A real-space stochastic density matrix approach for density functional electronic structure.
Beck, Thomas L
2015-12-21
The recent development of real-space grid methods has led to more efficient, accurate, and adaptable approaches for large-scale electrostatics and density functional electronic structure modeling. With the incorporation of multiscale techniques, linear-scaling real-space solvers are possible for density functional problems if localized orbitals are used to represent the Kohn-Sham energy functional. These methods still suffer from high computational and storage overheads, however, due to extensive matrix operations related to the underlying wave function grid representation. In this paper, an alternative stochastic method is outlined that aims to solve directly for the one-electron density matrix in real space. In order to illustrate aspects of the method, model calculations are performed for simple one-dimensional problems that display some features of the more general problem, such as spatial nodes in the density matrix. This orbital-free approach may prove helpful considering a future involving increasingly parallel computing architectures. Its primary advantage is the near-locality of the random walks, allowing for simultaneous updates of the density matrix in different regions of space partitioned across the processors. In addition, it allows for testing and enforcement of the particle number and idempotency constraints through stabilization of a Feynman-Kac functional integral as opposed to the extensive matrix operations in traditional approaches.
NASA Astrophysics Data System (ADS)
Nocera, A.; Alvarez, G.
2016-11-01
Frequency-dependent correlations, such as the spectral function and the dynamical structure factor, help illustrate condensed matter experiments. Within the density matrix renormalization group (DMRG) framework, an accurate method for calculating spectral functions directly in frequency is the correction-vector method. The correction vector can be computed by solving a linear equation or by minimizing a functional. This paper proposes an alternative to calculate the correction vector: to use the Krylov-space approach. This paper then studies the accuracy and performance of the Krylov-space approach, when applied to the Heisenberg, the t-J, and the Hubbard models. The cases studied indicate that the Krylov-space approach can be more accurate and efficient than the conjugate gradient, and that the error of the former integrates best when a Krylov-space decomposition is also used for ground state DMRG.
None, None
2016-11-21
Frequency-dependent correlations, such as the spectral function and the dynamical structure factor, help illustrate condensed matter experiments. Within the density matrix renormalization group (DMRG) framework, an accurate method for calculating spectral functions directly in frequency is the correction-vector method. The correction vector can be computed by solving a linear equation or by minimizing a functional. Our paper proposes an alternative to calculate the correction vector: to use the Krylov-space approach. This paper also studies the accuracy and performance of the Krylov-space approach, when applied to the Heisenberg, the t-J, and the Hubbard models. The cases we studied indicate that themore » Krylov-space approach can be more accurate and efficient than the conjugate gradient, and that the error of the former integrates best when a Krylov-space decomposition is also used for ground state DMRG.« less
None, None
2016-11-21
Frequency-dependent correlations, such as the spectral function and the dynamical structure factor, help illustrate condensed matter experiments. Within the density matrix renormalization group (DMRG) framework, an accurate method for calculating spectral functions directly in frequency is the correction-vector method. The correction vector can be computed by solving a linear equation or by minimizing a functional. Our paper proposes an alternative to calculate the correction vector: to use the Krylov-space approach. This paper also studies the accuracy and performance of the Krylov-space approach, when applied to the Heisenberg, the t-J, and the Hubbard models. The cases we studied indicate that the Krylov-space approach can be more accurate and efficient than the conjugate gradient, and that the error of the former integrates best when a Krylov-space decomposition is also used for ground state DMRG.
Nocera, A; Alvarez, G
2016-11-01
Frequency-dependent correlations, such as the spectral function and the dynamical structure factor, help illustrate condensed matter experiments. Within the density matrix renormalization group (DMRG) framework, an accurate method for calculating spectral functions directly in frequency is the correction-vector method. The correction vector can be computed by solving a linear equation or by minimizing a functional. This paper proposes an alternative to calculate the correction vector: to use the Krylov-space approach. This paper then studies the accuracy and performance of the Krylov-space approach, when applied to the Heisenberg, the t-J, and the Hubbard models. The cases studied indicate that the Krylov-space approach can be more accurate and efficient than the conjugate gradient, and that the error of the former integrates best when a Krylov-space decomposition is also used for ground state DMRG.
Metric-space approach to potentials and its relevance to density-functional theory
NASA Astrophysics Data System (ADS)
Sharp, P. M.; D'Amico, I.
2016-12-01
External potentials play a crucial role in modeling quantum systems, since, for a given interparticle interaction, they define the system Hamiltonian. We use the metric-space approach to quantum mechanics to derive, from the energy conservation law, two natural metrics for potentials. We show that these metrics are well defined for physical potentials, regardless of whether the system is in an eigenstate or if the potential is bounded. In addition, we discuss the gauge freedom of potentials and how to ensure that the metrics preserve physical relevance. Our metrics for potentials, together with the metrics for wave functions and densities from I. D'Amico et al. [Phys. Rev. Lett. 106, 050401 (2011), 10.1103/PhysRevLett.106.050401] paves the way for a comprehensive study of the two fundamental theorems of density-functional theory. We explore these by analyzing two many-body systems for which the related exact Kohn-Sham systems can be derived. First we consider the information provided by each of the metrics, and we find that the density metric performs best in distinguishing two many-body systems. Next we study for the systems at hand the one-to-one relationships among potentials, ground-state wave functions, and ground-state densities defined by the Hohenberg-Kohn theorem as relationships in metric spaces. We find that, in metric space, these relationships are monotonic and incorporate regions of linearity, at least for the systems considered. Finally, we use the metrics for wave functions and potentials in order to assess quantitatively how close the many-body and Kohn-Sham systems are: We show that, at least for the systems analyzed, both metrics provide a consistent picture, and for large regions of the parameter space the error in approximating the many-body wave function with the Kohn-Sham wave function lies under a threshold of 10%.
Lattice dynamics calculations based on density-functional perturbation theory in real space
NASA Astrophysics Data System (ADS)
Shang, Honghui; Carbogno, Christian; Rinke, Patrick; Scheffler, Matthias
2017-06-01
A real-space formalism for density-functional perturbation theory (DFPT) is derived and applied for the computation of harmonic vibrational properties in molecules and solids. The practical implementation using numeric atom-centered orbitals as basis functions is demonstrated exemplarily for the all-electron Fritz Haber Institute ab initio molecular simulations (FHI-aims) package. The convergence of the calculations with respect to numerical parameters is carefully investigated and a systematic comparison with finite-difference approaches is performed both for finite (molecules) and extended (periodic) systems. Finally, the scaling tests and scalability tests on massively parallel computer systems demonstrate the computational efficiency.
Density functional theory study of the conformational space of an infinitely long polypeptide chain
NASA Astrophysics Data System (ADS)
Ireta, Joel; Scheffler, Matthias
2009-08-01
The backbone conformational space of infinitely long polyalanine is investigated with density-functional theory and mapping the potential energy surface in terms of (L, θ) cylindrical coordinates. A comparison of the obtained (L, θ) Ramachandran-like plot with results from an extended set of protein structures shows excellent conformity, with the exception of the polyproline II region. It is demonstrated the usefulness of infinitely long polypeptide models for investigating the influence of hydrogen bonding and its cooperative effect on the backbone conformations. The results imply that hydrogen bonding together with long-range electrostatics is the main actuator for most of the structures assumed by protein residues.
Scalable real space pseudopotential-density functional codes for materials applications
NASA Astrophysics Data System (ADS)
Chelikowsky, James R.; Lena, Charles; Schofield, Grady; Saad, Yousef; Deslippe, Jack; Yang, Chao
2015-03-01
Real-space pseudopotential density functional theory has proven to be an efficient method for computing the properties of matter in many different states and geometries, including liquids, wires, slabs and clusters with and without spin polarization. Fully self-consistent solutions have been routinely obtained for systems with thousands of atoms. However, there are still systems where quantum mechanical accuracy is desired, but scalability proves to be a hindrance, such as large biological molecules or complex interfaces. We will present an overview of our work on new algorithms, which offer improved scalability by implementing another layer of parallelism, and by optimizing communication and memory management. Support provided by the SciDAC program, Department of Energy, Office of Science, Advanced Scientific Computing Research and Basic Energy Sciences. Grant Numbers DE-SC0008877 (Austin) and DE-FG02-12ER4 (Berkeley).
Modeling solvation effects in real-space and real-time within density functional approaches
Delgado, Alain; Corni, Stefano; Pittalis, Stefano; Rozzi, Carlo Andrea
2015-10-14
The Polarizable Continuum Model (PCM) can be used in conjunction with Density Functional Theory (DFT) and its time-dependent extension (TDDFT) to simulate the electronic and optical properties of molecules and nanoparticles immersed in a dielectric environment, typically liquid solvents. In this contribution, we develop a methodology to account for solvation effects in real-space (and real-time) (TD)DFT calculations. The boundary elements method is used to calculate the solvent reaction potential in terms of the apparent charges that spread over the van der Waals solute surface. In a real-space representation, this potential may exhibit a Coulomb singularity at grid points that are close to the cavity surface. We propose a simple approach to regularize such singularity by using a set of spherical Gaussian functions to distribute the apparent charges. We have implemented the proposed method in the OCTOPUS code and present results for the solvation free energies and solvatochromic shifts for a representative set of organic molecules in water.
Modeling solvation effects in real-space and real-time within density functional approaches.
Delgado, Alain; Corni, Stefano; Pittalis, Stefano; Rozzi, Carlo Andrea
2015-10-14
The Polarizable Continuum Model (PCM) can be used in conjunction with Density Functional Theory (DFT) and its time-dependent extension (TDDFT) to simulate the electronic and optical properties of molecules and nanoparticles immersed in a dielectric environment, typically liquid solvents. In this contribution, we develop a methodology to account for solvation effects in real-space (and real-time) (TD)DFT calculations. The boundary elements method is used to calculate the solvent reaction potential in terms of the apparent charges that spread over the van der Waals solute surface. In a real-space representation, this potential may exhibit a Coulomb singularity at grid points that are close to the cavity surface. We propose a simple approach to regularize such singularity by using a set of spherical Gaussian functions to distribute the apparent charges. We have implemented the proposed method in the Octopus code and present results for the solvation free energies and solvatochromic shifts for a representative set of organic molecules in water.
Modeling solvation effects in real-space and real-time within density functional approaches
NASA Astrophysics Data System (ADS)
Delgado, Alain; Corni, Stefano; Pittalis, Stefano; Rozzi, Carlo Andrea
2015-10-01
The Polarizable Continuum Model (PCM) can be used in conjunction with Density Functional Theory (DFT) and its time-dependent extension (TDDFT) to simulate the electronic and optical properties of molecules and nanoparticles immersed in a dielectric environment, typically liquid solvents. In this contribution, we develop a methodology to account for solvation effects in real-space (and real-time) (TD)DFT calculations. The boundary elements method is used to calculate the solvent reaction potential in terms of the apparent charges that spread over the van der Waals solute surface. In a real-space representation, this potential may exhibit a Coulomb singularity at grid points that are close to the cavity surface. We propose a simple approach to regularize such singularity by using a set of spherical Gaussian functions to distribute the apparent charges. We have implemented the proposed method in the Octopus code and present results for the solvation free energies and solvatochromic shifts for a representative set of organic molecules in water.
Scalable real space pseudopotential density functional codes for materials in the exascale regime
NASA Astrophysics Data System (ADS)
Lena, Charles; Chelikowsky, James; Schofield, Grady; Biller, Ariel; Kronik, Leeor; Saad, Yousef; Deslippe, Jack
Real-space pseudopotential density functional theory has proven to be an efficient method for computing the properties of matter in many different states and geometries, including liquids, wires, slabs, and clusters with and without spin polarization. Fully self-consistent solutions using this approach have been routinely obtained for systems with thousands of atoms. Yet, there are many systems of notable larger sizes where quantum mechanical accuracy is desired, but scalability proves to be a hindrance. Such systems include large biological molecules, complex nanostructures, or mismatched interfaces. We will present an overview of our new massively parallel algorithms, which offer improved scalability in preparation for exascale supercomputing. We will illustrate these algorithms by considering the electronic structure of a Si nanocrystal exceeding 104 atoms. Support provided by the SciDAC program, Department of Energy, Office of Science, Advanced Scientific Computing Research and Basic Energy Sciences. Grant Numbers DE-SC0008877 (Austin) and DE-FG02-12ER4 (Berkeley).
Hlushak, Stepan P; McCabe, Clare; Cummings, Peter T
2012-09-14
We present a Fourier space density functional approach for hard particles with attractive interactions, which is based on a previously developed two-dimensional approach [S. Hlushak, W. Rżysko, and S. Sokołowski, J. Chem. Phys. 131, 094904 (2009)] for hard-sphere chains. The interactions are incorporated by means of a three-dimensional Fourier image of the direct correlation function that is obtained from the first-order mean-spherical approximation. In order to improve the computational efficiency, we make extensive use of fast Fourier transforms for calculating density convolution integrals. A two-dimensional implementation of the new density functional approach, based on the expansion of the functional around the bulk fluid density, is used to study structure and adsorption of two model fluids in narrow cylindrical pores. We also investigate two methods that improve the accuracy of the theory as compared to the conventional DFT approach, which expands the free energy functional around the bulk fluid density: One a variant of the reference fluid density functional theory used by Gillespie et al. [Phys. Rev. E 68, 031503 (2003)], and the second a weighted density approach with energy route thermodynamics. Results from these two methods are compared to the conventional approach and also to the results of Monte Carlo simulations. We find that the method of Gillespie et al. and the weighted density approach with energy route thermodynamics yield significant improvement over the conventional approach.
Fading probability density function of free-space optical communication channels with pointing error
NASA Astrophysics Data System (ADS)
Zhao, Zhijun; Liao, Rui
2011-06-01
The turbulent atmosphere causes wavefront distortion, beam wander, and beam broadening of a laser beam. These effects result in average power loss and instantaneous power fading at the receiver aperture and thus degrade performance of a free-space optical (FSO) communication system. In addition to the atmospheric turbulence, a FSO communication system may also suffer from laser beam pointing error. The pointing error causes excessive power loss and power fading. This paper proposes and studies an analytical method for calculating the FSO channel fading probability density function (pdf) induced by both atmospheric turbulence and pointing error. This method is based on the fast-tracked laser beam fading profile and the joint effects of beam wander and pointing error. In order to evaluate the proposed analytical method, large-scale numerical wave-optics simulations are conducted. Three types of pointing errors are studied , namely, the Gaussian random pointing error, the residual tracking error, and the sinusoidal sway pointing error. The FSO system employs a collimated Gaussian laser beam propagating along a horizontal path. The propagation distances range from 0.25 miles to 2.5 miles. The refractive index structure parameter is chosen to be Cn2 = 5×10-15m-2/3 and Cn2 = 5×10-13m-2/3. The studied cases cover from weak to strong fluctuations. The fading pdf curves of channels with pointing error calculated using the analytical method match accurately the corresponding pdf curves obtained directly from large-scale wave-optics simulations. They also give accurate average bit-error-rate (BER) curves and outage probabilities. Both the lognormal and the best-fit gamma-gamma fading pdf curves deviate from those of corresponding simulation curves, and they produce overoptimistic average BER curves and outage probabilities.
Radiation dose rates in Space Shuttle as a function of atmospheric density.
Badhwar, G D
1999-06-01
Current models of the inner trapped belt describe the radiation environment at times of solar minimum and solar maximum, respectively. These two models were constructed using data acquired prior to 1970 during a small solar cycle, and no valid model for the past two high solar cycles exists. There is a clear need to accurately predict the radiation exposure of astronauts at all times between the solar minimum and solar maximum, not only on the short duration Space Shuttle flights, but on the longer term stay onboard the Mir orbital station and the planned International Space Station (ISS). An analysis of the trapped absorbed dose rate, D, at six fixed locations in the habitable volume of the Shuttle shows a power law relationship, D=A rho-n, where rho is the atmospheric density, rho. The index, n, is weakly dependent on the shielding, decreasing as the average shielding increases. A better representation is provided by D=A tan-1 [(Xi-Xi c)/(Xi c-Xi m)], where Xi=ln(rho), and A, Xi c, and Xi m are constants. Xi c is related to the atmospheric density near the altitude of atmospheric cutoff. These relationships hold over nearly four decades of density variation and throughout the solar cycle. This then provides a method of calculating absorbed dose rate at anytime in the solar cycle. These empirically derived relations were used to predict the dose rates for eleven Space Shuttle flights carried out since January 1997. The predictions are in excellent agreement with measured values. This method reduces the uncertainties of a factor of about 2 for the AP-8 MIN/MAX models to less than 30%.
NASA Astrophysics Data System (ADS)
Lee, Alex; Kim, Minjung; Chelikowsky, James
2015-03-01
Recent experimental noncontact atomic force microscopy (AFM) studies on 8-hydroxyquinoline (8-hq) assemblies have imaged distinct lines between molecules that are thought to represent intermolecular bonding. To aid the interpretation of these images, we calculate simulated AFM images of an 8-hq dimer with a CO functionalized tip using a real-space pseudopotential formalism. We examine the effects of Pauli repulsion and tip probe relaxation as explanations for the enhanced resolution that resolves these intermolecular force lines. Our study aims to compute ab initio real-space images of intermolecular interactions.
Ghosh, Soumen; Cramer, Christopher J; Truhlar, Donald G; Gagliardi, Laura
2017-04-01
Predicting ground- and excited-state properties of open-shell organic molecules by electronic structure theory can be challenging because an accurate treatment has to correctly describe both static and dynamic electron correlation. Strongly correlated systems, i.e., systems with near-degeneracy correlation effects, are particularly troublesome. Multiconfigurational wave function methods based on an active space are adequate in principle, but it is impractical to capture most of the dynamic correlation in these methods for systems characterized by many active electrons. We recently developed a new method called multiconfiguration pair-density functional theory (MC-PDFT), that combines the advantages of wave function theory and density functional theory to provide a more practical treatment of strongly correlated systems. Here we present calculations of the singlet-triplet gaps in oligoacenes ranging from naphthalene to dodecacene. Calculations were performed for unprecedently large orbitally optimized active spaces of 50 electrons in 50 orbitals, and we test a range of active spaces and active space partitions, including four kinds of frontier orbital partitions. We show that MC-PDFT can predict the singlet-triplet splittings for oligoacenes consistent with the best available and much more expensive methods, and indeed MC-PDFT may constitute the benchmark against which those other models should be compared, given the absence of experimental data.
Partition density functional theory
NASA Astrophysics Data System (ADS)
Nafziger, Jonathan
Partition density functional theory (PDFT) is a method for dividing a molecular electronic structure calculation into fragment calculations. The molecular density and energy corresponding to Kohn Sham density-functional theory (KS-DFT) may be exactly recovered from these fragments. Each fragment acts as an isolated system except for the influence of a global one-body 'partition' potential which deforms the fragment densities. In this work, the developments of PDFT are put into the context of other fragment-based density functional methods. We developed three numerical implementations of PDFT: One within the NWChem computational chemistry package using basis sets, and the other two developed from scratch using real-space grids. It is shown that all three of these programs can exactly reproduce a KS-DFT calculation via fragment calculations. The first of our in-house codes handles non-interacting electrons in arbitrary one-dimensional potentials with any number of fragments. This code is used to explore how the exact partition potential changes for different partitionings of the same system and also to study features which determine which systems yield non-integer PDFT occupations and which systems are locked into integer PDFT occupations. The second in-house code, CADMium, performs real-space calculations of diatomic molecules. Features of the exact partition potential are studied for a variety of cases and an analytical formula determining singularities in the partition potential is derived. We introduce an approximation for the non-additive kinetic energy and show how this quantity can be computed exactly. Finally a PDFT functional is developed to address the issues of static correlation and delocalization errors in approximations within DFT. The functional is applied to the dissociation of H2 + and H2.
NASA Astrophysics Data System (ADS)
Maitra, Neepa
2013-03-01
The usual approximations in Time-Dependent Density Functional Theory (TDDFT) have achieved an unprecedented balance between accuracy and efficiency for calculating excitation spectra and response. We show however that these approximations are less successful for time-resolved dynamics beyond the linear response regime. Step and peak structures develop in the exact exchange-correlation potential that have a density-dependence that is non-local both in time and in space, missed by all approximations in use today. The lack of these structures leads to their incorrect predictions of dynamics, such as faster time-scales, and incomplete charge-transfer. [P. Elliott, J.I. Fuks, A. Rubio, N.T. Maitra arXiv:1211.2012; J. I. Fuks, P. Elliott, A. Rubio, N. T. Maitra, arXiv:1211.2849] Support from NSF and DOE is gratefully acknowledged.
Flick, Johannes; Ruggenthaler, Michael; Appel, Heiko; Rubio, Angel
2015-12-15
The density-functional approach to quantum electrodynamics extends traditional density-functional theory and opens the possibility to describe electron-photon interactions in terms of effective Kohn-Sham potentials. In this work, we numerically construct the exact electron-photon Kohn-Sham potentials for a prototype system that consists of a trapped electron coupled to a quantized electromagnetic mode in an optical high-Q cavity. Although the effective current that acts on the photons is known explicitly, the exact effective potential that describes the forces exerted by the photons on the electrons is obtained from a fixed-point inversion scheme. This procedure allows us to uncover important beyond-mean-field features of the effective potential that mark the breakdown of classical light-matter interactions. We observe peak and step structures in the effective potentials, which can be attributed solely to the quantum nature of light; i.e., they are real-space signatures of the photons. Our findings show how the ubiquitous dipole interaction with a classical electromagnetic field has to be modified in real space to take the quantum nature of the electromagnetic field fully into account.
Flick, Johannes; Ruggenthaler, Michael; Appel, Heiko; Rubio, Angel
2015-01-01
The density-functional approach to quantum electrodynamics extends traditional density-functional theory and opens the possibility to describe electron–photon interactions in terms of effective Kohn–Sham potentials. In this work, we numerically construct the exact electron–photon Kohn–Sham potentials for a prototype system that consists of a trapped electron coupled to a quantized electromagnetic mode in an optical high-Q cavity. Although the effective current that acts on the photons is known explicitly, the exact effective potential that describes the forces exerted by the photons on the electrons is obtained from a fixed-point inversion scheme. This procedure allows us to uncover important beyond-mean-field features of the effective potential that mark the breakdown of classical light–matter interactions. We observe peak and step structures in the effective potentials, which can be attributed solely to the quantum nature of light; i.e., they are real-space signatures of the photons. Our findings show how the ubiquitous dipole interaction with a classical electromagnetic field has to be modified in real space to take the quantum nature of the electromagnetic field fully into account. PMID:26627715
Liu, Yu; Liu, Honglai; Hu, Ying; Jiang, Jianwen
2009-09-10
A density functional theory (DFT) is developed in three-dimensional nanoconfined space and applied for H(2) storage in metal-organic frameworks. Two different weighting functions based on the weighted density approximation (WDA) are adopted, respectively, for the repulsive and attractive contributions to the excess free energy. The Carnahan-Starling equation and a modified Benedicit-Webb-Rubin equation are used to calculate the excess free energy of uniform fluid. To compare with DFT predictions, grand canonical Monte Carlo simulations are carried out separately. For H(2) adsorption in MOF-5 and ZIF-8, the isotherms predicted from the DFT agree well with simulation and experiment results, and the DFT is found to be superior to the mean-field-approximation (MFA)-based theory. The adsorption energies and isosteric heats predicted are also in accord with simulation results. From the predicted density contours, the DFT shows that the preferential adsorption sites are the corners of metal clusters in MOF-5 and the top of organic linkers in ZIF-8, consistent with simulation and experimental observations.
All-electron Kohn-Sham density functional theory on hierarchic finite element spaces
NASA Astrophysics Data System (ADS)
Schauer, Volker; Linder, Christian
2013-10-01
In this work, a real space formulation of the Kohn-Sham equations is developed, making use of the hierarchy of finite element spaces from different polynomial order. The focus is laid on all-electron calculations, having the highest requirement onto the basis set, which must be able to represent the orthogonal eigenfunctions as well as the electrostatic potential. A careful numerical analysis is performed, which points out the numerical intricacies originating from the singularity of the nuclei and the necessity for approximations in the numerical setting, with the ambition to enable solutions within a predefined accuracy. In this context the influence of counter-charges in the Poisson equation, the requirement of a finite domain size, numerical quadratures and the mesh refinement are examined as well as the representation of the electrostatic potential in a high order finite element space. The performance and accuracy of the method is demonstrated in computations on noble gases. In addition the finite element basis proves its flexibility in the calculation of the bond-length as well as the dipole moment of the carbon monoxide molecule.
All-electron Kohn–Sham density functional theory on hierarchic finite element spaces
Schauer, Volker; Linder, Christian
2013-10-01
In this work, a real space formulation of the Kohn–Sham equations is developed, making use of the hierarchy of finite element spaces from different polynomial order. The focus is laid on all-electron calculations, having the highest requirement onto the basis set, which must be able to represent the orthogonal eigenfunctions as well as the electrostatic potential. A careful numerical analysis is performed, which points out the numerical intricacies originating from the singularity of the nuclei and the necessity for approximations in the numerical setting, with the ambition to enable solutions within a predefined accuracy. In this context the influence of counter-charges in the Poisson equation, the requirement of a finite domain size, numerical quadratures and the mesh refinement are examined as well as the representation of the electrostatic potential in a high order finite element space. The performance and accuracy of the method is demonstrated in computations on noble gases. In addition the finite element basis proves its flexibility in the calculation of the bond-length as well as the dipole moment of the carbon monoxide molecule.
Partition Density Functional Theory
NASA Astrophysics Data System (ADS)
Wasserman, Adam
2012-02-01
Partition Density Functional Theory (PDFT) is a formally exact method for obtaining molecular properties from self-consistent calculations on isolated fragments [1,2]. For a given choice of fragmentation, PDFT outputs the (in principle exact) molecular energy and density, as well as fragment densities that sum to the correct molecular density. I describe our progress understanding the behavior of the fragment energies as a function of fragment occupations, derivative discontinuities, practical implementation, and applications of PDFT to small molecules. I also discuss implications for ground-state Density Functional Theory, such as the promise of PDFT to circumvent the delocalization error of approximate density functionals. [4pt] [1] M.H. Cohen and A. Wasserman, J. Phys. Chem. A, 111, 2229(2007).[0pt] [2] P. Elliott, K. Burke, M.H. Cohen, and A. Wasserman, Phys. Rev. A 82, 024501 (2010).
NASA Astrophysics Data System (ADS)
Majumdar, Arun K.; Luna, Carlos E.; Idell, Paul S.
2007-09-01
A new method of reconstructing and predicting an unknown probability density function (PDF) characterizing the statistics of intensity fluctuations of optical beams propagating through atmospheric turbulence is presented in this paper. The method is based on a series expansion of generalized Laguerre polynomials ; the expansion coefficients are expressed in terms of the higher-order intensity moments of intensity statistics. This method generates the PDF from the data moments without any prior knowledge of specific statistics and converges smoothly. The utility of reconstructed PDF relevant to free-space laser communication in terms of calculating the average bit error rate and probability of fading is pointed out. Simulated numerical results are compared with some known non-Gaussian test PDFs: Log-Normal, Rice-Nakagami and Gamma-Gamma distributions and show excellent agreement obtained by the method developed. The accuracy of the reconstructed PDF is also evaluated.
Momentum-space properties from coordinate-space electron density
Harbola, Manoj K.; Zope, Rajendra R.; Kshirsagar, Anjali; Pathak, Rajeev K.
2005-05-22
Electron density and electron momentum density, while independently tractable experimentally, bear no direct connection without going through the many-electron wave function. However, invoking a variant of the constrained-search formulation of density-functional theory, we develop a general scheme (valid for arbitrary external potentials) yielding decent momentum-space properties, starting exclusively from the coordinate-space electron density. A numerical illustration of the scheme is provided for the closed-shell atomic systems He, Be, and Ne in their ground state and for 1s{sup 1} 2s{sup 1} singlet electronic excited state for helium by calculating the Compton profiles and the
expectation values derived from given coordinate-space electron densities.
NASA Astrophysics Data System (ADS)
Zhao, Zhijun; Liao, Rui
2011-03-01
Free-space optical (FSO) communication systems suffer from average power loss and instantaneous power fading due to the atmospheric turbulence. The channel fading probability density function (pdf) is of critical importance for FSO communication system design and evaluation. The performance and reliability of FSO communication systems can be greatly enhanced if fast-tacking devices are employed at the transmitter in order to compensate laser beam wander at the receiver aperture. The fast-tracking method is especially effective when communication distance is long. This paper studies the fading probability density functions of both fast-tracked and untracked FSO communication channels. Large-scale wave-optics simulations are conducted for both tracked and untracked lasers. In the simulations, the Kolmogorov spectrum is adopted, and it is assumed that the outer scale is infinitely large and the inner scale is negligibly small. The fading pdfs of both fast-tracked and untracked FSO channels are obtained from the simulations. Results show that the fast-tracked channel fading can be accurately modeled as gamma-distributed if receiver aperture size is smaller than the coherence radius. An analytical method is given for calculating the untracked fading pdfs of both point-like and finite-size receiver apertures from the fast-tracked fading pdf. For point-like apertures, the analytical method gives pdfs close to the well-known gamma-gamma pdfs if off-axis effects are omitted in the formulation. When off-axis effects are taken into consideration, the untracked pdfs obtained using the analytical method fit the simulation pdfs better than gamma-gamma distributions for point-like apertures, and closely fit the simulation pdfs for finite-size apertures where gamma-gamma pdfs deviate from those of the simulations significantly.
Herbst; Thompson; Fockenbrock; Rix; Beckwith
1999-11-20
We report preliminary results of a deep near-infrared search for methane-absorbing brown dwarfs; almost 5 yr after the discovery of Gl 229b, there are only a few confirmed examples of this type of object. New J-band, wide-field images, combined with preexisting R-band observations, allow efficient identification of candidates by their extreme (R-J) colors. Follow-up measurements with custom filters can then confirm objects with methane absorption. To date, we have surveyed a total of 11.4 deg2 to J approximately 20.5 and R approximately 25. Follow-up CH4 filter observations of promising candidates in one-fourth of these fields have turned up no methane-absorbing brown dwarfs. With 90% confidence, this implies that the space density of objects similar to Gl 229b is less than 0.012 pc-3. These calculations account for the vertical structure of the Galaxy, which can be important for sensitive measurements. Combining published theoretical atmospheric models with our observations sets an upper limit of alphafunction power law in this domain.
NASA Astrophysics Data System (ADS)
Han, Chu; Bongiorno, Angelo
2014-03-01
Yttrium-doped barium zirconate (BZY) is a proton conducting electrolyte forming a class of novel materials for new generation of solid oxide fuel cells, for hydrogen separation and purification, and for electrolysis of water. Here we use density functional theory calculations to compute the energy of protons and oxygen vacancies at the surface and in the bulk of lightly Y-doped BZY materials. We found that protons are energetically more stable at the surface termination than in the bulk of BZY by about 1 eV. In contrast, doubly-positively charged oxygen vacancies are found to form iso-energetic defects at both the terminal surface layer and in the bulk of BZY, while in the sub-surface region the defect energy raises by about 1 eV with respect to the value in the bulk. The energetic behavior of protons and oxygen vacancies in the near surface region of BZY is attributed to the competition of strain and electrostatic effects. Lattice model representations of BZY surfaces are then used in combination with Monte Carlo simulations to solve the Poisson-Boltzmann equation and investigate the implication of the results above on the structure of the space charge region at the surface of BZY materials.
Space race functional responses.
Sjödin, Henrik; Brännström, Åke; Englund, Göran
2015-02-22
We derive functional responses under the assumption that predators and prey are engaged in a space race in which prey avoid patches with many predators and predators avoid patches with few or no prey. The resulting functional response models have a simple structure and include functions describing how the emigration of prey and predators depend on interspecific densities. As such, they provide a link between dispersal behaviours and community dynamics. The derived functional response is general but is here modelled in accordance with empirically documented emigration responses. We find that the prey emigration response to predators has stabilizing effects similar to that of the DeAngelis-Beddington functional response, and that the predator emigration response to prey has destabilizing effects similar to that of the Holling type II response. A stability criterion describing the net effect of the two emigration responses on a Lotka-Volterra predator-prey system is presented. The winner of the space race (i.e. whether predators or prey are favoured) is determined by the relationship between the slopes of the species' emigration responses. It is predicted that predators win the space race in poor habitats, where predator and prey densities are low, and that prey are more successful in richer habitats. © 2015 The Author(s) Published by the Royal Society. All rights reserved.
NASA Astrophysics Data System (ADS)
Reylé, C.; Delorme, P.; Willott, C. J.; Albert, L.; Delfosse, X.; Forveille, T.; Artigau, E.; Malo, L.; Hill, G. J.; Doyon, R.
2010-11-01
Context. Thanks to recent and ongoing large scale surveys, hundreds of brown dwarfs have been discovered in the last decade. The Canada-France Brown Dwarf Survey is a wide-field survey for cool brown dwarfs conducted with the MegaCam camera on the Canada-France-Hawaii Telescope. Aims: Our objectives are to find ultracool brown dwarfs and to constrain the field brown-dwarf luminosity function and the mass function from a large and homogeneous sample of L and T dwarfs. Methods: We identify candidates in CFHT/MegaCam i' and z' images and follow them up with pointed near infrared (NIR) imaging on several telescopes. Halfway through our survey we found ~50 T dwarfs and ~170 L or ultra cool M dwarfs drawn from a larger sample of 1400 candidates with typical ultracool dwarfs i'-z' colours, found in 780 square degrees. Results: We have currently completed the NIR follow-up on a large part of the survey for all candidates from mid-L dwarfs down to the latest T dwarfs known with utracool dwarfs' colours. This allows us to draw on a complete and well defined sample of 102 ultracool dwarfs to investigate the luminosity function and space density of field dwarfs. Conclusions: We found the density of late L5 to T0 dwarfs to be 2.0+0.8-0.7 × 10-3 objects pc-3, the density of T0.5 to T5.5 dwarfs to be 1.4+0.3-0.2 × 10-3 objects pc-3, and the density of T6 to T8 dwarfs to be 5.3+3.1-2.2 × 10-3 objects pc-3. We found that these results agree better with a flat substellar mass function. Three latest dwarfs at the boundary between T and Y dwarfs give the high density 8.3+9.0-5.1 × 10-3 objects pc-3. Although the uncertainties are very large this suggests that many brown dwarfs should be found in this late spectral type range, as expected from the cooling of brown dwarfs, whatever their mass, down to very low temperature. Based on observations obtained with MegaPrime/MegaCam, a joint project of CFHT and CEA/DAPNIA, at the Canada-France-Hawaii Telescope (CFHT), which is operated by
NASA Technical Reports Server (NTRS)
Akhundova, E. A.; Dodonov, V. V.; Manko, V. I.
1993-01-01
The exact expressions for density matrix and Wigner functions of quantum systems are known only in special cases. Corresponding Hamiltonians are quadratic forms of Euclidean coordinates and momenta. In this paper we consider the problem of one-dimensional free particle movement in the bounded region 0 is less than x is less than a (including the case a = infinity).
Hempler, Daniela; Schmidt, Martin U; van de Streek, Jacco
2017-08-01
More than 600 molecular crystal structures with correct, incorrect and uncertain space-group symmetry were energy-minimized with dispersion-corrected density functional theory (DFT-D, PBE-D3). For the purpose of determining the correct space-group symmetry the required tolerance on the atomic coordinates of all non-H atoms is established to be 0.2 Å. For 98.5% of 200 molecular crystal structures published with missed symmetry, the correct space group is identified; there are no false positives. Very small, very symmetrical molecules can end up in artificially high space groups upon energy minimization, although this is easily detected through visual inspection. If the space group of a crystal structure determined from powder diffraction data is ambiguous, energy minimization with DFT-D provides a fast and reliable method to select the correct space group.
Semiclassics in Density Functional Theory
NASA Astrophysics Data System (ADS)
Lee, Donghyung; Cangi, Attila; Elliott, Peter; Burke, Kieron
2009-03-01
Recently, we published an article [1] about the semiclassical origin of density functional theory. We showed that the density and the kinetic energy density of one dimensional finite systems with hard walls can be expressed in terms of the external potential using the semiclassical Green's function method. Here, we show a uniformization scheme for the semiclassical density and the kinetic energy density for turning-point problems.[1] P. Elliott, D. Lee, A. Cangi, and K. Burke, Phys. Rev. Lett. 100, 256406 (2008).
Density-dependent covariant energy density functionals
Lalazissis, G. A.
2012-10-20
Relativistic nuclear energy density functionals are applied to the description of a variety of nuclear structure phenomena at and away fromstability line. Isoscalar monopole, isovector dipole and isoscalar quadrupole giant resonances are calculated using fully self-consistent relativistic quasiparticle randomphase approximation, based on the relativistic Hartree-Bogoliubovmodel. The impact of pairing correlations on the fission barriers in heavy and superheavy nuclei is examined. The role of pion in constructing desnity functionals is also investigated.
Noncollinear magnetism in density functional calculations
NASA Astrophysics Data System (ADS)
Peralta, Juan E.; Scuseria, Gustavo E.; Frisch, Michael J.
2007-03-01
We generalize the treatment of the electronic spin degrees of freedom in density functional calculations to the case where the spin vector variables employed in the definition of the energy functional can vary in any direction in space. The expression for the generalized exchange-correlation potential matrix elements is derived for general functionals which among their ingredients include the electron density, its gradient and Laplacian, the kinetic energy density, and nonlocal Hartree-Fock-type exchange. We present calculations on planar Cr clusters that exhibit ground states with noncollinear spin densities due to geometrically frustrated antiferromagnetic interactions.
Density functional theory of complex transition densities.
Ernzerhof, Matthias
2006-09-28
We present an extension of Hohenberg-Kohn-Sham density functional theory to the domain of complex local potentials and complex electron densities. The approach is applicable to resonance (Siegert) [Phys. Rev. 56, 750 (1939)] states and other scattering and transport problems that can be described by a normalized state of a Hamiltonian containing a complex local potential. Such Hamiltonians are non-Hermitian and their eigenvalues are in general complex, the imaginary part being inversely proportional to the lifetime of the system. The one-to-one correspondence between complex local potentials nu and complex electron densities rho is established provided that the complex variables are sufficiently close to real local potentials and densities of nondegenerate ground states. We show that the exchange-correlation functionals, contributing to the complex energy, are determined through analytic continuation of their ground-state-theory counterparts. This implies that the exchange-correlation effects on the lifetime of a resonance are, under appropriate conditions, already determined by the functionals of the ground-state theory.
Spatial Density Evolution of Space Debris Environment
NASA Astrophysics Data System (ADS)
Li, Canan; Pang, Baojun; Ding, Li
2009-03-01
It is known that the space debris provide great risks to the safety of on-orbit space vehicles, which makes it necessary to establish a model to evaluate their impact risks. In order to provide the scenario of the future space debris environment for space vehicle designers, this paper addresses a simplified mathematical model for the future evolution of space debris environment. While the spatial density is of more concern to engineers, this paper is devoted to study the evolution of the distribution of spatial density of space debris. Given the initial spatial density, this paper develops the algorithm to obtained the spatial density of space debris at any moment of future, by considering the orbital propagation and collisions.
Time-Dependent Current Density Functional Theory
NASA Astrophysics Data System (ADS)
Vignale, Giovanni
The nonlocality of the exchange-correlation (xc) potential, i.e., the fact that the xc potential at a certain position depends on the global distribution of the particles in space, is the curse of density functional theory. It is mainly because of this fact that, even after years of intensive studies, the exact form of the xc potential as a functional of the density remains unknown. Nevertheless, it is true that many accurate and useful results can be obtained from the use of an approximation - the local density approximation (LDA) - which ignores the problem altogether.
NASA Astrophysics Data System (ADS)
Shuai, Jing; Deog Yoo, Hyun; Liang, Yanliang; Li, Yifei; Yao, Yan; Grabow, Lars C.
2016-06-01
Layered materials, such as the transition metal dichalcogenide molybdenum disulfide (MoS2), are promising materials for ion storage in electrodes of rechargeable batteries. To extend the application range of these materials to ions beyond lithium-ions, we used van der Waals corrected density functional theory simulations to study the intercalation and diffusion of lithium (Li), sodium (Na), and magnesium (Mg) in the 2H structure of MoS2 as a function of interlayer spacing. All three species exhibit an optimal intercalation energy, which is reached at about 11% expansion for Li and Mg, and 23% expansion for Na. Similarly, the slow diffusion kinetics of large Na and divalent Mg-ions can be improved by layer expansion. When the interlayer spacing is increased by about 35% from its equilibrium value, the diffusion of Na and Mg-ions becomes more facile than the diffusion of small, monovalent Li-ions, with diffusion barriers similar to those of Li in graphene. Our results indicate that interlayer expansion is a promising technique to improve intercalation kinetics and thermodynamics for large and/or multivalent ions in MoS2, which can be a major limitation to battery performance. The rationalization of our results in terms of bonding geometries forms the basis of a battery electrode design framework with applications for a wide range of layered materials.
General performance of density functionals.
Sousa, Sérgio Filipe; Fernandes, Pedro Alexandrino; Ramos, Maria João
2007-10-25
The density functional theory (DFT) foundations date from the 1920s with the work of Thomas and Fermi, but it was after the work of Hohenberg, Kohn, and Sham in the 1960s, and particularly with the appearance of the B3LYP functional in the early 1990s, that the widespread application of DFT has become a reality. DFT is less computationally demanding than other computational methods with a similar accuracy, being able to include electron correlation in the calculations at a fraction of time of post-Hartree-Fock methodologies. In this review we provide a brief outline of the density functional theory and of the historic development of the field, focusing later on the several types of density functionals currently available, and finishing with a detailed analysis of the performance of DFT across a wide range of chemical properties and system types, reviewed from the most recent benchmarking studies, which encompass several well-established density functionals together with the most recent efforts in the field. Globally, an overall picture of the level of performance of the plethora of currently available density functionals for each chemical property is drawn, with particular attention being dedicated to the relative performance of the popular B3LYP density functional.
Phenomenological Relativistic Energy Density Functionals
Lalazissis, G. A.; Kartzikos, S.; Niksic, T.; Paar, N.; Vretenar, D.; Ring, P.
2009-08-26
The framework of relativistic nuclear energy density functionals is applied to the description of a variety of nuclear structure phenomena, not only in spherical and deformed nuclei along the valley of beta-stability, but also in exotic systems with extreme isospin values and close to the particle drip-lines. Dynamical aspects of exotic nuclear structure is explored using the fully consistent quasiparticle random-phase approximation based on the relativistic Hartree-Bogoliubov model. Recent applications of energy density functionals with explicit density dependence of the meson-nucleon couplings are presented.
NASA Astrophysics Data System (ADS)
Gagné, Jonathan; Faherty, Jacqueline K.; Mamajek, Eric E.; Malo, Lison; Doyon, René; Filippazzo, Joseph C.; Weinberger, Alycia J.; Donaldson, Jessica K.; Lépine, Sébastien; Lafrenière, David; Artigau, Étienne; Burgasser, Adam J.; Looper, Dagny; Boucher, Anne; Beletsky, Yuri; Camnasio, Sara; Brunette, Charles; Arboit, Geneviève
2017-02-01
A determination of the initial mass function (IMF) of the current, incomplete census of the 10 Myr-old TW Hya association (TWA) is presented. This census is built from a literature compilation supplemented with new spectra and 17 new radial velocities from ongoing membership surveys, as well as a reanalysis of Hipparcos data that confirmed HR 4334 (A2 Vn) as a member. Although the dominant uncertainty in the IMF remains census incompleteness, a detailed statistical treatment is carried out to make the IMF determination independent of binning while accounting for small number statistics. The currently known high-likelihood members are fitted by a log-normal distribution with a central mass of {0.21}-0.06+0.11 M ⊙ and a characteristic width of {0.8}-0.1+0.2 dex in the 12 M Jup-2 M ⊙ range, whereas a Salpeter power law with α ={2.2}-0.5+1.1 best describes the IMF slope in the 0.1-2 M ⊙ range. This characteristic width is higher than other young associations, which may be due to incompleteness in the current census of low-mass TWA stars. A tentative overpopulation of isolated planetary-mass members similar to 2MASS J11472421-2040204 and 2MASS J11193254-1137466 is identified: this indicates that there might be as many as {10}-5+13 similar members of TWA with hot-start model-dependent masses estimated at ˜5-7 M Jup, most of which would be too faint to be detected in 2MASS. Our new radial velocity measurements corroborate the membership of 2MASS J11472421-2040204, and secure TWA 28 (M8.5 γ), TWA 29 (M9.5 γ), and TWA 33 (M4.5 e) as members. The discovery of 2MASS J09553336-0208403, a young L7-type interloper unrelated to TWA, is also presented.
Carbó-Dorca, Ramon
2013-04-05
A general algorithm implementing a useful variant of quantum quantitative structure-property relationships (QQSPR) theory is described. Based on quantum similarity framework and previous theoretical developments on the subject, the present QQSPR procedure relies on the possibility to perform geometrical origin shifts over molecular density function sets. In this way, molecular collections attached to known properties can be easily used over other quantum mechanically well-described molecular structures for the estimation of their unknown property values. The proposed procedure takes quantum mechanical expectation value as provider of causal relation background and overcomes the dimensionality paradox, which haunts classical descriptor space QSPR. Also, contrarily to classical procedures, which are also attached to heavy statistical gear, the present QQSPR approach might use a geometrical assessment only or just some simple statistical outline or both. From an applied point of view, several easily reachable computational levels can be set up. A Fortran 95 program: QQSPR-n is described with two versions, which might be downloaded from a dedicated web site. Various practical examples are provided, yielding excellent results. Finally, it is also shown that an equivalent molecular space classical QSPR formalism can be easily developed.
Density Functionals of Chemical Bonding
Putz, Mihai V.
2008-01-01
The behavior of electrons in general many-electronic systems throughout the density functionals of energy is reviewed. The basic physico-chemical concepts of density functional theory are employed to highlight the energy role in chemical structure while its extended influence in electronic localization function helps in chemical bonding understanding. In this context the energy functionals accompanied by electronic localization functions may provide a comprehensive description of the global-local levels electronic structures in general and of chemical bonds in special. Becke-Edgecombe and author’s Markovian electronic localization functions are discussed at atomic, molecular and solid state levels. Then, the analytical survey of the main workable kinetic, exchange, and correlation density functionals within local and gradient density approximations is undertaken. The hierarchy of various energy functionals is formulated by employing both the parabolic and statistical correlation degree of them with the electronegativity and chemical hardness indices by means of quantitative structure-property relationship (QSPR) analysis for basic atomic and molecular systems. PMID:19325846
NASA Technical Reports Server (NTRS)
West, J. B.; Elliott, A. R.; Guy, H. J.; Prisk, G. K.
1997-01-01
The lung is exquisitely sensitive to gravity, and so it is of interest to know how its function is altered in the weightlessness of space. Studies on National Aeronautics and Space Administration (NASA) Spacelabs during the last 4 years have provided the first comprehensive data on the extensive changes in pulmonary function that occur in sustained microgravity. Measurements of pulmonary function were made on astronauts during space shuttle flights lasting 9 and 14 days and were compared with extensive ground-based measurements before and after the flights. Compared with preflight measurements, cardiac output increased by 18% during space flight, and stroke volume increased by 46%. Paradoxically, the increase in stroke volume occurred in the face of reductions in central venous pressure and circulating blood volume. Diffusing capacity increased by 28%, and the increase in the diffusing capacity of the alveolar membrane was unexpectedly large based on findings in normal gravity. The change in the alveolar membrane may reflect the effects of uniform filling of the pulmonary capillary bed. Distributions of blood flow and ventilation throughout the lung were more uniform in space, but some unevenness remained, indicating the importance of nongravitational factors. A surprising finding was that airway closing volume was approximately the same in microgravity and in normal gravity, emphasizing the importance of mechanical properties of the airways in determining whether they close. Residual volume was unexpectedly reduced by 18% in microgravity, possibly because of uniform alveolar expansion. The findings indicate that pulmonary function is greatly altered in microgravity, but none of the changes observed so far will apparently limit long-term space flight. In addition, the data help to clarify how gravity affects pulmonary function in the normal gravity environment on Earth.
NASA Astrophysics Data System (ADS)
Lee, M.; Leiter, K.; Eisner, C.; Breuer, A.; Wang, X.
2017-09-01
In this work, we investigate a block Jacobi-Davidson (J-D) variant suitable for sparse symmetric eigenproblems where a substantial number of extremal eigenvalues are desired (e.g., ground-state real-space quantum chemistry). Most J-D algorithm variations tend to slow down as the number of desired eigenpairs increases due to frequent orthogonalization against a growing list of solved eigenvectors. In our specification of block J-D, all of the steps of the algorithm are performed in clusters, including the linear solves, which allows us to greatly reduce computational effort with blocked matrix-vector multiplies. In addition, we move orthogonalization against locked eigenvectors and working eigenvectors outside of the inner loop but retain the single Ritz vector projection corresponding to the index of the correction vector. Furthermore, we minimize the computational effort by constraining the working subspace to the current vectors being updated and the latest set of corresponding correction vectors. Finally, we incorporate accuracy thresholds based on the precision required by the Fermi-Dirac distribution. The net result is a significant reduction in the computational effort against most previous block J-D implementations, especially as the number of wanted eigenpairs grows. We compare our approach with another robust implementation of block J-D (JDQMR) and the state-of-the-art Chebyshev filter subspace (CheFSI) method for various real-space density functional theory systems. Versus CheFSI, for first-row elements, our method yields competitive timings for valence-only systems and 4-6× speedups for all-electron systems with up to 10× reduced matrix-vector multiplies. For all-electron calculations on larger elements (e.g., gold) where the wanted spectrum is quite narrow compared to the full spectrum, we observe 60× speedup with 200× fewer matrix-vector multiples vs. CheFSI.
Lee, M; Leiter, K; Eisner, C; Breuer, A; Wang, X
2017-09-21
In this work, we investigate a block Jacobi-Davidson (J-D) variant suitable for sparse symmetric eigenproblems where a substantial number of extremal eigenvalues are desired (e.g., ground-state real-space quantum chemistry). Most J-D algorithm variations tend to slow down as the number of desired eigenpairs increases due to frequent orthogonalization against a growing list of solved eigenvectors. In our specification of block J-D, all of the steps of the algorithm are performed in clusters, including the linear solves, which allows us to greatly reduce computational effort with blocked matrix-vector multiplies. In addition, we move orthogonalization against locked eigenvectors and working eigenvectors outside of the inner loop but retain the single Ritz vector projection corresponding to the index of the correction vector. Furthermore, we minimize the computational effort by constraining the working subspace to the current vectors being updated and the latest set of corresponding correction vectors. Finally, we incorporate accuracy thresholds based on the precision required by the Fermi-Dirac distribution. The net result is a significant reduction in the computational effort against most previous block J-D implementations, especially as the number of wanted eigenpairs grows. We compare our approach with another robust implementation of block J-D (JDQMR) and the state-of-the-art Chebyshev filter subspace (CheFSI) method for various real-space density functional theory systems. Versus CheFSI, for first-row elements, our method yields competitive timings for valence-only systems and 4-6× speedups for all-electron systems with up to 10× reduced matrix-vector multiplies. For all-electron calculations on larger elements (e.g., gold) where the wanted spectrum is quite narrow compared to the full spectrum, we observe 60× speedup with 200× fewer matrix-vector multiples vs. CheFSI.
Wave-function functionals for the density
Slamet, Marlina; Pan Xiaoyin; Sahni, Viraht
2011-11-15
We extend the idea of the constrained-search variational method for the construction of wave-function functionals {psi}[{chi}] of functions {chi}. The search is constrained to those functions {chi} such that {psi}[{chi}] reproduces the density {rho}(r) while simultaneously leading to an upper bound to the energy. The functionals are thereby normalized and automatically satisfy the electron-nucleus coalescence condition. The functionals {psi}[{chi}] are also constructed to satisfy the electron-electron coalescence condition. The method is applied to the ground state of the helium atom to construct functionals {psi}[{chi}] that reproduce the density as given by the Kinoshita correlated wave function. The expectation of single-particle operators W={Sigma}{sub i}r{sub i}{sup n}, n=-2,-1,1,2, W={Sigma}{sub i}{delta}(r{sub i}) are exact, as must be the case. The expectations of the kinetic energy operator W=-(1/2){Sigma}{sub i}{nabla}{sub i}{sup 2}, the two-particle operators W={Sigma}{sub n}u{sup n}, n=-2,-1,1,2, where u=|r{sub i}-r{sub j}|, and the energy are accurate. We note that the construction of such functionals {psi}[{chi}] is an application of the Levy-Lieb constrained-search definition of density functional theory. It is thereby possible to rigorously determine which functional {psi}[{chi}] is closer to the true wave function.
Studies in Density Functional Theory
NASA Astrophysics Data System (ADS)
Lee, Hsing
The first chapter begins with reviews of density -functional theory and Green's function method. The connections between these two theories are emphasized. Then we present an approximate model of kinetic energy functional and a possible form of the universal functional is given through an equality obeyed by true ground state densities. Chapter two is aimed at developing a general formulation of the response function in density-functional theory. We first give our definition of response functions in the context of functional derivative. The parameter-differentiation technique employed greatly reduces the efforts for computations. The advantage of this method is its numerical simplicity. It is also the aim of this chapter to elucidate the connections between exchange-correlation potential and the response functions. We show that the computations of response functions in the Kohn-Sham formulation will be exact if the so-called uniqueness assumption we present here is true. Various integral formulas for nonlinear response functions are derived here for the first time. In the third chapter we demonstrate that the exchange -correlation functional given in the form of Pade approximation to gradient expansion approximation, yields excellent results when applied to atoms. The coefficients for the Pade approximation are derived by numerical fits to the exchange and exchange -correlation energies of the atoms He through Ar. The fitted non-local gradient corrections are used in the minimization of the Kohn-Sham functional to solve for the exchange and exchange-correlation total energies. The resulting standard deviations in the calculated total energies are 0.0043 for exchange only and 0.0014 for exchange-correlation. The conjoint relation of kinetic and exchange energy functionals is proposed in the fourth chapter. Supportive evidence is given numerically and theoretically. Test cases are the second-row atoms and a group of small molecules with Becke equivalent form, and
Density functional theory: Foundations reviewed
NASA Astrophysics Data System (ADS)
Kryachko, Eugene S.; Ludeña, Eduardo V.
2014-11-01
Guided by the above motto (quotation), we review a broad range of issues lying at the foundations of Density Functional Theory, DFT, a theory which is currently omnipresent in our everyday computational study of atoms and molecules, solids and nano-materials, and which lies at the heart of modern many-body computational technologies. The key goal is to demonstrate that there are definitely the ways to improve DFT. We start by considering DFT in the larger context provided by reduced density matrix theory (RDMT) and natural orbital functional theory (NOFT), and examine the implications that N-representability conditions on the second-order reduced density matrix (2-RDM) have not only on RDMT and NOFT but, also, by extension, on the functionals of DFT. This examination is timely in view of the fact that necessary and sufficient N-representability conditions on the 2-RDM have recently been attained. In the second place, we review some problems appearing in the original formulation of the first Hohenberg-Kohn theorem which is still a subject of some controversy. In this vein we recall Lieb's comment on this proof and the extension to this proof given by Pino et al. (2009), and in this context examine the conditions that must be met in order that the one-to-one correspondence between ground-state densities and external potentials remains valid for finite subspaces (namely, the subspaces where all Kohn-Sham solutions are obtained in practical applications). We also consider the issue of whether the Kohn-Sham equations can be derived from basic principles or whether they are postulated. We examine this problem in relation to ab initio DFT. The possibility of postulating arbitrary Kohn-Sham-type equations, where the effective potential is by definition some arbitrary mixture of local and non-local terms, is discussed. We also deal with the issue of whether there exists a universal functional, or whether one should advocate instead the construction of problem
Density functionals from deep learning
NASA Astrophysics Data System (ADS)
McMahon, Jeffrey
Density-functional theory is a formally exact description of a many-body quantum system in terms of its density; in practice, however, approximations to the universal density functional (DF) are necessary. Machine learning has recently been proposed as a novel approach to discover such a DF (or components of it). Conventional machine learning algorithms, however, are limited in their ability to process data in their raw form, leading to invariance and/or sensitivity issues. In this presentation, an alternative approach based on deep learning will be demonstrated. Deep learning allows computational models that are capable of discovering intricate structure in large and/or high-dimensional data sets with multiple levels of abstraction, and do not suffer from the aforementioned issues. Results from the application of this approach to the prediction of the kinetic-energy DF of noninteracting electrons will be presented. Using theoretical results from computer science, a connection between the underlying model and the theorems of Hohenberg and Kohn will also be suggested.
Scaled density functional theory correlation functionals.
Ghouri, Mohammed M; Singh, Saurabh; Ramachandran, B
2007-10-18
We show that a simple one-parameter scaling of the dynamical correlation energy estimated by the density functional theory (DFT) correlation functionals helps increase the overall accuracy for several local and nonlocal functionals. The approach taken here has been described as the "scaled dynamical correlation" (SDC) method [Ramachandran, J. Phys. Chem. A 2006, 110, 396], and its justification is the same as that of the scaled external correlation (SEC) method of Brown and Truhlar. We examine five local and five nonlocal (hybrid) DFT functionals, the latter group including three functionals developed specifically for kinetics by the Truhlar group. The optimum scale factors are obtained by use of a set of 98 data values consisting of molecules, ions, and transition states. The optimum scale factors, found with a linear regression relationship, are found to differ from unity with a high degree of correlation in nearly every case, indicating that the deviation of calculated results from the experimental values are systematic and proportional to the dynamic correlation energy. As a consequence, the SDC scaling of dynamical correlation decreases the mean errors (signed and unsigned) by significant amounts in an overwhelming majority of cases. These results indicate that there are gains to be realized from further parametrization of several popular exchange-correlation functionals.
Weaver, Michael N.; Ma, Dongxia; Kim, Hyun Jung
2013-01-01
Heats of formation were predicted for nine ZnX complexes (X= Zn, H, O, F2, S, Cl, Cl2, CH3, (CH3)2) using fourteen density functionals, MP2 calculations and the CCSD and CCSD(T) coupled-cluster methods. Calculations utilized the correlation consistent cc-pVTZ and aug-cc-pVTZ basis sets. Heats of formation were most accurately predicted by the TPSSTPSS and TPSSKCIS density functionals, and the BLYP, B3LYP, MP2, CCSD and CCSD(T) levels were among the poorest performing methods based on accuracy. A wide range of Zn2 equilibrium bond distances were predicted, indicating that many of the studied levels of theory may be unable to adequately describe this transition metal dimer. To further benchmark the accuracy of the density functional methods, high-level CASSCF and CASPT2 calculations were performed to estimate bond dissociation energies, equilibrium bond lengths and heats of formation for the diatomic Zn complexes and the latter two quantities were compared with the results of DFT, MP2 and coupled-cluster calculations as well as experimental values. PMID:24409106
Parameterized local hybrid functionals from density-matrix similarity metrics.
Janesko, Benjamin G; Scuseria, Gustavo E
2008-02-28
We recently proposed a real-space similarity metric comparing the Kohn-Sham one-particle density matrix to the local spin-density approximation model density matrix [Janesko and Scuseria, J. Chem. Phys. 127, 164117 (2007)]. This metric provides a useful ingredient for constructing local hybrid density functionals that locally mix exact exchange and semilocal density functional theory exchange. Here we present two lines of inquiry: An approximate similarity metric comparing exact versus generalized gradient approximation (GGA), exchange and parameterized mixing functions using these similarity metrics. This approach yields significantly improved thermochemistry, including GGA local hybrids whose thermochemical performance approaches GGA global hybrids.
Gedanken densities and exact constraints in density functional theory
Perdew, John P.; Ruzsinszky, Adrienn; Sun, Jianwei; Burke, Kieron
2014-05-14
Approximations to the exact density functional for the exchange-correlation energy of a many-electron ground state can be constructed by satisfying constraints that are universal, i.e., valid for all electron densities. Gedanken densities are designed for the purpose of this construction, but need not be realistic. The uniform electron gas is an old gedanken density. Here, we propose a spherical two-electron gedanken density in which the dimensionless density gradient can be an arbitrary positive constant wherever the density is non-zero. The Lieb-Oxford lower bound on the exchange energy can be satisfied within a generalized gradient approximation (GGA) by bounding its enhancement factor or simplest GGA exchange-energy density. This enhancement-factor bound is well known to be sufficient, but our gedanken density shows that it is also necessary. The conventional exact exchange-energy density satisfies no such local bound, but energy densities are not unique, and the simplest GGA exchange-energy density is not an approximation to it. We further derive a strongly and optimally tightened bound on the exchange enhancement factor of a two-electron density, which is satisfied by the local density approximation but is violated by all published GGA's or meta-GGA’s. Finally, some consequences of the non-uniform density-scaling behavior for the asymptotics of the exchange enhancement factor of a GGA or meta-GGA are given.
Space: The Final Frontier of Bone Density
NASA Technical Reports Server (NTRS)
Sibonga, Jean D.
2011-01-01
It is a medical requirement at NASA to evaluate the skeletal integrity of "long-duration" astronauts by measuring bone mineral density [BMD] with DXA technology. A long-duration mission is a spaceflight that is greater than 30 days but is typically the continuous 120-180 day missions aboard the International Space Station [ISS]. Not only does NASA use the BMD index to monitor fracture risk in this astronaut population, but these measures are also used to describe the effects of spaceflight, to certify skeletal health readiness for flight, to monitor the recovery of lost bone mass after return to earth, and to evaluate the efficacy of countermeasures to bone loss. However, despite the fact that DXA-based BMD is a widely-applied surrogate for bone strength that is grounded in an abundance of population-based fracture data, its applicability to the long-duration astronaut is limited. The cohort of long-duration astronauts is not the typical group for evaluating osteoporosis or determining age-related fracture risk. The cohort is young (< 55 years), predominantly male and exposed to novel risk factors for bone loss besides the weightlessness of space. NASA is concerned about early onset osteoporosis in the astronaut exposed to long-duration spaceflight, especially since any detectable symptoms are likely to manifest after return to earth and perhaps years after space travel. This risk raises the question: is NASA doing enough now to mitigate a fracture event that may manifest later? This presentation will discuss the limitations and constraints to understanding skeletal changes due to prolonged spaceflight and the recommendations, by clinical experts in osteoporosis and BMD, to transition research technologies for clinical decision-making by NASA.
Distribution function approach to redshift space distortions
Seljak, Uroš; McDonald, Patrick E-mail: pvmcdonald@lbl.gov
2011-11-01
We develop a phase space distribution function approach to redshift space distortions (RSD), in which the redshift space density can be written as a sum over velocity moments of the distribution function. These moments are density weighted and have well defined physical interpretation: their lowest orders are density, momentum density, and stress energy density. The series expansion is convergent if kμu/aH < 1, where k is the wavevector, H the Hubble parameter, u the typical gravitational velocity and μ = cos θ, with θ being the angle between the Fourier mode and the line of sight. We perform an expansion of these velocity moments into helicity modes, which are eigenmodes under rotation around the axis of Fourier mode direction, generalizing the scalar, vector, tensor decomposition of perturbations to an arbitrary order. We show that only equal helicity moments correlate and derive the angular dependence of the individual contributions to the redshift space power spectrum. We show that the dominant term of μ{sup 2} dependence on large scales is the cross-correlation between the density and scalar part of momentum density, which can be related to the time derivative of the matter power spectrum. Additional terms contributing to μ{sup 2} and dominating on small scales are the vector part of momentum density-momentum density correlations, the energy density-density correlations, and the scalar part of anisotropic stress density-density correlations. The second term is what is usually associated with the small scale Fingers-of-God damping and always suppresses power, but the first term comes with the opposite sign and always adds power. Similarly, we identify 7 terms contributing to μ{sup 4} dependence. Some of the advantages of the distribution function approach are that the series expansion converges on large scales and remains valid in multi-stream situations. We finish with a brief discussion of implications for RSD in galaxies relative to dark matter
Density-functional study of paramagnetic iron
NASA Astrophysics Data System (ADS)
Zhang, Hualei; Johansson, Börje; Vitos, Levente
2011-10-01
By using density-functional theory in combination with the coherent-potential approximation and the disordered local magnetic moment picture, we demonstrate that the competing high-temperature cubic phases of paramagnetic Fe correspond to two distinct total energy minima in the tetragonal (Bain) configurational space. Both the face-centered-cubic (fcc) and the body-centered-cubic (bcc) lattices are dynamically stable, and at static conditions the fcc structure is found to be the thermodynamically stable phase. The theoretical bcc and fcc bulk parameters are in agreement with the experimental data. Due to the shallow energy minimum around the bcc structure, increasing temperature is predicted to stabilize the bcc (δ) phase against the fcc (γ) one.
NASA Astrophysics Data System (ADS)
Joubert, Daniel P.
2012-03-01
It is shown that the density-functional-theory exchange and correlation functionals satisfy 0=γEhx[ρN]+2Ecγ[ρN]-γEhx[ρN-1γ]-2Ecγ[ρN-1γ]+2∫d3r'[ρN-10(r)-ρN-1γ(r)]v0([ρN];r)+∫d3r'[ρN-10(r)-ρN-1γ(r)]r·∇v0([ρN];r)+∫d3r'ρN(r)r·∇vcγ([ρN];r)-∫d3r'ρN-1γ(r)r·∇vcγ([ρN-1γ];r)-∫d3r'fγ(r)r·∇vhxcγ([ρN];r)-2∫d3r'fγ(r)vhxcγ([ρN];r). In the derivation of this equation the adiabatic connection formulation is used, where the ground-state density of an N-electron system ρN is kept constant independent of the electron-electron coupling strength γ. Here Ehx[ρ] is the Hartree plus exchange energy, Ecγ[ρ] is the correlation energy, vhxcγ[ρ] is the Hartree plus exchange-correlation potential, vc[ρ] is the correlation potential, and v0[ρ]is the Kohn-Sham potential. The charge densities ρN and ρN-1γ are the N- and (N-1)-electron ground-state densities of the same Hamiltonian at electron-electron coupling strength γ. fγ(r)=ρN(r)-ρN-1γ(r) is the Fukui function. This equation can be useful in testing the internal self-consistency of approximations to the exchange and correlation functionals. As an example the identity is tested on the analytical Hooke's atom charge density for some frequently used approximate functionals.
Casimir effect for scalar current densities in topologically nontrivial spaces
NASA Astrophysics Data System (ADS)
Bellucci, S.; Saharian, A. A.; Saharyan, N. A.
2015-08-01
We evaluate the Hadamard function and the vacuum expectation value (VEV) of the current density for a charged scalar field, induced by flat boundaries in spacetimes with an arbitrary number of toroidally compactified spatial dimensions. The field operator obeys the Robin conditions on the boundaries and quasiperiodicity conditions with general phases along compact dimensions. In addition, the presence of a constant gauge field is assumed. The latter induces Aharonov-Bohm-type effect on the VEVs. There is a region in the space of the parameters in Robin boundary conditions where the vacuum state becomes unstable. The stability condition depends on the lengths of compact dimensions and is less restrictive than that for background with trivial topology. The vacuum current density is a periodic function of the magnetic flux, enclosed by compact dimensions, with the period equal to the flux quantum. It is explicitly decomposed into the boundary-free and boundary-induced contributions. In sharp contrast to the VEVs of the field squared and the energy-momentum tensor, the current density does not contain surface divergences. Moreover, for Dirichlet condition it vanishes on the boundaries. The normal derivative of the current density on the boundaries vanish for both Dirichlet and Neumann conditions and is nonzero for general Robin conditions. When the separation between the plates is smaller than other length scales, the behavior of the current density is essentially different for non-Neumann and Neumann boundary conditions. In the former case, the total current density in the region between the plates tends to zero. For Neumann boundary condition on both plates, the current density is dominated by the interference part and is inversely proportional to the separation.
On Approximation of Distribution and Density Functions.
ERIC Educational Resources Information Center
Wolff, Hans
Stochastic approximation algorithms for least square error approximation to density and distribution functions are considered. The main results are necessary and sufficient parameter conditions for the convergence of the approximation processes and a generalization to some time-dependent density and distribution functions. (Author)
Density functional theory for carbon dioxide crystal
Chang, Yiwen; Mi, Jianguo Zhong, Chongli
2014-05-28
We present a density functional approach to describe the solid−liquid phase transition, interfacial and crystal structure, and properties of polyatomic CO{sub 2}. Unlike previous phase field crystal model or density functional theory, which are derived from the second order direct correlation function, the present density functional approach is based on the fundamental measure theory for hard-sphere repulsion in solid. More importantly, the contributions of enthalpic interactions due to the dispersive attractions and of entropic interactions arising from the molecular architecture are integrated in the density functional model. Using the theoretical model, the predicted liquid and solid densities of CO{sub 2} at equilibrium triple point are in good agreement with the experimental values. Based on the structure of crystal-liquid interfaces in different planes, the corresponding interfacial tensions are predicted. Their respective accuracies need to be tested.
Magnetic fields and density functional theory
Salsbury Jr., Freddie
1999-02-01
A major focus of this dissertation is the development of functionals for the magnetic susceptibility and the chemical shielding within the context of magnetic field density functional theory (BDFT). These functionals depend on the electron density in the absence of the field, which is unlike any other treatment of these responses. There have been several advances made within this theory. The first of which is the development of local density functionals for chemical shieldings and magnetic susceptibilities. There are the first such functionals ever proposed. These parameters have been studied by constructing functionals for the current density and then using the Biot-Savart equations to obtain the responses. In order to examine the advantages and disadvantages of the local functionals, they were tested numerically on some small molecules.
Space station functional relationships analysis
NASA Technical Reports Server (NTRS)
Tullis, Thomas S.; Bied, Barbra R.
1988-01-01
A systems engineering process is developed to assist Space Station designers to understand the underlying operational system of the facility so that it can be physically arranged and configured to support crew productivity. The study analyzes the operational system proposed for the Space Station in terms of mission functions, crew activities, and functional relationships in order to develop a quantitative model for evaluation of interior layouts, configuration, and traffic analysis for any Station configuration. Development of the model involved identification of crew functions, required support equipment, criteria of assessing functional relationships, and tools for analyzing functional relationship matrices, as well as analyses of crew transition frequency, sequential dependencies, support equipment requirements, potential for noise interference, need for privacy, and overall compatability of functions. The model can be used for analyzing crew functions for the Initial Operating Capability of the Station and for detecting relationships among these functions. Note: This process (FRA) was used during Phase B design studies to test optional layouts of the Space Station habitat module. The process is now being automated as a computer model for use in layout testing of the Space Station laboratory modules during Phase C.
Maps of current density using density-functional methods.
Soncini, A; Teale, A M; Helgaker, T; De Proft, F; Tozer, D J
2008-08-21
The performance of several density-functional theory (DFT) methods for the calculation of current densities induced by a uniform magnetic field is examined. Calculations are performed using the BLYP and KT3 generalized-gradient approximations, together with the B3LYP hybrid functional. For the latter, both conventional and optimized effective potential (OEP) approaches are used. Results are also determined from coupled-cluster singles-and-doubles (CCSD) electron densities by a DFT constrained search procedure using the approach of Wu and Yang (WY). The current densities are calculated within the CTOCD-DZ2 distributed origin approach. Comparisons are made with results from Hartree-Fock (HF) theory. Several small molecules for which correlation is known to be especially important in the calculation of magnetic response properties are considered-namely, O(3), CO, PN, and H(2)CO. As examples of aromatic and antiaromatic systems, benzene and planarized cyclooctatetraene molecules are considered, with specific attention paid to the ring current phenomenon and its Kohn-Sham orbital origin. Finally, the o-benzyne molecule is considered as a computationally challenging case. The HF and DFT induced current maps show qualitative differences, while among the DFT methods the maps show a similar qualitative structure. To assess quantitative differences in the calculated current densities with different methods, the maximal moduli of the induced current densities are compared and integration of the current densities to yield shielding constants is performed. In general, the maximal modulus is reduced in moving from HF to B3LYP and BLYP, and further reduced in moving to KT3, OEP(B3LYP), and WY(CCSD). The latter three methods offer the most accurate shielding constants in comparison with both experimental and ab initio data and hence the more reliable route to DFT calculation of induced current density in molecules.
Maps of current density using density-functional methods
NASA Astrophysics Data System (ADS)
Soncini, A.; Teale, A. M.; Helgaker, T.; de Proft, F.; Tozer, D. J.
2008-08-01
The performance of several density-functional theory (DFT) methods for the calculation of current densities induced by a uniform magnetic field is examined. Calculations are performed using the BLYP and KT3 generalized-gradient approximations, together with the B3LYP hybrid functional. For the latter, both conventional and optimized effective potential (OEP) approaches are used. Results are also determined from coupled-cluster singles-and-doubles (CCSD) electron densities by a DFT constrained search procedure using the approach of Wu and Yang (WY). The current densities are calculated within the CTOCD-DZ2 distributed origin approach. Comparisons are made with results from Hartree-Fock (HF) theory. Several small molecules for which correlation is known to be especially important in the calculation of magnetic response properties are considered-namely, O3, CO, PN, and H2CO. As examples of aromatic and antiaromatic systems, benzene and planarized cyclooctatetraene molecules are considered, with specific attention paid to the ring current phenomenon and its Kohn-Sham orbital origin. Finally, the o-benzyne molecule is considered as a computationally challenging case. The HF and DFT induced current maps show qualitative differences, while among the DFT methods the maps show a similar qualitative structure. To assess quantitative differences in the calculated current densities with different methods, the maximal moduli of the induced current densities are compared and integration of the current densities to yield shielding constants is performed. In general, the maximal modulus is reduced in moving from HF to B3LYP and BLYP, and further reduced in moving to KT3, OEP(B3LYP), and WY(CCSD). The latter three methods offer the most accurate shielding constants in comparison with both experimental and ab initio data and hence the more reliable route to DFT calculation of induced current density in molecules.
A perturbative density functional theory for square-well fluids.
Jin, Zhehui; Tang, Yiping; Wu, Jianzhong
2011-05-07
We report a perturbative density functional theory for quantitative description of the structural and thermodynamic properties of square-well fluids in the bulk or at inhomogeneous conditions. The free-energy functional combines a modified fundamental measure theory to account for the short-range repulsion and a quadratic density expansion for the long-range attraction. The long-correlation effects are taken into account by using analytical expressions of the direct correlation functions of bulk fluids recently obtained from the first-order mean-spherical approximation. The density functional theory has been calibrated by extensive comparison with simulation data from this work and from the literature. The theory yields good agreement with simulation results for the radial distribution function of bulk systems and for the density profiles of square-well fluids near the surfaces of spherical cavities or in slit pores over a broad range of the parameter space and thermodynamic conditions.
A density functional for sparse matter.
Langreth, D C; Lundqvist, B I; Chakarova-Käck, S D; Cooper, V R; Dion, M; Hyldgaard, P; Kelkkanen, A; Kleis, J; Kong, Lingzhu; Li, Shen; Moses, P G; Murray, E; Puzder, A; Rydberg, H; Schröder, E; Thonhauser, T
2009-02-25
Sparse matter is abundant and has both strong local bonds and weak nonbonding forces, in particular nonlocal van der Waals (vdW) forces between atoms separated by empty space. It encompasses a broad spectrum of systems, like soft matter, adsorption systems and biostructures. Density-functional theory (DFT), long since proven successful for dense matter, seems now to have come to a point, where useful extensions to sparse matter are available. In particular, a functional form, vdW-DF (Dion et al 2004 Phys. Rev. Lett. 92 246401; Thonhauser et al 2007 Phys. Rev. B 76 125112), has been proposed for the nonlocal correlations between electrons and applied to various relevant molecules and materials, including to those layered systems like graphite, boron nitride and molybdenum sulfide, to dimers of benzene, polycyclic aromatic hydrocarbons (PAHs), doped benzene, cytosine and DNA base pairs, to nonbonding forces in molecules, to adsorbed molecules, like benzene, naphthalene, phenol and adenine on graphite, alumina and metals, to polymer and carbon nanotube (CNT) crystals, and hydrogen storage in graphite and metal-organic frameworks (MOFs), and to the structure of DNA and of DNA with intercalators. Comparison with results from wavefunction calculations for the smaller systems and with experimental data for the extended ones show the vdW-DF path to be promising. This could have great ramifications.
Spin Density Matrices for Nuclear Density Functionals with Parity Violation
NASA Astrophysics Data System (ADS)
Barrett, Bruce; Giraud, Bertrand
2010-11-01
Within the context of the radial density functional [1], we apply the spin density matrix (SDM) used in atomic and molecular physics [2] to nuclear physics. The vector part of the SDM defines a ``hedgehog'' situation, which exists only if nuclear states contain some amount of parity violation. Thus, looking for the vector profile of the SDM could be used as a test for parity violation in nuclei. The difference between the scalar profile and the vector profile of the SDM will be illustrated by a toy model. [4pt] [1] B. G. Giraud, Phys. Rev. C 78, 014307 (2008).[0pt] [2] A. Goerling, Phys. Rev. A 47, 2783 (1993).
Nagy, A.
2011-09-15
A link between density and pair density functional theories is presented. Density and pair density scaling are used to derive the Euler equation in both theories. Density scaling provides a constructive way of obtaining approximations for the Pauli potential. The Pauli potential (energy) of the density functional theory is expressed as the difference of the scaled and original exchange-correlation potentials (energies).
Cardiovascular function in space flight
NASA Technical Reports Server (NTRS)
Nicogossian, A. E.; Charles, J. B.; Bungo, M. W.; Leach-Huntoon, C. S.
1990-01-01
Postflight orthostatic intolerance and cardiac hemodynamics associated with manned space flight have been investigated on seven STS missions. Orthostatic heart rates appear to be influenced by the mission duration. The rates increase during the first 7-10 days of flight and recover partially after that. Fluid loading is used as a countermeasure to the postflight orthostatic intolerance. The carotid baroreceptor function shows only slight responsiveness to orthostatic stimulation. Plots of the baroreceptor function are presented. It is concluded that an early adaptation to the space flight conditions involves a fluid shift and that the subsequent alterations in the neutral controlling mechanisms contribute to the orthoststic intolerance.
Cardiovascular function in space flight
NASA Technical Reports Server (NTRS)
Nicogossian, A. E.; Charles, J. B.; Bungo, M. W.; Leach-Huntoon, C. S.
1990-01-01
Postflight orthostatic intolerance and cardiac hemodynamics associated with manned space flight have been investigated on seven STS missions. Orthostatic heart rates appear to be influenced by the mission duration. The rates increase during the first 7-10 days of flight and recover partially after that. Fluid loading is used as a countermeasure to the postflight orthostatic intolerance. The carotid baroreceptor function shows only slight responsiveness to orthostatic stimulation. Plots of the baroreceptor function are presented. It is concluded that an early adaptation to the space flight conditions involves a fluid shift and that the subsequent alterations in the neutral controlling mechanisms contribute to the orthoststic intolerance.
Nuclear Energy Density Functional for KIDS
NASA Astrophysics Data System (ADS)
Gil, H.; Papakonstantinou, P.; Hyun, C. H.; Park, T.-S.; Oh, Y.
The density functional theory (DFT) is based on the existence and uniqueness of a universal functional $E[\\rho]$, which determines the dependence of the total energy on single-particle density distributions. However, DFT says nothing about the form of the functional. Our strategy is to first look at what we know, from independent considerations, about the analytical density dependence of the energy of nuclear matter and then, for practical applications, to obtain an appropriate density-dependent effective interaction by reverse engineering. In a previous work on homogeneous matter, we identified the most essential terms to include in our "KIDS" functional, named after the early-stage participating institutes. We now present first results for finite nuclei, namely the energies and radii of $^{16,28}$O, $^{40,60}$Ca.
Density Scaling of Noninteracting Kinetic Energy Functionals.
Borgoo, Alex; Tozer, David J
2013-05-14
The influence of imposing an approximate density scaling condition on a noninteracting kinetic energy functional is investigated. A simple generalized gradient approximation (GGA) is presented, which satisfies both the density scaling condition and the usual coordinate scaling condition; the remaining multiplicative constant is determined from an energy criterion. In post-Kohn-Sham calculations, noninteracting kinetic energies of the closed-shell molecules of the G1 set determined using the GGA are a modest improvement over those determined using the corresponding local functional, which does not satisfy the density scaling condition. Potential energy curves of CO, F2, and P2 exhibit binding with the GGA, compared to purely repulsive curves with the local functional. Adjusting the exponent in the GGA form in order to optimize energy accuracy violates the density scaling condition, and two of the diatomics no longer exhibit binding. Results are compared with those from other local/GGA functionals in the literature.
Development of New Density Functional Approximations
NASA Astrophysics Data System (ADS)
Su, Neil Qiang; Xu, Xin
2017-05-01
Kohn-Sham density functional theory has become the leading electronic structure method for atoms, molecules, and extended systems. It is in principle exact, but any practical application must rely on density functional approximations (DFAs) for the exchange-correlation energy. Here we emphasize four aspects of the subject: (a) philosophies and strategies for developing DFAs; (b) classification of DFAs; (c) major sources of error in existing DFAs; and (d) some recent developments and future directions.
NASA Astrophysics Data System (ADS)
Ho, Gregory S.; Lignères, Vincent L.; Carter, Emily A.
2008-07-01
We derive an analytic form of the Wang-Govind-Carter (WGC) [Wang , Phys. Rev. B 60, 16350 (1999)] kinetic energy density functional (KEDF) with the density-dependent response kernel. A real-space aperiodic implementation of the WGC KEDF is then described and used in linear scaling orbital-free density functional theory (OF-DFT) calculations.
Vowel space density as an indicator of speech performance.
Story, Brad H; Bunton, Kate
2017-05-01
The purpose of this study was to develop a method for visualizing and assessing the characteristics of vowel production by measuring the local density of normalized F1 and F2 formant frequencies. The result is a three-dimensional plot called the vowel space density (VSD) and indicates the regions in the vowel space most heavily used by a talker during speech production. The area of a convex hull enclosing the vowel space at specific threshold density values was proposed as a means of quantifying the VSD.
Gourlaouen, Christophe; Piquemal, Jean-Philip; Parisel, Olivier
2006-05-07
Within the scope of studying the molecular implications of the Pb(2+) cation in environmental and polluting processes, this paper reports Hartree-Fock and density functional theory (B3LYP) four-component relativistic calculations using an all-electron basis set applied to [Pb(H(2)O)](2+) and [Pb(OH)](+), two complexes expected to be found in the terrestrial atmosphere. It is shown that full-relativistic calculations validate the use of scalar relativistic approaches within the framework of density functional theory. [Pb(H(2)O)](2+) is found C(2v) at any level of calculations whereas [Pb(OH)](+) can be found bent or linear depending of the computational methodology used. When C(s) is found the barrier to inversion through the C(infinityv) structure is very low, and can be overcome at high enough temperature, making the molecule floppy. In order to get a better understanding of the bonding occurring between the Pb(2+) cation and the H(2)O and OH(-) ligands, natural bond orbital and atoms-in-molecule calculations have been performed. These approaches are supplemented by a topological analysis of the electron localization function. Finally, the description of these complexes is refined using constrained-space orbital variation complexation energy decompositions.
Function Spaces for Liquid Crystals
NASA Astrophysics Data System (ADS)
Bedford, Stephen
2016-02-01
We consider the relationship between three continuum liquid crystal theories: Oseen-Frank, Ericksen and Landau-de Gennes. It is known that the function space is an important part of the mathematical model and by considering various function space choices for the order parameters s, n, and Q, we establish connections between the variational formulations of these theories. We use these results to justify a version of the Oseen-Frank theory using special functions of bounded variation. This proposed model can describe both orientable and non-orientable defects. Finally we study a number of frustrated nematic and cholesteric liquid crystal systems and show that the model predicts the existence of point and surface discontinuities in the director.
WSN-Based Space Charge Density Measurement System
Deng, Dawei; Yuan, Haiwen; Lv, Jianxun; Ju, Yong
2017-01-01
It is generally acknowledged that high voltage direct current (HVDC) transmission line endures the drawback of large area, because of which the utilization of cable for space charge density monitoring system is of inconvenience. Compared with the traditional communication network, wireless sensor network (WSN) shows advantages in small volume, high flexibility and strong self-organization, thereby presenting great potential in solving the problem. Additionally, WSN is more suitable for the construction of distributed space charge density monitoring system as it has longer distance and higher mobility. A distributed wireless system is designed for collecting and monitoring the space charge density under HVDC transmission lines, which has been widely applied in both Chinese state grid HVDC test base and power transmission projects. Experimental results of the measuring system demonstrated its adaptability in the complex electromagnetic environment under the transmission lines and the ability in realizing accurate, flexible, and stable demands for the measurement of space charge density. PMID:28052105
WSN-Based Space Charge Density Measurement System.
Deng, Dawei; Yuan, Haiwen; Lv, Jianxun; Ju, Yong
2017-01-01
It is generally acknowledged that high voltage direct current (HVDC) transmission line endures the drawback of large area, because of which the utilization of cable for space charge density monitoring system is of inconvenience. Compared with the traditional communication network, wireless sensor network (WSN) shows advantages in small volume, high flexibility and strong self-organization, thereby presenting great potential in solving the problem. Additionally, WSN is more suitable for the construction of distributed space charge density monitoring system as it has longer distance and higher mobility. A distributed wireless system is designed for collecting and monitoring the space charge density under HVDC transmission lines, which has been widely applied in both Chinese state grid HVDC test base and power transmission projects. Experimental results of the measuring system demonstrated its adaptability in the complex electromagnetic environment under the transmission lines and the ability in realizing accurate, flexible, and stable demands for the measurement of space charge density.
Whitenack, Daniel L; Wasserman, Adam
2012-04-28
Aspects of density functional resonance theory (DFRT) [D. L. Whitenack and A. Wasserman, Phys. Rev. Lett. 107, 163002 (2011)], a recently developed complex-scaled version of ground-state density functional theory (DFT), are studied in detail. The asymptotic behavior of the complex density function is related to the complex resonance energy and system's threshold energy, and the function's local oscillatory behavior is connected with preferential directions of electron decay. Practical considerations for implementation of the theory are addressed including sensitivity to the complex-scaling parameter, θ. In Kohn-Sham DFRT, it is shown that almost all θ-dependence in the calculated energies and lifetimes can be extinguished via use of a proper basis set or fine grid. The highest occupied Kohn-Sham orbital energy and lifetime are related to physical affinity and width, and the threshold energy of the Kohn-Sham system is shown to be equal to the threshold energy of the interacting system shifted by a well-defined functional. Finally, various complex-scaling conditions are derived which relate the functionals of ground-state DFT to those of DFRT via proper scaling factors and a non-Hermitian coupling-constant system.
"Sloppy" nuclear energy density functionals: Effective model reduction
NASA Astrophysics Data System (ADS)
Nikšić, Tamara; Vretenar, Dario
2016-08-01
Concepts from information geometry are used to analyze parameter sensitivity for a nuclear energy density functional, representative of a class of semiempirical functionals that start from a microscopically motivated ansatz for the density dependence of the energy of a system of protons and neutrons. It is shown that such functionals are "sloppy," namely, characterized by an exponential range of sensitivity to parameter variations. Responsive to only a few stiff parameter combinations, sloppy functionals exhibit an exponential decrease of sensitivity to variations of the remaining soft parameters. By interpreting the space of model predictions as a manifold embedded in the data space, with the parameters of the functional as coordinates on the manifold, it is also shown that the exponential distribution of model manifold widths corresponds to the range of parameter sensitivity. Using the manifold boundary approximation method, we illustrate how to systematically construct effective nuclear density functionals of successively lower dimension in parameter space until sloppiness is eventually eliminated and the resulting functional contains only stiff combinations of parameters.
Nonlocal kinetic-energy-density functionals
Garcia-Gonzalez, P.; Alvarellos, J.E.; Chacon, E. |
1996-04-01
In this paper we present nonlocal kinetic-energy functionals {ital T}[{ital n}] within the average density approximation (ADA) framework, which do not require any extra input when applied to any electron system and recover the exact kinetic energy and the linear response function of a homogeneous system. In contrast with previous ADA functionals, these present good behavior of the long-range tail of the exact weight function. The averaging procedure for the kinetic functional (averaging the Fermi momentum of the electron gas, instead of averaging the electron density) leads to a functional without numerical difficulties in the calculation of extended systems, and it gives excellent results when applied to atoms and jellium surfaces. {copyright} {ital 1996 The American Physical Society.}
Optimization of an exchange-correlation density functional for water
NASA Astrophysics Data System (ADS)
Fritz, Michelle; Fernández-Serra, Marivi; Soler, José M.
2016-06-01
We describe a method, that we call data projection onto parameter space (DPPS), to optimize an energy functional of the electron density, so that it reproduces a dataset of experimental magnitudes. Our scheme, based on Bayes theorem, constrains the optimized functional not to depart unphysically from existing ab initio functionals. The resulting functional maximizes the probability of being the "correct" parameterization of a given functional form, in the sense of Bayes theory. The application of DPPS to water sheds new light on why density functional theory has performed rather poorly for liquid water, on what improvements are needed, and on the intrinsic limitations of the generalized gradient approximation to electron exchange and correlation. Finally, we present tests of our water-optimized functional, that we call vdW-DF-w, showing that it performs very well for a variety of condensed water systems.
Periodic subsystem density-functional theory
Genova, Alessandro; Pavanello, Michele; Ceresoli, Davide
2014-11-07
By partitioning the electron density into subsystem contributions, the Frozen Density Embedding (FDE) formulation of subsystem Density Functional Theory (DFT) has recently emerged as a powerful tool for reducing the computational scaling of Kohn–Sham DFT. To date, however, FDE has been employed to molecular systems only. Periodic systems, such as metals, semiconductors, and other crystalline solids have been outside the applicability of FDE, mostly because of the lack of a periodic FDE implementation. To fill this gap, in this work we aim at extending FDE to treat subsystems of molecular and periodic character. This goal is achieved by a dual approach. On one side, the development of a theoretical framework for periodic subsystem DFT. On the other, the realization of the method into a parallel computer code. We find that periodic FDE is capable of reproducing total electron densities and (to a lesser extent) also interaction energies of molecular systems weakly interacting with metallic surfaces. In the pilot calculations considered, we find that FDE fails in those cases where there is appreciable density overlap between the subsystems. Conversely, we find FDE to be in semiquantitative agreement with Kohn–Sham DFT when the inter-subsystem density overlap is low. We also conclude that to make FDE a suitable method for describing molecular adsorption at surfaces, kinetic energy density functionals that go beyond the GGA level must be employed.
Periodic subsystem density-functional theory
NASA Astrophysics Data System (ADS)
Genova, Alessandro; Ceresoli, Davide; Pavanello, Michele
2014-11-01
By partitioning the electron density into subsystem contributions, the Frozen Density Embedding (FDE) formulation of subsystem Density Functional Theory (DFT) has recently emerged as a powerful tool for reducing the computational scaling of Kohn-Sham DFT. To date, however, FDE has been employed to molecular systems only. Periodic systems, such as metals, semiconductors, and other crystalline solids have been outside the applicability of FDE, mostly because of the lack of a periodic FDE implementation. To fill this gap, in this work we aim at extending FDE to treat subsystems of molecular and periodic character. This goal is achieved by a dual approach. On one side, the development of a theoretical framework for periodic subsystem DFT. On the other, the realization of the method into a parallel computer code. We find that periodic FDE is capable of reproducing total electron densities and (to a lesser extent) also interaction energies of molecular systems weakly interacting with metallic surfaces. In the pilot calculations considered, we find that FDE fails in those cases where there is appreciable density overlap between the subsystems. Conversely, we find FDE to be in semiquantitative agreement with Kohn-Sham DFT when the inter-subsystem density overlap is low. We also conclude that to make FDE a suitable method for describing molecular adsorption at surfaces, kinetic energy density functionals that go beyond the GGA level must be employed.
Periodic subsystem density-functional theory.
Genova, Alessandro; Ceresoli, Davide; Pavanello, Michele
2014-11-07
By partitioning the electron density into subsystem contributions, the Frozen Density Embedding (FDE) formulation of subsystem Density Functional Theory (DFT) has recently emerged as a powerful tool for reducing the computational scaling of Kohn-Sham DFT. To date, however, FDE has been employed to molecular systems only. Periodic systems, such as metals, semiconductors, and other crystalline solids have been outside the applicability of FDE, mostly because of the lack of a periodic FDE implementation. To fill this gap, in this work we aim at extending FDE to treat subsystems of molecular and periodic character. This goal is achieved by a dual approach. On one side, the development of a theoretical framework for periodic subsystem DFT. On the other, the realization of the method into a parallel computer code. We find that periodic FDE is capable of reproducing total electron densities and (to a lesser extent) also interaction energies of molecular systems weakly interacting with metallic surfaces. In the pilot calculations considered, we find that FDE fails in those cases where there is appreciable density overlap between the subsystems. Conversely, we find FDE to be in semiquantitative agreement with Kohn-Sham DFT when the inter-subsystem density overlap is low. We also conclude that to make FDE a suitable method for describing molecular adsorption at surfaces, kinetic energy density functionals that go beyond the GGA level must be employed.
Density Functionals with Broad Applicability in Chemistry
Zhao, Yan; Truhlar, Donald G.
2008-02-01
The research described in this product was performed in part in the Environmental Molecular Sciences Laboratory, a national scientific user facility sponsored by the Department of Energy's Office of Biological and Environmental Research and located at Pacific Northwest National Laboratory. Although density functional theory is widely used in the computational chemistry community, the most popular density functional, B3LYP, has some serious shortcomings: (i) it is better for main-group chemistry than for transition metals; (ii) it systematically underestimates reaction barrier heights; (iii) it is inaccurate for interactions dominated by mediumrange correlation energy, such as van der Waals attraction, aromatic-aromatic stacking, and alkane isomerization energies. We have developed a variety of databases for testing and designing new density functionals. We used these data to design new density functionals, called M06-class (and, earlier, M05-class) functionals, for which we enforced some fundamental exact constraints such as the uniform-electron-gas limit and the absence of self-correlation energy. Our M06-class functionals depend on spin-up and spin-down electron densities (i.e., spin densities), spin density gradients, spin kinetic energy densities, and, for nonlocal (also called hybrid) functionals, Hartree-Fock exchange. We have developed four new functionals that overcome the above-mentioned difficulties: (a) M06, a hybrid meta functional, is a functional with good accuracy “across-theboard” for transition metals, main group thermochemistry, medium-range correlation energy, and barrier heights; (b) M06- 2X, another hybrid meta functional, is not good for transition metals but has excellent performance for main group chemistry, predicts accurate valence and Rydberg electronic excitation energies, and is an excellent functional for aromatic-aromatic stacking interactions; (c) M06-L is not as accurate as M06 for barrier heights but is the most accurate
Nucleon localization within nuclear density functional theory
NASA Astrophysics Data System (ADS)
Zhang, Chunli; Schuetrumpf, Bastian; Nazarewicz, Witold
2016-09-01
Recently, a nucleon localization measure based on Hartree-Fock densities has been introduced to investigate α-cluster structures in light nuclei. Compared to the local nucleonic density, the nucleon localization function (NLF) has been shown to be an excellent indicator of cluster correlations. To investigate the cluster structures in light nuclei and study the development of fission fragments in heavy nuclei, we analyse NLFs in deformed nuclei. We use both the deformed harmonic oscillator model and self-consistent nuclear density functional theory (DFT) with energy density functionals UNEDF1 and UNEDF1-HFB, which were optimized for fission studies. In this contribution, we will discuss particle densities and spatial localization functions for deformed configurations of 8Be and 20Ne and along fission pathways of 232Th and 240Pu. We illustrate the usefulness of the NLF by showing how the third hyperdeformed minimum of 232Th can be understood in terms of the ground states of 132Sn and 100Zr. This material is based upon work supported by the U.S. Department of Energy, Office of Science under Award Numbers DOE-DE-NA0002847, DE-SC0013365 (Michigan State University), and DE-SC0008511 (NUCLEI SciDAC-3 collaboration).
Van der Waals density functional: An appropriate exchange functional
NASA Astrophysics Data System (ADS)
Cooper, Valentino R.
2010-04-01
In this Rapid Communication, an exchange functional which is compatible with the nonlocal Rutgers-Chalmers correlation functional [van der Waals density functional (vdW-DF)] is presented. This functional, when employed with vdW-DF, demonstrates remarkable improvements on intermolecular separation distances while further improving the accuracy of vdW-DF interaction energies. The key to the success of this three-parameter functional is its reduction in short-range exchange repulsion through matching to the gradient expansion approximation in the slowly varying/high-density limit while recovering the large reduced gradient, s , limit set in the revised Perdew-Burke-Ernzerhof (revPBE) exchange functional. This augmented exchange functional could be a solution to long-standing issues of vdW-DF lending to further applicability of density-functional theory to the study of relatively large, dispersion bound (van der Waals) complexes.
Error analysis in nuclear density functional theory
NASA Astrophysics Data System (ADS)
Schunck, Nicolas; McDonnell, Jordan D.; Sarich, Jason; Wild, Stefan M.; Higdon, Dave
2015-03-01
Nuclear density functional theory (DFT) is the only microscopic, global approach to the structure of atomic nuclei. It is used in numerous applications, from determining the limits of stability to gaining a deep understanding of the formation of elements in the Universe or the mechanisms that power stars and reactors. The predictive power of the theory depends on the amount of physics embedded in the energy density functional as well as on efficient ways to determine a small number of free parameters and solve the DFT equations. In this article, we discuss the various sources of uncertainties and errors encountered in DFT and possible methods to quantify these uncertainties in a rigorous manner.
Connection formulas for thermal density functional theory
Pribram-Jones, A.; Burke, K.
2016-05-23
We show that the adiabatic connection formula of ground-state density functional theory relates the correlation energy to a coupling-constant integral over a purely potential contribution, and is widely used to understand and improve approximations. The corresponding formula for thermal density functional theory is cast as an integral over temperatures instead, ranging upward from the system's physical temperature. We also show how to relate different correlation components to each other, either in terms of temperature or coupling-constant integrations. Lastly, we illustrate our results on the uniform electron gas.
Error Analysis in Nuclear Density Functional Theory
Schunck, Nicolas; McDonnell, Jordan D.; Sarich, Jason; Wild, Stefan M.; Higdon, Dave
2015-03-01
Nuclear density functional theory (DFT) is the only microscopic, global approach to the structure of atomic nuclei. It is used in numerous applications, from determining the limits of stability to gaining a deep understanding of the formation of elements in the Universe or the mechanisms that power stars and reactors. The predictive power of the theory depends on the amount of physics embedded in the energy density functional as well as on efficient ways to determine a small number of free parameters and solve the DFT equations. In this article, we discuss the various sources of uncertainties and errors encountered in DFT and possible methods to quantify these uncertainties in a rigorous manner.
Koopmans' condition for density-functional theory
Dabo, Ismaila; Ferretti, Andrea; Poilvert, Nicolas; Marzari, Nicola; Li, Yanli; Cococcioni, Matteo
2010-09-15
In approximate Kohn-Sham density-functional theory, self-interaction manifests itself as the dependence of the energy of an orbital on its fractional occupation. This unphysical behavior translates into qualitative and quantitative errors that pervade many fundamental aspects of density-functional predictions. Here, we first examine self-interaction in terms of the discrepancy between total and partial electron removal energies, and then highlight the importance of imposing the generalized Koopmans' condition - that identifies orbital energies as opposite total electron removal energies - to resolve this discrepancy. In the process, we derive a correction to approximate functionals that, in the frozen-orbital approximation, eliminates the unphysical occupation dependence of orbital energies up to the third order in the single-particle densities. This non-Koopmans correction brings physical meaning to single-particle energies; when applied to common local or semilocal density functionals it provides results that are in excellent agreement with experimental data - with an accuracy comparable to that of GW many-body perturbation theory - while providing an explicit total energy functional that preserves or improves on the description of established structural properties.
Cardiovascular function in space flight
NASA Technical Reports Server (NTRS)
Nicogossian, A. E.; Charles, J. B.; Bungo, M. W.; Leach-Huntoon, C. S.; Nicgossian, A. E.
1991-01-01
Changes in orthostatic heart rate have been noted universally in Soviet and U.S. crewmembers post space flight. The magnitude of these changes appears to be influenced by mission duration, with increasing orthostatic intolerance for the first 7-10 days of flight and then a partial recovery in the orthostatic heart rate response. Fluid loading has been used as a countermeasure to this postflight orthostatic intolerance. Previous reports have documented the effectiveness of this technique, but it has also been noted that the effectiveness of volume expansion diminishes as flight duration exceeds one week. The response of carotid baroreceptor function was investigated utilizing a commercially available neck collar which could apply positive and negative pressure to effect receptor stimulation. Bedrest studies had validated the usefulness and validity of the device. In these studies it was shown that carotid baroreceptor function curves demonstrated less responsiveness to orthostatic stimulation than control individuals. Twelve Space Shuttle crewmembers were examined pre- and postflight from flights lasting from 4-5 days. Plots of baroreceptor function were constructed and plotted as change in R-R interval vs. carotid distending pressure (an orthostatic stimulus). Typical sigmoidal curves were obtained. Postflight the resting heart rate was higher (smaller R-R interval) and the range of R-R value and the slope of the carotid sigmoidal response were both depressed. These changes were not significant immediately postflight (L + O), but did become significant by the second day postflight (L + 2), and remained suppressed for several days thereafter. It is hypothesized that the early adaptation to space flight involves a central fluid shift during the initial days of flight, but subsequent alterations in neural controlling mechanisms (such as carotid baroreceptor function) contribute to orthostatic intolerance.
Cardiovascular function in space flight
NASA Technical Reports Server (NTRS)
Nicogossian, A. E.; Charles, J. B.; Bungo, M. W.; Leach-Huntoon, C. S.; Nicgossian, A. E.
1991-01-01
Changes in orthostatic heart rate have been noted universally in Soviet and U.S. crewmembers post space flight. The magnitude of these changes appears to be influenced by mission duration, with increasing orthostatic intolerance for the first 7-10 days of flight and then a partial recovery in the orthostatic heart rate response. Fluid loading has been used as a countermeasure to this postflight orthostatic intolerance. Previous reports have documented the effectiveness of this technique, but it has also been noted that the effectiveness of volume expansion diminishes as flight duration exceeds one week. The response of carotid baroreceptor function was investigated utilizing a commercially available neck collar which could apply positive and negative pressure to effect receptor stimulation. Bedrest studies had validated the usefulness and validity of the device. In these studies it was shown that carotid baroreceptor function curves demonstrated less responsiveness to orthostatic stimulation than control individuals. Twelve Space Shuttle crewmembers were examined pre- and postflight from flights lasting from 4-5 days. Plots of baroreceptor function were constructed and plotted as change in R-R interval vs. carotid distending pressure (an orthostatic stimulus). Typical sigmoidal curves were obtained. Postflight the resting heart rate was higher (smaller R-R interval) and the range of R-R value and the slope of the carotid sigmoidal response were both depressed. These changes were not significant immediately postflight (L + O), but did become significant by the second day postflight (L + 2), and remained suppressed for several days thereafter. It is hypothesized that the early adaptation to space flight involves a central fluid shift during the initial days of flight, but subsequent alterations in neural controlling mechanisms (such as carotid baroreceptor function) contribute to orthostatic intolerance.
Communication: Embedded fragment stochastic density functional theory
Neuhauser, Daniel; Baer, Roi; Rabani, Eran
2014-07-28
We develop a method in which the electronic densities of small fragments determined by Kohn-Sham density functional theory (DFT) are embedded using stochastic DFT to form the exact density of the full system. The new method preserves the scaling and the simplicity of the stochastic DFT but cures the slow convergence that occurs when weakly coupled subsystems are treated. It overcomes the spurious charge fluctuations that impair the applications of the original stochastic DFT approach. We demonstrate the new approach on a fullerene dimer and on clusters of water molecules and show that the density of states and the total energy can be accurately described with a relatively small number of stochastic orbitals.
Density functional calculation of intermolecular potentials.
Nyeland, Carl
2011-06-30
Calculations of intermolecular potentials following the density functional theory (DFT) turn out to be very complicated without using some appropriate approximations. Most often the following three approximations have been considered. In one approximation the disturbed charge distributions during collisions are reduced to sums of undisturbed charge distributions from the colliding species. In another approximation, the so-called local density approximation (LDA), one neglects the fact that the intermolecular potentials that depend on charge densities also depend on gradients in the densities. In a third approximation one assumes that the intermolecular potential can be considered as a sum of two terms: a term for the long-range geometry and a term for the short-range geometry. In this Article the three approximations mentioned will be discussed for numerical accuracy for calculations of potentials between inert gas atoms and for calculations of potentials between surfaces and inert gas atoms. In the discussion a few other approximations will be mentioned too.
Kvaal, Simen; Helgaker, Trygve
2015-11-14
The relationship between the densities of ground-state wave functions (i.e., the minimizers of the Rayleigh-Ritz variation principle) and the ground-state densities in density-functional theory (i.e., the minimizers of the Hohenberg-Kohn variation principle) is studied within the framework of convex conjugation, in a generic setting covering molecular systems, solid-state systems, and more. Having introduced admissible density functionals as functionals that produce the exact ground-state energy for a given external potential by minimizing over densities in the Hohenberg-Kohn variation principle, necessary and sufficient conditions on such functionals are established to ensure that the Rayleigh-Ritz ground-state densities and the Hohenberg-Kohn ground-state densities are identical. We apply the results to molecular systems in the Born-Oppenheimer approximation. For any given potential v ∈ L(3/2)(ℝ(3)) + L(∞)(ℝ(3)), we establish a one-to-one correspondence between the mixed ground-state densities of the Rayleigh-Ritz variation principle and the mixed ground-state densities of the Hohenberg-Kohn variation principle when the Lieb density-matrix constrained-search universal density functional is taken as the admissible functional. A similar one-to-one correspondence is established between the pure ground-state densities of the Rayleigh-Ritz variation principle and the pure ground-state densities obtained using the Hohenberg-Kohn variation principle with the Levy-Lieb pure-state constrained-search functional. In other words, all physical ground-state densities (pure or mixed) are recovered with these functionals and no false densities (i.e., minimizing densities that are not physical) exist. The importance of topology (i.e., choice of Banach space of densities and potentials) is emphasized and illustrated. The relevance of these results for current-density-functional theory is examined.
Lehtovaara, Lauri; Havu, Ville; Puska, Martti
2009-08-07
We present for static density functional theory and time-dependent density functional theory calculations an all-electron method which employs high-order hierarchical finite-element bases. Our mesh generation scheme, in which structured atomic meshes are merged to an unstructured molecular mesh, allows a highly nonuniform discretization of the space. Thus it is possible to represent the core and valence states using the same discretization scheme, i.e., no pseudopotentials or similar treatments are required. The nonuniform discretization also allows the use of large simulation cells, and therefore avoids any boundary effects.
NASA Astrophysics Data System (ADS)
Mukamel, Shaul
2005-02-01
Time-ordered superoperators are used to develop a unified description of nonlinear density response and spontaneous fluctuations of many-electron systems. The pth -order density response functions are decomposed into 2p+1 non-causal Liouville space pathways. Individual pathways are symmetric to the interchange of their space, time, and superoperator indices and can thus be calculated as functional derivatives. Other combinations of these pathways represent spontaneous density fluctuations and the response of such fluctuations to an external field. The resolution of the causality paradox of time-dependent density-functional theory (TDDFT) is shown to be intimately connected with the nonretarded nature of fluctuations.
Density functional theory studies of etoricoxib
NASA Astrophysics Data System (ADS)
Sachdeva, Ritika; Kaur, Prabhjot; Singh, V. P.; Saini, G. S. S.
2016-05-01
Etoricoxib is a COX-2 selective inhibitor drug with molecular formula C18H15ClN2O2S. It is primarily used for the treatment of arthritis(rheumatoid, psoriatic, osteoarthritis), ankylosing spondylitis, gout and chronic low back pain. Theoretical studies of the molecule including geometry optimization and vibrational frequency calculations were carried out with the help of density functional theory calculations using 6-311++ g (d, p) basis set and B3LYP functional.
Radiative Strength Functions and Level Densities
Schiller, A; Becker, J A; Bernstein, L A; Voinov, A; Guttormsen, M; Hjorth-Jensen, M; Rekstad, J; Siem, S; Mitchell, G E; Tavukcu, E
2002-08-28
Radiative strength functions and level densities have been extracted from primary {gamma}-ray spectra for {sup 27,28}Si, {sup 56,57}Fe, {sup 96,97}Mo, and several rare earth nuclei. An unexpectedly strong ({approx} 1 mb MeV) resonance at 3 MeV in the radiative strength function has been observed for well-deformed rare earth nuclei. The physical origin of this resonance and its connection to the scissors mode is discussed.
Density functional theory: Fixing Jacob's ladder
NASA Astrophysics Data System (ADS)
Car, Roberto
2016-09-01
Density functional theory calculations can be carried out with different levels of accuracy, forming a hierarchy that is often represented by the rungs of a ladder. Now a new method has been developed that significantly improves the accuracy of the 'third rung' when calculating the properties of diversely bonded systems.
Uncertainty Quantification for Nuclear Density Functional Theory
NASA Astrophysics Data System (ADS)
McDonnell, Jordan; Schunck, Nicolas; Nazarewicz, Witold; Higdon, Dave; Sarich, Jason; Wild, Stefan
2014-09-01
Nuclear density functional theory exhibits good overall agreement with measured nuclear masses for medium-mass to heavy nuclei. But the predictions of various models diverge substantially near the neutron and proton drip lines. Quantifying the theory's inherent uncertainty is essential for making reliable predictions. Through a Bayesian analysis, we calculate the theoretical uncertainty for nuclear masses obtained with a Skyrme-class energy density functional. We also assess whether a recent set of mass measurements of neutron-rich nuclei reduces the uncertainty in this model's predictions near the neutron drip line. Nuclear density functional theory exhibits good overall agreement with measured nuclear masses for medium-mass to heavy nuclei. But the predictions of various models diverge substantially near the neutron and proton drip lines. Quantifying the theory's inherent uncertainty is essential for making reliable predictions. Through a Bayesian analysis, we calculate the theoretical uncertainty for nuclear masses obtained with a Skyrme-class energy density functional. We also assess whether a recent set of mass measurements of neutron-rich nuclei reduces the uncertainty in this model's predictions near the neutron drip line. This work was supported by the US Department of Energy under Contracts No. DE-SC0008499 and No. DE-AC52-07NA27344.
Space Shuttle critical function audit
NASA Technical Reports Server (NTRS)
Sacks, Ivan J.; Dipol, John; Su, Paul
1990-01-01
A large fault-tolerance model of the main propulsion system of the US space shuttle has been developed. This model is being used to identify single components and pairs of components that will cause loss of shuttle critical functions. In addition, this model is the basis for risk quantification of the shuttle. The process used to develop and analyze the model is digraph matrix analysis (DMA). The DMA modeling and analysis process is accessed via a graphics-based computer user interface. This interface provides coupled display of the integrated system schematics, the digraph models, the component database, and the results of the fault tolerance and risk analyses.
Space Shuttle critical function audit
NASA Technical Reports Server (NTRS)
Sacks, Ivan J.; Dipol, John; Su, Paul
1990-01-01
A large fault-tolerance model of the main propulsion system of the US space shuttle has been developed. This model is being used to identify single components and pairs of components that will cause loss of shuttle critical functions. In addition, this model is the basis for risk quantification of the shuttle. The process used to develop and analyze the model is digraph matrix analysis (DMA). The DMA modeling and analysis process is accessed via a graphics-based computer user interface. This interface provides coupled display of the integrated system schematics, the digraph models, the component database, and the results of the fault tolerance and risk analyses.
Optimization of a van der Waals Density Functional for water
NASA Astrophysics Data System (ADS)
Fritz, Michelle; Fernandez-Serra, Marivi; Soler, Jose M.
2015-03-01
In particularly delicate systems, like liquid water, ab initio exchange and correlation functionals are simply not accurate enough for many practical applications. In these cases, fitting the functional to reference data is a sensible alternative to empirical interatomic potentials. However, a global optimization requires functional forms that depend on many parameters and the usual trial and error strategy becomes cumbersome and suboptimal. We present a general and powerful optimization scheme called data projection onto parameter space (DPPS). In an arbitrarily large parameter space, DPPS expands the vector of unknown parameters in vectors of known data. Poorly sampled subspaces are determined by the physically-motivated functional shape of ab initio functionals, using Bayes' theory to combine this prior information with reference energies and electron densities of monomers, clusters, and condensed phases of water. We aknowledge support from FIS2012-37549 (MF and JMS) and DOE Early Career Award No. DE-SC0003871 (M.-V.F.-S.)
Lee, Jin-Woong; Singh, Satendra Pal; Kim, Minseuk; Hong, Sung Un; Park, Woon Bae; Sohn, Kee-Sun
2017-08-21
A metaheuristics-based design would be of great help in relieving the enormous experimental burdens faced during the combinatorial screening of a huge, multidimensional search space, while providing the same effect as total enumeration. In order to tackle the high-throughput powder processing complications and to secure practical phosphors, metaheuristics, an elitism-reinforced nondominated sorting genetic algorithm (NSGA-II), was employed in this study. The NSGA-II iteration targeted two objective functions. The first was to search for a higher emission efficacy. The second was to search for narrow-band green color emissions. The NSGA-II iteration finally converged on BaLi2Al2Si2N6:Eu(2+) phosphors in the Eu(2+)-doped Ca-Sr-Ba-Li-Mg-Al-Si-Ge-N compositional search space. The BaLi2Al2Si2N6:Eu(2+) phosphor, which was synthesized with no human intervention via the assistance of NSGA-II, was a clear single phase and gave an acceptable luminescence. The BaLi2Al2Si2N6:Eu(2+) phosphor as well as all other phosphors that appeared during the NSGA-II iterations were examined in detail by employing powder X-ray diffraction-based Rietveld refinement, X-ray absorption near edge structure, density functional theory calculation, and time-resolved photoluminescence. The thermodynamic stability and the band structure plausibility were confirmed, and more importantly a novel approach to the energy transfer analysis was also introduced for BaLi2Al2Si2N6:Eu(2+) phosphors.
Density-functional description of electrides.
Dale, Stephen G; Otero-de-la-Roza, Alberto; Johnson, Erin R
2014-07-28
Electrides are a unique class of ionic solids in which the anions are stoichiometrically replaced by electrons localised within the crystal voids. There are only nine electrides with known crystal structures and their study represents a challenge for theory. A systematic investigation of their electronic structure is conducted using semilocal density-functional theory (DFT) in this article. The band structure is calculated for each electride and a range of techniques including plots of the valence densities, procrystal densities, non-covalent interaction isosurfaces, and Bader's quantum-chemical topology are applied. All of these methods provide consistent results, confirming the presence of localised interstitial electrons and demonstrating that these crystals display a characteristic electronic structure.
Frozen density embedding with hybrid functionals
NASA Astrophysics Data System (ADS)
Laricchia, S.; Fabiano, E.; Della Sala, F.
2010-10-01
The Kohn-Sham equations with constrained electron density are extended to hybrid exchange-correlation (XC) functionals. We derive the frozen density embedding generalized Kohn-Sham (FDE-GKS) scheme which allows to treat the nonlocal exact-exchange in the subsystems. For practical calculations we propose an approximated version of the FDE-GKS in which the nonadditive exchange potential is computed at a semilocal level. The proposed method is applied to compute the ground-state electronic properties of small test systems and selected DNA base pairs. The results of calculations employing the hierarchy of XC functionals BLYP/B3LYP/BHLYP and PBE/PBE0 are presented, in order to analyze the effect of nonlocal exchange contributions, and compared with reference coupled-cluster singles and doubles results. We find that the use of hybrid functionals leads to a significant improvement in the description of ground-state electronic properties of the investigated systems. The semilocal version of the FDE-GKS correctly reproduces the dipole and the electron density distribution of the exact GKS supramolecular system, with errors smaller than the ones obtained using conventional semilocal XC functionals.
NASA Astrophysics Data System (ADS)
Toshihiro, Handa; Takahiro, Yoda; Nario, Kuno
2015-03-01
In the steady state, the probability density function (PDF) of the gaseous interstellar matter (ISM) can be observed as a gas density histogram (GDH) of all cells in the system. We made GDHs of the Milky Way Galaxy (MWG) using Galactic plane surveys in CO lines. We found that the GDH in the MWG is log-normal which suggests that the density structure of the molecular gas is a result of many stochastic processes. Using the Nobeyama CO atlas, we made GDHs of nearby galaxies but in column density. Although some galaxies show log-normal, the others show completely different shapes, suggesting that the density structure of galaxies may be different from galaxy to galaxy.
Dynamic density functional theory versus kinetic theory of simple fluids.
Marini Bettolo Marconi, Umberto; Melchionna, Simone
2010-09-15
By combining methods of kinetic and density functional theory, we present a description of molecular fluids which accounts for their microscopic structure and thermodynamic properties as well as their hydrodynamic behavior. We focus on the evolution of the one-particle phase space distribution, rather than on the evolution of the average particle density which features in dynamic density functional theory. The resulting equation can be studied in two different physical limits: diffusive dynamics, typical of colloidal fluids without hydrodynamic interaction where particles are subject to overdamped motion resulting from coupling with a solvent at rest, and inertial dynamics, typical of molecular fluids. Finally, we propose an algorithm to solve numerically and efficiently the resulting kinetic equation by employing a discretization procedure analogous to the one used in the lattice Boltzmann method.
Teaching Density Functional Theory Through Experiential Learning
NASA Astrophysics Data System (ADS)
Narasimhan, Shobhana
2015-09-01
Today, quantum mechanical density functional theory is often the method of choice for performing accurate calculations on atomic, molecular and condensed matter systems. Here, I share some of my experiences in teaching the necessary basics of solid state physics, as well as the theory and practice of density functional theory, in a number of workshops held in developing countries over the past two decades. I discuss the advantages of supplementing the usual mathematically formal teaching methods, characteristic of graduate courses, with the use of visual imagery and analogies. I also describe a successful experiment we carried out, which resulted in a joint publication co-authored by 67 lecturers and students participating in a summer school.
"Sloppy" nuclear energy density functionals. II. Finite nuclei
NASA Astrophysics Data System (ADS)
Nikšić, T.; Imbrišak, M.; Vretenar, D.
2017-05-01
A study of parameter sensitivity of nuclear energy density functionals, initiated in the first part of this work [Nikšić and Vretenar, Phys. Rev. C 94, 024333 (2016), 10.1103/PhysRevC.94.024333], is extended by the inclusion of data on ground-state properties of finite nuclei in the application of the manifold boundary approximation method (MBAM). Density functionals used in self-consistent mean-field calculations, and nuclear structure models based on them, are generally "sloppy" and exhibit an exponential range of sensitivity to parameter variations. Concepts of information geometry are used to identify the presence of effective functionals of lower dimension in parameter space associated with parameter combinations that can be tightly constrained by data. The MBAM is used in an iterative procedure that systematically reduces the complexity and dimension of parameter space of a sloppy functional, with properties of nuclear matter and data on finite nuclei determining not only the values of model parameters but also the optimal functional form of the density dependence.
The problem of the universal density functional and the density matrix functional theory
Bobrov, V. B. Trigger, S. A.
2013-04-15
The analysis in this paper shows that the Hohenberg-Kohn theorem is the constellation of two statements: (i) the mathematically rigorous Hohenberg-Kohn lemma, which demonstrates that the same ground-state density cannot correspond to two different potentials of an external field, and (ii) the hypothesis of the existence of the universal density functional. Based on the obtained explicit expression for the nonrel-ativistic particle energy in a local external field, we prove that the energy of the system of more than two non-interacting electrons cannot be a functional of the inhomogeneous density. This result is generalized to the system of interacting electrons. It means that the Hohenberg-Kohn lemma cannot provide justification of the universal density functional for fermions. At the same time, statements of the density functional theory remain valid when considering any number of noninteracting ground-state bosons due to the Bose condensation effect. In the framework of the density matrix functional theory, the hypothesis of the existence of the universal density matrix functional corresponds to the cases of noninteracting particles and to interaction in the Hartree-Fock approximation.
NASA Astrophysics Data System (ADS)
Pribram-Jones, Aurora
Warm dense matter (WDM) is a high energy phase between solids and plasmas, with characteristics of both. It is present in the centers of giant planets, within the earth's core, and on the path to ignition of inertial confinement fusion. The high temperatures and pressures of warm dense matter lead to complications in its simulation, as both classical and quantum effects must be included. One of the most successful simulation methods is density functional theory-molecular dynamics (DFT-MD). Despite great success in a diverse array of applications, DFT-MD remains computationally expensive and it neglects the explicit temperature dependence of electron-electron interactions known to exist within exact DFT. Finite-temperature density functional theory (FT DFT) is an extension of the wildly successful ground-state DFT formalism via thermal ensembles, broadening its quantum mechanical treatment of electrons to include systems at non-zero temperatures. Exact mathematical conditions have been used to predict the behavior of approximations in limiting conditions and to connect FT DFT to the ground-state theory. An introduction to FT DFT is given within the context of ensemble DFT and the larger field of DFT is discussed for context. Ensemble DFT is used to describe ensembles of ground-state and excited systems. Exact conditions in ensemble DFT and the performance of approximations depend on ensemble weights. Using an inversion method, exact Kohn-Sham ensemble potentials are found and compared to approximations. The symmetry eigenstate Hartree-exchange approximation is in good agreement with exact calculations because of its inclusion of an ensemble derivative discontinuity. Since ensemble weights in FT DFT are temperature-dependent Fermi weights, this insight may help develop approximations well-suited to both ground-state and FT DFT. A novel, highly efficient approach to free energy calculations, finite-temperature potential functional theory, is derived, which has the
Spaces defined by the Paley function
Astashkin, S V; Semenov, E M
2013-07-31
The paper is concerned with Haar and Rademacher series in symmetric spaces, and also with the properties of spaces defined by the Paley function. In particular, the symmetric hull of the space of functions with uniformly bounded Paley function is found. Bibliography: 27 titles.
Computing dispersion interactions in density functional theory
NASA Astrophysics Data System (ADS)
Cooper, V. R.; Kong, L.; Langreth, D. C.
2010-02-01
In this article techniques for including dispersion interactions within density functional theory are examined. In particular comparisons are made between four popular methods: dispersion corrected DFT, pseudopotential correction schemes, symmetry adapted perturbation theory, and a non-local density functional - the so called Rutgers-Chalmers van der Waals density functional (vdW-DF). The S22 benchmark data set is used to evaluate the relative accuracy of these methods and factors such as scalability and transferability are also discussed. We demonstrate that vdW-DF presents an excellent compromise between computational speed and accuracy and lends most easily to full scale application in solid materials. This claim is supported through a brief discussion of a recent large scale application to H2 in a prototype metal organic framework material (MOF), Zn2BDC2TED. The vdW-DF shows overwhelming promise for first-principles studies of physisorbed molecules in porous extended systems; thereby having broad applicability for studies as diverse as molecular adsorption and storage, battery technology, catalysis and gas separations.
A density functional approach to ferrogels
NASA Astrophysics Data System (ADS)
Cremer, P.; Heinen, M.; Menzel, A. M.; Löwen, H.
2017-07-01
Ferrogels consist of magnetic colloidal particles embedded in an elastic polymer matrix. As a consequence, their structural and rheological properties are governed by a competition between magnetic particle-particle interactions and mechanical matrix elasticity. Typically, the particles are permanently fixed within the matrix, which makes them distinguishable by their positions. Over time, particle neighbors do not change due to the fixation by the matrix. Here we present a classical density functional approach for such ferrogels. We map the elastic matrix-induced interactions between neighboring colloidal particles distinguishable by their positions onto effective pairwise interactions between indistinguishable particles similar to a ‘pairwise pseudopotential’. Using Monte-Carlo computer simulations, we demonstrate for one-dimensional dipole-spring models of ferrogels that this mapping is justified. We then use the pseudopotential as an input into classical density functional theory of inhomogeneous fluids and predict the bulk elastic modulus of the ferrogel under various conditions. In addition, we propose the use of an ‘external pseudopotential’ when one switches from the viewpoint of a one-dimensional dipole-spring object to a one-dimensional chain embedded in an infinitely extended bulk matrix. Our mapping approach paves the way to describe various inhomogeneous situations of ferrogels using classical density functional concepts of inhomogeneous fluids.
A density functional approach to ferrogels.
Cremer, P; Heinen, M; Menzel, A M; Löwen, H
2017-07-12
Ferrogels consist of magnetic colloidal particles embedded in an elastic polymer matrix. As a consequence, their structural and rheological properties are governed by a competition between magnetic particle-particle interactions and mechanical matrix elasticity. Typically, the particles are permanently fixed within the matrix, which makes them distinguishable by their positions. Over time, particle neighbors do not change due to the fixation by the matrix. Here we present a classical density functional approach for such ferrogels. We map the elastic matrix-induced interactions between neighboring colloidal particles distinguishable by their positions onto effective pairwise interactions between indistinguishable particles similar to a 'pairwise pseudopotential'. Using Monte-Carlo computer simulations, we demonstrate for one-dimensional dipole-spring models of ferrogels that this mapping is justified. We then use the pseudopotential as an input into classical density functional theory of inhomogeneous fluids and predict the bulk elastic modulus of the ferrogel under various conditions. In addition, we propose the use of an 'external pseudopotential' when one switches from the viewpoint of a one-dimensional dipole-spring object to a one-dimensional chain embedded in an infinitely extended bulk matrix. Our mapping approach paves the way to describe various inhomogeneous situations of ferrogels using classical density functional concepts of inhomogeneous fluids.
Kinetic energy in density-functional theory
NASA Astrophysics Data System (ADS)
Nesbet, R. K.
1998-07-01
While Kohn-Sham theory uses the quantum-mechanical operator for kinetic energy, Thomas-Fermi theory replaces this with an effective local potential. If both theories are based on the exact universal density functional defined by Hohenberg-Kohn theory, it is an interesting question whether they should give the same results for N-electron ground states. This question is examined and answered in the negative. The inconsistency is resolved only by extending the definition of functional derivatives to encompass linear operators. An exact theory must incorporate one-electron energies and occupation numbers derived from Kohn-Sham theory.
Multiple Streaming and the Probability Distribution of Density in Redshift Space
NASA Astrophysics Data System (ADS)
Hui, Lam; Kofman, Lev; Shandarin, Sergei F.
2000-07-01
We examine several aspects of redshift distortions by expressing the redshift-space density in terms of the eigenvalues and orientation of the local Lagrangian deformation tensor. We explore the importance of multiple streaming using the Zeldovich approximation (ZA), and compute the average number of streams in both real and redshift space. We find that multiple streaming can be significant in redshift space but negligible in real space, even at moderate values of the linear fluctuation amplitude (σl<~1). Moreover, unlike their real-space counterparts, redshift-space multiple streams can flow past each other with minimal interactions. Such nonlinear redshift-space effects, which are physically distinct from the fingers-of-God due to small-scale virialized motions, might in part explain the well-known departure of redshift distortions from the classic linear prediction by Kaiser, even at relatively large scales where the corresponding density field in real space is well described by linear perturbation theory. We also compute, using the ZA, the probability distribution function (PDF) of the density, as well as S3, in real and redshift space, and compare it with the PDF measured from N-body simulations. The role of caustics in defining the character of the high-density tail is examined. We find that (non-Lagrangian) smoothing, due to both finite resolution or discreteness and small-scale velocity dispersions, is very effective in erasing caustic structures, unless the initial power spectrum is sufficiently truncated.
Extended screened exchange functional derived from transcorrelated density functional theory
NASA Astrophysics Data System (ADS)
Umezawa, Naoto
2017-09-01
We propose a new formulation of the correlation energy functional derived from the transcorrelated method in use in density functional theory (TC-DFT). An effective Hamiltonian, HTC, is introduced by a similarity transformation of a many-body Hamiltonian, H , with respect to a complex function F: HTC=1/F H F . It is proved that an expectation value of HTC for a normalized single Slater determinant, Dn, corresponds to the total energy: E [n ] = ⟨Ψn|H |Ψn ⟩ /⟨Ψn|Ψn ⟩ = ⟨Dn|HTC|Dn ⟩ under the two assumptions: (1) The electron density n (r ) associated with a trial wave function Ψn = DnF is v -representable and (2) Ψn and Dn give rise to the same electron density n (r ). This formulation, therefore, provides an alternative expression of the total energy that is useful for the development of novel correlation energy functionals. By substituting a specific function for F, we successfully derived a model correlation energy functional, which resembles the functional form of the screened exchange method. The proposed functional, named the extended screened exchange (ESX) functional, is described within two-body integrals and is parametrized for a numerically exact correlation energy of the homogeneous electron gas. The ESX functional does not contain any ingredients of (semi-)local functionals and thus is totally free from self-interactions. The computational cost for solving the self-consistent-field equation is comparable to that of the Hartree-Fock method. We apply the ESX functional to electronic structure calculations for a solid silicon, H- ion, and small atoms. The results demonstrate that the TC-DFT formulation is promising for the systematic improvement of the correlation energy functional.
Extended screened exchange functional derived from transcorrelated density functional theory.
Umezawa, Naoto
2017-09-14
We propose a new formulation of the correlation energy functional derived from the transcorrelated method in use in density functional theory (TC-DFT). An effective Hamiltonian, HTC, is introduced by a similarity transformation of a many-body Hamiltonian, H, with respect to a complex function F: HTC=1FHF. It is proved that an expectation value of HTC for a normalized single Slater determinant, D(n), corresponds to the total energy: E[n] = ⟨Ψ(n)|H|Ψ(n)⟩/⟨Ψ(n)|Ψ(n)⟩ = ⟨D(n)|HTC|D(n)⟩ under the two assumptions: (1) The electron density nr associated with a trial wave function Ψ(n) = D(n)F is v-representable and (2) Ψ(n) and D(n) give rise to the same electron density nr. This formulation, therefore, provides an alternative expression of the total energy that is useful for the development of novel correlation energy functionals. By substituting a specific function for F, we successfully derived a model correlation energy functional, which resembles the functional form of the screened exchange method. The proposed functional, named the extended screened exchange (ESX) functional, is described within two-body integrals and is parametrized for a numerically exact correlation energy of the homogeneous electron gas. The ESX functional does not contain any ingredients of (semi-)local functionals and thus is totally free from self-interactions. The computational cost for solving the self-consistent-field equation is comparable to that of the Hartree-Fock method. We apply the ESX functional to electronic structure calculations for a solid silicon, H(-) ion, and small atoms. The results demonstrate that the TC-DFT formulation is promising for the systematic improvement of the correlation energy functional.
Density functional theory for atomic Fermi gases
NASA Astrophysics Data System (ADS)
Ma, Ping Nang; Pilati, Sebastiano; Troyer, Matthias; Dai, Xi
2012-08-01
The interplay between interaction and inhomogeneity for electrons in solids generates many interesting phenomena, including insulating and metallic behaviour, magnetism, superconductivity, quantum criticality and more exotic phases. Many of the same phenomena appear in ultracold fermionic atoms in optical lattices, which provide clean, controlled and tunable `quantum simulators' to explore the intriguing physics of fermionic systems. Although density functional theory (DFT) is widely used to calculate material properties, it has not yet been applied to cold atomic gases in optical lattices. Here we present a new density functional for short-range interactions (as opposed to Coulomb interactions of electrons), which renders DFT suitable for atomic Fermi gases. This grants us access to an extensive toolset, previously developed for materials simulations, to calculate the static and dynamic properties of atomic Fermi gases in optical lattices and external potentials. Ultracold atom quantum simulators can in turn be used to explore limitations of DFT functionals, and to further improve hybrid functionals, thus forming a bridge between materials simulations and atomic physics.
Sublinear scaling for time-dependent stochastic density functional theory
Gao, Yi; Neuhauser, Daniel; Baer, Roi; Rabani, Eran
2015-01-21
A stochastic approach to time-dependent density functional theory is developed for computing the absorption cross section and the random phase approximation (RPA) correlation energy. The core idea of the approach involves time-propagation of a small set of stochastic orbitals which are first projected on the occupied space and then propagated in time according to the time-dependent Kohn-Sham equations. The evolving electron density is exactly represented when the number of random orbitals is infinite, but even a small number (≈16) of such orbitals is enough to obtain meaningful results for absorption spectrum and the RPA correlation energy per electron. We implement the approach for silicon nanocrystals using real-space grids and find that the overall scaling of the algorithm is sublinear with computational time and memory.
Morphology Effects on Space Charge Characteristics of Low Density Polyethylene
NASA Astrophysics Data System (ADS)
Zhou; Yuanxiang; Wang; Yunshan; Zahn, Markus; Wang; Ninghua; Sun; Qinghua; Liang; Xidong; Guan; Zhichen
2011-01-01
Low density polyethylene (LDPE) film samples with different morphology were prepared by three kinds of annealing methods which were different in cooling rates in this study. A pulsed electro-acoustic (PEA) space charge measurement system was improved to solve the surface discharge problems for small samples applied with a high voltage. Negative direct current (DC) fields from 50 to above 220 kV/mm were applied to the samples. The influences of morphologies on space charge and space charge packet characteristics were measured by the improved high voltage withstand (HVW) PEA system. Mobility and trap depth of released charges were calculated by space charge decay. It was found that there is a different probability of space charge packet initiation under applied field from -60 to -100 kV/mm. Average velocity and mobility of the space charge packets were calculated by space charge packet dynamics. It was found that the lower cooling rate samples have higher crystallinity, more homo-charge accumulation, lower mobility and deeper trap depth. The mechanism of morphological effects on space charge phenomena have been presumed to give a plausible explanation for their inherent relationships. The morphology in the metal-dielectric interface and in the bulk is convincingly suggested to be responsible for the injection and propagation processes of space charge. A model of positive space charge initiation in LDPE samples was also suggested and analyzed. The mechanism of morphological effects and the charge injection model are well fit with the injection and propagation processes of space charge. The different effects of morphology in the metal-dielectric interface and in the bulk of polymers are stressed.
Optimization of constrained density functional theory
NASA Astrophysics Data System (ADS)
O'Regan, David D.; Teobaldi, Gilberto
2016-07-01
Constrained density functional theory (cDFT) is a versatile electronic structure method that enables ground-state calculations to be performed subject to physical constraints. It thereby broadens their applicability and utility. Automated Lagrange multiplier optimization is necessary for multiple constraints to be applied efficiently in cDFT, for it to be used in tandem with geometry optimization, or with molecular dynamics. In order to facilitate this, we comprehensively develop the connection between cDFT energy derivatives and response functions, providing a rigorous assessment of the uniqueness and character of cDFT stationary points while accounting for electronic interactions and screening. In particular, we provide a nonperturbative proof that stable stationary points of linear density constraints occur only at energy maxima with respect to their Lagrange multipliers. We show that multiple solutions, hysteresis, and energy discontinuities may occur in cDFT. Expressions are derived, in terms of convenient by-products of cDFT optimization, for quantities such as the dielectric function and a condition number quantifying ill definition in multiple constraint cDFT.
Recent progress in density functional theory
NASA Astrophysics Data System (ADS)
Truhlar, Donald
2014-03-01
Ongoing work involves several areas of density functional theory: new methods for computing electronic excitation energies, including a new way to remove spin contamination in the spin-flip Tamm-Dancoff approximation and a configuration-interaction-corrected Tamm-Dancoff Approximation for treating conical intersections; new ways to treat open-shell states, including a reinterpreted broken-symmetry method and multi-configuration Kohn-Sham theory; a new exchange-correlation functional; new tests of density functional theory against databases for electronic transition energies and molecules and solids containing metal atoms; and applications. A selection of results will be presented. I am grateful to the following collaborators for contributions to the ongoing work: Boris Averkiev, Rebecca Carlson, Laura Fernandez, Laura Gagliardi, Chad Hoyer, Francesc Illas, Miho Isegawa, Shaohong Li, Giovanni Li Manni, Sijie Luo, Dongxia Ma, Remi Maurice, Rubén Means-Pañeda, Roberto Peverati, Nora Planas, Prasenjit Seal, Pragya Verma, Bo Wang, Xuefei Xu, Ke R. Yang, Haoyu Yu, Wenjing Zhang, and Jingjing Zheng. Supported in part by the AFOSR and U.S. DOE.
Modulation Based on Probability Density Functions
NASA Technical Reports Server (NTRS)
Williams, Glenn L.
2009-01-01
A proposed method of modulating a sinusoidal carrier signal to convey digital information involves the use of histograms representing probability density functions (PDFs) that characterize samples of the signal waveform. The method is based partly on the observation that when a waveform is sampled (whether by analog or digital means) over a time interval at least as long as one half cycle of the waveform, the samples can be sorted by frequency of occurrence, thereby constructing a histogram representing a PDF of the waveform during that time interval.
Insight and progress in density functional theory
NASA Astrophysics Data System (ADS)
Yang, Weitao; Mori-Sanchez, Paula; Cohen, Aron J.
2012-12-01
Density functional theory of electronic structure is widely and successfully applied in simulations throughout engineering and sciences. However, there are spectacular failures for many predicted properties. The errors include underestimation of the barriers of chemical reactions, the band gaps of materials, the energies of dissociating molecular ions and charge transfer excitation energies. Typical DFT calculations also fail to describe degenerate or near degenerate systems, as arise in the breaking of chemical bonds, and strongly correlated materials. These errors can all be characterized and understood through the perspective of fractional charges and fractional spins introduced recently.
Probability density functions in turbulent channel flow
NASA Technical Reports Server (NTRS)
Dinavahi, Surya P. G.
1992-01-01
The probability density functions (pdf's) of the fluctuating velocity components, as well as their first and second derivatives, are calculated using data from the direct numerical simulations (DNS) of fully developed turbulent channel flow. It is observed that, beyond the buffer region, the pdf of each of these quantities is independent of the distance from the channel wall. It is further observed that, beyond the buffer region, the pdf's for all the first derivatives collapse onto a single universal curve and those of the second derivatives also collapse onto another universal curve, irrespective of the distance from the wall. The kinetic-energy dissipation rate exhibits log normal behavior.
Density functional theory of charged colloidal systems
Chan, Derek Y. C.
2001-06-01
The phase behavior of charged colloidal systems has been studied recently by the density functional theory formalism (DFT) [R. van Roij, M. Dijkstra, and J. P. Hansen, Phys. Rev. E >59, 2010 (1999)]. A key feature of this approach is the appearance of a density and temperature-dependent effective Hamiltonian between the charged colloids. Under certain approximations, the effective Hamiltonian is made up only of a sum of position-independent one-body or volume terms and two-body colloid-separation dependent terms. In the limit of low colloidal densities, the DFT results do not reduce to the familiar Debye-Huckel limiting law nor do the results agree with previous work based on an identical approach but were developed using traditional statistical-mechanical methods [B. Beresford-Smith, D. Y. C. Chan, and D. J. Mitchell J. Colloid Interface Sci. >105, 216 (1985)]. This paper provides a reconciliation of these differences and comments on the significance of the one-body volume terms in the effective Hamiltonian of a system of charged colloids in determining thermodynamics and phase behavior.
Positive spaces, generalized semi-densities, and quantum interactions
NASA Astrophysics Data System (ADS)
Canarutto, Daniel
2012-03-01
The basics of quantum particle physics on a curved Lorentzian background are expressed in a formulation which has original aspects and exploits some non-standard mathematical notions. In particular, positive spaces and generalized semi-densities (in a distributional sense) are shown to link, in a natural way, discrete multi-particle spaces to distributional bundles of quantum states. The treatment of spinor and boson fields is partly original also from an algebraic point of view and suggests a non-standard approach to quantum interactions. The case of electroweak interactions provides examples.
Constrained density functional for noncollinear magnetism
NASA Astrophysics Data System (ADS)
Ma, Pui-Wai; Dudarev, S. L.
2015-02-01
Energies of arbitrary small- and large-angle noncollinear excited magnetic configurations are computed using a highly accurate constrained density functional theory approach. Numerical convergence and accuracy are controlled by the choice of Lagrange multipliers λI entering the constraining conditions. The penalty part Ep of the constrained energy functional at its minimum is shown to be inversely proportional to λI, enabling a simple, robust, and accurate iterative procedure to be followed to find a convergent solution. The method is implemented as a part of ab initio vasp package, and applied to the investigation of noncollinear B2-like and <001 > double-layer antiferromagnetic configurations of bcc iron, Fe2 dimer, and amorphous iron. Forces acting on atoms depend on the orientations of magnetic moments, and the proposed approach enables constrained self-consistent noncollinear magnetic and structural relaxation of large atomic systems to be carried out.
New algebraic formulation of density functional calculation
NASA Astrophysics Data System (ADS)
Ismail-Beigi, Sohrab; Arias, T. A.
2000-06-01
This article addresses a fundamental problem faced by the community employing single-particle ab initio methods: the lack of an effective formalism for the rapid exploration and exchange of new methods. To rectify this, we introduce a new, basis-set independent, matrix-based formulation of generalized density functional theories which reduces the development, implementation, and dissemination of new techniques to the derivation and transcription of a few lines of algebra. This new framework enables us to concisely demystify the inner workings of fully functional, highly efficient modern ab initio codes and to give complete instructions for their construction for calculations employing arbitrary basis sets. Within this framework, we also discuss in full detail a variety of leading-edge techniques, minimization algorithms, and highly efficient computational kernels for use with scalar as well as shared and distributed-memory supercomputer architectures.
Density-functional theory for complex fluids.
Wu, Jianzhong; Li, Zhidong
2007-01-01
Density-functional theory (DFT) and its variations provide a fruitful approach to the computational modeling of the microscopic structures and phase behavior of soft-condensed matter. The methodology takes deep root in quantum mechanics but shares a mathematical similarity with a number of classical approaches in statistical mechanics. This review discusses different strategies commonly used to formulate the free-energy functional of complex fluids for either phenomena-oriented applications or as a generic description of the thermodynamic nonideality owing to various components of intermolecular forces. We emphasize the connections among different schemes of DFT approximations, their underlying assumptions, and inherent limitations. We also address extensions of equilibrium DFT to phenomenological theories for the dynamic properties of complex fluids and for the kinetics of phase transitions. In addition, we highlight the recent literature concerning applications of DFT to diverse static and time-dependent phenomena in complex fluids.
Lieleg, Corinna; Ketterer, Philip; Nuebler, Johannes; Ludwigsen, Johanna; Gerland, Ulrich; Dietz, Hendrik
2015-01-01
Arrays of regularly spaced nucleosomes are a hallmark of chromatin, but it remains unclear how they are generated. Recent genome-wide studies, in vitro and in vivo, showed constant nucleosome spacing even if the histone concentration was experimentally reduced. This counters the long-held assumption that nucleosome density determines spacing and calls for factors keeping spacing constant regardless of nucleosome density. We call this a clamping activity. Here, we show in a purified system that ISWI- and CHD1-type nucleosome remodelers have a clamping activity such that they not only generate regularly spaced nucleosome arrays but also generate constant spacing regardless of nucleosome density. This points to a functionally attractive nucleosome interaction that could be mediated either directly by nucleosome-nucleosome contacts or indirectly through the remodelers. Mutant Drosophila melanogaster ISWI without the HAND-SANT-SLIDE (HSS) domain had no detectable spacing activity even though it is known to remodel and slide nucleosomes. This suggests that the role of ISWI remodelers in generating constant spacing is not just to mediate nucleosome sliding; they actively contribute to the attractive interaction. Additional factors are necessary to set physiological spacing in absolute terms. PMID:25733687
Lieleg, Corinna; Ketterer, Philip; Nuebler, Johannes; Ludwigsen, Johanna; Gerland, Ulrich; Dietz, Hendrik; Mueller-Planitz, Felix; Korber, Philipp
2015-05-01
Arrays of regularly spaced nucleosomes are a hallmark of chromatin, but it remains unclear how they are generated. Recent genome-wide studies, in vitro and in vivo, showed constant nucleosome spacing even if the histone concentration was experimentally reduced. This counters the long-held assumption that nucleosome density determines spacing and calls for factors keeping spacing constant regardless of nucleosome density. We call this a clamping activity. Here, we show in a purified system that ISWI- and CHD1-type nucleosome remodelers have a clamping activity such that they not only generate regularly spaced nucleosome arrays but also generate constant spacing regardless of nucleosome density. This points to a functionally attractive nucleosome interaction that could be mediated either directly by nucleosome-nucleosome contacts or indirectly through the remodelers. Mutant Drosophila melanogaster ISWI without the Hand-Sant-Slide (HSS) domain had no detectable spacing activity even though it is known to remodel and slide nucleosomes. This suggests that the role of ISWI remodelers in generating constant spacing is not just to mediate nucleosome sliding; they actively contribute to the attractive interaction. Additional factors are necessary to set physiological spacing in absolute terms.
Self-contained filtered density function
NASA Astrophysics Data System (ADS)
Nouri, A. G.; Nik, M. B.; Givi, P.; Livescu, D.; Pope, S. B.
2017-09-01
The filtered density function (FDF) closure is extended to a "self-contained" format to include the subgrid-scale (SGS) statistics of all of the hydro-thermo-chemical variables in turbulent flows. These are the thermodynamic pressure, the specific internal energy, the velocity vector, and the composition field. In this format, the model is comprehensive and facilitates large-eddy simulation (LES) of flows at both low and high compressibility levels. A transport equation is developed for the joint pressure-energy-velocity-composition filtered mass density function (PEVC-FMDF). In this equation, the effect of convection appears in closed form. The coupling of the hydrodynamics and thermochemistry is modeled via a set of stochastic differential equation for each of the transport variables. This yields a self-contained SGS closure. For demonstration, LES is conducted of a turbulent shear flow with transport of a passive scalar. The consistency of the PEVC-FMDF formulation is established, and its overall predictive capability is appraised via comparison with direct numerical simulation (DNS) data.
Band terminations in density functional theory
Afanasjev, A. V.
2008-11-15
The analysis of the terminating bands has been performed in the relativistic mean field framework. It was shown that nuclear magnetism provides an additional binding to the energies of the specific configuration and this additional binding increases with spin and has its maximum exactly at the terminating state. This suggests that the terminating states can be an interesting probe of the time-odd mean fields provided that other effects can be reliably isolated. Unfortunately, a reliable isolation of these effects is not that simple: many terms of the density functional theories contribute into the energies of the terminating states and the deficiencies in the description of those terms affect the result. The recent suggestion [H. Zdunczuk, W. Satula, and R. A. Wyss, Phys. Rev. C 71, 024305 (2005)] that the relative energies of the terminating states in the N{ne}Z,A{approx}44 mass region given by {delta}E provide unique and reliable constraints on time-odd mean fields and the strength of spin-orbit interaction in density functional theories has been reanalyzed. The current investigation shows that the {delta}E value is affected also by the relative placement of the states with different orbital angular momentum l, namely, the placement of the d (l=2) and f (l=3) states. This indicates the dependence of the {delta}E value on the properties of the central potential.
Adiabatic corrections to density functional theory energies and wave functions.
Mohallem, José R; Coura, Thiago de O; Diniz, Leonardo G; de Castro, Gustavo; Assafrão, Denise; Heine, Thomas
2008-09-25
The adiabatic finite-nuclear-mass-correction (FNMC) to the electronic energies and wave functions of atoms and molecules is formulated for density-functional theory and implemented in the deMon code. The approach is tested for a series of local and gradient corrected density functionals, using MP2 results and diagonal-Born-Oppenheimer corrections from the literature for comparison. In the evaluation of absolute energy corrections of nonorganic molecules the LDA PZ81 functional works surprisingly better than the others. For organic molecules the GGA BLYP functional has the best performance. FNMC with GGA functionals, mainly BLYP, show a good performance in the evaluation of relative corrections, except for nonorganic molecules containing H atoms. The PW86 functional stands out with the best evaluation of the barrier of linearity of H2O and the isotopic dipole moment of HDO. In general, DFT functionals display an accuracy superior than the common belief and because the corrections are based on a change of the electronic kinetic energy they are here ranked in a new appropriate way. The approach is applied to obtain the adiabatic correction for full atomization of alcanes C(n)H(2n+2), n = 4-10. The barrier of 1 mHartree is approached for adiabatic corrections, justifying its insertion into DFT.
Nitrogenase structure and function relationships by density functional theory.
Harris, Travis V; Szilagyi, Robert K
2011-01-01
Modern density functional theory has tremendous potential with matching popularity in metalloenzymology to reveal the unseen atomic and molecular details of structural data, spectroscopic measurements, and biochemical experiments by providing insights into unobservable structures and states, while also offering theoretical justifications for observed trends and differences. An often untapped potential of this theoretical approach is to bring together diverse experimental structural and reactivity information and allow for these to be critically evaluated at the same level. This is particularly applicable for the tantalizingly complex problem of the structure and molecular mechanism of biological nitrogen fixation. In this chapter we provide a review with extensive practical details of the compilation and evaluation of experimental data for an unbiased and systematic density functional theory analysis that can lead to remarkable new insights about the structure-function relationships of the iron-sulfur clusters of nitrogenase.
Efficient molecular density functional theory using generalized spherical harmonics expansions
NASA Astrophysics Data System (ADS)
Ding, Lu; Levesque, Maximilien; Borgis, Daniel; Belloni, Luc
2017-09-01
We show that generalized spherical harmonics are well suited for representing the space and orientation molecular density in the resolution of the molecular density functional theory. We consider the common system made of a rigid solute of arbitrary complexity immersed in a molecular solvent, both represented by molecules with interacting atomic sites and classical force fields. The molecular solvent density ρ (r, Ω) around the solute is a function of the position r ≡(x ,y ,z ) and of the three Euler angles Ω≡(θ ,ϕ ,ψ ) describing the solvent orientation. The standard density functional, equivalent to the hypernetted-chain closure for the solute-solvent correlations in the liquid theory, is minimized with respect to ρ (r, Ω). The up-to-now very expensive angular convolution products are advantageously replaced by simple products between projections onto generalized spherical harmonics. The dramatic gain in speed of resolution enables to explore in a systematic way molecular solutes of up to nanometric sizes in arbitrary solvents and to calculate their solvation free energy and associated microscopic solvent structure in at most a few minutes. We finally illustrate the formalism by tackling the solvation of molecules of various complexities in water.
Voyager observations of Saturnian ion and electron phase space densities
Armstrong, T.P.; Paonessa, M.T.; Bell, E.V. II; Krimigis, S.M.
1983-11-01
Voyager 1 and 2 low-energy charged particle (LECP) observations of 30-keV to 2-MeV electron and ion energy spectra and angular distributions have been used to calculate phase space densities at constant first and second adiabatic invariant in the Saturnian magnetosphere. The results are generally consistent with inward radial diffusion from a external source. The data obtained also indicate a source of ions located within the orbital distance of enceladus capable of producing 10-to 40-MeV/Gauss ions as well as a source of electrons at about 3.5 R/sub S/ which produces particles at 100 to 200 MeV/Gauss. Higher magnetic moment (200--400 MeV/Gauss) ions extend from the sunward boundary between a plasma mantle and the region of durable trapping at R/sub S/: the behavior of the phase space density suggests inward diffusion of these particles from a source at the boundary. The identification of sources of low (10 to 200 MeV/Gauss) magnetic moment particles deep in the Saturnian magnetosphere is a new result of this work. Several analyses of the observed phase space densities in terms of time-independent radial diffusion are presented.
NASA Astrophysics Data System (ADS)
García-Aldea, David; Alvarellos, J. E.
2009-03-01
We present several nonlocal exchange energy density functionals that reproduce the linear response function of the free electron gas. These nonlocal functionals are constructed following a similar procedure used previously for nonlocal kinetic energy density functionals by Chac'on-Alvarellos-Tarazona, Garc'ia-Gonz'alez et al., Wang-Govind-Carter and Garc'ia-Aldea-Alvarellos. The exchange response function is not known but we have used the approximate response function developed by Utsumi and Ichimaru, even we must remark that the same ansatz can be used to reproduce any other response function with the same scaling properties. We have developed two families of new nonlocal functionals: one is constructed with a mathematical structure based on the LDA approximation -- the Dirac functional for the exchange - and for the second one the structure of the second order gradient expansion approximation is took as a model. The functionals are constructed is such a way that they can be used in localized systems (using real space calculations) and in extended systems (using the momentum space, and achieving a quasilinear scaling with the system size if a constant reference electron density is defined).
Dispersion interactions in Density Functional Theory
NASA Astrophysics Data System (ADS)
Andrinopoulos, Lampros; Hine, Nicholas; Mostofi, Arash
2012-02-01
Semilocal functionals in Density Functional Theory (DFT) achieve high accuracy simulating a wide range of systems, but miss the effect of dispersion (vdW) interactions, important in weakly bound systems. We study two different methods to include vdW in DFT: First, we investigate a recent approach [1] to evaluate the vdW contribution to the total energy using maximally-localized Wannier functions. Using a set of simple dimers, we show that it has a number of shortcomings that hamper its predictive power; we then develop and implement a series of improvements [2] and obtain binding energies and equilibrium geometries in closer agreement to quantum-chemical coupled-cluster calculations. Second, we implement the vdW-DF functional [3], using Soler's method [4], within ONETEP [5], a linear-scaling DFT code, and apply it to a range of systems. This method within a linear-scaling DFT code allows the simulation of weakly bound systems of larger scale, such as organic/inorganic interfaces, biological systems and implicit solvation models. [1] P. Silvestrelli, JPC A 113, 5224 (2009). [2] L. Andrinopoulos et al, JCP 135, 154105 (2011). [3] M. Dion et al, PRL 92, 246401 (2004). [4] G. Rom'an-P'erez, J.M. Soler, PRL 103, 096102 (2009). [5] C. Skylaris et al, JCP 122, 084119 (2005).
Graphical functions in parametric space
NASA Astrophysics Data System (ADS)
Golz, Marcel; Panzer, Erik; Schnetz, Oliver
2016-12-01
Graphical functions are positive functions on the punctured complex plane Csetminus {0,1} which arise in quantum field theory. We generalize a parametric integral representation for graphical functions due to Lam, Lebrun and Nakanishi, which implies the real analyticity of graphical functions. Moreover, we prove a formula that relates graphical functions of planar dual graphs.
Density functional theory with fractional orbital occupations.
Chai, Jeng-Da
2012-04-21
In contrast to the original Kohn-Sham (KS) formalism, we propose a density functional theory (DFT) with fractional orbital occupations for the study of ground states of many-electron systems, wherein strong static correlation is shown to be described. Even at the simplest level represented by the local density approximation (LDA), our resulting DFT-LDA is shown to improve upon KS-LDA for multi-reference systems, such as dissociation of H(2) and N(2), and twisted ethylene, while performing similar to KS-LDA for single-reference systems, such as reaction energies and equilibrium geometries. Because of its computational efficiency (similar to KS-LDA), this DFT-LDA is applied to the study of the singlet-triplet energy gaps (ST gaps) of acenes, which are "challenging problems" for conventional electronic structure methods due to the presence of strong static correlation effects. Our calculated ST gaps are in good agreement with the existing experimental and high-level ab initio data. The ST gaps are shown to decrease monotonically with the increase of chain length, and become vanishingly small (within 0.1 kcal/mol) in the limit of an infinitely large polyacene. In addition, based on our calculated active orbital occupation numbers, the ground states for large acenes are shown to be polyradical singlets.
When Density Functional Approximations Meet Iron Oxides.
Meng, Yu; Liu, Xing-Wu; Huo, Chun-Fang; Guo, Wen-Ping; Cao, Dong-Bo; Peng, Qing; Dearden, Albert; Gonze, Xavier; Yang, Yong; Wang, Jianguo; Jiao, Haijun; Li, Yongwang; Wen, Xiao-Dong
2016-10-11
Three density functional approximations (DFAs), PBE, PBE+U, and Heyd-Scuseria-Ernzerhof screened hybrid functional (HSE), were employed to investigate the geometric, electronic, magnetic, and thermodynamic properties of four iron oxides, namely, α-FeOOH, α-Fe2O3, Fe3O4, and FeO. Comparing our calculated results with available experimental data, we found that HSE (a = 0.15) (containing 15% "screened" Hartree-Fock exchange) can provide reliable values of lattice constants, Fe magnetic moments, band gaps, and formation energies of all four iron oxides, while standard HSE (a = 0.25) seriously overestimates the band gaps and formation energies. For PBE+U, a suitable U value can give quite good results for the electronic properties of each iron oxide, but it is challenging to accurately get other properties of the four iron oxides using the same U value. Subsequently, we calculated the Gibbs free energies of transformation reactions among iron oxides using the HSE (a = 0.15) functional and plotted the equilibrium phase diagrams of the iron oxide system under various conditions, which provide reliable theoretical insight into the phase transformations of iron oxides.
Chemistry by Way of Density Functional Theory
NASA Technical Reports Server (NTRS)
Bauschlicher, Charles W., Jr.; Ricca, Alessandra; Partridge, Harry; Langohff, Stephen R.; Arnold, James O. (Technical Monitor)
1996-01-01
In this work we demonstrate that density functional theory (DFT) methods make an important contribution to understanding chemical systems and are an important additional method for the computational chemist. We report calibration calculations obtained with different functionals for the 55 G2 molecules to justify our selection of the B3LYP functional. We show that accurate geometries and vibrational frequencies obtained at the B3LYP level can be combined with traditional methods to simplify the calculation of accurate heats of formation. We illustrate the application of the B3LYP approach to a variety of chemical problems from the vibrational frequencies of polycyclic aromatic hydrocarbons to transition metal systems. We show that the B3LYP method typically performs better than the MP2 method at a significantly lower computational cost. Thus the B3LYP method allows us to extend our studies to much larger systems while maintaining a high degree of accuracy. We show that for transition metal systems, the B3LYP bond energies are typically of sufficient accuracy that they can be used to explain experimental trends and even differentiate between different experimental values. We show that for boron clusters the B3LYP energetics are not as good as for many of the other systems presented, but even in this case the B3LYP approach is able to help understand the experimental trends.
Chemistry by Way of Density Functional Theory
NASA Technical Reports Server (NTRS)
Bauschlicher, Charles W., Jr.; Ricca, Alessandra; Partridge, Harry; Langohff, Stephen R.; Arnold, James O. (Technical Monitor)
1996-01-01
In this work we demonstrate that density functional theory (DFT) methods make an important contribution to understanding chemical systems and are an important additional method for the computational chemist. We report calibration calculations obtained with different functionals for the 55 G2 molecules to justify our selection of the B3LYP functional. We show that accurate geometries and vibrational frequencies obtained at the B3LYP level can be combined with traditional methods to simplify the calculation of accurate heats of formation. We illustrate the application of the B3LYP approach to a variety of chemical problems from the vibrational frequencies of polycyclic aromatic hydrocarbons to transition metal systems. We show that the B3LYP method typically performs better than the MP2 method at a significantly lower computational cost. Thus the B3LYP method allows us to extend our studies to much larger systems while maintaining a high degree of accuracy. We show that for transition metal systems, the B3LYP bond energies are typically of sufficient accuracy that they can be used to explain experimental trends and even differentiate between different experimental values. We show that for boron clusters the B3LYP energetics are not as good as for many of the other systems presented, but even in this case the B3LYP approach is able to help understand the experimental trends.
Immune function during space flight
NASA Technical Reports Server (NTRS)
Sonnenfeld, Gerald; Shearer, William T.
2002-01-01
It is very likely that the human immune system will be altered in astronauts exposed to the conditions of long-term space flight: isolation, containment, microgravity, radiation, microbial contamination, sleep disruption, and insufficient nutrition. In human and animal subjects flown in space, there is evidence of immune compromise, reactivation of latent virus infection, and possible development of a premalignant or malignant condition. Moreover, in ground-based space flight model investigations, there is evidence of immune compromise and reactivation of latent virus infection. All of these observations in space flight itself or in ground-based models of space flight have a strong resonance in a wealth of human pathologic conditions involving the immune system where reactivated virus infections and cancer appear as natural consequences. The clinical conditions of Epstein-Barr-driven lymphomas in transplant patients and Kaposi's sarcoma in patients with autoimmune deficiency virus come easily to mind in trying to identify these conditions. With these thoughts in mind, it is highly appropriate, indeed imperative, that careful investigations of human immunity, infection, and cancer be made by space flight researchers.
Immune function during space flight.
Sonnenfeld, Gerald; Shearer, William T
2002-10-01
It is very likely that the human immune system will be altered in astronauts exposed to the conditions of long-term space flight: isolation, containment, microgravity, radiation, microbial contamination, sleep disruption, and insufficient nutrition. In human and animal subjects flown in space, there is evidence of immune compromise, reactivation of latent virus infection, and possible development of a premalignant or malignant condition. Moreover, in ground-based space flight model investigations, there is evidence of immune compromise and reactivation of latent virus infection. All of these observations in space flight itself or in ground-based models of space flight have a strong resonance in a wealth of human pathologic conditions involving the immune system where reactivated virus infections and cancer appear as natural consequences. The clinical conditions of Epstein-Barr-driven lymphomas in transplant patients and Kaposi's sarcoma in patients with autoimmune deficiency virus come easily to mind in trying to identify these conditions. With these thoughts in mind, it is highly appropriate, indeed imperative, that careful investigations of human immunity, infection, and cancer be made by space flight researchers.
General degeneracy in density functional perturbation theory
NASA Astrophysics Data System (ADS)
Palenik, Mark C.; Dunlap, Brett I.
2017-07-01
Degenerate perturbation theory from quantum mechanics is inadequate in density functional theory (DFT) because of nonlinearity in the Kohn-Sham potential. Herein, we develop the fully general perturbation theory for open-shell, degenerate systems in Kohn-Sham DFT, without assuming the presence of symmetry or equal occupation of degenerate orbitals. To demonstrate the resulting methodology, we apply it to the iron atom in the central field approximation, perturbed by an electric quadrupole. This system was chosen because it displays both symmetry required degeneracy, between the five 3 d orbitals, as well as accidental degeneracy, between the 3 d and 4 s orbitals. The quadrupole potential couples the degenerate 3 d and 4 s states, serving as an example of the most general perturbation.
Modeling NMR lineshapes using logspline density functions.
Raz, J; Fernandez, E J; Gillespie, J
1997-08-01
Distortions in the FID and spin echo due to magnetic field inhomogeneity are proved to have a representation as the characteristic function of some probability distribution. In the special case that the distribution is Cauchy, the model reduces to the conventional Lorentzian model. A more general and flexible representation is presented using the Fourier transform of a logspline density. An algorithm for fitting the model is described, the performance of the model and algorithm is investigated in applications to real and simulated data sets, and the logspline approach is compared to a previous Hermitian spline approach and to the Lorentzian model. The logspline model is more parsimonious than the Hermitian spline model, provides a better fit to real data, and is much less biased than the Lorentzian model.
Phases of Polonium via Density Functional Theory
NASA Astrophysics Data System (ADS)
Verstraete, Matthieu J.
2010-01-01
The thermodynamical properties of the main phases of metallic polonium are examined using density functional theory. The exceptional nature of the solid-solid phase transition of α to β Po is underlined: it induces a lowering in symmetry, from cubic to rhombohedral, with increasing temperature. This is explained as the result of a delicate balance between bonding and entropic effects. Overall agreement with existing experimental data is good by state-of-the-art standards. The phonons of Po present Kohn anomalies, and it is shown that the effect of spin-orbit interactions is the inverse of that in normal metals: due to the nonspherical nature of the Fermi Surface, spin-orbit effects reduce nesting and harden most phonon frequencies.
Carrier Modulation Via Waveform Probability Density Function
NASA Technical Reports Server (NTRS)
Williams, Glenn L.
2006-01-01
Beyond the classic modes of carrier modulation by varying amplitude (AM), phase (PM), or frequency (FM), we extend the modulation domain of an analog carrier signal to include a class of general modulations which are distinguished by their probability density function histogram. Separate waveform states are easily created by varying the pdf of the transmitted waveform. Individual waveform states are assignable as proxies for digital one's or zero's. At the receiver, these states are easily detected by accumulating sampled waveform statistics and performing periodic pattern matching, correlation, or statistical filtering. No fundamental physical laws are broken in the detection process. We show how a typical modulation scheme would work in the digital domain and suggest how to build an analog version. We propose that clever variations of the modulating waveform (and thus the histogram) can provide simple steganographic encoding.
Carrier Modulation Via Waveform Probability Density Function
NASA Technical Reports Server (NTRS)
Williams, Glenn L.
2004-01-01
Beyond the classic modes of carrier modulation by varying amplitude (AM), phase (PM), or frequency (FM), we extend the modulation domain of an analog carrier signal to include a class of general modulations which are distinguished by their probability density function histogram. Separate waveform states are easily created by varying the pdf of the transmitted waveform. Individual waveform states are assignable as proxies for digital ONEs or ZEROs. At the receiver, these states are easily detected by accumulating sampled waveform statistics and performing periodic pattern matching, correlation, or statistical filtering. No fundamental natural laws are broken in the detection process. We show how a typical modulation scheme would work in the digital domain and suggest how to build an analog version. We propose that clever variations of the modulating waveform (and thus the histogram) can provide simple steganographic encoding.
Augmented Lagrangian method for constrained nuclear density functional theory
NASA Astrophysics Data System (ADS)
Staszczak, A.; Stoitsov, M.; Baran, A.; Nazarewicz, W.
2010-10-01
The augmented Lagrangiam method (ALM), widely used in quantum chemistry constrained optimization problems, is applied in the context of the nuclear Density Functional Theory (DFT) in the self-consistent constrained Skyrme Hartree-Fock-Bogoliubov (CHFB) variant. The ALM allows precise calculations of multi-dimensional energy surfaces in the space of collective coordinates that are needed to, e.g., determine fission pathways and saddle points; it improves the accuracy of computed derivatives with respect to collective variables that are used to determine collective inertia; and is well adapted to supercomputer applications.
Some new function spaces of variable smoothness
Tyulenev, A I
2015-06-30
A new Besov space of variable smoothness is introduced on which the norm is defined in terms of difference relations. This space is shown to be the trace of a weighted Sobolev space with a weight in the corresponding Muckenhoupt class. Methods of nonlinear spline approximation are applied to derive an atomic decomposition theorem for functions in a Besov space of variable smoothness. A complete description of traces on the hyperplane of a Besov space of variable smoothness and of a weighted Besov space with a weight in the corresponding Muckenhoupt class is given. Bibliography: 27 titles.
NASA Astrophysics Data System (ADS)
Balthazor, R. L.; McHarg, M. G.; Wilson, G.
2016-12-01
The Integrated Miniaturized Electrostatic Analyzer (IMESA) is a space weather sensor developed by the United States Air Force Academy and integrated and flown by the DoD's Space Test Program. IMESA records plasma spectrograms from which can be derived plasma density, temperature, and spacecraft frame charging. Results from IMESA currently orbiting on STPSat-3 are presented, showing frame charging effects dependent on a complex function of the number of solar panel cell strings switched in, solar panel current, and plasma density. IMESA will fly on four more satellites launching in the next two calendar years, enabling an undergraduate DoD space weather constellation in Low Earth Orbit that has the ability to significantly improve space weather forecasting capabilities using assimilative forecast models.
Building a Universal Nuclear Energy Density Functional
Carlson, Joe A.; Furnstahl, Dick; Horoi, Mihai; Lust, Rusty; Nazaewicc, Witek; Ng, Esmond; Thompson, Ian; Vary, James
2012-12-30
During the period of Dec. 1 2006 – Jun. 30, 2012, the UNEDF collaboration carried out a comprehensive study of all nuclei, based on the most accurate knowledge of the strong nuclear interaction, the most reliable theoretical approaches, the most advanced algorithms, and extensive computational resources, with a view towards scaling to the petaflop platforms and beyond. The long-term vision initiated with UNEDF is to arrive at a comprehensive, quantitative, and unified description of nuclei and their reactions, grounded in the fundamental interactions between the constituent nucleons. We seek to replace current phenomenological models of nuclear structure and reactions with a well-founded microscopic theory that delivers maximum predictive power with well-quantified uncertainties. Specifically, the mission of this project has been three-fold: First, to find an optimal energy density functional (EDF) using all our knowledge of the nucleonic Hamiltonian and basic nuclear properties; Second, to apply the EDF theory and its extensions to validate the functional using all the available relevant nuclear structure and reaction data; Third, to apply the validated theory to properties of interest that cannot be measured, in particular the properties needed for reaction theory.
Internal density functional theory of molecular systems
NASA Astrophysics Data System (ADS)
Nalewajski, Roman F.
1984-08-01
A thermodynamiclike theory of internal equilibrium and constrained equilibrium states of individual molecular systems is formulated, based on the Legendre transformed density functional theory (LT DFT). The molecular system (nonrelativistic, field free, Born-Oppenheimer or non-Born-Oppenheimer) is treated as the closed composite thermodynamic system, consisting of very small, rigid (open) subsystems (simple systems) containing a multi-(m)-component charged fluid in the presence of an external field. The generalized Levy constrained search construction of various ``thermodynamic'' potentials of LT DFT is given and the local Maxwell relations are derived. The reduction of various second-order partial functional derivatives (system sensitivities) in terms of few independent, basic kernels is described, using the Jacobian determinants technique. The qualitative implications for the basic kernels of the theory, from the Maxwell relations and stability criteria (generalized Le Châtelier and Le Châtelier-Braun principles) are systematically examined. Finally, possible applications of the general formalism in the thermodynamic analysis of the chemical bond, molecular stability, and chemical reactivity are identified.
Density Functional O(N) Calculations
NASA Astrophysics Data System (ADS)
Ordejón, Pablo
1998-03-01
We have developed a scheme for performing Density Functional Theory calculations with O(N) scaling.(P. Ordejón, E. Artacho and J. M. Soler, Phys. Rev. B, 53), 10441 (1996) The method uses arbitrarily flexible and complete Atomic Orbitals (AO) basis sets. This gives a wide range of choice, from extremely fast calculations with minimal basis sets, to greatly accurate calculations with complete sets. The size-efficiency of AO bases, together with the O(N) scaling of the algorithm, allow the application of the method to systems with many hundreds of atoms, in single processor workstations. I will present the SIESTA code,(D. Sanchez-Portal, P. Ordejón, E. Artacho and J. M. Soler, Int. J. Quantum Chem., 65), 453 (1997) in which the method is implemented, with several LDA, LSD and GGA functionals available, and using norm-conserving, non-local pseudopotentials (in the Kleinman-Bylander form) to eliminate the core electrons. The calculation of static properties such as energies, forces, pressure, stress and magnetic moments, as well as molecular dynamics (MD) simulations capabilities (including variable cell shape, constant temperature and constant pressure MD) are fully implemented. I will also show examples of the accuracy of the method, and applications to large-scale materials and biomolecular systems.
Improving Density Functionals with Quantum Harmonic Oscillators
NASA Astrophysics Data System (ADS)
Tkatchenko, Alexandre
2013-03-01
Density functional theory (DFT) is the most widely used and successful approach for electronic structure calculations. However, one of the pressing challenges for DFT is developing efficient functionals that can accurately capture the omnipresent long-range electron correlations, which determine the structure and stability of many molecules and materials. Here we show that, under certain conditions, the problem of computing the long-range correlation energy of interacting electrons can be mapped to a system of coupled quantum harmonic oscillators (QHOs). The proposed model allows us to synergistically combine concepts from DFT, quantum chemistry, and the widely discussed random-phase approximation for the correlation energy. In the dipole limit, the interaction energy for a system of coupled QHOs can be calculated exactly, thereby leading to an efficient and accurate model for the many-body dispersion energy of complex molecules and materials. The studied examples include intermolecular binding energies, the conformational hierarchy of DNA structures, the geometry and stability of molecular crystals, and supramolecular host-guest complexes (A. Tkatchenko, R. A. DiStasio Jr., R. Car, M. Scheffler, Phys. Rev. Lett. 108, 236402 (2012); R. A. DiStasio Jr., A. von Lilienfeld, A. Tkatchenko, PNAS 109, 14791 (2012); A. Tkatchenko, D. Alfe, K. S. Kim, J. Chem. Theory and Comp. (2012), doi: 10.1021/ct300711r; A. Tkatchenko, A. Ambrosetti, R. A. DiStasio Jr., arXiv:1210.8343v1).
Polynomial approximation of functions in Sobolev spaces
Dupont, T.; Scott, R.
1980-04-01
Constructive proofs and several generalizations of approximation results of J. H. Bramble and S. R. Hilbert are presented. Using an averaged Taylor series, we represent a function as a polynomical plus a remainder. The remainder can be manipulated in many ways to give different types of bounds. Approximation of functions in fractional order Sobolev spaces is treated as well as the usual integer order spaces and several nonstandard Sobolev-like spaces.
Polynomial approximation of functions in Sobolev spaces
NASA Technical Reports Server (NTRS)
Dupont, T.; Scott, R.
1980-01-01
Constructive proofs and several generalizations of approximation results of J. H. Bramble and S. R. Hilbert are presented. Using an averaged Taylor series, we represent a function as a polynomial plus a remainder. The remainder can be manipulated in many ways to give different types of bounds. Approximation of functions in fractional order Sobolev spaces is treated as well as the usual integer order spaces and several nonstandard Sobolev-like spaces.
Polynomial approximation of functions in Sobolev spaces
NASA Technical Reports Server (NTRS)
Dupont, T.; Scott, R.
1980-01-01
Constructive proofs and several generalizations of approximation results of J. H. Bramble and S. R. Hilbert are presented. Using an averaged Taylor series, we represent a function as a polynomial plus a remainder. The remainder can be manipulated in many ways to give different types of bounds. Approximation of functions in fractional order Sobolev spaces is treated as well as the usual integer order spaces and several nonstandard Sobolev-like spaces.
Revisiting the Fermi Surface in Density Functional Theory
NASA Astrophysics Data System (ADS)
Das, Mukunda P.; Green, Frederick
2016-06-01
The Fermi surface is an abstract object in the reciprocal space of a crystal lattice, enclosing the set of all those electronic band states that are filled according to the Pauli principle. Its topology is dictated by the underlying lattice structure and its volume is the carrier density in the material. The Fermi surface is central to predictions of thermal, electrical, magnetic, optical and superconducting properties in metallic systems. Density functional theory is a first-principles method used to estimate the occupied-band energies and, in particular, the isoenergetic Fermi surface. In this review we survey several key facts about Fermi surfaces in complex systems, where a proper theoretical understanding is still lacking. We address some critical difficulties.
A Wigner Monte Carlo approach to density functional theory
Sellier, J.M. Dimov, I.
2014-08-01
In order to simulate quantum N-body systems, stationary and time-dependent density functional theories rely on the capacity of calculating the single-electron wave-functions of a system from which one obtains the total electron density (Kohn–Sham systems). In this paper, we introduce the use of the Wigner Monte Carlo method in ab-initio calculations. This approach allows time-dependent simulations of chemical systems in the presence of reflective and absorbing boundary conditions. It also enables an intuitive comprehension of chemical systems in terms of the Wigner formalism based on the concept of phase-space. Finally, being based on a Monte Carlo method, it scales very well on parallel machines paving the way towards the time-dependent simulation of very complex molecules. A validation is performed by studying the electron distribution of three different systems, a Lithium atom, a Boron atom and a hydrogenic molecule. For the sake of simplicity, we start from initial conditions not too far from equilibrium and show that the systems reach a stationary regime, as expected (despite no restriction is imposed in the choice of the initial conditions). We also show a good agreement with the standard density functional theory for the hydrogenic molecule. These results demonstrate that the combination of the Wigner Monte Carlo method and Kohn–Sham systems provides a reliable computational tool which could, eventually, be applied to more sophisticated problems.
Neutral Orbital Altitude Density Effects on the International Space Station
NASA Technical Reports Server (NTRS)
Smith, O.E.; Adelfang, S. I.; Smith, R. E.
1997-01-01
One of the design requirements of the International Space Station (ISS) is that each year accelerations of one micro-g cannot be exceeded at the ISS internal payload location for 6 periods of not less than 30 consecutive days. Although there are other causes, this study deals only with the accelerations caused by atmospheric drag. The critical ambient neutral density, computed using the Marshall Engineering Thermosphere Model, required to produce accelerations of one micro-g on the ISS, is estimated using an atmospheric drag acceleration equation. Results show that the design requirements may be difficult to meet during periods of extremely high solar activity; the planned reboost and altitude strategies for the ISS may have to be revised to allow for the uncertainty in the prediction of neutral atmospheric density within the 100-day period established for orbital decay before reboost.
Bone Density Following Long Duration Space Flight and Recovery
NASA Technical Reports Server (NTRS)
Amin, Shreyasee; Achenbach, Sara J.; Atkinson, Elizabeth J.; Melton, L. Joseph; Khosla, Sundeep; Sibonga, Jean
2010-01-01
At approx.12 months, Bone Mineral Density (BMD) at most sites in men remained lower than would be predicted, raising concerns for long-term bone health consequences following space flight. Additional analyses based on longer follow-up are being conducted. Although the N is too small for definitive conclusions, women had lower rates of loss at load-bearing sites of the hip and spine immediately post-flight relative to men and smaller differences between observed vs. predicted BMD at most sites, both immediately and 12 months post-flight, relative to men. The role of other exposures/risk factors need to be explored to further understand these possible gender differences in BMD loss and recovery following long-duration space flight.
An interpretation of electrostatic density shocks in space plasma
Shi Jiankui; Zhang Tielong; Torkar, Klaus; Liu Zhenxing
2005-08-15
A physical model of electrostatic shocks observed in space plasma is established by deriving the 'Sagdeev potential' from the magnetohydrodynamic equations in a cylindrical coordinate system. The results show that the electrostatic density shock and its corresponding solitary electric-field structure can develop from an ion acoustic wave or an ion cyclotron wave if the Mach number and the initial electric field satisfy some conditions. Some features of the shock wave are discussed. The result can be used to interpret the electrostatic shock observed in geospace plasma.
Reduced density-matrix functionals from many-particle theory
NASA Astrophysics Data System (ADS)
Schade, Robert; Kamil, Ebad; Blöchl, Peter
2017-07-01
In materials with strong electron correlation the proper treatment of local atomic physics described by orbital occupations is crucial. Reduced density-matrix functional theory is a natural extension of density functional theory for systems that are dominated by orbital physics. We review the current state of reduced density-matrix functional theory (RDMFT). For atomic structure relaxations or ab-initio molecular dynamics the combination of density functional theory (DFT) and dynamical mean-field theory (DMFT) possesses a number of disadvantages, like the cumbersome evaluation of forces. We therefore describe a method, DFT+RDMFT, that combines many-particle effects based on reduced density-matrix functional theory with a density functional-like framework. A recent development is the construction of density-matrix functionals directly from many-particle theory such as methods from quantum chemistry or many-particle Green's functions. We present the underlying exact theorems and describe current progress towards quantitative functionals.
Garcia-Aldea, David; Alvarellos, J. E.
2008-02-15
We propose a kinetic energy density functional scheme with nonlocal terms based on the von Weizsaecker functional, instead of the more traditional approach where the nonlocal terms have the structure of the Thomas-Fermi functional. The proposed functionals recover the exact kinetic energy and reproduce the linear response function of homogeneous electron systems. In order to assess their quality, we have tested the total kinetic energies as well as the kinetic energy density for atoms. The results show that these nonlocal functionals give as good results as the most sophisticated functionals in the literature. The proposed scheme for constructing the functionals means a step ahead in the field of fully nonlocal kinetic energy functionals, because they are capable of giving better local behavior than the semilocal functionals, yielding at the same time accurate results for total kinetic energies. Moreover, the functionals enjoy the possibility of being evaluated as a single integral in momentum space if an adequate reference density is defined, and then quasilinear scaling for the computational cost can be achieved.
Multiple Streaming and the Probability Distribution of Density in Redshift Space
Hui, Lam; Kofman, Lev; Shandarin, Sergei F.
2000-07-01
We examine several aspects of redshift distortions by expressing the redshift-space density in terms of the eigenvalues and orientation of the local Lagrangian deformation tensor. We explore the importance of multiple streaming using the Zeldovich approximation (ZA), and compute the average number of streams in both real and redshift space. We find that multiple streaming can be significant in redshift space but negligible in real space, even at moderate values of the linear fluctuation amplitude ({sigma}{sub l}(less-or-similar sign)1). Moreover, unlike their real-space counterparts, redshift-space multiple streams can flow past each other with minimal interactions. Such nonlinear redshift-space effects, which are physically distinct from the fingers-of-God due to small-scale virialized motions, might in part explain the well-known departure of redshift distortions from the classic linear prediction by Kaiser, even at relatively large scales where the corresponding density field in real space is well described by linear perturbation theory. We also compute, using the ZA, the probability distribution function (PDF) of the density, as well as S{sub 3}, in real and redshift space, and compare it with the PDF measured from N-body simulations. The role of caustics in defining the character of the high-density tail is examined. We find that (non-Lagrangian) smoothing, due to both finite resolution or discreteness and small-scale velocity dispersions, is very effective in erasing caustic structures, unless the initial power spectrum is sufficiently truncated. (c) 2000 The American Astronomical Society.
Parker, Shane M.; Shiozaki, Toru
2014-12-07
We extend the active space decomposition method, recently developed by us, to more than two active sites using the density matrix renormalization group algorithm. The fragment wave functions are described by complete or restricted active-space wave functions. Numerical results are shown on a benzene pentamer and a perylene diimide trimer. It is found that the truncation errors in our method decrease almost exponentially with respect to the number of renormalization states M, allowing for numerically exact calculations (to a few μE{sub h} or less) with M = 128 in both cases. This rapid convergence is because the renormalization steps are used only for the interfragment electron correlation.
Parker, Shane M; Shiozaki, Toru
2014-12-07
We extend the active space decomposition method, recently developed by us, to more than two active sites using the density matrix renormalization group algorithm. The fragment wave functions are described by complete or restricted active-space wave functions. Numerical results are shown on a benzene pentamer and a perylene diimide trimer. It is found that the truncation errors in our method decrease almost exponentially with respect to the number of renormalization states M, allowing for numerically exact calculations (to a few μE(h) or less) with M = 128 in both cases. This rapid convergence is because the renormalization steps are used only for the interfragment electron correlation.
Particle number and probability density functional theory and A-representability.
Pan, Xiao-Yin; Sahni, Viraht
2010-04-28
In Hohenberg-Kohn density functional theory, the energy E is expressed as a unique functional of the ground state density rho(r): E = E[rho] with the internal energy component F(HK)[rho] being universal. Knowledge of the functional F(HK)[rho] by itself, however, is insufficient to obtain the energy: the particle number N is primary. By emphasizing this primacy, the energy E is written as a nonuniversal functional of N and probability density p(r): E = E[N,p]. The set of functions p(r) satisfies the constraints of normalization to unity and non-negativity, exists for each N; N = 1, ..., infinity, and defines the probability density or p-space. A particle number N and probability density p(r) functional theory is constructed. Two examples for which the exact energy functionals E[N,p] are known are provided. The concept of A-representability is introduced, by which it is meant the set of functions Psi(p) that leads to probability densities p(r) obtained as the quantum-mechanical expectation of the probability density operator, and which satisfies the above constraints. We show that the set of functions p(r) of p-space is equivalent to the A-representable probability density set. We also show via the Harriman and Gilbert constructions that the A-representable and N-representable probability density p(r) sets are equivalent.
Flexoelectricity from density-functional perturbation theory
NASA Astrophysics Data System (ADS)
Stengel, Massimiliano
2013-11-01
We derive the complete flexoelectric tensor, including electronic and lattice-mediated effects, of an arbitrary insulator in terms of the microscopic linear response of the crystal to atomic displacements. The basic ingredient, which can be readily calculated from first principles in the framework of density-functional perturbation theory, is the quantum-mechanical probability current response to a long-wavelength acoustic phonon. Its second-order Taylor expansion in the wave vector q around the Γ (q=0) point in the Brillouin zone naturally yields the flexoelectric tensor. At order one in q we recover Martin's theory of piezoelectricity [Martin, Phys. Rev. B 5, 1607 (1972)], thus providing an alternative derivation thereof. To put our derivations on firm theoretical grounds, we perform a thorough analysis of the nonanalytic behavior of the dynamical matrix and other response functions in a vicinity of Γ. Based on this analysis, we find that there is an ambiguity in the specification of the “zero macroscopic field” condition in the flexoelectric case; such arbitrariness can be related to an analytic band-structure term, in close analogy to the theory of deformation potentials. As a by-product, we derive a rigorous generalization of the Cochran-Cowley formula [Cochran and Cowley, J. Phys. Chem. Solids 23, 447 (1962)] to higher orders in q. This can be of great utility in building reliable atomistic models of electromechanical phenomena, as well as for improving the accuracy of the calculation of phonon dispersion curves. Finally, we discuss the physical interpretation of the various contributions to the flexoelectric response, either in the static or dynamic regime, and we relate our findings to earlier theoretical works on the subject.
Dynamical density functional theory for microswimmers.
Menzel, Andreas M; Saha, Arnab; Hoell, Christian; Löwen, Hartmut
2016-01-14
Dynamical density functional theory (DDFT) has been successfully derived and applied to describe on one hand passive colloidal suspensions, including hydrodynamic interactions between individual particles. On the other hand, active "dry" crowds of self-propelled particles have been characterized using DDFT. Here, we go one essential step further and combine these two approaches. We establish a DDFT for active microswimmer suspensions. For this purpose, simple minimal model microswimmers are introduced. These microswimmers self-propel by setting the surrounding fluid into motion. They hydrodynamically interact with each other through their actively self-induced fluid flows and via the common "passive" hydrodynamic interactions. An effective soft steric repulsion is also taken into account. We derive the DDFT starting from common statistical approaches. Our DDFT is then tested and applied by characterizing a suspension of microswimmers, the motion of which is restricted to a plane within a three-dimensional bulk fluid. Moreover, the swimmers are confined by a radially symmetric trapping potential. In certain parameter ranges, we find rotational symmetry breaking in combination with the formation of a "hydrodynamic pumping state," which has previously been observed in the literature as a result of particle-based simulations. An additional instability of this pumping state is revealed.
Dynamical density functional theory for microswimmers
NASA Astrophysics Data System (ADS)
Menzel, Andreas M.; Saha, Arnab; Hoell, Christian; Löwen, Hartmut
2016-01-01
Dynamical density functional theory (DDFT) has been successfully derived and applied to describe on one hand passive colloidal suspensions, including hydrodynamic interactions between individual particles. On the other hand, active "dry" crowds of self-propelled particles have been characterized using DDFT. Here, we go one essential step further and combine these two approaches. We establish a DDFT for active microswimmer suspensions. For this purpose, simple minimal model microswimmers are introduced. These microswimmers self-propel by setting the surrounding fluid into motion. They hydrodynamically interact with each other through their actively self-induced fluid flows and via the common "passive" hydrodynamic interactions. An effective soft steric repulsion is also taken into account. We derive the DDFT starting from common statistical approaches. Our DDFT is then tested and applied by characterizing a suspension of microswimmers, the motion of which is restricted to a plane within a three-dimensional bulk fluid. Moreover, the swimmers are confined by a radially symmetric trapping potential. In certain parameter ranges, we find rotational symmetry breaking in combination with the formation of a "hydrodynamic pumping state," which has previously been observed in the literature as a result of particle-based simulations. An additional instability of this pumping state is revealed.
Density functional theory in the solid state
Hasnip, Philip J.; Refson, Keith; Probert, Matt I. J.; Yates, Jonathan R.; Clark, Stewart J.; Pickard, Chris J.
2014-01-01
Density functional theory (DFT) has been used in many fields of the physical sciences, but none so successfully as in the solid state. From its origins in condensed matter physics, it has expanded into materials science, high-pressure physics and mineralogy, solid-state chemistry and more, powering entire computational subdisciplines. Modern DFT simulation codes can calculate a vast range of structural, chemical, optical, spectroscopic, elastic, vibrational and thermodynamic phenomena. The ability to predict structure–property relationships has revolutionized experimental fields, such as vibrational and solid-state NMR spectroscopy, where it is the primary method to analyse and interpret experimental spectra. In semiconductor physics, great progress has been made in the electronic structure of bulk and defect states despite the severe challenges presented by the description of excited states. Studies are no longer restricted to known crystallographic structures. DFT is increasingly used as an exploratory tool for materials discovery and computational experiments, culminating in ex nihilo crystal structure prediction, which addresses the long-standing difficult problem of how to predict crystal structure polymorphs from nothing but a specified chemical composition. We present an overview of the capabilities of solid-state DFT simulations in all of these topics, illustrated with recent examples using the CASTEP computer program. PMID:24516184
Bone mineral density, adiposity, and cognitive functions
Sohrabi, Hamid R.; Bates, Kristyn A.; Weinborn, Michael; Bucks, Romola S.; Rainey-Smith, Stephanie R.; Rodrigues, Mark A.; Bird, Sabine M.; Brown, Belinda M.; Beilby, John; Howard, Matthew; Criddle, Arthur; Wraith, Megan; Taddei, Kevin; Martins, Georgia; Paton, Athena; Shah, Tejal; Dhaliwal, Satvinder S.; Mehta, Pankaj D.; Foster, Jonathan K.; Martins, Ian J.; Lautenschlager, Nicola T.; Mastaglia, Francis; Laws, Simon M.; Martins, Ralph N.
2015-01-01
Cognitive decline and dementia due to Alzheimer's disease (AD) have been associated with genetic, lifestyle, and environmental factors. A number of potentially modifiable risk factors should be taken into account when preventive or ameliorative interventions targeting dementia and its preclinical stages are investigated. Bone mineral density (BMD) and body composition are two such potentially modifiable risk factors, and their association with cognitive decline was investigated in this study. 164 participants, aged 34–87 years old (62.78 ± 9.27), were recruited for this longitudinal study and underwent cognitive and clinical examinations at baseline and after 3 years. Blood samples were collected for apolipoprotein E (APOE) genotyping and dual energy x-ray absorptiometry (DXA) was conducted at the same day as cognitive assessment. Using hierarchical regression analysis, we found that BMD and lean body mass, as measured using DXA were significant predictors of episodic memory. Age, gender, APOE status, and premorbid IQ were controlled for. Specifically, the List A learning from California Verbal Learning Test was significantly associated with BMD and lean mass both at baseline and at follow up assessment. Our findings indicate that there is a significant association between BMD and lean body mass and episodic verbal learning. While the involvement of modifiable lifestyle factors in human cognitive function has been examined in different studies, there is a need for further research to understand the potential underlying mechanisms. PMID:25741279
Density functional theory in the solid state.
Hasnip, Philip J; Refson, Keith; Probert, Matt I J; Yates, Jonathan R; Clark, Stewart J; Pickard, Chris J
2014-03-13
Density functional theory (DFT) has been used in many fields of the physical sciences, but none so successfully as in the solid state. From its origins in condensed matter physics, it has expanded into materials science, high-pressure physics and mineralogy, solid-state chemistry and more, powering entire computational subdisciplines. Modern DFT simulation codes can calculate a vast range of structural, chemical, optical, spectroscopic, elastic, vibrational and thermodynamic phenomena. The ability to predict structure-property relationships has revolutionized experimental fields, such as vibrational and solid-state NMR spectroscopy, where it is the primary method to analyse and interpret experimental spectra. In semiconductor physics, great progress has been made in the electronic structure of bulk and defect states despite the severe challenges presented by the description of excited states. Studies are no longer restricted to known crystallographic structures. DFT is increasingly used as an exploratory tool for materials discovery and computational experiments, culminating in ex nihilo crystal structure prediction, which addresses the long-standing difficult problem of how to predict crystal structure polymorphs from nothing but a specified chemical composition. We present an overview of the capabilities of solid-state DFT simulations in all of these topics, illustrated with recent examples using the CASTEP computer program.
A method for calculating phase-space densities in ion-optical systems
NASA Astrophysics Data System (ADS)
Hanelt, E.; Schmidt, K.-H.
1992-10-01
A method for calculating the motion of an ensemble of beam particles through an ion-optical system is presented. The collective motion of the ensemble which covers a finite phase-space volume is described by an analytical transformation of the corresponding particle density distribution in phase space. This density distribution is represented by a convolution of generating functions. It is transformed by applying the ion-optical matrix formalism tto the generating functions. Physical effects acting on the particle ensemble on its way through the ion-optical system are taken into account by additional generating functions. This method allows to calculate rare processes in ion-optical systems with low computational effort.
Armstrong Laboratory Space Visual Function Tester Program
NASA Technical Reports Server (NTRS)
Oneal, Melvin R.; Task, H. Lee; Gleason, Gerald A.
1992-01-01
Viewgraphs on space visual function tester program are presented. Many astronauts and cosmonauts have commented on apparent changes in their vision while on-orbit. Comments have included descriptions of earth features and objects that would suggest enhanced distance visual acuity. In contrast, some cosmonaut observations suggest a slight loss in their object discrimination during initial space flight. Astronauts have also mentioned a decreased near vision capability that did not recover to normal until return to earth. Duntley space vision experiment, USSR space vision experiments, and visual function testers are described.
Adaptive density trajectory cluster based on time and space distance
NASA Astrophysics Data System (ADS)
Liu, Fagui; Zhang, Zhijie
2017-10-01
There are some hotspot problems remaining in trajectory cluster for discovering mobile behavior regularity, such as the computation of distance between sub trajectories, the setting of parameter values in cluster algorithm and the uncertainty/boundary problem of data set. As a result, based on the time and space, this paper tries to define the calculation method of distance between sub trajectories. The significance of distance calculation for sub trajectories is to clearly reveal the differences in moving trajectories and to promote the accuracy of cluster algorithm. Besides, a novel adaptive density trajectory cluster algorithm is proposed, in which cluster radius is computed through using the density of data distribution. In addition, cluster centers and number are selected by a certain strategy automatically, and uncertainty/boundary problem of data set is solved by designed weighted rough c-means. Experimental results demonstrate that the proposed algorithm can perform the fuzzy trajectory cluster effectively on the basis of the time and space distance, and obtain the optimal cluster centers and rich cluster results information adaptably for excavating the features of mobile behavior in mobile and sociology network.
Generalized Pauli constraints in reduced density matrix functional theory
Theophilou, Iris; Helbig, Nicole; Lathiotakis, Nektarios N.; Marques, Miguel A. L.
2015-04-21
Functionals of the one-body reduced density matrix (1-RDM) are routinely minimized under Coleman’s ensemble N-representability conditions. Recently, the topic of pure-state N-representability conditions, also known as generalized Pauli constraints, received increased attention following the discovery of a systematic way to derive them for any number of electrons and any finite dimensionality of the Hilbert space. The target of this work is to assess the potential impact of the enforcement of the pure-state conditions on the results of reduced density-matrix functional theory calculations. In particular, we examine whether the standard minimization of typical 1-RDM functionals under the ensemble N-representability conditions violates the pure-state conditions for prototype 3-electron systems. We also enforce the pure-state conditions, in addition to the ensemble ones, for the same systems and functionals and compare the correlation energies and optimal occupation numbers with those obtained by the enforcement of the ensemble conditions alone.
Time-dependent density-functional description of nuclear dynamics
NASA Astrophysics Data System (ADS)
Nakatsukasa, Takashi; Matsuyanagi, Kenichi; Matsuo, Masayuki; Yabana, Kazuhiro
2016-10-01
The basic concepts and recent developments in the time-dependent density-functional theory (TDDFT) for describing nuclear dynamics at low energy are presented. The symmetry breaking is inherent in nuclear energy density functionals, which provides a practical description of important correlations at the ground state. Properties of elementary modes of excitation are strongly influenced by the symmetry breaking and can be studied with TDDFT. In particular, a number of recent developments in the linear response calculation have demonstrated their usefulness in the description of collective modes of excitation in nuclei. Unrestricted real-time calculations have also become available in recent years, with new developments for quantitative description of nuclear collision phenomena. There are, however, limitations in the real-time approach; for instance, it cannot describe the many-body quantum tunneling. Thus, the quantum fluctuations associated with slow collective motions are explicitly treated assuming that time evolution of densities is determined by a few collective coordinates and momenta. The concept of collective submanifold is introduced in the phase space associated with the TDDFT and used to quantize the collective dynamics. Selected applications are presented to demonstrate the usefulness and quality of the new approaches. Finally, conceptual differences between nuclear and electronic TDDFT are discussed, with some recent applications to studies of electron dynamics in the linear response and under a strong laser field.
Partitioned density functional approach for a Lennard-Jones fluid.
Zhou, Shiqi
2003-12-01
The existing classical density functional approach for nonuniform Lennard-Jones fluid, which is based on dividing the Lennard-Jones interaction potential into a short-range, repulsive part, and a smoothly varying, long-range, attractive tail, was improved by dividing the bulk second-order direct correlation function into strongly density-depending short-range part and weakly density-depending long-range part. The latter is treated by functional perturbation expansion truncated at the lowest order whose accuracy depends on how weakly the long-range part depends on the bulk density. The former is treated by the truncated functional perturbation expansion which is rewritten in the form of the simple weighted density approximation and incorporates the omitted higher-order terms by applying Lagrangian theorem of differential calculus to the reformulated form. The two approximations are put into the density profile equation of the density functional theory formalism to predict the density distribution for Lennard-Jones fluid in contact with a hard wall or between two hard walls within the whole density range for reduced temperature T(*)=1.35 and a density point for reduced temperature T(*)=1. The present partitioned density functional theory performs much better than several previous density functional perturbation theory approaches and a recently proposed bridge density functional approximation.
NASA Astrophysics Data System (ADS)
Granett, B. R.; Branchini, E.; Guzzo, L.; Abbas, U.; Adami, C.; Arnouts, S.; Bel, J.; Bolzonella, M.; Bottini, D.; Cappi, A.; Coupon, J.; Cucciati, O.; Davidzon, I.; De Lucia, G.; de la Torre, S.; Fritz, A.; Franzetti, P.; Fumana, M.; Garilli, B.; Ilbert, O.; Iovino, A.; Krywult, J.; Le Brun, V.; Le Fèvre, O.; Maccagni, D.; Małek, K.; Marulli, F.; McCracken, H. J.; Polletta, M.; Pollo, A.; Scodeggio, M.; Tasca, L. A. M.; Tojeiro, R.; Vergani, D.; Zanichelli, A.; Burden, A.; Di Porto, C.; Marchetti, A.; Marinoni, C.; Mellier, Y.; Moutard, T.; Moscardini, L.; Nichol, R. C.; Peacock, J. A.; Percival, W. J.; Zamorani, G.
2015-11-01
Aims: Using the VIMOS Public Extragalactic Redshift Survey (VIPERS) we aim to jointly estimate the keyparameters that describe the galaxy density field and its spatial correlations in redshift space. Methods: We use the Bayesian formalism to jointly reconstruct the redshift-space galaxy density field, power spectrum, galaxy bias and galaxy luminosity function given the observations and survey selection function. The high-dimensional posterior distribution is explored using the Wiener filter within a Gibbs sampler. We validate the analysis using simulated catalogues and apply it to VIPERS data taking into consideration the inhomogeneous selection function. Results: We present joint constraints on the anisotropic power spectrum, and the bias and number density of red and blue galaxy classes in luminosity and redshift bins as well as the measurement covariances of these quantities. We find that the inferred galaxy bias and number density parameters are strongly correlated although they are only weakly correlated with the galaxy power spectrum. The power spectrum and redshift-space distortion parameters are in agreement with previous VIPERS results with the value of the growth rate fσ8 = 0.38 with 18% uncertainty at redshift 0.7. Appendices are available in electronic form at http://www.aanda.org
Density of a semigroup in a Banach space
NASA Astrophysics Data System (ADS)
Borodin, P. A.
2014-12-01
We study conditions on a set M in a Banach space X which are necessary or sufficient for the set R(M) of all sums x_1+\\dots+x_n, x_k\\in M, to be dense in X. We distinguish conditions under which the closure \\overline{R(M)} is an additive subgroup of X, and conditions under which this additive subgroup is dense in X. In particular, we prove that if M is a closed rectifiable curve in a uniformly convex and uniformly smooth Banach space X, and does not lie in a closed half-space \\{x\\in X\\colon f(x)≥0\\}, f\\in X^*, and is minimal in the sense that every proper subarc of M lies in an open half-space \\{x\\in X\\colon f(x)>0\\}, then \\overline{R(M)}=X. We apply our results to questions of approximation in various function spaces.
Brorsen, Kurt R; Yang, Yang; Pak, Michael V; Hammes-Schiffer, Sharon
2017-05-04
The development of approximate exchange-correlation functionals is critical for modern density functional theory. A recent analysis of atomic systems suggested that some modern functionals are straying from the path toward the exact functional because electron densities are becoming less accurate while energies are becoming more accurate since the year 2000. To investigate this trend for more chemically relevant systems, the electron densities in the bonding regions and the atomization energies are analyzed for a series of diatomic molecules with 90 different functionals. For hybrid generalized gradient approximation functionals developed since the year 2000, the errors in densities and atomization energies are decoupled; the accuracy of the energies remains relatively consistent while the accuracy of the densities varies significantly. Such decoupling is not observed for generalized gradient and meta-generalized gradient approximation functionals. Analysis of electron densities in bonding regions is found to be important for the evaluation of functionals for chemical systems.
Charge transfer in time-dependent density functional theory
NASA Astrophysics Data System (ADS)
Maitra, Neepa T.
2017-10-01
Charge transfer plays a crucial role in many processes of interest in physics, chemistry, and bio-chemistry. In many applications the size of the systems involved calls for time-dependent density functional theory (TDDFT) to be used in their computational modeling, due to its unprecedented balance between accuracy and efficiency. However, although exact in principle, in practise approximations must be made for the exchange-correlation functional in this theory, and the standard functional approximations perform poorly for excitations which have a long-range charge-transfer component. Intense progress has been made in developing more sophisticated functionals for this problem, which we review. We point out an essential difference between the properties of the exchange-correlation kernel needed for an accurate description of charge-transfer between open-shell fragments and between closed-shell fragments. We then turn to charge-transfer dynamics, which, in contrast to the excitation problem, is a highly non-equilibrium, non-perturbative, process involving a transfer of one full electron in space. This turns out to be a much more challenging problem for TDDFT functionals. We describe dynamical step and peak features in the exact functional evolving over time, that are missing in the functionals currently used. The latter underestimate the amount of charge transferred and manifest a spurious shift in the charge transfer resonance position. We discuss some explicit examples.
Linear and nonlinear density response functions for a simple atomic fluid.
Dalton, Benjamin A; Glavatskiy, Kirill S; Daivis, Peter J; Todd, B D; Snook, Ian K
2013-07-28
We use molecular dynamics simulations to investigate the linear and nonlinear density response functions for simple fluids under the influence of spatially periodic external fields. Using a direct Fourier space decomposition of the instantaneous microscopic density for the perturbed fluid we can clearly identify the distinct order of response. Using a single component sinusoidal longitudinal force for a set of wavelengths and amplitudes we show that in the linear response regime the proportionality between the external field amplitude and the density perturbation can be used to determine the linear density response function, and hence the pair correlation function, static liquid structure factor, and lowest order direct correlation function. We show also that for large external field amplitudes a single component external field can be used to determine the form for lowest order and second lowest order nonlinear response functions for restricted regions of the total response function spaces.
A half century of density functional theory
Zangwill, Andrew
2015-07-15
Today’s most popular method for calculating the electronic structure of atoms, molecules, liquids, solids, and plasmas began as a bold hypothesis: The electron density distribution completely characterizes the ground state of a many-electron system.
Validation of density-functional versus density-functional+U approaches for oxide ultrathin films
NASA Astrophysics Data System (ADS)
Barcaro, Giovanni; Thomas, Iorwerth Owain; Fortunelli, Alessandro
2010-03-01
A comparison between available experimental information and the predictions of density-functional and density-functional+U approaches is presented for oxide ultrathin films grown on single-crystal metal surfaces. Prototypical examples of monolayer phases of an ionic oxide (ZnO), a late transition metal oxide (NiO), and an early transition metal oxide (TiO2) are considered. The aim is to validate the theoretical approaches, focusing on the prediction of structural features and the reproduction of scanning tunneling microscopy images, rationalized in terms of the local density of states of the systems. It is found that it is possible to reasonably estimate the optimal lattice constant of ultrathin supported films and that the inclusion of the Hubbard U term appreciably improves the accuracy of theoretical predictions, especially in the case of nonpolar ultrathin phases of a transition metal oxide. Moreover, the optimal value of U for the oxide layer at the interface with the metal support is found to differ from that appropriate for the bulk oxide, as a consequence of the intermixing of oxide and support electronic states and screening effects.
[Capillary density and respiratory function in the external intercostal muscle].
Jiménez-Fuentes, M A; Gea, J; Aguar, M C; Minguella, J; Lloreta, J; Félez, M; Broquetas, J
1999-11-01
Changes in lung function have been related to adaptive structural modifications in respiratory muscles. To evaluate the capillary density (Dcap) of the external intercostal muscle in patients with chronic obstructive pulmonary disease (COPD), and its possible relation to respiratory function. Forty-two individuals (61 +/- 9 years old) underwent conventional lung function testing and evaluation of respiratory muscles (maximum pressures at rest and a tolerance test using Martyn's technique). The sample included 10 subjects with normal lung function and 32 COPD patients (FEV1 between 13 and 78% of reference), in stable phase and with no respiratory insufficiency (PaO2 > 60 mmHg). A local biopsy of the external intercostal muscle was taken from all subjects at the fifth intercostal space (anterior axillary [correction of axile]) on the non-dominant side. The sample was processed for morphometry and fiber typing with ATPase staining and for quantifying capillarity with Gomori's trichrome staining. The mean diameter was 61 +/- 10 micrograms, with type I fibers predominating (56 +/- 11%). Dcap was 2.8 +/- 0.6 capillaries/fiber (equivalent to 1.02 +/- 0.37 capillaries/mm2 of fibrillary surface). The number of capillaries/fiber was significantly higher in patients with severe COPD (FEV1 < 50% ref) than in controls (3.0 +/- 0.6 versus 2.3 +/- 0.5, p < 0.01) and was inversely related to FEV1 (r = -0.395, p < 0.01). Muscle capillarity was unrelated to other function variables, including markers of respiratory muscle function and gas exchange. The structural remodelling of external intercostal muscles in COPD patients also includes an increase in density of interfibrillary capillaries. This increase is proportional to the severity of obstruction and probably reflects an adaptive phenomenon.
Coulomb wave functions in momentum space
Eremenko, V.; Upadhyay, N. J.; Thompson, I. J.; Elster, Ch.; Nunes, F. M.; Arbanas, G.; Escher, J. E.; Hlophe, L.
2015-10-15
We present an algorithm to calculate non-relativistic partial-wave Coulomb functions in momentum space. The arguments are the Sommerfeld parameter η, the angular momentum l, the asymptotic momentum q and the 'running' momentum p, where both momenta are real. Since the partial-wave Coulomb functions exhibit singular behavior when p → q, different representations of the Legendre functions of the 2nd kind need to be implemented in computing the functions for the values of p close to the singularity and far away from it. The code for the momentum-space Coulomb wave functions is applicable for values of vertical bar eta vertical bar in the range of 10^{-1} to 10, and thus is particularly suited for momentum space calculations of nuclear reactions.
Coulomb wave functions in momentum space
Eremenko, V.; Upadhyay, N. J.; Thompson, I. J.; ...
2015-10-15
We present an algorithm to calculate non-relativistic partial-wave Coulomb functions in momentum space. The arguments are the Sommerfeld parameter η, the angular momentum l, the asymptotic momentum q and the 'running' momentum p, where both momenta are real. Since the partial-wave Coulomb functions exhibit singular behavior when p → q, different representations of the Legendre functions of the 2nd kind need to be implemented in computing the functions for the values of p close to the singularity and far away from it. The code for the momentum-space Coulomb wave functions is applicable for values of vertical bar eta vertical barmore » in the range of 10-1 to 10, and thus is particularly suited for momentum space calculations of nuclear reactions.« less
Mezei, Pal Daniel; Csonka, Gabor I; Kallay, Mihaly
2017-09-11
Since its formal introduction, density functional theory has achieved many successes on the fields of molecular and solid-state chemistry. According to its central theorems, the ground state of a many-electron system is fully described by its electron density, and the exact functional minimizes the energy at the exact electron density. For many years of density functional development, it was assumed that the improvements in the energy are accompanied by the improvements in the density, and the approximations approach the exact functional. In a recent analysis (Medvedev et al. Science 2017, 355, 49-52.), it has been pointed out for fourteen first row (Be-Ne) atoms and cations with 2, 4, or 10 electrons that the nowadays popular flexible but physically less rigorous approximate density functionals may provide large errors in the calculated electron densities despite the accurate energies. Although far-reaching conclusions have been drawn in this work, the methodology used by the authors may need improvements. Most importantly, their benchmark set was biased towards small atomic cations with compressed, high electron densities. In our paper, we construct a molecular test set with chemically relevant densities and analyze the performance of several density functional approximations including the less-investigated double hybrids. We apply an intensive error measure for the density, its gradient, and its Laplacian and examine how the errors in the density propagate into the semi-local exchange-correlation energy. While we have confirmed the broad conclusions of Medvedev et al., our different way of analyzing the data has led to conclusions that differ in detail. Finally, seeking for a rationale behind the global hybrid or double hybrid methods from the density's point of view, we also analyze the role of the exact exchange and second-order perturbative correlation mixing in PBE-based global hybrid and double hybrid functional forms.
a Renormalization Group Calculation of the Velocity - and Density-Density Correlation Functions.
NASA Astrophysics Data System (ADS)
Cowan, Mark Timothy
The velocity-velocity correlation function of a free field theory is obtained. The renormalization group, along with a 4-varepsilon expansion, is then used to find the leading order behavior of the velocity-velocity correlation function for an interacting field theory in the high temperature phase near the critical point. The details of the calculation of the density-density correlation function for Hedgehogs, in the context of a free field theory, is presented next. Finally the renormalization group, along with a 4-varepsilon expansion, is used to find the leading order behavior of the density-density correlation function for Hedgehogs in an interacting field theory near the critical point.
Characterizing high-energy-density propellants for space propulsion applications
NASA Astrophysics Data System (ADS)
Kokan, Timothy
There exists wide ranging research interest in high-energy-density matter (HEDM) propellants as a potential replacement for existing industry standard fuels for liquid rocket engines. The U.S. Air Force Research Laboratory, the U.S. Army Research Lab, the NASA Marshall Space Flight Center, and the NASA Glenn Research Center each either recently concluded or currently has ongoing programs in the synthesis and development of these potential new propellants. In order to perform conceptual designs using these new propellants, most conceptual rocket engine powerhead design tools (e.g. NPSS, ROCETS, and REDTOP-2) require several thermophysical properties of a given propellant over a wide range of temperature and pressure. These properties include enthalpy, entropy, density, viscosity, and thermal conductivity. Very little thermophysical property data exists for most of these potential new HEDM propellants. Experimental testing of these properties is both expensive and time consuming and is impractical in a conceptual vehicle design environment. A new technique for determining these thermophysical properties of potential new rocket engine propellants is presented. The technique uses a combination of three different computational methods to determine these properties. Quantum mechanics and molecular dynamics are used to model new propellants at a molecular level in order to calculate density, enthalpy, and entropy. Additivity methods are used to calculate the kinematic viscosity and thermal conductivity of new propellants. This new technique is validated via a series of verification experiments of HEDM compounds. Results are provided for two HEDM propellants: quadricyclane and 2-azido-N,N-dimethylethanamine (DMAZ). In each case, the new technique does a better job than the best current computational methods at accurately matching the experimental data of the HEDM compounds of interest. A case study is provided to help quantify the vehicle level impacts of using HEDM
Fluids Density Functional Theory of Diblock Copolymers for Electrolyte Applications
NASA Astrophysics Data System (ADS)
Brown, Jonathan R.; Hall, Lisa M.
We use classical, fluids density functional theory (fDFT) to study microphase separation in block copolymer systems. We are motivated by systems used as battery electrolytes or in other transport applications, in which the two blocks of the system have different mechanical, dielectric, and transport properties that allow one phase to act as a charge/penetrant carrier and the other to make the film mechanically strong. We find density profiles of penetrants, showing to what degree they segregate into the A phase and their concentration near the interface, depending on the penetrant-A and penetrant-B interaction strengths as well as the A-B segregation strength. We also study the effect of tapering, or adding a gradient region (taper) between the pure A and B blocks of an AB diblock copolymer; the taper changes in composition along its length from pure A to pure B (or from B to A for an inverse taper). The effect of both penetrants and tapering on microphase domain spacing as a function of segregation strength will be discussed. Adjusting taper length allows one to tune the phase behavior of the system for easier processing or access to specific desired microphase structures. Based upon work supported by NSF Grant 1454343 and DOE Grant SC0014209.
Prox-regular functions in Hilbert spaces
NASA Astrophysics Data System (ADS)
Bernard, Frédéric; Thibault, Lionel
2005-03-01
This paper studies the prox-regularity concept for functions in the general context of Hilbert space. In particular, a subdifferential characterization is established as well as several other properties. It is also shown that the Moreau envelopes of such functions are continuously differentiable.
Direct recursive identification of the Preisach hysteresis density function
NASA Astrophysics Data System (ADS)
Ruderman, Michael
2013-12-01
In this paper, a novel direct method of recursive identification of the Preisach hysteresis density function is proposed. Using the discrete dynamic Preisach model, which is a state-space realization of the classical scalar Preisach model, the method is designed based on the output increment error. After giving the general formulation, the identification scheme implemented for a discretized Preisach plane is introduced and evaluated through the use of numerical simulations. Two cases of Gaussian mixtures are considered for mapping the hysteresis system to be identified. The parameter convergence is shown for a low-pass filtered white-noise input. Further, the proposed identification method is applied to a magnetism-related application example, where the flux linkage hysteresis of a proportional solenoid is assumed from the measurements, and then the inverse of a standard demagnetization procedure is utilized as the identification sequence.
Fundamental gap of molecular crystals via constrained density functional theory
NASA Astrophysics Data System (ADS)
Droghetti, Andrea; Rungger, Ivan; Das Pemmaraju, Chaitanya; Sanvito, Stefano
2016-05-01
The energy gap of a molecular crystal is one of the most important properties since it determines the crystal charge transport when the material is utilized in electronic devices. This is, however, a quantity difficult to calculate and standard theoretical approaches based on density functional theory (DFT) have proven unable to provide accurate estimates. In fact, besides the well-known band-gap problem, DFT completely fails in capturing the fundamental gap reduction occurring when molecules are packed in a crystal structures. The failure has to be associated with the inability of describing the electronic polarization and the real space localization of the charged states. Here we describe a scheme based on constrained DFT, which can improve upon the shortcomings of standard DFT. The method is applied to the benzene crystal, where we show that accurate results can be achieved for both the band gap and also the energy level alignment.
Characterizing the Spatial Density Functions of Neural Arbors
NASA Astrophysics Data System (ADS)
Teeter, Corinne Michelle
Recently, it has been proposed that a universal function describes the way in which all arbors (axons and dendrites) spread their branches over space. Data from fish retinal ganglion cells as well as cortical and hippocampal arbors from mouse, rat, cat, monkey and human provide evidence that all arbor density functions (adf) can be described by a Gaussian function truncated at approximately two standard deviations. A Gaussian density function implies that there is a minimal set of parameters needed to describe an adf: two or three standard deviations (depending on the dimensionality of the arbor) and an amplitude. However, the parameters needed to completely describe an adf could be further constrained by a scaling law found between the product of the standard deviations and the amplitude of the function. In the following document, I examine the scaling law relationship in order to determine the minimal set of parameters needed to describe an adf. First, I find that the at, two-dimensional arbors of fish retinal ganglion cells require only two out of the three fundamental parameters to completely describe their density functions. Second, the three-dimensional, volume filling, cortical arbors require four fundamental parameters: three standard deviations and the total length of an arbor (which corresponds to the amplitude of the function). Next, I characterize the shape of arbors in the context of the fundamental parameters. I show that the parameter distributions of the fish retinal ganglion cells are largely homogenous. In general, axons are bigger and less dense than dendrites; however, they are similarly shaped. The parameter distributions of these two arbor types overlap and, therefore, can only be differentiated from one another probabilistically based on their adfs. Despite artifacts in the cortical arbor data, different types of arbors (apical dendrites, non-apical dendrites, and axons) can generally be differentiated based on their adfs. In addition, within
Density Functional Theory Embedding for Correlated Wavefunctions
2014-01-01
The H2 molecules are oriented parallel to the z axis, with a bond length of 0.8 Å, and the centers-of-mass for the molecules are spaced by 3.0 Å...Bickelhaupt, E. J. Baerends, C. Fonseca Guerra , S. J. A. Van Gisbergen, J. G. Snijders, and T. Ziegler, J. Comput. Chem. 22, 931 (2001). [56] Y
Density functional theory for Yukawa fluids.
Hatlo, Marius M; Banerjee, Priyanka; Forsman, Jan; Lue, Leo
2012-08-14
We develop an approximate field theory for particles interacting with a generalized Yukawa potential. This theory improves and extends a previous splitting field theory, originally developed for counterions around a fixed charge distribution. The resulting theory bridges between the second virial approximation, which is accurate at low particle densities, and the mean-field approximation, accurate at high densities. We apply this theory to charged, screened ions in bulk solution, modeled to interact with a Yukawa potential; the theory is able to accurately reproduce the thermodynamic properties of the system over a broad range of conditions. The theory is also applied to "dressed counterions," interacting with a screened electrostatic potential, contained between charged plates. It is found to work well from the weak coupling to the strong coupling limits. The theory is able to reproduce the counterion profiles and force curves for closed and open systems obtained from Monte Carlo simulations.
Multiscale time-dependent density functional theory: Demonstration for plasmons
NASA Astrophysics Data System (ADS)
Jiang, Jiajian; Abi Mansour, Andrew; Ortoleva, Peter J.
2017-08-01
Plasmon properties are of significant interest in pure and applied nanoscience. While time-dependent density functional theory (TDDFT) can be used to study plasmons, it becomes impractical for elucidating the effect of size, geometric arrangement, and dimensionality in complex nanosystems. In this study, a new multiscale formalism that addresses this challenge is proposed. This formalism is based on Trotter factorization and the explicit introduction of a coarse-grained (CG) structure function constructed as the Weierstrass transform of the electron wavefunction. This CG structure function is shown to vary on a time scale much longer than that of the latter. A multiscale propagator that coevolves both the CG structure function and the electron wavefunction is shown to bring substantial efficiency over classical propagators used in TDDFT. This efficiency follows from the enhanced numerical stability of the multiscale method and the consequence of larger time steps that can be used in a discrete time evolution. The multiscale algorithm is demonstrated for plasmons in a group of interacting sodium nanoparticles (15-240 atoms), and it achieves improved efficiency over TDDFT without significant loss of accuracy or space-time resolution.
Molecular dynamics simulation of liquid water: Hybrid density functionals
Todorova, T; Seitsonen, A; Hutter, J; Kuo, W; Mundy, C
2005-09-12
The structure, dynamical and electronic properties of liquid water utilizing different hybrid density functionals were tested within the plane wave framework of first principles molecular dynamics simulations. The computational approach, which employs modified functionals with short-ranged Hartree-Fock exchange, was first tested in calculations of the structural and bonding properties of the water dimer and cyclic water trimer. Liquid water simulations were performed at the state point of 350 K at the experimental density. Simulations included three different hybrid functionals, a meta functional, four gradient corrected functionals, the local density and Hartree-Fock approximation. It is found that hybrid functionals are superior in reproducing the experimental structure and dynamical properties as measured by the radial distribution function and self diffusion constant when compared to the pure density functionals. The local density and Hartree-Fock approximations show strongly over- and under-structured liquids, respectively. Hydrogen bond analysis shows that the hybrid functionals give slightly smaller averaged numbers of hydrogen bonds and similar hydrogen bond populations as pure density functionals. The average molecular dipole moments in the liquid from the three hybrid functionals are lower than from the corresponding pure density functionals.
Orbital-free kinetic-energy density functionals with a density-dependent kernel
NASA Astrophysics Data System (ADS)
Wang, Yan Alexander; Govind, Niranjan; Carter, Emily A.
1999-12-01
We report linear-response kinetic-energy density functionals, which show significant improvement over the Wang-Teter, Perrot, Smargiassi-Madden, Wang-Govind-Carter functionals, yet still maintain O(N ln N) scaling. Numerical tests show that these functionals, which contain a double-density-dependent kernel, can reproduce the Kohn-Sham results almost exactly for several aluminum bulk phases. We further show that with a sensible choice of the uniform background density, energies of formation for the low-index aluminum surfaces, where the density variations are very large, can be reproduced to within reasonable accuracy.
On the estimation of the current density in space plasmas: Multi- versus single-point techniques
NASA Astrophysics Data System (ADS)
Perri, Silvia; Valentini, Francesco; Sorriso-Valvo, Luca; Reda, Antonio; Malara, Francesco
2017-06-01
Thanks to multi-spacecraft mission, it has recently been possible to directly estimate the current density in space plasmas, by using magnetic field time series from four satellites flying in a quasi perfect tetrahedron configuration. The technique developed, commonly called ;curlometer; permits a good estimation of the current density when the magnetic field time series vary linearly in space. This approximation is generally valid for small spacecraft separation. The recent space missions Cluster and Magnetospheric Multiscale (MMS) have provided high resolution measurements with inter-spacecraft separation up to 100 km and 10 km, respectively. The former scale corresponds to the proton gyroradius/ion skin depth in ;typical; solar wind conditions, while the latter to sub-proton scale. However, some works have highlighted an underestimation of the current density via the curlometer technique with respect to the current computed directly from the velocity distribution functions, measured at sub-proton scales resolution with MMS. In this paper we explore the limit of the curlometer technique studying synthetic data sets associated to a cluster of four artificial satellites allowed to fly in a static turbulent field, spanning a wide range of relative separation. This study tries to address the relative importance of measuring plasma moments at very high resolution from a single spacecraft with respect to the multi-spacecraft missions in the current density evaluation.
Transition from Fowler-Nordheim field emission to space charge limited current density
NASA Astrophysics Data System (ADS)
Feng, Y.; Verboncoeur, J. P.
2006-07-01
The Fowler-Nordheim law gives the current density extracted from a surface under strong fields, by treating the emission of electrons from a metal-vacuum interface in the presence of an electric field normal to the surface as a quantum mechanical tunneling process. Child's law predicts the maximum transmitted current density by considering the space charge effect. When the electric field becomes high enough, the emitted current density will be limited by Child's law. This work analyzes the transition of the transmitted current density from the Fowler-Nordheim law to Child's law space charge limit using a one-dimensional particle-in-cell code. Also studied is the response of the emission model to strong electric fields near the transition point. We find the transition without geometrical effort is smooth and much slower than reported previously [J. P. Barbour, W. W. Dolan, J. K. Trolan, E. E. Martin, and W. P. Dyke, Phys. Rev. 92, 45 (1953)]. We analyze the effects of geometric field enhancement and work function on the transition. Using our previous model for effective field enhancement [Y. Feng and J. P. Verboncoeur, Phys. Plasmas 12, 103301 (2005)], we find the geometric effect dominates, and enhancement β >10 can accelerate the approach to the space charge limit at practical electric field. A damped oscillation near the local plasma frequency is observed in the transient system response.
Transition from Fowler-Nordheim field emission to space charge limited current density
Feng, Y.; Verboncoeur, J. P.
2006-07-15
The Fowler-Nordheim law gives the current density extracted from a surface under strong fields, by treating the emission of electrons from a metal-vacuum interface in the presence of an electric field normal to the surface as a quantum mechanical tunneling process. Child's law predicts the maximum transmitted current density by considering the space charge effect. When the electric field becomes high enough, the emitted current density will be limited by Child's law. This work analyzes the transition of the transmitted current density from the Fowler-Nordheim law to Child's law space charge limit using a one-dimensional particle-in-cell code. Also studied is the response of the emission model to strong electric fields near the transition point. We find the transition without geometrical effort is smooth and much slower than reported previously [J. P. Barbour, W. W. Dolan, J. K. Trolan, E. E. Martin, and W. P. Dyke, Phys. Rev. 92, 45 (1953)]. We analyze the effects of geometric field enhancement and work function on the transition. Using our previous model for effective field enhancement [Y. Feng and J. P. Verboncoeur, Phys. Plasmas 12, 103301 (2005)], we find the geometric effect dominates, and enhancement {beta}>10 can accelerate the approach to the space charge limit at practical electric field. A damped oscillation near the local plasma frequency is observed in the transient system response.
Curtis, Robert O.; Bansal, Sheel; Harrington, Constance A.
2016-01-01
This report presents updated information on a 1981 Douglas-fir (Pseudotsuga menziesii (Mirb.) Franco var. menziesii) plantation spacing trial at 33 years from planting. Stand statistics at the most recent measurement were compared for initial spacing of 1 through 6 meters and associated relative densities. There was no clear relationship of spacing to top height. Diameter, live crown ratio, and percent survival increased with spacing; basal area and relative density decreased with increase in spacing. Volume in trees ≥ 4 cm diameter was greatest at 2 m spacing, while utilizable volume (trees ≥20 cm dbh) was greatest at 4 m spacing. Live crown ratio decreased and total crown projectional area increased with increasing relative density indices. Total crown projectional area was more closely related to relative density than to basal area.
Topological analysis of electron densities from Kohn-Sham and subsystem density functional theory.
Kiewisch, Karin; Eickerling, Georg; Reiher, Markus; Neugebauer, Johannes
2008-01-28
In this study, we compare the electron densities for a set of hydrogen-bonded complexes obtained with either conventional Kohn-Sham density functional theory (DFT) calculations or with the frozen-density embedding (FDE) method, which is a subsystem approach to DFT. For a detailed analysis of the differences between these two methods, we compare the topology of the electron densities obtained from Kohn-Sham DFT and FDE in terms of deformation densities, bond critical points, and the negative Laplacian of the electron density. Different kinetic-energy functionals as needed for the frozen-density embedding method are tested and compared to a purely electrostatic embedding. It is shown that FDE is able to reproduce the characteristics of the density in the bonding region even in systems such as the F-H-F(-) molecule, which contains one of the strongest hydrogen bonds. Basis functions on the frozen system are usually required to accurately reproduce the electron densities of supermolecular calculations. However, it is shown here that it is in general sufficient to provide just a few basis functions in the boundary region between the two subsystems so that the use of the full supermolecular basis set can be avoided. It also turns out that electron-density deformations upon bonding predicted by FDE lack directionality with currently available functionals for the nonadditive kinetic-energy contribution.
Interpolating Functions on Lines in 3-Space
2000-01-01
numbers comprise the compilation report: ADP011967 thru ADPO12009 UNCLASSIFIED Interpolating Functions on Lines in 3-Space Martin Peternell and Helmut...reproduction in any form reserved. 352 M. Peternell and H. Pottmann §2. Lines in Space An oriented line L in Euclidean 3-space E 3 is determined by a...intersection r = Q n T is a quadratic cone with vertex Z. The intersection e = E n T is a hyperplane 354 M. Peternell and H. Pottmann X t) Fig. 2. Local
Filtered density function approach for reactive transport in groundwater
NASA Astrophysics Data System (ADS)
Suciu, Nicolae; Schüler, Lennart; Attinger, Sabine; Knabner, Peter
2016-04-01
Spatial filtering may be used in coarse-grained simulations (CGS) of reactive transport in groundwater, similar to the large eddy simulations (LES) in turbulence. The filtered density function (FDF), stochastically equivalent to a probability density function (PDF), provides a statistical description of the sub-grid, unresolved, variability of the concentration field. Besides closing the chemical source terms in the transport equation for the mean concentration, like in LES-FDF methods, the CGS-FDF approach aims at quantifying the uncertainty over the whole hierarchy of heterogeneity scales exhibited by natural porous media. Practically, that means estimating concentration PDFs on coarse grids, at affordable computational costs. To cope with the high dimensionality of the problem in case of multi-component reactive transport and to reduce the numerical diffusion, FDF equations are solved by particle methods. But, while trajectories of computational particles are modeled as stochastic processes indexed by time, the concentration's heterogeneity is modeled as a random field, with multi-dimensional, spatio-temporal sets of indices. To overcome this conceptual inconsistency, we consider FDFs/PDFs of random species concentrations weighted by conserved scalars and we show that their evolution equations can be formulated as Fokker-Planck equations describing stochastically equivalent processes in concentration-position spaces. Numerical solutions can then be approximated by the density in the concentration-position space of an ensemble of computational particles governed by the associated Itô equations. Instead of sequential particle methods we use a global random walk (GRW) algorithm, which is stable, free of numerical diffusion, and practically insensitive to the increase of the number of particles. We illustrate the general FDF approach and the GRW numerical solution for a reduced complexity problem consisting of the transport of a single scalar in groundwater
Exact conditions on the temperature dependence of density functionals
Burke, K.; Smith, J. C.; Grabowski, P. E.; ...
2016-05-15
Universal exact conditions guided the construction of most ground-state density functional approximations in use today. Here, we derive the relation between the entropy and Mermin free energy density functionals for thermal density functional theory. Both the entropy and sum of kinetic and electron-electron repulsion functionals are shown to be monotonically increasing with temperature, while the Mermin functional is concave downwards. Analogous relations are found for both exchange and correlation. The importance of these conditions is illustrated in two extremes: the Hubbard dimer and the uniform gas.
Boosting BOLD fMRI by K-Space Density Weighted Echo Planar Imaging
Zeller, Mario; Müller, Alexander; Gutberlet, Marcel; Nichols, Thomas; Hahn, Dietbert; Köstler, Herbert; Bartsch, Andreas J.
2013-01-01
Functional magnetic resonance imaging (fMRI) has become a powerful and influential method to non-invasively study neuronal brain activity. For this purpose, the blood oxygenation level-dependent (BOLD) effect is most widely used. T2* weighted echo planar imaging (EPI) is BOLD sensitive and the prevailing fMRI acquisition technique. Here, we present an alternative to its standard Cartesian recordings, i.e. k-space density weighted EPI, which is expected to increase the signal-to-noise ratio in fMRI data. Based on in vitro and in vivo pilot measurements, we show that fMRI by k-space density weighted EPI is feasible and that this new acquisition technique in fact boosted spatial and temporal SNR as well as the detection of local fMRI activations. Spatial resolution, spatial response function and echo time were identical for density weighted and conventional Cartesian EPI. The signal-to-noise ratio gain of density weighting can improve activation detection and has the potential to further increase the sensitivity of fMRI investigations. PMID:24040262
Factor levels for density comparisons in the split-block spacing design
Kurt H. Riitters; Brian J. Stanton; Robbert H. Walkup
1989-01-01
The split-block spacing design is a compact test of the effects of within-row and between-row spacings. But the sometimes awkward analysis of density (i.e., trees/ha) effects may deter use of the design. The analysis is simpler if the row spacings are chosen to obtain a balanced set of equally spaced density and rectangularity treatments. A spacing study in poplar (...
Introduction to Classical Density Functional Theory by a Computational Experiment
ERIC Educational Resources Information Center
Jeanmairet, Guillaume; Levy, Nicolas; Levesque, Maximilien; Borgis, Daniel
2014-01-01
We propose an in silico experiment to introduce the classical density functional theory (cDFT). Density functional theories, whether quantum or classical, rely on abstract concepts that are nonintuitive; however, they are at the heart of powerful tools and active fields of research in both physics and chemistry. They led to the 1998 Nobel Prize in…
Introduction to Classical Density Functional Theory by a Computational Experiment
ERIC Educational Resources Information Center
Jeanmairet, Guillaume; Levy, Nicolas; Levesque, Maximilien; Borgis, Daniel
2014-01-01
We propose an in silico experiment to introduce the classical density functional theory (cDFT). Density functional theories, whether quantum or classical, rely on abstract concepts that are nonintuitive; however, they are at the heart of powerful tools and active fields of research in both physics and chemistry. They led to the 1998 Nobel Prize in…
General dynamical density functional theory for classical fluids.
Goddard, Benjamin D; Nold, Andreas; Savva, Nikos; Pavliotis, Grigorios A; Kalliadasis, Serafim
2012-09-21
We study the dynamics of a colloidal fluid including inertia and hydrodynamic interactions, two effects which strongly influence the nonequilibrium properties of the system. We derive a general dynamical density functional theory which shows very good agreement with full Langevin dynamics. In suitable limits, we recover existing dynamical density functional theories and a Navier-Stokes-like equation with additional nonlocal terms.
Hybrid-space density matrix renormalization group study of the doped two-dimensional Hubbard model
NASA Astrophysics Data System (ADS)
Ehlers, G.; White, S. R.; Noack, R. M.
2017-03-01
The performance of the density matrix renormalization group (DMRG) is strongly influenced by the choice of the local basis of the underlying physical lattice. We demonstrate that, for the two-dimensional Hubbard model, the hybrid-real-momentum-space formulation of the DMRG is computationally more efficient than the standard real-space formulation. In particular, we show that the computational cost for fixed bond dimension of the hybrid-space DMRG is approximately independent of the width of the lattice, in contrast to the real-space DMRG, for which it is proportional to the width squared. We apply the hybrid-space algorithm to calculate the ground state of the doped two-dimensional Hubbard model on cylinders of width four and six sites; at n =0.875 filling, the ground state exhibits a striped charge-density distribution with a wavelength of eight sites for both U /t =4.0 and 8.0 . We find that the strength of the charge ordering depends on U /t and on the boundary conditions. Furthermore, we investigate the magnetic ordering as well as the decay of the static spin, charge, and pair-field correlation functions.
Efficiency issues related to probability density function comparison
NASA Astrophysics Data System (ADS)
Kelly, Patrick M.; Cannon, T. Michael; Barros, Julio E.
1996-03-01
The CANDID project (comparison algorithm for navigating digital image databases) employs probability density functions (PDFs) of localized feature information to represent the content of an image for search and retrieval purposes. A similarity measure between PDFs is used to identify database images that are similar to a user-provided query image. Unfortunately, signature comparison involving PDFs is a very time-consuming operation. In this paper, we look into some efficiency considerations when working with PDFs. Since PDFs can take on many forms, we look into tradeoffs between accurate representation and efficiency of manipulation for several data sets. In particular, we typically represent each PDF as a Gaussian mixture (e.g. as a weighted sum of Gaussian kernels) in the feature space. We find that by constraining all Gaussian kernels to have principal axes that are aligned to the natural axes of the feature space, computations involving these PDFs are simplified. We can also constrain the Gaussian kernels to be hyperspherical rather than hyperellipsoidal, simplifying computations even further, and yielding an order of magnitude speedup in signature comparison. This paper illustrates the tradeoffs encountered when using these constraints.
NASA Astrophysics Data System (ADS)
Mattsson, Thomas R.
2007-06-01
Atomistic simulations employing Density Functional Theory (DFT) have recently emerged as a powerful way of increasing our understanding of materials and processes in high energy density physics. Knowledge of the properties of water (equation of state, electrical conductivity, diffusion, low-energy opacity) is essential for correctly describing the physics of giant planets as well as shock waves in water. Although a qualitative picture of water electrical conductivity has emerged, the necessary quantitative information is scarce over a wide range of temperature and density. Since experiments can only access certain areas of phase space, and often require modeling as a part of the analysis, Quantum Molecular Dynamics simulations play a vital role. Using finite-temperature density functional theory (FT-DFT), we have investigated the structure and electronic conductivity of water across three phase transitions (molecular liquid/ ionic liquid/ superionic/ electronic liquid). The ionic contribution to the conduction is calculated from proton diffusion and the electronic contribution is calculated using the Kubo-Greenwood formula. The calculations are performed with VASP, a plane-wave pseudo-potential code. There is a rapid transition to ionic conduction at 2000 K and 2 g/cm^3, whereas electronic conduction dominates at temperatures at and above 6000 K&[tilde;1]. Contrary to earlier results using the Car-Parrinello method&[tilde;2], we predict that the fluid bordering the superionic phase is conducting above 4000 K and 100 GPa. Our comprehensive use of FT-DFT explains the new findings. The calculated conductivity is compared to experimental data. I gratefully acknowledge Mike Desjarlais, my collaborator in this effort. The LDRD office at Sandia supported this work. Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL
Rapid modelling of the redshift-space power spectrum multipoles for a masked density field
NASA Astrophysics Data System (ADS)
Wilson, M. J.; Peacock, J. A.; Taylor, A. N.; de la Torre, S.
2017-01-01
In this work, we reformulate the forward modelling of the redshift-space power spectrum multipole moments for a masked density field, as encountered in galaxy redshift surveys. Exploiting the symmetries of the redshift-space correlation function, we provide a masked-field generalization of the Hankel transform relation between the multipole moments in real and Fourier space. Using this result, we detail how a likelihood analysis requiring computation for a broad range of desired P(k) models may be executed 103-104 times faster than with other common approaches, together with significant gains in spectral resolution. We present a concrete application to the complex angular geometry of the VIMOS Public Extragalactic Redshift Survey PDR-1 release and discuss the validity of this technique for finite-angle surveys.
NASA Astrophysics Data System (ADS)
Petrenko, Taras; Kossmann, Simone; Neese, Frank
2011-02-01
In this paper, we present the implementation of efficient approximations to time-dependent density functional theory (TDDFT) within the Tamm-Dancoff approximation (TDA) for hybrid density functionals. For the calculation of the TDDFT/TDA excitation energies and analytical gradients, we combine the resolution of identity (RI-J) algorithm for the computation of the Coulomb terms and the recently introduced "chain of spheres exchange" (COSX) algorithm for the calculation of the exchange terms. It is shown that for extended basis sets, the RIJCOSX approximation leads to speedups of up to 2 orders of magnitude compared to traditional methods, as demonstrated for hydrocarbon chains. The accuracy of the adiabatic transition energies, excited state structures, and vibrational frequencies is assessed on a set of 27 excited states for 25 molecules with the configuration interaction singles and hybrid TDDFT/TDA methods using various basis sets. Compared to the canonical values, the typical error in transition energies is of the order of 0.01 eV. Similar to the ground-state results, excited state equilibrium geometries differ by less than 0.3 pm in the bond distances and 0.5° in the bond angles from the canonical values. The typical error in the calculated excited state normal coordinate displacements is of the order of 0.01, and relative error in the calculated excited state vibrational frequencies is less than 1%. The errors introduced by the RIJCOSX approximation are, thus, insignificant compared to the errors related to the approximate nature of the TDDFT methods and basis set truncation. For TDDFT/TDA energy and gradient calculations on Ag-TB2-helicate (156 atoms, 2732 basis functions), it is demonstrated that the COSX algorithm parallelizes almost perfectly (speedup ˜26-29 for 30 processors). The exchange-correlation terms also parallelize well (speedup ˜27-29 for 30 processors). The solution of the Z-vector equations shows a speedup of ˜24 on 30 processors. The
Petrenko, Taras; Kossmann, Simone; Neese, Frank
2011-02-07
In this paper, we present the implementation of efficient approximations to time-dependent density functional theory (TDDFT) within the Tamm-Dancoff approximation (TDA) for hybrid density functionals. For the calculation of the TDDFT/TDA excitation energies and analytical gradients, we combine the resolution of identity (RI-J) algorithm for the computation of the Coulomb terms and the recently introduced "chain of spheres exchange" (COSX) algorithm for the calculation of the exchange terms. It is shown that for extended basis sets, the RIJCOSX approximation leads to speedups of up to 2 orders of magnitude compared to traditional methods, as demonstrated for hydrocarbon chains. The accuracy of the adiabatic transition energies, excited state structures, and vibrational frequencies is assessed on a set of 27 excited states for 25 molecules with the configuration interaction singles and hybrid TDDFT/TDA methods using various basis sets. Compared to the canonical values, the typical error in transition energies is of the order of 0.01 eV. Similar to the ground-state results, excited state equilibrium geometries differ by less than 0.3 pm in the bond distances and 0.5° in the bond angles from the canonical values. The typical error in the calculated excited state normal coordinate displacements is of the order of 0.01, and relative error in the calculated excited state vibrational frequencies is less than 1%. The errors introduced by the RIJCOSX approximation are, thus, insignificant compared to the errors related to the approximate nature of the TDDFT methods and basis set truncation. For TDDFT/TDA energy and gradient calculations on Ag-TB2-helicate (156 atoms, 2732 basis functions), it is demonstrated that the COSX algorithm parallelizes almost perfectly (speedup ~26-29 for 30 processors). The exchange-correlation terms also parallelize well (speedup ~27-29 for 30 processors). The solution of the Z-vector equations shows a speedup of ~24 on 30 processors. The
Schlüns, Danny; Franchini, Mirko; Götz, Andreas W; Neugebauer, Johannes; Jacob, Christoph R; Visscher, Lucas
2017-02-05
We present a new implementation of analytical gradients for subsystem density-functional theory (sDFT) and frozen-density embedding (FDE) into the Amsterdam Density Functional program (ADF). The underlying theory and necessary expressions for the implementation are derived and discussed in detail for various FDE and sDFT setups. The parallel implementation is numerically verified and geometry optimizations with different functional combinations (LDA/TF and PW91/PW91K) are conducted and compared to reference data. Our results confirm that sDFT-LDA/TF yields good equilibrium distances for the systems studied here (mean absolute deviation: 0.09 Å) compared to reference wave-function theory results. However, sDFT-PW91/PW91k quite consistently yields smaller equilibrium distances (mean absolute deviation: 0.23 Å). The flexibility of our new implementation is demonstrated for an HCN-trimer test system, for which several different setups are applied. © 2016 Wiley Periodicals, Inc. © 2016 Wiley Periodicals, Inc.
Phase-space structures - I. A comparison of 6D density estimators
NASA Astrophysics Data System (ADS)
Maciejewski, M.; Colombi, S.; Alard, C.; Bouchet, F.; Pichon, C.
2009-03-01
In the framework of particle-based Vlasov systems, this paper reviews and analyses different methods recently proposed in the literature to identify neighbours in 6D space and estimate the corresponding phase-space density. Specifically, it compares smoothed particle hydrodynamics (SPH) methods based on tree partitioning to 6D Delaunay tessellation. This comparison is carried out on statistical and dynamical realizations of single halo profiles, paying particular attention to the unknown scaling, SG, used to relate the spatial dimensions to the velocity dimensions. It is found that, in practice, the methods with local adaptive metric provide the best phase-space estimators. They make use of a Shannon entropy criterion combined with a binary tree partitioning and with subsequent SPH interpolation using 10-40 nearest neighbours. We note that the local scaling SG implemented by such methods, which enforces local isotropy of the distribution function, can vary by about one order of magnitude in different regions within the system. It presents a bimodal distribution, in which one component is dominated by the main part of the halo and the other one is dominated by the substructures of the halo. While potentially better than SPH techniques, since it yields an optimal estimate of the local softening volume (and therefore the local number of neighbours required to perform the interpolation), the Delaunay tessellation in fact generally poorly estimates the phase-space distribution function. Indeed, it requires, prior to its implementation, the choice of a global scaling SG. We propose two simple but efficient methods to estimate SG that yield a good global compromise. However, the Delaunay interpolation still remains quite sensitive to local anisotropies in the distribution. To emphasize the advantages of 6D analysis versus traditional 3D analysis, we also compare realistic 6D phase-space density estimation with the proxy proposed earlier in the literature, Q = ρ/σ3
The Performance of Density Functionals for Sulfate-Water Clusters.
Mardirossian, Narbe; Lambrecht, Daniel S; McCaslin, Laura; Xantheas, Sotiris S; Head-Gordon, Martin
2013-03-12
The performance of 24 density functionals, Hartree-Fock, and MP2 is assessed with respect to the CCSD(T)/CBS* energetics of 49 sulfate-water clusters with three to six water molecules. Included among the density functionals are GGA, meta-GGA, hybrid GGA, hybrid meta-GGA, and double hybrid density functionals, as well as the LDA. Three types of dispersion corrections (VV10, XDM, and -D) are tested in conjunction with these functionals. The 26 methods are compared using the relative and binding energies of the sulfate-water clusters as the main criteria. It was discovered that a majority of the tested density functionals are unable to simultaneously capture the physics necessary to describe both the relative and binding energies of the anionic solvation clusters. The three density functionals with the best overall performance are XYG3, ωB97X-2, and XYGJ-OS. The only other density functional that performs comparably to these three double hybrids is M11. A majority of the density functionals that contain a fraction of exact exchange tend to perform well only for the relative energies, while functionals lacking exact exchange generally perform poorly with respect to both criteria. However, the meta-GGA functional, M11-L, stands out due to its superior performance for the relative energies. While dispersion correction functionals cannot replace the accuracy provided by MP2 correlation, it is shown that the proper combination of a hybrid GGA functional (LC-ωPBE) with a dispersion correction functional (VV10) can lead to drastic improvements in the binding energies of the parent functional, while preserving its performance with respect to the relative energies. Ultimately, however, MP2 has the best overall performance out of the 26 benchmarked methods.
Origin of anomeric effect: A density functional steric analysis
Huang, Ying; Zhong, Ai-Guo; Yang, Qinsong; Liu, Shubin
2011-01-01
The anomeric effect (the tendency of heteroatomic substituents adjacent to a heteroatom within the cyclohexane ring to prefer the axial orientation instead of the sterically less hindered equatorial position) is traditionally explained through either the dipole moment repulsion or the hyperconjugation effect. In this work, by employing our recent work in density functional steric analysis, we provide a novel two-component explanation, which is consistent with the common belief in chemistry that the effect has a stereoelectronic origin. With α-D-glucopyranose as the prototype, we systematically explore its conformational space and generate 32 isomers, leading to a total of 80 axial–equatorial conformation pairs. The energy difference analysis of these pairs shows that while statistically speaking the tendency is valid, the anomeric effect is not always true and can be violated. Three energy components, exchange–correlation, classical electrostatic, and density functional steric, are found to be directly proportional to the total energy difference between axial and equatorial isomers. We also found that the total dipole moment change, not the hyperconjugation effect, is a reasonable indicator of the total energy difference. However, all these correlations alone are not strong enough to provide a compellingly convincing explanation for the general validity of the effect. With the help of strong correlations between energy components, an explanation with two energy components, steric and electrostatic, was proposed in this work. We show that the axial–equatorial energy difference in general, with the anomeric effect as a special case, is dictated by two factors of the stereoelectronic origin, steric hindrance and classical electrostaticinteractions, synchronously working together. Another explanation in terms of exchange–correlation and electrostaticinteractions has also been obtained in this work.
Augmented Lagrangian formulation of orbital-free density functional theory
Suryanarayana, Phanish Phanish, Deepa
2014-10-15
We present an Augmented Lagrangian formulation and its real-space implementation for non-periodic Orbital-Free Density Functional Theory (OF-DFT) calculations. In particular, we rewrite the constrained minimization problem of OF-DFT as a sequence of minimization problems without any constraint, thereby making it amenable to powerful unconstrained optimization algorithms. Further, we develop a parallel implementation of this approach for the Thomas–Fermi–von Weizsacker (TFW) kinetic energy functional in the framework of higher-order finite-differences and the conjugate gradient method. With this implementation, we establish that the Augmented Lagrangian approach is highly competitive compared to the penalty and Lagrange multiplier methods. Additionally, we show that higher-order finite-differences represent a computationally efficient discretization for performing OF-DFT simulations. Overall, we demonstrate that the proposed formulation and implementation are both efficient and robust by studying selected examples, including systems consisting of thousands of atoms. We validate the accuracy of the computed energies and forces by comparing them with those obtained by existing plane-wave methods.
Augmented Lagrangian formulation of orbital-free density functional theory
NASA Astrophysics Data System (ADS)
Suryanarayana, Phanish; Phanish, Deepa
2014-10-01
We present an Augmented Lagrangian formulation and its real-space implementation for non-periodic Orbital-Free Density Functional Theory (OF-DFT) calculations. In particular, we rewrite the constrained minimization problem of OF-DFT as a sequence of minimization problems without any constraint, thereby making it amenable to powerful unconstrained optimization algorithms. Further, we develop a parallel implementation of this approach for the Thomas-Fermi-von Weizsacker (TFW) kinetic energy functional in the framework of higher-order finite-differences and the conjugate gradient method. With this implementation, we establish that the Augmented Lagrangian approach is highly competitive compared to the penalty and Lagrange multiplier methods. Additionally, we show that higher-order finite-differences represent a computationally efficient discretization for performing OF-DFT simulations. Overall, we demonstrate that the proposed formulation and implementation are both efficient and robust by studying selected examples, including systems consisting of thousands of atoms. We validate the accuracy of the computed energies and forces by comparing them with those obtained by existing plane-wave methods.
Loop expansion in a functional space
Kroger, H.; Labelle, P.
1989-07-15
As an alternative to the loop expansion of the effective potential, wesuggest a functional expansion of the generating functional for an/ital n/-point Euclidean Green's function. The formulation of the scheme isindependent of the space-time dimension of the model. The scheme yieldsstandard perturbation theory in the regime of a small coupling constant andallows to extract information on the regime of strong coupling. As an explicitexample we consider the scalar /Phi//sup 4/ model and computecontributions up to the four-loop level.
Density-functional calculations of structures and absorption spectra of sulfur cluster S-6
NASA Astrophysics Data System (ADS)
Zhu, J.; Cheng, Y.; Bai, Y. L.; Chen, X. R.
2005-01-01
A finite-difference pseudopotential density-functional theory in real space and the Langevin molecular dynamics annealing technique as well as the adiabatic time-dependent density functional theory within the time-dependent local density approximation (TDLDA) are applied to the descriptions of structures and optical absorption spectra of sulfur cluster S-6. It is found that the ground-state structure of S-6 belongs to either a boat-shaped C-2v or chair-shaped D-3d symmetry structure and the calculated spectra exhibit a variety of features that can be used for comparison against future experimental investigations.
Density functional calculations on hydrocarbon isodesmic reactions
NASA Astrophysics Data System (ADS)
Fortunelli, Alessandro; Selmi, Massimo
1994-06-01
Hartree—Fock, Hartree—Fock-plus-correlation and self-consistent Kohn—Sham calculations are performed on a set of hydrocarbon isodesmic reactions, i.e. reactions among hydrocarbons in which the number and type of carbon—carbon and carbon—hydrogen bonds is conserved. It is found that neither Hartree—Fock nor Kohn—Sham methods correctly predict standard enthalpies, Δ Hr(298 K), of these reactions, even though — for reactions involving molecules containing strained double bonds — the agreement between the theoretical estimates and the experimental values of Δ Hr seems to be improved by the self-consistent solution of the Kohn—Sham equations. The remaining discrepancies are attributed to intramolecular dispersion effects, that are not described by ordinary exchange—correlation functionals, and are eliminated by introducing corrections based on a simple semi-empirical model.
[VESTIBULAR FUNCTION AFTER REPEATED SPACE FLIGHTS].
Naumov, I A; Kornilova, L N; Glukhikh, D O; Pavlova, A S; Khabarova, E V; Ekimovsky, G A; Vasin, A V
2015-01-01
Results of the vestibular function testing of 32 cosmonauts on return from repeated 125- to 215-day space flights (SF) on the International space station are presented. The cosmonauts were tested twice before flight (baseline data collection) and on days 1-2, 4-5 and 8-9 after landing. Electro- and video-oculography were used to register simultaneously eye and head movements. It was found that deadaptation following a repeated stay in long-duration SF takes statistically much shorter time. Most often, atypical vestibular disorders and changed patterns of the otolith-semicircular canal interaction are observed in cosmonauts who have made their maiden flights to microgravity.
Testing for parity violation in nuclei using spin density matrices for nuclear density functionals
NASA Astrophysics Data System (ADS)
Barrett, B. R.; Giraud, B. G.
2015-06-01
The spin density matrix (SDM) used in atomic and molecular physics is revisited for nuclear physics, in the context of the radial density functional theory. The vector part of the SDM defines a ‘hedgehog’ situation, which exists only if nuclear states contain some amount of parity violation. A toy model is given as an illustrative example.
Postfragmentation density function for bacterial aggregates in laminar flow
NASA Astrophysics Data System (ADS)
Byrne, Erin; Bortz, David M.; Dzul, Steve; Solomon, Michael; Younger, John
2011-04-01
The postfragmentation probability density of daughter flocs is one of the least well-understood aspects of modeling flocculation. We use three-dimensional positional data of Klebsiella pneumoniae bacterial flocs in suspension and the knowledge of hydrodynamic properties of a laminar flow field to construct a probability density function of floc volumes after a fragmentation event. We provide computational results which predict that the primary fragmentation mechanism for large flocs is erosion. The postfragmentation probability density function has a strong dependence on the size of the original floc and indicates that most fragmentation events result in clumps of one to three bacteria eroding from the original floc. We also provide numerical evidence that exhaustive fragmentation yields a limiting density inconsistent with the log-normal density predicted in the literature, most likely due to the heterogeneous nature of K. pneumoniae flocs. To support our conclusions, artificial flocs were generated and display similar postfragmentation density and exhaustive fragmentation.
Pérez-Jiménez, Angel J; Pérez-Jordá, José M; Illas, Francesc
2004-01-01
A new method to improve the excess spin density obtained from unrestricted Hartree-Fock wave functions in terms of natural orbitals is proposed. Using this modified excess spin density to evaluate the correlation energy by means of density functionals leads to large improvements in the computed magnetic coupling constants of several materials without need to modify the exchange contribution. This is important because it reconciles the density functional theory description with the one provided by multi-determinant wave functions. Using the present approach, the leading contribution to the magnetic coupling constant arises from electron correlation effects. The performance of the new method is illustrated on various materials including high-critical-temperature superconductors parent compounds.
Quantum fluid density functional theory of time-dependent phenomena: Ion-atom collisions
NASA Astrophysics Data System (ADS)
Deb, B. M.; Chattaraj, P. K.
1988-07-01
Using a recently proposed kinetic energy density functional and an amalgamation of density functional theory with quantum fluid dynamics, a time-dependent Kohn-Sham-type equation in three-dimensional space, which is a new non-linear Schrödinger equation, has been derived. The equation is also derived through the stochastic interpretation of quantum mechanics. A molecular "thermodynamic" viewpoint is suggested in terms of space-time-dependent quantities. Numerical solution of the above equation yields the time-dependent charge density, current density, effective potential and chemical potential. Perspective plots of these quantities for the proton-neon 25 keV head-on collision are presented.
Carlson, Rebecca K; Li Manni, Giovanni; Sonnenberger, Andrew L; Truhlar, Donald G; Gagliardi, Laura
2015-01-13
Kohn-Sham density functional theory, resting on the representation of the electronic density and kinetic energy by a single Slater determinant, has revolutionized chemistry, but for open-shell systems, the Kohn-Sham Slater determinant has the wrong symmetry properties as compared to an accurate wave function. We have recently proposed a theory, called multiconfiguration pair-density functional theory (MC-PDFT), in which the electronic kinetic energy and classical Coulomb energy are calculated from a multiconfiguration wave function with the correct symmetry properties, and the rest of the energy is calculated from a density functional, called the on-top density functional, that depends on the density and the on-top pair density calculated from this wave function. We also proposed a simple way to approximate the on-top density functional by translation of Kohn-Sham exchange-correlation functionals. The method is much less expensive than other post-SCF methods for calculating the dynamical correlation energy starting with a multiconfiguration self-consistent-field wave function as the reference wave function, and initial tests of the theory were quite encouraging. Here, we provide a broader test of the theory by applying it to bond energies of main-group molecules and transition metal complexes, barrier heights and reaction energies for diverse chemical reactions, proton affinities, and the water dimerization energy. Averaged over 56 data points, the mean unsigned error is 3.2 kcal/mol for MC-PDFT, as compared to 6.9 kcal/mol for Kohn-Sham theory with a comparable density functional. MC-PDFT is more accurate on average than complete active space second-order perturbation theory (CASPT2) for main-group small-molecule bond energies, alkyl bond dissociation energies, transition-metal-ligand bond energies, proton affinities, and the water dimerization energy.
Density functional theory of the crystal field in dioxides
NASA Astrophysics Data System (ADS)
Diviš, M.; Kuriplach, J.; Richter, M.; Steinbeck, L.
1996-04-01
Presented are the results of ab-initio density functional calculations for PrO2 and UO2 using the general potential LAPW and optimized LCAO method in the local density approximation. The crystal field splitting of ionic Pr4+ and U4+ ground states was calculated and compared with predictions of a superposition model.
Applications and validations of the Minnesota density functionals
NASA Astrophysics Data System (ADS)
Zhao, Yan; Truhlar, Donald G.
2011-01-01
We discuss and review selected recent applications and validations of the Minnesota density functionals, especially the M06 family, emphasizing nanochemistry, organic, inorganic, and biological chemistry, and catalysis and highlighting the broad accuracy of these functionals as compared to previous popular functionals for thermochemistry, kinetics, and noncovalent interactions.
Integration, Continuity and a Connection with Probability Density Functions
ERIC Educational Resources Information Center
Samuels, M.
2006-01-01
This note considers functions of two variables which are continuous on a possibly unbounded closed region in [vertical bar]R[squared], and the functions of one variable obtained by integrating out the other variable over this region. The question of continuity of these functions is investigated, as are connections with joint density and marginal…
The correlation function for density perturbations in an expanding universe. II - Nonlinear theory
NASA Technical Reports Server (NTRS)
Mcclelland, J.; Silk, J.
1977-01-01
A formalism is developed to find the two-point and higher-order correlation functions for a given distribution of sizes and shapes of perturbations which are randomly placed in three-dimensional space. The perturbations are described by two parameters such as central density and size, and the two-point correlation function is explicitly related to the luminosity function of groups and clusters of galaxies
NASA Astrophysics Data System (ADS)
Xia, Junchao; Carter, Emily A.
2012-12-01
We propose a density decomposition scheme using a Wang-Govind-Carter- (WGC-) based kinetic energy density functional (KEDF) to accurately and efficiently simulate various covalently bonded molecules and materials within orbital-free (OF) density functional theory (DFT). By using a local, density-dependent scale function, the total density is decomposed into a highly localized density within covalent bond regions and a flattened delocalized density, with the former described by semilocal KEDFs and the latter treated by the WGC KEDF. The new model predicts reasonable equilibrium volumes, bulk moduli, and phase-ordering energies for various semiconductors compared to Kohn-Sham (KS) DFT benchmarks. The decomposition formalism greatly improves numerical stability and accuracy, while retaining computational speed compared to simply applying the original WGC KEDF to covalent materials. The surface energy of Si(100) and various diatomic molecule properties can be stably calculated and also agree well with KSDFT benchmarks. This linear-scaled, computationally efficient, density-partitioned, multi-KEDF scheme opens the door to large-scale simulations of molecules, semiconductors, and insulators with OFDFT.
Applying the density matrix expansion with coordinate-space chiral interactions
NASA Astrophysics Data System (ADS)
Dyhdalo, A.; Bogner, S. K.; Furnstahl, R. J.
2017-05-01
We apply the density matrix expansion (DME) at Hartree-Fock level with long-range chiral effective field theory interactions defined in coordinate space up to next-to-next-to-leading order. We consider chiral potentials both with and without explicit Δ isobars. The challenging algebra associated with applying the DME to three-nucleon forces is tamed using a new organization scheme, which will also facilitate generalizations. We include local regulators on the interactions to mitigate the effects of singular potentials on the DME couplings and simplify the optimization of generalized Skyrme-like functionals.
Making a happy match between orbital-free density functional theory and information energy density
NASA Astrophysics Data System (ADS)
Alipour, Mojtaba
2015-08-01
In the field of computational chemistry within density functional theory (DFT), the orbital-free DFT (OF-DFT) can be considered as a promising approach for simulating large systems. In OF-DFT, only a single relation, the Euler equation, has to be solved independently from the number of electrons. In this work, the Euler equation of OF-DFT is rewritten through a new partition scheme for energy density functional. Next, based on information theory, we reformulate the resulting equation in terms of Onicescu information energy density. Plus, the new forms of Euler equation based on Shannon entropy and Fisher information are presented.
Density Functional Calculations for the Neutron Star Matter at Subnormal Density
NASA Astrophysics Data System (ADS)
Kashiwaba, Yu; Nakatsukasa, Takashi
The pasta phases of nuclear matter, whose existence is suggested at low density, may influence observable properties of neutron stars. In order to investigate properties of the neutron star matter, we calculate self-consistent solutions for the ground states of slab-like phase using the microscopic density functional theory with Bloch wave functions. The calculations are performed at each point of fixed average density and proton fraction (\\bar{ρ },Yp), varying the lattice constant of the unit cell. For small Yp values, the dripped neutrons emerge in the ground state, while the protons constitute the slab (crystallized) structure. The shell effect of protons affects the thickness of the slab nuclei.
Space shuttle configuration accounting functional design specification
NASA Technical Reports Server (NTRS)
1974-01-01
An analysis is presented of the requirements for an on-line automated system which must be capable of tracking the status of requirements and engineering changes and of providing accurate and timely records. The functional design specification provides the definition, description, and character length of the required data elements and the interrelationship of data elements to adequately track, display, and report the status of active configuration changes. As changes to the space shuttle program levels II and III configuration are proposed, evaluated, and dispositioned, it is the function of the configuration management office to maintain records regarding changes to the baseline and to track and report the status of those changes. The configuration accounting system will consist of a combination of computers, computer terminals, software, and procedures, all of which are designed to store, retrieve, display, and process information required to track proposed and proved engineering changes to maintain baseline documentation of the space shuttle program levels II and III.
Simple Fully Nonlocal Density Functionals for Electronic Repulsion Energy.
Vuckovic, Stefan; Gori-Giorgi, Paola
2017-07-06
From a simplified version of the mathematical structure of the strong coupling limit of the exact exchange-correlation functional, we construct an approximation for the electronic repulsion energy at physical coupling strength, which is fully nonlocal. This functional is self-interaction free and yields energy densities within the definition of the electrostatic potential of the exchange-correlation hole that are locally accurate and have the correct asymptotic behavior. The model is able to capture strong correlation effects that arise from chemical bond dissociation, without relying on error cancellation. These features, which are usually missed by standard density functional theory (DFT) functionals, are captured by the highly nonlocal structure, which goes beyond the "Jacob's ladder" framework for functional construction, by using integrals of the density as the key ingredient. Possible routes for obtaining the full exchange-correlation functional by recovering the missing kinetic component of the correlation energy are also implemented and discussed.
Free energy density functional for adsorption of fluids in nanopores.
Zhou, Shiqi
2010-11-16
A classical free energy density functional, which is isomorphic to a usual effective hard sphere model + mean field approximation for tail contribution, is proposed for treatment of real fluids in inhomogeneous states. In the framework of the classical density functional theory (DFT), the present functional is applied to two representative model fluids, namely, a Lennard-Jones fluid and a hard core attractive Yukawa fluid, subject to influence of various external fields. A comprehensive comparison with simulation results and a detailed analysis show that the present functional holds simultaneously all of the desirable properties inherent in an excellent functional, such as high accuracy, computational simplicity, consistency with a hard wall sum rule, nonrecourse to use of adjustable parameter(s) and weighted densities, reproduction of bulk second-order direct correlation function (DCF) in bulk limit, and applicability to subcritical fluid phenomena.
Towards a more accurate van der Waals density functional
NASA Astrophysics Data System (ADS)
Hamada, Ikutaro
2014-03-01
The van der Waals density functional (vdW-DF) of Dion et al. [1] has attracted considerable attention, because the functional is able to describe intra- and intermolecular bondings with different natures, e.g., covalent and van der Waals bondings in a seamless fashion within the framework of density functional theory. However, the accuracy of the functional is yet to be improved for the applications to various systems. Here I propose an exchange functional for the second version of vdW-DF [2], which improves the accuracy of vdW-DF. The keys in the improved exchange are the matching to the gradient expansion approximation in the slowly varying limit and the large density gradient behavior set in Becke's exchange (B86b)[3]. Systematic study on gas phase molecules, solids, and molecular adsorption demonstrates the applicability of the proposed functional to a wide variety of materials.
Density functional study of the electric double layer formed by a high density electrolyte.
Henderson, Douglas; Lamperski, Stanisław; Jin, Zhehui; Wu, Jianzhong
2011-11-10
We use a classical density functional theory (DFT) to study the electric double layer formed by charged hard spheres near a planar charged surface. The DFT predictions are found to be in good agreement with recent computer simulation results. We study the capacitance of the charged hard-sphere system at a range of densities and surface charges and find that the capacitance exhibits a local minimum at low ionic densities and small electrode charge. Although this charging behavior is typical for an aqueous electrolyte solution, the local minimum gradually turns into a maximum as the density of the hard spheres increases. Charged hard spheres at high density provide a reasonable first approximation for ionic liquids. In agreement with experiment, the capacitance of this model ionic liquid double layer has a maximum at small electrode charge density.
Gutzwiller density functional theory for correlated electron systems
Ho, K. M.; Schmalian, J.; Wang, C. Z.
2008-02-04
We develop a density functional theory (DFT) and formalism for correlated electron systems by taking as reference an interacting electron system that has a ground state wave function which exactly obeys the Gutzwiller approximation for all one-particle operators. The solution of the many-electron problem is mapped onto the self-consistent solution of a set of single-particle Schroedinger equations, analogously to standard DFT-local density approximation calculations.
Density Functional Theory with Dissipation: Transport through Single Molecules
Kieron Burke
2012-04-30
A huge amount of fundamental research was performed on this grant. Most of it focussed on fundamental issues of electronic structure calculations of transport through single molecules, using density functional theory. Achievements were: (1) First density functional theory with dissipation; (2) Pseudopotential plane wave calculations with master equation; (3) Weak bias limit; (4) Long-chain conductance; and (5) Self-interaction effects in tunneling.
Reflection-Asymmetric Nuclear Deformations within the Density Functional Theory
Olsen, E; Erler, J; Nazarewicz, W.; Stoitsov, M
2012-01-01
Within the nuclear density functional theory (DFT) we study the effect of reflection- asymmetric shapes on ground-state binding energies and binding energy differences. To this end, we developed the new DFT solver axialhfb that uses an approximate second-order gradient to solve the Hartree-Fock-Bogoliubov equations of superconducting DFT with the quasi-local Skyrme energy density functionals. Illustrative calculations are carried out for even- even isotopes of radium and thorium.
Density Functional Studies of Decomposition Processes of Energetic Molecules
1994-11-03
34-- I of Energetic Molecules Dr. Richard S. Miller 6. AUTHOR(S) Peter Politzer, Jorge M. Seminario and M. Edward Grice R&T Code 4131DO2 7. PERFORMING...49) ,’i. " o MW U of. tongi.ig2 Density Functional Studies of Decomposition Processes of Energetic Molecules Peter Politzer, Jorge M. Seminario and...Initio Molecular Orbital Theory, (Wiley-Interscience, New York, 1986). 9. J. M. Seminario , M. Grodzicki and P. Politzer, in Density Functional Methods
Constraints on parton density functions from D0
Hays, Jonathan M.; /Imperial Coll., London
2008-04-01
Five recent results from D0 which either impact or have the potential to impact on uncertainties in parton density functions are presented. Many analyses at D0 are sensitive to the modeling of the partonic structure of the proton. When theoretical and experimental uncertainties are well controlled there exists the possibility for additional constraints on parton density functions (PDF). Five measurements are presented which either have already been included in global parton fits or have the potential to contribute in the future.
Preface: Special Topic on Advances in Density Functional Theory
Yang, Weitao
2014-05-14
This Special Topic Issue on the Advances in Density Functional Theory, published as a celebration of the fifty years of density functional theory, contains a retrospective article, a perspective article, and a collection of original research articles that showcase recent theoretical advances in the field. It provides a timely discussion reflecting a cross section of our understanding, and the theoretical and computational developments, which have significant implications in broad areas of sciences and engineering.
Conditional Probability Density Functions Arising in Bearing Estimation
1994-05-01
and a better known performance measure: the Cramer-Rao bound . 14. SUMECT TEm IL5 NUlMN OF PAMES Probability Density Function, bearing angle estimation...results obtained using the calculated density functions and a better known performance measure: the Cramer-Rao bound . The major results obtained are as...48 15. Sampling Inteval , Propagation Delay, and Covariance Singularities ....... 52 viii List of Figures (continued
A revised density function for molecular surface definition in continuum solvent models
Ye, Xiang; Wang, Jun; Luo, Ray
2014-01-01
A revised density function is developed to define the molecular surface for the numerical Poisson-Boltzmann methods to achieve a better convergence and higher numerical stability. The new density function does not use any predefined functional form but is numerically optimized to reproduce the reaction field energies computed with the solvent excluded surface definition. An exhaustive search in the parameter space is utilized in the optimization using a wide-range training molecules including proteins, nucleic acids, and peptides in both folded and unfolded conformations. A cubic-spline function is introduced to guarantee good numerical behavior of the new density function. Our test results show that the average relative energy errors computed with the revised density function are uniformly lower than 1% for both training and test molecules with different sizes and conformations. Our transferability analysis shows that the performance of the new method is mostly size and conformation independent. A detailed analysis further shows that the numerical forces computed with the revised density function converge better with respect to the grid spacing and are numerically more stable in tested peptides. PMID:24723844
Average protein density is a molecular-weight-dependent function.
Fischer, Hannes; Polikarpov, Igor; Craievich, Aldo F
2004-10-01
The mass density of proteins is a relevant basic biophysical quantity. It is also a useful input parameter, for example, for three-dimensional structure determination by protein crystallography and studies of protein oligomers in solution by analytic ultracentrifugation. We have performed a critical analysis of published, theoretical, and experimental investigations about this issue and concluded that the average density of proteins is not a constant as often assumed. For proteins with a molecular weight below 20 kDa, the average density exhibits a positive deviation that increases for decreasing molecular weight. A simple molecular-weight-depending function is proposed that provides a more accurate estimate of the average protein density.
Density functional theory for polymeric systems in 2D.
Słyk, Edyta; Roth, Roland; Bryk, Paweł
2016-06-22
We propose density functional theory for polymeric fluids in two dimensions. The approach is based on Wertheim's first order thermodynamic perturbation theory (TPT) and closely follows density functional theory for polymers proposed by Yu and Wu (2002 J. Chem. Phys. 117 2368). As a simple application we evaluate the density profiles of tangent hard-disk polymers at hard walls. The theoretical predictions are compared against the results of the Monte Carlo simulations. We find that for short chain lengths the theoretical density profiles are in an excellent agreement with the Monte Carlo data. The agreement is less satisfactory for longer chains. The performance of the theory can be improved by recasting the approach using the self-consistent field theory formalism. When the self-avoiding chain statistics is used, the theory yields a marked improvement in the low density limit. Further improvements for long chains could be reached by going beyond the first order of TPT.
Density-functional study of plutonium monoxide monohydride
NASA Astrophysics Data System (ADS)
Qiu, Ruizhi; Lu, Haiyan; Ao, Bingyun; Tang, Tao; Chen, Piheng
2017-03-01
The structural, electronic, mechanical, optical, thermodynamic properties of plutonium monoxide monohydride (PuOH) are studied by density-functional calculations within the framework of LDA/GGA and LDA/GGA+U. From the total energy calculation, the lowest-energy crystal structure of PuOH is predicted to have space group F 4 bar 3 m (No. 216). Within the LDA+U framework, the calculated lattice parameter of F 4 bar 3 m -PuOH is in good agreement with the experimental value and the corresponding ground state is predicted to be an antiferromagnetic charge-transfer insulator. Furthermore, we investigate the bonding character of PuOH by analyzing the electron structure and find that there are a stronger Pu-O bond and a weaker Pu-H bond. The mechanical properties including the elastic constants, elastic moduli and Debye's temperature, and the optical properties including the reflectivity and absorption coefficient are also calculated. We then compute the phonon spectrum which verified the dynamical stability of F 4 bar 3 m -PuOH. Some thermodynamic quantities such as the specific heat are evaluated. Finally we calculate the formation energy of PuOH, and the reaction energies for the oxidation of PuOH and PuOH-coated Pu, which are in reasonable agreement with the experimental values.
Parameterizing deep convection using the assumed probability density function method
Storer, R. L.; Griffin, B. M.; Höft, J.; ...
2015-01-06
Due to their coarse horizontal resolution, present-day climate models must parameterize deep convection. This paper presents single-column simulations of deep convection using a probability density function (PDF) parameterization. The PDF parameterization predicts the PDF of subgrid variability of turbulence, clouds, and hydrometeors. That variability is interfaced to a prognostic microphysics scheme using a Monte Carlo sampling method.The PDF parameterization is used to simulate tropical deep convection, the transition from shallow to deep convection over land, and midlatitude deep convection. These parameterized single-column simulations are compared with 3-D reference simulations. The agreement is satisfactory except when the convective forcing is weak.more » The same PDF parameterization is also used to simulate shallow cumulus and stratocumulus layers. The PDF method is sufficiently general to adequately simulate these five deep, shallow, and stratiform cloud cases with a single equation set. This raises hopes that it may be possible in the future, with further refinements at coarse time step and grid spacing, to parameterize all cloud types in a large-scale model in a unified way.« less
Parameterizing deep convection using the assumed probability density function method
Storer, R. L.; Griffin, B. M.; Höft, J.; ...
2014-06-11
Due to their coarse horizontal resolution, present-day climate models must parameterize deep convection. This paper presents single-column simulations of deep convection using a probability density function (PDF) parameterization. The PDF parameterization predicts the PDF of subgrid variability of turbulence, clouds, and hydrometeors. That variability is interfaced to a prognostic microphysics scheme using a Monte Carlo sampling method. The PDF parameterization is used to simulate tropical deep convection, the transition from shallow to deep convection over land, and mid-latitude deep convection. These parameterized single-column simulations are compared with 3-D reference simulations. The agreement is satisfactory except when the convective forcing ismore » weak. The same PDF parameterization is also used to simulate shallow cumulus and stratocumulus layers. The PDF method is sufficiently general to adequately simulate these five deep, shallow, and stratiform cloud cases with a single equation set. This raises hopes that it may be possible in the future, with further refinements at coarse time step and grid spacing, to parameterize all cloud types in a large-scale model in a unified way.« less
Parameterizing deep convection using the assumed probability density function method
Storer, R. L.; Griffin, B. M.; Hoft, Jan; Weber, J. K.; Raut, E.; Larson, Vincent E.; Wang, Minghuai; Rasch, Philip J.
2015-01-06
Due to their coarse horizontal resolution, present-day climate models must parameterize deep convection. This paper presents single-column simulations of deep convection using a probability density function (PDF) parameterization. The PDF parameterization predicts the PDF of subgrid variability of turbulence, clouds, and hydrometeors. That variability is interfaced to a prognostic microphysics scheme using a Monte Carlo sampling method.The PDF parameterization is used to simulate tropical deep convection, the transition from shallow to deep convection over land, and mid-latitude deep convection.These parameterized single-column simulations are compared with 3-D reference simulations. The agreement is satisfactory except when the convective forcing is weak. The same PDF parameterization is also used to simulate shallow cumulus and stratocumulus layers. The PDF method is sufficiently general to adequately simulate these five deep, shallow, and stratiform cloud cases with a single equation set. This raises hopes that it may be possible in the future, with further refinements at coarse time step and grid spacing, to parameterize all cloud types in a large-scale model in a unified way.
Cooling Function in Wide Range of Density and Metallicity
NASA Astrophysics Data System (ADS)
Wang, Ye; Ferland, G. J.
2013-06-01
This work focuses on how the plasma cooling function changes with density and metallicity over a wide range of temperature (104 K
Linear response of homogeneous nuclear matter with energy density functionals
NASA Astrophysics Data System (ADS)
Pastore, A.; Davesne, D.; Navarro, J.
2015-03-01
Response functions of infinite nuclear matter with arbitrary isospin asymmetry are studied in the framework of the random phase approximation. The residual interaction is derived from a general nuclear Skyrme energy density functional. Besides the usual central, spin-orbit and tensor terms it could also include other components as new density-dependent terms or three-body terms. Algebraic expressions for the response functions are obtained from the Bethe-Salpeter equation for the particle-hole propagator. Applications to symmetric nuclear matter, pure neutron matter and asymmetric nuclear matter are presented and discussed. Spin-isospin strength functions are analyzed for varying conditions of density, momentum transfer, isospin asymmetry, and temperature for some representative Skyrme functionals. Particular attention is paid to the discussion of instabilities, either real or unphysical, which could manifest in finite nuclei.
Density functionals and dimensional renormalization for an exactly solvable model
NASA Astrophysics Data System (ADS)
Kais, S.; Herschbach, D. R.; Handy, N. C.; Murray, C. W.; Laming, G. J.
1993-07-01
We treat an analytically solvable version of the ``Hooke's Law'' model for a two-electron atom, in which the electron-electron repulsion is Coulombic but the electron-nucleus attraction is replaced by a harmonic oscillator potential. Exact expressions are obtained for the ground-state wave function and electron density, the Hartree-Fock solution, the correlation energy, the Kohn-Sham orbital, and, by inversion, the exchange and correlation functionals. These functionals pertain to the ``intermediate'' density regime (rs≥1.4) for an electron gas. As a test of customary approximations employed in density functional theory, we compare our exact density, exchange, and correlation potentials and energies with results from two approximations. These use Becke's exchange functional and either the Lee-Yang-Parr or the Perdew correlation functional. Both approximations yield rather good results for the density and the exchange and correlation energies, but both deviate markedly from the exact exchange and correlation potentials. We also compare properties of the Hooke's Law model with those of two-electron atoms, including the large dimension limit. A renormalization procedure applied to this very simple limit yields correlation energies as good as those obtained from the approximate functionals, for both the model and actual atoms.
High-temperature, high-power-density thermionic energy conversion for space
NASA Technical Reports Server (NTRS)
Morris, J. F.
1977-01-01
Theoretic converter outputs and efficiencies indicate the need to consider thermionic energy conversion (TEC) with greater power densities and higher temperatures within reasonable limits for space missions. Converter-output power density, voltage, and efficiency as functions of current density were determined for 1400-to-2000 K emitters with 725-to-1000 K collectors. The results encourage utilization of TEC with hotter-than-1650 K emitters and greater-than-6W sq cm outputs to attain better efficiencies, greater voltages, and higher waste-heat-rejection temperatures for multihundred-kilowatt space-power applications. For example, 1800 K, 30 A sq cm TEC operation for NEP compared with the 1650 K, 5 A/sq cm case should allow much lower radiation weights, substantially fewer and/or smaller emitter heat pipes, significantly reduced reactor and shield-related weights, many fewer converters and associated current-collecting bus bars, less power conditioning, and lower transmission losses. Integration of these effects should yield considerably reduced NEP specific weights.
Range Separation and Local Hybridization in Density Functional Theory†
Henderson, Thomas M.; Janesko, Benjamin G.; Scuseria, Gustavo E.
2016-01-01
Kohn–Sham density functional theory has become a standard method for modeling energetic, spectroscopic, and chemical reactivity properties of large molecules and solids. Density functional theory provides a rigorous theoretical framework for modeling the many-body exchange-correlation effects that dominate the computational cost of traditional wave function approaches. The advent of hybrid exchange-correlation functionals which incorporate a fraction of nonlocal exact exchange has solidified the prominence of density functional theory within computational chemistry. Hybrids provide accurate treatments of properties such as thermochemistry and molecular geometry. But they also exhibit some rather spectacular failures, and often contain multiple empirical parameters. This article reviews our work on developing novel exchange-correlation functionals that build upon the successes of global hybrids. We focus on more flexible functional forms, including local and range-separated hybrid functionals, constructed to obey known exact constraints and (ideally) to incorporate a minimum of empirical parametrization. The article places our work within the context of some other new approximate density functionals and discusses prospects for future work. PMID:19006280
Reduction of functional capillary density in human brain after stroke.
Gjedde, A; Kuwabara, H; Hakim, A M
1990-05-01
The blood flow of brain tissue often returns to normal after an ischemic episode. As "luxury" rather than "reactive" reperfusion, this hyperemia is associated with low metabolism. It is not known to what extent the high blood flow accompanies a high, normal, or low density of capillaries. The resolution of this question may indicate whether the functional capillary density is variable and, if so, whether it is coupled to blood flow or metabolism. To answer these questions, we defined functional capillaries as capillaries that transport glucose. We then calculated the density of functional capillaries (Dcap) and the mean time of transit of blood through the capillaries (tcap) from hemodynamic variables obtained in vivo by positron tomography of five patients afflicted by cerebral ischemic stroke. Each patient was studied twice, within 36 h of the insult and 1 week later. We identified nominally "ischemic" regions in the first study as cortical gray matter regions, contiguous with the ischemic focus, in which the magnitude of blood flow did not exceed 20 ml 100 g-1 min-1. In these regions, values of metabolism and functional capillary density were proportionately low compared with normal values obtained in the contralateral hemisphere. The studies revealed a reduction of the functional density of exchange vessels in postischemic brain tissue as soon as 36 h after the insult. In "ischemic" regions, within 36 h of the insult, the net extraction of oxygen was inversely related to the capillary transit time and appeared to be limited mainly by the low functional density of the capillaries. Contrary to expectations, the reduced density persisted, even when more than adequate perfusion of the tissue returned. For these reasons, we concluded that changes of the capillary density were associated with changes of the metabolism of the tissue rather than with blood flow.
Putz, Mihai V.
2009-01-01
The density matrix theory, the ancestor of density functional theory, provides the immediate framework for Path Integral (PI) development, allowing the canonical density be extended for the many-electronic systems through the density functional closure relationship. Yet, the use of path integral formalism for electronic density prescription presents several advantages: assures the inner quantum mechanical description of the system by parameterized paths; averages the quantum fluctuations; behaves as the propagator for time-space evolution of quantum information; resembles Schrödinger equation; allows quantum statistical description of the system through partition function computing. In this framework, four levels of path integral formalism were presented: the Feynman quantum mechanical, the semiclassical, the Feynman-Kleinert effective classical, and the Fokker-Planck non-equilibrium ones. In each case the density matrix or/and the canonical density were rigorously defined and presented. The practical specializations for quantum free and harmonic motions, for statistical high and low temperature limits, the smearing justification for the Bohr’s quantum stability postulate with the paradigmatic Hydrogen atomic excursion, along the quantum chemical calculation of semiclassical electronegativity and hardness, of chemical action and Mulliken electronegativity, as well as by the Markovian generalizations of Becke-Edgecombe electronic focalization functions – all advocate for the reliability of assuming PI formalism of quantum mechanics as a versatile one, suited for analytically and/or computationally modeling of a variety of fundamental physical and chemical reactivity concepts characterizing the (density driving) many-electronic systems. PMID:20087467
Putz, Mihai V
2009-11-10
The density matrix theory, the ancestor of density functional theory, provides the immediate framework for Path Integral (PI) development, allowing the canonical density be extended for the many-electronic systems through the density functional closure relationship. Yet, the use of path integral formalism for electronic density prescription presents several advantages: assures the inner quantum mechanical description of the system by parameterized paths; averages the quantum fluctuations; behaves as the propagator for time-space evolution of quantum information; resembles Schrödinger equation; allows quantum statistical description of the system through partition function computing. In this framework, four levels of path integral formalism were presented: the Feynman quantum mechanical, the semiclassical, the Feynman-Kleinert effective classical, and the Fokker-Planck non-equilibrium ones. In each case the density matrix or/and the canonical density were rigorously defined and presented. The practical specializations for quantum free and harmonic motions, for statistical high and low temperature limits, the smearing justification for the Bohr's quantum stability postulate with the paradigmatic Hydrogen atomic excursion, along the quantum chemical calculation of semiclassical electronegativity and hardness, of chemical action and Mulliken electronegativity, as well as by the Markovian generalizations of Becke-Edgecombe electronic focalization functions - all advocate for the reliability of assuming PI formalism of quantum mechanics as a versatile one, suited for analytically and/or computationally modeling of a variety of fundamental physical and chemical reactivity concepts characterizing the (density driving) many-electronic systems.
Basis convergence of range-separated density-functional theory.
Franck, Odile; Mussard, Bastien; Luppi, Eleonora; Toulouse, Julien
2015-02-21
Range-separated density-functional theory (DFT) is an alternative approach to Kohn-Sham density-functional theory. The strategy of range-separated density-functional theory consists in separating the Coulomb electron-electron interaction into long-range and short-range components and treating the long-range part by an explicit many-body wave-function method and the short-range part by a density-functional approximation. Among the advantages of using many-body methods for the long-range part of the electron-electron interaction is that they are much less sensitive to the one-electron atomic basis compared to the case of the standard Coulomb interaction. Here, we provide a detailed study of the basis convergence of range-separated density-functional theory. We study the convergence of the partial-wave expansion of the long-range wave function near the electron-electron coalescence. We show that the rate of convergence is exponential with respect to the maximal angular momentum L for the long-range wave function, whereas it is polynomial for the case of the Coulomb interaction. We also study the convergence of the long-range second-order Møller-Plesset correlation energy of four systems (He, Ne, N2, and H2O) with cardinal number X of the Dunning basis sets cc - p(C)V XZ and find that the error in the correlation energy is best fitted by an exponential in X. This leads us to propose a three-point complete-basis-set extrapolation scheme for range-separated density-functional theory based on an exponential formula.
Basis convergence of range-separated density-functional theory
Franck, Odile Mussard, Bastien; Luppi, Eleonora Toulouse, Julien
2015-02-21
Range-separated density-functional theory (DFT) is an alternative approach to Kohn-Sham density-functional theory. The strategy of range-separated density-functional theory consists in separating the Coulomb electron-electron interaction into long-range and short-range components and treating the long-range part by an explicit many-body wave-function method and the short-range part by a density-functional approximation. Among the advantages of using many-body methods for the long-range part of the electron-electron interaction is that they are much less sensitive to the one-electron atomic basis compared to the case of the standard Coulomb interaction. Here, we provide a detailed study of the basis convergence of range-separated density-functional theory. We study the convergence of the partial-wave expansion of the long-range wave function near the electron-electron coalescence. We show that the rate of convergence is exponential with respect to the maximal angular momentum L for the long-range wave function, whereas it is polynomial for the case of the Coulomb interaction. We also study the convergence of the long-range second-order Møller-Plesset correlation energy of four systems (He, Ne, N{sub 2}, and H{sub 2}O) with cardinal number X of the Dunning basis sets cc − p(C)V XZ and find that the error in the correlation energy is best fitted by an exponential in X. This leads us to propose a three-point complete-basis-set extrapolation scheme for range-separated density-functional theory based on an exponential formula.
Linscheid, A; Sanna, A; Floris, A; Gross, E K U
2015-08-28
We show that the superconducting order parameter and condensation energy density of phonon-mediated superconductors can be calculated in real space from first principles density functional theory for superconductors. This method highlights the connection between the chemical bonding structure and the superconducting condensation and reveals new and interesting properties of superconducting materials. Understanding this connection is essential to describe nanostructured superconducting systems where the usual reciprocal space analysis hides the basic physical mechanism. In a first application we present results for MgB2, CaC6 and hole-doped graphane.
NASA Astrophysics Data System (ADS)
Linscheid, A.; Sanna, A.; Floris, A.; Gross, E. K. U.
2015-08-01
We show that the superconducting order parameter and condensation energy density of phonon-mediated superconductors can be calculated in real space from first principles density functional theory for superconductors. This method highlights the connection between the chemical bonding structure and the superconducting condensation and reveals new and interesting properties of superconducting materials. Understanding this connection is essential to describe nanostructured superconducting systems where the usual reciprocal space analysis hides the basic physical mechanism. In a first application we present results for MgB2 , CaC6 and hole-doped graphane.
2016-05-23
AFRL-AFOSR-VA-TR-2016-0199 FUNDAMENTAL STUDY OF INTERACTIONS BETWEEN PULSED HIGH-DENSITY PLASMAS AND MATERIALS FOR SPACE PROPULSION LAXAMIRIAN RAJA...CONTRACT NUMBER FA9550-11-1-0062 FUNDAMENTAL STUDY OF INTERACTIONS BETWEEN PULSED HIGH-DENSITY LASMAS AND MATERIALS FOR SPACE PROPULSION 5b. GRANT... SPACE PROPULSION Principal Investigators: L. L. Raja, I. McNab, F. Stefani, R. D. Bengtson, G. Henkelman, F. Stefani The University of Texas at
The Deep Space Network. [tracking and communication functions and facilities
NASA Technical Reports Server (NTRS)
1974-01-01
The objectives, functions, and organization of the Deep Space Network are summarized. The Deep Space Instrumentation Facility, the Ground Communications Facility, and the Network Control System are described.
Robert O. Curtis; Sheel Bansal; Constance A. Harrington
2016-01-01
This report presents updated information on a 1981 Douglas-fir (Pseudotsuga menziesii (Mirb.) Franco var. menziesii ) plantation spacing trial at 33 years from planting. Stand statistics at the most recent measurement were compared for initial spacing of 1 through 6 meters and associated relative densities. There was no clear...
Density Functional Theory for General Hard-Core Lattice Gases
NASA Astrophysics Data System (ADS)
Lafuente, Luis; Cuesta, José A.
2004-09-01
We put forward a general procedure to obtain an approximate free-energy density functional for any hard-core lattice gas, regardless of the shape of the particles, the underlying lattice, or the dimension of the system. The procedure is conceptually very simple and recovers effortlessly previous results for some particular systems. Also, the obtained density functionals belong to the class of fundamental measure functionals and, therefore, are always consistent through dimensional reduction. We discuss possible extensions of this method to account for attractive lattice models.
Can orbital-free density functional theory simulate molecules?
NASA Astrophysics Data System (ADS)
Xia, Junchao; Huang, Chen; Shin, Ilgyou; Carter, Emily A.
2012-02-01
Orbital-free density functional theory (OFDFT), with its attractive linearly scaling computation cost and low prefactor, is one of the most powerful first principles methods for simulating large systems (˜104-106 atoms). However, approximating the electron kinetic energy with density functionals limits the accuracy and generality of OFDFT compared to Kohn-Sham density functional theory (KSDFT). In this work, we test whether the Huang-Carter (HC) kinetic energy density functional (KEDF), which contains the physics to properly describe covalently bonded semiconductor materials, can also be used to describe covalent bonds in molecules. In particular, we calculate a variety of homonuclear diatomic molecules with the HC functional within OFDFT. The OFDFT bond dissociation energy, equilibrium bond length, and vibrational frequency of these dimers are in remarkably good agreement with benchmark KSDFT results, given the lack of orbitals in the calculation. We vary the two parameters λ (controlling the reduced density gradient contribution to the nonlocal kernel) and β (the exponent of the density in the nonlocal term) present in the HC KEDF and find that the optimal λ correlates with the magnitude of the highest occupied molecular orbital - lowest unoccupied molecular orbital energy gap. Although the HC KEDF represents a significant improvement over previous KEDFs in describing covalent systems, deficiencies still exist. Despite the similar overall shape of the KSDFT and OFDFT ground state electron densities, the electron density within the bonding region is still quite different. Furthermore, OFDFT is not yet able to give reasonable description of magnetic states. The energy orderings of the triplet and singlet states of Si2 and Al family dimers are not consistent with KSDFT or experimental results and the spin polarization distributions also differ widely between the two theories.
Force Density Function Relationships in 2-D Granular Media
NASA Technical Reports Server (NTRS)
Youngquist, Robert C.; Metzger, Philip T.; Kilts, Kelly N.
2004-01-01
An integral transform relationship is developed to convert between two important probability density functions (distributions) used in the study of contact forces in granular physics. Developing this transform has now made it possible to compare and relate various theoretical approaches with one another and with the experimental data despite the fact that one may predict the Cartesian probability density and another the force magnitude probability density. Also, the transforms identify which functional forms are relevant to describe the probability density observed in nature, and so the modified Bessel function of the second kind has been identified as the relevant form for the Cartesian probability density corresponding to exponential forms in the force magnitude distribution. Furthermore, it is shown that this transform pair supplies a sufficient mathematical framework to describe the evolution of the force magnitude distribution under shearing. Apart from the choice of several coefficients, whose evolution of values must be explained in the physics, this framework successfully reproduces the features of the distribution that are taken to be an indicator of jamming and unjamming in a granular packing. Key words. Granular Physics, Probability Density Functions, Fourier Transforms
Density functional for ternary non-additive hard sphere mixtures.
Schmidt, Matthias
2011-10-19
Based on fundamental measure theory, a Helmholtz free energy density functional for three-component mixtures of hard spheres with general, non-additive interaction distances is constructed. The functional constitutes a generalization of the previously given theory for binary non-additive mixtures. The diagrammatic structure of the spatial integrals in both functionals is of star-like (or tree-like) topology. The ternary diagrams possess a higher degree of complexity than the binary diagrams. Results for partial pair correlation functions, obtained via the Ornstein-Zernike route from the second functional derivatives of the excess free energy functional, agree well with Monte Carlo simulation data. © 2011 IOP Publishing Ltd
Improved association in a classical density functional theory for water
Krebs, Eric J.; Schulte, Jeff B.; Roundy, David
2014-03-28
We present a modification to our recently published statistical associating fluid theory-based classical density functional theory for water. We have recently developed and tested a functional for the averaged radial distribution function at contact of the hard-sphere fluid that is dramatically more accurate at interfaces than earlier approximations. We now incorporate this improved functional into the association term of our free energy functional for water, improving its description of hydrogen bonding. We examine the effect of this improvement by studying two hard solutes (a hard hydrophobic rod and a hard sphere) and a Lennard-Jones approximation of a krypton atom solute. The improved functional leads to a moderate change in the density profile and a large decrease in the number of hydrogen bonds broken in the vicinity of the hard solutes. We find an improvement of the partial radial distribution for a krypton atom in water when compared with experiment.
Forward and backward galaxy evolution in comoving cumulative number density space
NASA Astrophysics Data System (ADS)
Torrey, Paul; Wellons, Sarah; Ma, Chung-Pei; Hopkins, Philip F.; Vogelsberger, Mark
2017-06-01
Galaxy cumulative comoving number density is commonly used to forge progenitor/descendant links between observed galaxy populations at different epochs. However, this method breaks down in the presence of galaxy mergers, or when galaxies experience stochastic growth rates. We present a simple analytic framework to treat the physical processes that drive the evolution and diffusion of galaxies within comoving number density space. The evolution in mass rank order of a galaxy population with time is influenced by (1) the non-conservative nature of total galaxy number density driven by galaxies combining in mergers (which we tabulate as a galaxy 'coagulation' rate) and (2) galaxy 'mass rank scatter' driven by stochasticity in stellar-mass growth rates from in situ star formation and mergers. We quantify the relative contribution of these two effects to the total mass rank order evolution using the Illustris simulation. We show that galaxy coagulation is dominant at lower redshifts and stellar masses, while scattered growth rates dominate the mass rank evolution at higher redshifts and stellar masses. For a galaxy population at 1010 M⊙, coagulation has been the dominant effect since z = 2.2, but a galaxy population at 1011 M⊙ was dominated by mass rank scatter until z = 0.6. We show that although the forward and backward median cumulative number density evolution tracks are asymmetric, the backward median cumulative number density evolution can be obtained by convolving the descendant distribution function with progenitor relative abundances. We tabulate fits for the median cumulative number density evolution and scatter that can be applied to improve the way galaxy populations are linked in multi-epoch observational data sets.
Density functional calculations of spin-wave dispersion curves.
NASA Astrophysics Data System (ADS)
Kleinman, Leonard; Niu, Qian
1998-03-01
Extending the density functional method of Kubler et al( J. Kubler et al, J. Phys. F 18, 469 (1983) and J. Phys. Condens. Matter 1, 8155 (1989). ) for calcuating spin density wave ground states (but not making their atomic sphere approximation which requires a constant spin polarization direction in each WS sphere) we dicuss the calculation of frozen spin-wave eigenfunctions and their total energies. From these and the results of Niu's talk, we describe the calculation of spin-wave frequencies.
New link between conceptual density functional theory and electron delocalization.
Matito, Eduard; Putz, Mihai V
2011-11-17
In this paper we give a new definition of the softness kernel based on the exchange-correlation density. This new kernel is shown to correspond to the change of electron fluctuation upon external perturbation, thus helping to bridge the gap between conceptual density functional theory and some tools describing electron localization in molecules. With the aid of a few computational calculations on diatomics we illustrate the performance of this new computational tool.
Density functionals that recognize covalent, metallic, and weak bonds.
Sun, Jianwei; Xiao, Bing; Fang, Yuan; Haunschild, Robin; Hao, Pan; Ruzsinszky, Adrienn; Csonka, Gábor I; Scuseria, Gustavo E; Perdew, John P
2013-09-06
Computationally efficient semilocal approximations of density functional theory at the level of the local spin density approximation (LSDA) or generalized gradient approximation (GGA) poorly describe weak interactions. We show improved descriptions for weak bonds (without loss of accuracy for strong ones) from a newly developed semilocal meta-GGA (MGGA), by applying it to molecules, surfaces, and solids. We argue that this improvement comes from using the right MGGA dimensionless ingredient to recognize all types of orbital overlap.
NASA Astrophysics Data System (ADS)
Schuetrumpf, B.; Nazarewicz, W.; Reinhard, P.-G.
2017-08-01
Background: The central depression of nucleonic density, i.e., a reduction of density in the nuclear interior, has been attributed to many factors. For instance, bubble structures in superheavy nuclei are believed to be due to the electrostatic repulsion. In light nuclei, the mechanism behind the density reduction in the interior has been discussed in terms of shell effects associated with occupations of s orbits. Purpose: The main objective of this work is to reveal mechanisms behind the formation of central depression in nucleonic densities in light and heavy nuclei. To this end, we introduce several measures of the internal nucleonic density. Through the statistical analysis, we study the information content of these measures with respect to nuclear matter properties. Method: We apply nuclear density functional theory with Skyrme functionals. Using the statistical tools of linear least square regression, we inspect correlations between various measures of central depression and model parameters, including nuclear matter properties. We study bivariate correlations with selected quantities as well as multiple correlations with groups of parameters. Detailed correlation analysis is carried out for 34Si for which a bubble structure has been reported recently, 48Ca, and N =82 , 126, and 184 isotonic chains. Results: We show that the central depression in medium-mass nuclei is very sensitive to shell effects, whereas for superheavy systems it is firmly driven by the electrostatic repulsion. An appreciable semibubble structure in proton density is predicted for 294Og, which is currently the heaviest nucleus known experimentally. Conclusion: Our correlation analysis reveals that the central density indicators in nuclei below 208Pb carry little information on parameters of nuclear matter; they are predominantly driven by shell structure. On the other hand, in the superheavy nuclei there exists a clear relationship between the central nucleonic density and symmetry energy.
Experimental study of high density foods for the Space Operations Center
NASA Technical Reports Server (NTRS)
Ahmed, S. M.
1981-01-01
The experimental study of high density foods for the Space Operations Center is described. A sensory evaluation of the high density foods was conducted first to test the acceptability of the products. A shelf-life study of the high density foods was also conducted for three different time lengths at three different temperatures. The nutritional analysis of the high density foods is at present incomplete.
Experimental study of high density foods for the Space Operations Center
NASA Technical Reports Server (NTRS)
Ahmed, S. M.
1981-01-01
The experimental study of high density foods for the Space Operations Center is described. A sensory evaluation of the high density foods was conducted first to test the acceptability of the products. A shelf-life study of the high density foods was also conducted for three different time lengths at three different temperatures. The nutritional analysis of the high density foods is at present incomplete.
Density functional theory for semiflexible and cyclic polyatomic fluids.
Cao, Dapeng; Wu, Jianzhong
2004-09-01
The effects of bond angle and chain stiffness on the structures of semiflexible polyatomic fluids are investigated by incorporating the bending potential into a density functional theory [Y. X. Yu and J. Z. Wu, J. Chem. Phys. 117, 2368 (2002)] that combines a modified fundamental measure theory for the excluded-volume effects and the first-order thermodynamics perturbation theory for the chain connectivity. The refined density functional theory faithfully reproduces the density profiles and conformational properties of a variety of triatomic fluids near a hard wall in which extensive Monte Carlo simulation data are available. In particular, the theory is able to capture the structures of rigid cyclic trimers where all segments are identical. The variation of local density profiles with respect to the chain length of confined polyatomic fluids is also explored. For quadratomic fluids confined in slit pores, the density profile of the middle segments exhibits novel double peaks that are absent in a fully flexible chain model. In addition, the density functional theory is applied to predicting the conformational properties and adsorption behavior of heterogeneous triatomic fluids of type "ABB" mimicking surfactant molecules. The competition between surface adsorption and self-association of trimers consisting of surface active and self-binding "A" segments and neutral "B" segment is explored. (c) 2004 American Institute of Physics
NASA Astrophysics Data System (ADS)
Chen, Y.; Friedel, R. H. W.; Reeves, G. D.; Cayton, T. E.; Christensen, R.
2007-11-01
An integrated investigation method, which can study the relativistic electron phase space density distribution and check the reliability of employed magnetic field models simultaneously, is developed and applied to the geosynchronous orbit region for 53 geomagnetic storms during a ˜190-d period. First, to test how the magnetospheric magnetic field affects the study of phase space density, two approaches are taken on handling the magnetic field model: One is to use an existing empirical model through the whole storm period; the other is to select one from a list of existing magnetic field models for each time bin during the period by fitting to multipoint in situ measurements. The magnetic field models in both approaches are again tested by Liouville's theorem, which requires the conserved phase space density for fixed phase space coordinates given no local losses and sources. Then on the basis of the selected magnetic field model, the phase space density is calculated by transforming the flux data from three Los Alamos National Laboratory geosynchronous satellites. By following the procedure developed here and using the cross-satellite calibration achieved in previous work, we deduce the storm time electron phase space density distribution for the region near geosynchronous orbit, covering a range of L shells with L* centered ˜6. This work establishes the radial phase space density gradient at constant adiabatic invariants as a function of universal time during storm times, and three types of geomagnetic storms are defined according to the degree of energy-dependent enhancements of energetic electrons during recovery phases. Initial results from this study suggest a source outside geosynchronous orbit for low-energy electrons and a major source inside for high-energy electrons.
Sorption on deformable solids. Density functional theory approach.
Berim, Gersh O; Ruckenstein, Eli
2011-11-17
A modified density functional theory is proposed to describe fluid adsorption and absorption by a solid, the density of which is nonhomogeneous near the interface. The density distribution of the solid is not provided by apriori assumptions, but is obtained via the minimization of an appropriate thermodynamic potential. The theory considers a mixture of two components in a slitlike pore. One of them, the fluid, is in contact with a reservoir containing the same kind of molecules and can be described through a grand canonical ensemble. The other component has strong interactions between its molecules. As a consequence, it forms a solid in the slit which can be treated as a canonical ensemble of a fixed number of molecules. The theory predicts both an intrinsic (in the absence of fluid) change in the solid density near the interface and a solid density variation as the fluid density in the reservoir is changed. In addition, it reveals that the oscillations that occur in the fluid density when the solid density is uniform are damped by the nonuniform solid. The theory provides the amounts of fluid adsorbed as well as absorbed by the solid.
Determination of atmospheric density using a space-launched projectile
NASA Technical Reports Server (NTRS)
Menees, G. P.; Park, C.; Brown, K. G.; Wilson, J. F.
1985-01-01
A method is proposed that provides advance information about unpredictable atmospheric density dispersions that must be accommodated during random operations of aeroassisted-orbital-transfer vehicles (AOTVs). The principal feature is that a test or 'scout' projectile precedes the AOTV through the same region of the atmosphere as that of the predicted transatmospheric flight trajectory. The atmospheric density structure is determined from the vehicle's aerodynamic deceleration characteristics by on-board or ground-based tracking equipment. The time lag between passage of the projectile and the AOTV can be adjusted to only that time necessary to implement required guidance, navigation, and control (GN&C) corrections. The various strategies available to control the projectile's flight characteristics are analyzed in detail. The results are correlated with aerothermodynamic heating and materials requirements to ensure the survival of the projectile and, consequently, the capability of the AOTV to navigate a variable upper atmosphere within specified limits.
Configuration interaction in symmetry-conserving covariant density functional theory
NASA Astrophysics Data System (ADS)
Zhao, P. W.; Ring, P.; Meng, J.
2016-10-01
A new method to calculate spectroscopic properties of deformed nuclei is proposed: configuration interaction on top of projected density functional theory (CI-PDFT). The general concept of this approach is discussed in the framework of covariant density functional theory and its validity is illustrated in an application to the yrast band of the nucleus 54Cr. It is found that the experimentally observed excitation energies for the yrast band in 54Cr can be well reproduced. In contrast to conventional shell-model calculations, there is no core and only a relatively small number of configurations is sufficient for a satisfying description. No new parameters are necessary, because the effective interaction is derived from an universal density functional given in the literature.
The AM05 density functional applied to solids.
Mattsson, Ann E; Armiento, Rickard; Paier, Joachim; Kresse, Georg; Wills, John M; Mattsson, Thomas R
2008-02-28
We show that the AM05 functional [Armiento and Mattsson, Phys. Rev. B 72, 085108 (2005)] has the same excellent performance for solids as the hybrid density functionals tested in Paier et al. [J. Chem. Phys. 124, 154709 (2006); 125, 249901 (2006)]. This confirms the original finding that AM05 performs exceptionally well for solids and surfaces. Hartree-Fock hybrid calculations are typically an order of magnitude slower than local or semilocal density functionals such as AM05, which is of a regular semilocal generalized gradient approximation form. The performance of AM05 is on average found to be superior to selecting the best of local density approximation and PBE for each solid. By comparing data from several different electronic-structure codes, we have determined that the numerical errors in this study are equal to or smaller than the corresponding experimental uncertainties.
Bakosi, Jozsef; Ristorcelli, Raymond J
2010-01-01
Probability density function (PDF) methods are extended to variable-density pressure-gradient-driven turbulence. We apply the new method to compute the joint PDF of density and velocity in a non-premixed binary mixture of different-density molecularly mixing fluids under gravity. The full time-evolution of the joint PDF is captured in the highly non-equilibrium flow: starting from a quiescent state, transitioning to fully developed turbulence and finally dissipated by molecular diffusion. High-Atwood-number effects (as distinguished from the Boussinesq case) are accounted for: both hydrodynamic turbulence and material mixing are treated at arbitrary density ratios, with the specific volume, mass flux and all their correlations in closed form. An extension of the generalized Langevin model, originally developed for the Lagrangian fluid particle velocity in constant-density shear-driven turbulence, is constructed for variable-density pressure-gradient-driven flows. The persistent small-scale anisotropy, a fundamentally 'non-Kolmogorovian' feature of flows under external acceleration forces, is captured by a tensorial diffusion term based on the external body force. The material mixing model for the fluid density, an active scalar, is developed based on the beta distribution. The beta-PDF is shown to be capable of capturing the mixing asymmetry and that it can accurately represent the density through transition, in fully developed turbulence and in the decay process. The joint model for hydrodynamics and active material mixing yields a time-accurate evolution of the turbulent kinetic energy and Reynolds stress anisotropy without resorting to gradient diffusion hypotheses, and represents the mixing state by the density PDF itself, eliminating the need for dubious mixing measures. Direct numerical simulations of the homogeneous Rayleigh-Taylor instability are used for model validation.
Perspective: Kohn-Sham density functional theory descending a staircase.
Yu, Haoyu S; Li, Shaohong L; Truhlar, Donald G
2016-10-07
This article presents a perspective on Kohn-Sham density functional theory (KS-DFT) for electronic structure calculations in chemical physics. This theory is in widespread use for applications to both molecules and solids. We pay special attention to several aspects where there are both concerns and progress toward solutions. These include: 1. The treatment of open-shell and inherently multiconfigurational systems (the latter are often called multireference systems and are variously classified as having strong correlation, near-degeneracy correlation, or high static correlation; KS-DFT must treat these systems with broken-symmetry determinants). 2. The treatment of noncovalent interactions. 3. The choice between developing new functionals by parametrization, by theoretical constraints, or by a combination. 4. The ingredients of the exchange-correlation functionals used by KS-DFT, including spin densities, the magnitudes of their gradients, spin-specific kinetic energy densities, nonlocal exchange (Hartree-Fock exchange), nonlocal correlation, and subshell-dependent corrections (DFT+U). 5. The quest for a universal functional, where we summarize some of the success of the latest Minnesota functionals, namely MN15-L and MN15, which were obtained by optimization against diverse databases. 6. Time-dependent density functional theory, which is an extension of DFT to treat time-dependent problems and excited states. The review is a snapshot of a rapidly moving field, and-like Marcel Duchamp-we hope to convey progress in a stimulating way.
Perspective: Kohn-Sham density functional theory descending a staircase
NASA Astrophysics Data System (ADS)
Yu, Haoyu S.; Li, Shaohong L.; Truhlar, Donald G.
2016-10-01
This article presents a perspective on Kohn-Sham density functional theory (KS-DFT) for electronic structure calculations in chemical physics. This theory is in widespread use for applications to both molecules and solids. We pay special attention to several aspects where there are both concerns and progress toward solutions. These include: 1. The treatment of open-shell and inherently multiconfigurational systems (the latter are often called multireference systems and are variously classified as having strong correlation, near-degeneracy correlation, or high static correlation; KS-DFT must treat these systems with broken-symmetry determinants). 2. The treatment of noncovalent interactions. 3. The choice between developing new functionals by parametrization, by theoretical constraints, or by a combination. 4. The ingredients of the exchange-correlation functionals used by KS-DFT, including spin densities, the magnitudes of their gradients, spin-specific kinetic energy densities, nonlocal exchange (Hartree-Fock exchange), nonlocal correlation, and subshell-dependent corrections (DFT+U). 5. The quest for a universal functional, where we summarize some of the success of the latest Minnesota functionals, namely MN15-L and MN15, which were obtained by optimization against diverse databases. 6. Time-dependent density functional theory, which is an extension of DFT to treat time-dependent problems and excited states. The review is a snapshot of a rapidly moving field, and—like Marcel Duchamp—we hope to convey progress in a stimulating way.
Non-Periodic Finite-Element Formulation of Orbital-Free Density Functional Theory
Gavini, V; Knap, J; Bhattacharya, K; Ortiz, M
2006-10-06
We propose an approach to perform orbital-free density functional theory calculations in a non-periodic setting using the finite-element method. We consider this a step towards constructing a seamless multi-scale approach for studying defects like vacancies, dislocations and cracks that require quantum mechanical resolution at the core and are sensitive to long range continuum stresses. In this paper, we describe a local real space variational formulation for orbital-free density functional theory, including the electrostatic terms and prove existence results. We prove the convergence of the finite-element approximation including numerical quadratures for our variational formulation. Finally, we demonstrate our method using examples.
Multiconfiguration Pair-Density Functional Theory: A New Way To Treat Strongly Correlated Systems.
Gagliardi, Laura; Truhlar, Donald G; Li Manni, Giovanni; Carlson, Rebecca K; Hoyer, Chad E; Bao, Junwei Lucas
2017-01-17
The electronic energy of a system provides the Born-Oppenheimer potential energy for internuclear motion and thus determines molecular structure and spectra, bond energies, conformational energies, reaction barrier heights, and vibrational frequencies. The development of more efficient and more accurate ways to calculate the electronic energy of systems with inherently multiconfigurational electronic structure is essential for many applications, including transition metal and actinide chemistry, systems with partially broken bonds, many transition states, and most electronically excited states. Inherently multiconfigurational systems are called strongly correlated systems or multireference systems, where the latter name refers to the need for using more than one ("multiple") configuration state function to provide a good zero-order reference wave function. This Account describes multiconfiguration pair-density functional theory (MC-PDFT), which was developed as a way to combine the advantages of wave function theory (WFT) and density functional theory (DFT) to provide a better treatment of strongly correlated systems. First we review background material: the widely used Kohn-Sham DFT (which uses only a single Slater determinant as reference wave function), multiconfiguration WFT methods that treat inherently multiconfigurational systems based on an active space, and previous attempts to combine multiconfiguration WFT with DFT. Then we review the formulation of MC-PDFT. It is a generalization of Kohn-Sham DFT in that the electron kinetic energy and classical electrostatic energy are calculated from a reference wave function, while the rest of the energy is obtained from a density functional. However, there are two main differences with respent to Kohn-Sham DFT: (i) The reference wave function is multiconfigurational rather than being a single Slater determinant. (ii) The density functional is a function of the total density and the on-top pair density rather than
Energy density functional for nuclei and neutron stars
NASA Astrophysics Data System (ADS)
Erler, J.; Horowitz, C. J.; Nazarewicz, W.; Rafalski, M.; Reinhard, P.-G.
2013-04-01
Background: Recent observational data on neutron star masses and radii provide stringent constraints on the equation of state of neutron rich matter [Annu. Rev. Nucl. Part. Sci.ARPSDF0163-899810.1146/annurev-nucl-102711-095018 62, 485 (2012)].Purpose: We aim to develop a nuclear energy density functional that can be simultaneously applied to finite nuclei and neutron stars.Methods: We use the self-consistent nuclear density functional theory (DFT) with Skyrme energy density functionals and covariance analysis to assess correlations between observables for finite nuclei and neutron stars. In a first step two energy functionals—a high density energy functional giving reasonable neutron properties, and a low density functional fitted to nuclear properties—are matched. In a second step, we optimize a new functional using exactly the same protocol as in earlier studies pertaining to nuclei but now including neutron star data. This allows direct comparisons of performance of the new functional relative to the standard one.Results: The new functional TOV-min yields results for nuclear bulk properties (energy, rms radius, diffraction radius, and surface thickness) that are of the same quality as those obtained with the established Skyrme functionals, including SV-min. When comparing SV-min and TOV-min, isoscalar nuclear matter indicators vary slightly while isovector properties are changed considerably. We discuss neutron skins, dipole polarizability, separation energies of the heaviest elements, and proton and neutron drip lines. We confirm a correlation between the neutron skin of 208Pb and the neutron star radius.Conclusions: We demonstrate that standard energy density functionals optimized to nuclear data do not carry information on the expected maximum neutron star mass, and that predictions can only be made within an extremely broad uncertainty band. For atomic nuclei, the new functional TOV-min performs at least as well as the standard nuclear functionals, but
Exploration of a modified density dependence in the Skyrme functional
Erler, J.; Reinhard, P.-G.; Kluepfel, P.
2010-10-15
A variant of the basic Skyrme-Hartree-Fock functional is considered dealing with a new form of density dependence. It employs only integer powers and thus will allow a more sound basis for projection schemes (particle number, angular momentum). We optimize the new functional with exactly the same adjustment strategy as used in an earlier study with a standard Skyrme functional. This allows direct comparisons of the performance of the new functional relative to the standard one. We discuss various observables: bulk properties of finite nuclei, nuclear matter, giant resonances, superheavy elements, and energy systematics. The new functional performs at least as well as the standard one, but offers a wider range of applicability (e.g., for projection) and more flexibility in the regime of high densities.
Kinetic-energy density functional: Atoms and shell structure
Garcia-Gonzalez, P.; Alvarellos, J.E.; Chacon, E. |
1996-09-01
We present a nonlocal kinetic-energy functional which includes an anisotropic average of the density through a symmetrization procedure. This functional allows a better description of the nonlocal effects of the electron system. The main consequence of the symmetrization is the appearance of a clear shell structure in the atomic density profiles, obtained after the minimization of the total energy. Although previous results with some of the nonlocal kinetic functionals have given incipient structures for heavy atoms, only our functional shows a clear shell structure for most of the atoms. The atomic total energies have a good agreement with the exact calculations. Discussion of the chemical potential and the first ionization potential in atoms is included. The functional is also extended to spin-polarized systems. {copyright} {ital 1996 The American Physical Society.}
On the evolution of the density probability density function in strongly self-gravitating systems
Girichidis, Philipp; Konstandin, Lukas; Klessen, Ralf S.; Whitworth, Anthony P.
2014-02-01
The time evolution of the probability density function (PDF) of the mass density is formulated and solved for systems in free-fall using a simple approximate function for the collapse of a sphere. We demonstrate that a pressure-free collapse results in a power-law tail on the high-density side of the PDF. The slope quickly asymptotes to the functional form P{sub V} (ρ)∝ρ{sup –1.54} for the (volume-weighted) PDF and P{sub M} (ρ)∝ρ{sup –0.54} for the corresponding mass-weighted distribution. From the simple approximation of the PDF we derive analytic descriptions for mass accretion, finding that dynamically quiet systems with narrow density PDFs lead to retarded star formation and low star formation rates (SFRs). Conversely, strong turbulent motions that broaden the PDF accelerate the collapse causing a bursting mode of star formation. Finally, we compare our theoretical work with observations. The measured SFRs are consistent with our model during the early phases of the collapse. Comparison of observed column density PDFs with those derived from our model suggests that observed star-forming cores are roughly in free-fall.
On the Evolution of the Density Probability Density Function in Strongly Self-gravitating Systems
NASA Astrophysics Data System (ADS)
Girichidis, Philipp; Konstandin, Lukas; Whitworth, Anthony P.; Klessen, Ralf S.
2014-02-01
The time evolution of the probability density function (PDF) of the mass density is formulated and solved for systems in free-fall using a simple approximate function for the collapse of a sphere. We demonstrate that a pressure-free collapse results in a power-law tail on the high-density side of the PDF. The slope quickly asymptotes to the functional form PV (ρ)vpropρ-1.54 for the (volume-weighted) PDF and PM (ρ)vpropρ-0.54 for the corresponding mass-weighted distribution. From the simple approximation of the PDF we derive analytic descriptions for mass accretion, finding that dynamically quiet systems with narrow density PDFs lead to retarded star formation and low star formation rates (SFRs). Conversely, strong turbulent motions that broaden the PDF accelerate the collapse causing a bursting mode of star formation. Finally, we compare our theoretical work with observations. The measured SFRs are consistent with our model during the early phases of the collapse. Comparison of observed column density PDFs with those derived from our model suggests that observed star-forming cores are roughly in free-fall.
Course 4: Density Functional Theory, Methods, Techniques, and Applications
NASA Astrophysics Data System (ADS)
Chrétien, S.; Salahub, D. R.
Contents 1 Introduction 2 Density functional theory 2.1 Hohenberg and Kohn theorems 2.2 Levy's constrained search 2.3 Kohn-Sham method 3 Density matrices and pair correlation functions 4 Adiabatic connection or coupling strength integration 5 Comparing and constrasting KS-DFT and HF-CI 6 Preparing new functionals 7 Approximate exchange and correlation functionals 7.1 The Local Spin Density Approximation (LSDA) 7.2 Gradient Expansion Approximation (GEA) 7.3 Generalized Gradient Approximation (GGA) 7.4 meta-Generalized Gradient Approximation (meta-GGA) 7.5 Hybrid functionals 7.6 The Optimized Effective Potential method (OEP) 7.7 Comparison between various approximate functionals 8 LAP correlation functional 9 Solving the Kohn-Sham equations 9.1 The Kohn-Sham orbitals 9.2 Coulomb potential 9.3 Exchange-correlation potential 9.4 Core potential 9.5 Other choices and sources of error 9.6 Functionality 10 Applications 10.1 Ab initio molecular dynamics for an alanine dipeptide model 10.2 Transition metal clusters: The ecstasy, and the agony... 10.3 The conversion of acetylene to benzene on Fe clusters 11 Conclusions
Nonlinear eigenvalue problems in Density Functional Theory calculations
Fattebert, J
2009-08-28
Developed in the 1960's by W. Kohn and coauthors, Density Functional Theory (DFT) is a very popular quantum model for First-Principles simulations in chemistry and material sciences. It allows calculations of systems made of hundreds of atoms. Indeed DFT reduces the 3N-dimensional Schroedinger electronic structure problem to the search for a ground state electronic density in 3D. In practice it leads to the search for N electronic wave functions solutions of an energy minimization problem in 3D, or equivalently the solution of an eigenvalue problem with a non-linear operator.
Crystallization induced by multiple seeds: dynamical density functional approach.
Neuhaus, T; Schmiedeberg, M; Löwen, H
2013-12-01
Using microscopic dynamical density functional theory, we calculate the dynamical formation of polycrystals by following the crystal growth around multiple crystalline seeds imposed to an undercooled fluid. Depending on the undercooling and the size ratio as well as the relative crystal orientation of two neighboring seeds, three possibilities of the final state emerge, namely no crystallization at all, formation of a monocrystal, or two crystallites separated by a curved grain boundary. Our results, which are obtained for two-dimensional hard disk systems using a fundamental-measure density functional, shed new light on the particle-resolved structure and growth of polycrystalline material in general.
Abstracting Attribute Space for Transfer Function Exploration and Design.
Maciejewski, Ross; Jang, Yun; Woo, Insoo; Jänicke, Heike; Gaither, Kelly P; Ebert, David S
2013-01-01
Currently, user centered transfer function design begins with the user interacting with a one or two-dimensional histogram of the volumetric attribute space. The attribute space is visualized as a function of the number of voxels, allowing the user to explore the data in terms of the attribute size/magnitude. However, such visualizations provide the user with no information on the relationship between various attribute spaces (e.g., density, temperature, pressure, x, y, z) within the multivariate data. In this work, we propose a modification to the attribute space visualization in which the user is no longer presented with the magnitude of the attribute; instead, the user is presented with an information metric detailing the relationship between attributes of the multivariate volumetric data. In this way, the user can guide their exploration based on the relationship between the attribute magnitude and user selected attribute information as opposed to being constrained by only visualizing the magnitude of the attribute. We refer to this modification to the traditional histogram widget as an abstract attribute space representation. Our system utilizes common one and two-dimensional histogram widgets where the bins of the abstract attribute space now correspond to an attribute relationship in terms of the mean, standard deviation, entropy, or skewness. In this manner, we exploit the relationships and correlations present in the underlying data with respect to the dimension(s) under examination. These relationships are often times key to insight and allow us to guide attribute discovery as opposed to automatic extraction schemes which try to calculate and extract distinct attributes a priori. In this way, our system aids in the knowledge discovery of the interaction of properties within volumetric data.
Density functional theory study of neutral and oxidized thiophene oligomers
NASA Astrophysics Data System (ADS)
Dai, Yafei; Wei, Chengwei; Blaisten-Barojas, Estela
2013-11-01
The effect of oxidation on the energetics and structure of thiophene (Th) oligomers is studied with density functional theory at the B3PW91/6-311++G(d,p) level. Neutral n-Th oligomers (2 < n < 13) are gently curved planar chains. Ionization potential and electron affinity results show that n-Th oligomers are easier to be oxidized as their chain length increases. Oxidation states +2, +4, +6, and +8 are energetically stable in 12-Th. Upon oxidation the conjugated backbone of 12-Th switches from extended benzenoid phase to quinoid phase localized on groups of monomers regularly spaced along the chain. Oxidized states +2, +4, +6, and +8 of 12-Th display two +1e localized at the ends of their chains only because of the finite size of the chains. In 12-Th this end-effect extends over the two terminal monomers forming a positive-negative charge duet. This peculiar charge localization makes n-Th oligomers different from other conducting polymers with similar structure, such as polypyrrole. The spectrum of single-electron molecular states of oxidized 12-Th displays two localized single-electron states in the HOMO-LUMO energy gap per +2 oxidation state. Oligothiophene 12-Th doped with F atoms at 1:2 concentration presents a charge transfer of 3.4 e from oligomer to dopants that increases to 4.8 e in the presence of solvent. The charge distribution in these F-doped oligomers is similar to the +4 oxidation state of 12-Th. It is predicted that dopants produce an enhanced charge transfer localized in the proximity of their locations enhancing the formation of bipolarons in the central part of the oligomer chain.
García-Aldea, David; Alvarellos, J E
2008-08-21
Following some recent ideas on the construction of kinetic energy density functionals that reproduce the linear response function of the homogeneous electron gas, a family of them with a nonlocal term based on the von Weizsacker functional and with a dependence on the logarithm of the density is presented. As localized systems are the most difficult to study with explicit kinetic functionals, in this paper we apply to atomic systems a number of families of fully nonlocal kinetic functionals. We have put our attention in both the total kinetic energy and the local behavior of the kinetic energy density, and the results clearly show the quality of these fully nonlocal functionals. They make a good description of the local behavior of the kinetic energy density and maintain good results for the total kinetic energies. We must remark that almost all the functionals discussed in the paper, when using an adequate reference density, can be evaluated as a single integral in momentum space, with a quasilinear scaling for the computational cost.
Effects of high density on spacing behaviour and reproduction in Akodon azarae: A fencing experiment
NASA Astrophysics Data System (ADS)
Ávila, Belén; Bonatto, Florencia; Priotto, José; Steinmann, Andrea R.
2016-01-01
We studied the short term spacing behavioural responses of Pampean grassland mouse (Akodon azarae) with regard to population density in four 0.25 ha enclosures (two control and two experimental) in the 2011 breeding season. Based on the hypothesis that A. azarae breeding females exhibit spacing behaviour, and breeding males show a fusion spatial response, we tested the following predictions: (1) home range size and intrasexual overlap degree of females are independent of population density values; (2) at high population density, home range size of males decreases and the intrasexual home range overlap degree increases. To determine if female reproductive success decreases at high population density, we analyzed pregnancy rate, size and weight of litters, and period until fecundation in both low and high enclosure population density. We found that both males and females varied their home range size in relation to population density. Although male home ranges were always bigger than those of females in populations with high density, home range sizes of both sexes decreased. Females kept exclusive home ranges independent of density values meanwhile males decreased home range overlap in high breeding density populations. Although females produced litters of similar size in both treatments, weight of litter, pregnant rate and period until fecundation varied in relation to population density. Our results did not support the hypothesis that at high density females of A. azarae exhibit spacing behaviour neither that males exhibit a fusion spatial response.
Dynamics of localized particles from density functional theory
NASA Astrophysics Data System (ADS)
Reinhardt, J.; Brader, J. M.
2012-01-01
A fundamental assumption of the dynamical density functional theory (DDFT) of colloidal systems is that a grand-canonical free-energy functional may be employed to generate the thermodynamic driving forces. Using one-dimensional hard rods as a model system, we analyze the validity of this key assumption and show that unphysical self-interactions of the tagged particle density fields, arising from coupling to a particle reservoir, are responsible for the excessively fast relaxation predicted by the theory. Moreover, our findings suggest that even employing a canonical functional would not lead to an improvement for many-particle systems, if only the total density is considered. We present several possible schemes to suppress these effects by incorporating tagged densities. When applied to confined systems, we demonstrate, using a simple example, that DDFT necessarily leads to delocalized tagged particle density distributions, which do not respect the fundamental geometrical constraints apparent in Brownian dynamics simulation data. The implication of these results for possible applications of DDFT to treat the glass transition are discussed.
Density functionals for the strong-interaction limit
NASA Astrophysics Data System (ADS)
Seidl, Michael; Perdew, John P.; Kurth, Stefan
2000-07-01
The strong-interaction limit of density-functional (DF) theory is simple and provides information required for an accurate resummation of DF perturbation theory. Here we derive the point-charge-plus-continuum (PC) model for that limit, and its gradient expansion. The exchange-correlation (xc) energy Exc[ρ]≡∫10dαWα[ρ] follows from the xc potential energies Wα at different interaction strengths α>=0 [but at fixed density ρ(r)]. For small α~0, the integrand Wα is obtained accurately from perturbation theory, but the perturbation expansion requires resummation for moderate and large α. For that purpose, we present density functionals for the coefficients in the asymptotic expansion Wα-->W∞+W'∞α-1/2 for α-->∞ in the PC model. WPC∞ arises from strict correlation, and W'PC∞ from zero-point vibration of the electrons around their strictly correlated distributions. The PC values for W∞ and W'∞ agree with those from a self-correlation-free meta-generalized gradient approximation, both for atoms and for atomization energies of molecules. We also (i) explain the difference between the PC cell and the exchange-correlation hole, (ii) present a density-functional measure of correlation strength, (iii) describe the electron localization and spin polarization energy in a highly stretched H2 molecule, and (iv) discuss the soft-plasmon instability of the low-density uniform electron gas.
Nuclear energy density functional and the nuclear α decay
NASA Astrophysics Data System (ADS)
Lim, Yeunhwan; Oh, Yongseok
2017-03-01
The nuclear α decay of heavy nuclei is investigated based on the nuclear energy density functional, which leads to the α potential inside the parent nucleus in terms of the proton and neutron density profiles of the daughter nucleus. We use the Skyrme force model, Gogny force model, and relativistic mean-field model to get the nucleon density profiles inside heavy nuclei. Once the nucleon density profiles are determined, the parameters of the nuclear α potential are fitted to the observed α decay half-lives of heavy nuclei. This approach is then applied to predict unknown α decay half-lives of heavy nuclei. To estimate the Q values of unobserved α decays, we make use of the liquid droplet model.
Average protein density is a molecular-weight-dependent function
Fischer, Hannes; Polikarpov, Igor; Craievich, Aldo F.
2004-01-01
The mass density of proteins is a relevant basic biophysical quantity. It is also a useful input parameter, for example, for three-dimensional structure determination by protein crystallography and studies of protein oligomers in solution by analytic ultracentrifugation. We have performed a critical analysis of published, theoretical, and experimental investigations about this issue and concluded that the average density of proteins is not a constant as often assumed. For proteins with a molecular weight below 20 kDa, the average density exhibits a positive deviation that increases for decreasing molecular weight. A simple molecular-weight-depending function is proposed that provides a more accurate estimate of the average protein density. PMID:15388866
Fractional spin in reduced density-matrix functional theory.
Helbig, N; Theodorakopoulos, G; Lathiotakis, N N
2011-08-07
We study the behavior of different functionals of the one-body reduced density matrix (1RDM) for systems with fractional z-component of the total spin. We define these systems as ensembles of integer spin states. It is shown that, similarly to density functional theory, the error in the dissociation of diatomic molecules is directly related to the deviation from constancy of the atomic total energies as functions of the fractional spin. However, several functionals of the 1RDM show a size inconsistency which leads to additional errors. We also investigate the difference between a direct evaluation of the energy of an ensemble of integer-spin systems and a direct minimization of the energy of a fractional-spin system.
Density-based mixing parameter for hybrid functionals
NASA Astrophysics Data System (ADS)
Marques, Miguel A. L.; Vidal, Julien; Oliveira, Micael J. T.; Reining, Lucia; Botti, Silvana
2011-01-01
A very popular ab initio scheme to calculate electronic properties in solids is the use of hybrid functionals in density functional theory (DFT) that mixes a portion of the Fock exchange with DFT functionals. In spite of its success, a major problem still remains, related to the use of one single mixing parameter for all materials. Guided by physical arguments that connect the mixing parameter to the dielectric properties of the solid, and ultimately to its band gap, we propose a method to calculate this parameter from the electronic density alone. This approach is able to cut significantly the error of traditional hybrid functionals for large and small gap materials, while retaining a good description of the structural properties. Moreover, its implementation is simple and leads to a negligible increase of the computational time.
Enabling Exploration of Deep Space: High Density Storage of Antimatter
NASA Technical Reports Server (NTRS)
Smith, Gerald A.; Kramer, Kevin J.
1999-01-01
Portable electromagnetic antiproton traps are now in a state of realization. This allows facilities like NASA Marshall Space Flight Center to conduct antimatter research remote to production sites. MSFC is currently developing a trap to store 10(exp 12) antiprotons for a twenty-day half-life period to be used in future experiments including antimatter plasma guns, antimatter-initiated microfusion, and the synthesis of antihydrogen for space propulsion applications. In 1998, issues including design, safety and transportation were considered for the MSFC High Performance Antimatter Trap (HiPAT). Radial diffusion and annihilation losses of antiprotons prompted the use of a 4 Tesla superconducting magnet and a 20 KV electrostatic potential at 10(exp -12) Torr pressure. Cryogenic fluids used to maintain a trap temperature of 4K were sized accordingly to provide twenty days of stand-alone storage time (half-life). Procurement of the superconducting magnet with associated cryostat has been completed. The inner, ultra-high vacuum system with electrode structures has been fabricated, tested and delivered to MSFC along with the magnet and cryostat. Assembly of these systems is currently in progress. Testing under high vacuum conditions, using electrons and hydrogen ions will follow in the months ahead.
Semilocal density functional obeying a strongly tightened bound for exchange
Sun, Jianwei; Perdew, John P.; Ruzsinszky, Adrienn
2015-01-01
Because of its useful accuracy and efficiency, density functional theory (DFT) is one of the most widely used electronic structure theories in physics, materials science, and chemistry. Only the exchange-correlation energy is unknown, and needs to be approximated in practice. Exact constraints provide useful information about this functional. The local spin-density approximation (LSDA) was the first constraint-based density functional. The Lieb–Oxford lower bound on the exchange-correlation energy for any density is another constraint that plays an important role in the development of generalized gradient approximations (GGAs) and meta-GGAs. Recently, a strongly and optimally tightened lower bound on the exchange energy was proved for one- and two-electron densities, and conjectured for all densities. In this article, we present a realistic “meta-GGA made very simple” (MGGA-MVS) for exchange that respects this optimal bound, which no previous beyond-LSDA approximation satisfies. This constraint might have been expected to worsen predicted thermochemical properties, but in fact they are improved over those of the Perdew–Burke–Ernzerhof GGA, which has nearly the same correlation part. MVS exchange is however radically different from that of other GGAs and meta-GGAs. Its exchange enhancement factor has a very strong dependence upon the orbital kinetic energy density, which permits accurate energies even with the drastically tightened bound. When this nonempirical MVS meta-GGA is hybridized with 25% of exact exchange, the resulting global hybrid gives excellent predictions for atomization energies, reaction barriers, and weak interactions of molecules. PMID:25561554
Semilocal density functional obeying a strongly tightened bound for exchange.
Sun, Jianwei; Perdew, John P; Ruzsinszky, Adrienn
2015-01-20
Because of its useful accuracy and efficiency, density functional theory (DFT) is one of the most widely used electronic structure theories in physics, materials science, and chemistry. Only the exchange-correlation energy is unknown, and needs to be approximated in practice. Exact constraints provide useful information about this functional. The local spin-density approximation (LSDA) was the first constraint-based density functional. The Lieb-Oxford lower bound on the exchange-correlation energy for any density is another constraint that plays an important role in the development of generalized gradient approximations (GGAs) and meta-GGAs. Recently, a strongly and optimally tightened lower bound on the exchange energy was proved for one- and two-electron densities, and conjectured for all densities. In this article, we present a realistic "meta-GGA made very simple" (MGGA-MVS) for exchange that respects this optimal bound, which no previous beyond-LSDA approximation satisfies. This constraint might have been expected to worsen predicted thermochemical properties, but in fact they are improved over those of the Perdew-Burke-Ernzerhof GGA, which has nearly the same correlation part. MVS exchange is however radically different from that of other GGAs and meta-GGAs. Its exchange enhancement factor has a very strong dependence upon the orbital kinetic energy density, which permits accurate energies even with the drastically tightened bound. When this nonempirical MVS meta-GGA is hybridized with 25% of exact exchange, the resulting global hybrid gives excellent predictions for atomization energies, reaction barriers, and weak interactions of molecules.
Clustering and pasta phases in nuclear density functional theory
Schuetrumpf, Bastian; Zhang, Chunli; Nazarewicz, Witold
2017-05-23
Nuclear density functional theory is the tool of choice in describing properties of complex nuclei and intricate phases of bulk nucleonic matter. It is a microscopic approach based on an energy density functional representing the nuclear interaction. An attractive feature of nuclear DFT is that it can be applied to both finite nuclei and pasta phases appearing in the inner crust of neutron stars. While nuclear pasta clusters in a neutron star can be easily characterized through their density distributions, the level of clustering of nucleons in a nucleus can often be difficult to assess. To this end, we usemore » the concept of nucleon localization. We demonstrate that the localization measure provides us with fingerprints of clusters in light and heavy nuclei, including fissioning systems. Furthermore we investigate the rod-like pasta phase using twist-averaged boundary conditions, which enable calculations in finite volumes accessible by state of the art DFT solvers.« less
Subsystem real-time time dependent density functional theory.
Krishtal, Alisa; Ceresoli, Davide; Pavanello, Michele
2015-04-21
We present the extension of Frozen Density Embedding (FDE) formulation of subsystem Density Functional Theory (DFT) to real-time Time Dependent Density Functional Theory (rt-TDDFT). FDE is a DFT-in-DFT embedding method that allows to partition a larger Kohn-Sham system into a set of smaller, coupled Kohn-Sham systems. Additional to the computational advantage, FDE provides physical insight into the properties of embedded systems and the coupling interactions between them. The extension to rt-TDDFT is done straightforwardly by evolving the Kohn-Sham subsystems in time simultaneously, while updating the embedding potential between the systems at every time step. Two main applications are presented: the explicit excitation energy transfer in real time between subsystems is demonstrated for the case of the Na4 cluster and the effect of the embedding on optical spectra of coupled chromophores. In particular, the importance of including the full dynamic response in the embedding potential is demonstrated.
Subsystem real-time time dependent density functional theory
NASA Astrophysics Data System (ADS)
Krishtal, Alisa; Ceresoli, Davide; Pavanello, Michele
2015-04-01
We present the extension of Frozen Density Embedding (FDE) formulation of subsystem Density Functional Theory (DFT) to real-time Time Dependent Density Functional Theory (rt-TDDFT). FDE is a DFT-in-DFT embedding method that allows to partition a larger Kohn-Sham system into a set of smaller, coupled Kohn-Sham systems. Additional to the computational advantage, FDE provides physical insight into the properties of embedded systems and the coupling interactions between them. The extension to rt-TDDFT is done straightforwardly by evolving the Kohn-Sham subsystems in time simultaneously, while updating the embedding potential between the systems at every time step. Two main applications are presented: the explicit excitation energy transfer in real time between subsystems is demonstrated for the case of the Na4 cluster and the effect of the embedding on optical spectra of coupled chromophores. In particular, the importance of including the full dynamic response in the embedding potential is demonstrated.
Probability density functions of instantaneous Stokes parameters on weak scattering
NASA Astrophysics Data System (ADS)
Chen, Xi; Korotkova, Olga
2017-10-01
The single-point probability density functions (PDF) of the instantaneous Stokes parameters of a polarized plane-wave light field scattered from a three-dimensional, statistically stationary, weak medium with Gaussian statistics and Gaussian correlation function have been studied for the first time. Apart from the scattering geometry the PDF distributions of the scattered light have been related to the illumination's polarization state and the correlation properties of the medium.
Plasma density fluctuations observed during Space Shuttle Orbiter water releases
NASA Technical Reports Server (NTRS)
Pickett, J. S.; D'Angelo, N.; Kurth, W. S.
1989-01-01
Observations by the Langmuir probe on the Plasma Diagnostics Package flown as part of the Spacelab 2 mission in the summer of 1985 show a strong increase in the level of turbulence near the Shuttle Orbiter during operations in which liquid water is released. The spectrum of the plasma density fluctuations peaks at the lowest frequencies measured (a few Hz) and extends up to a few kHz, near the lower hybrid frequency. Two potential mechanisms for generating the plasma turbulence are suggested which are both based on the production of water ions as a result of charge exchange with the ambient oxygen ions in the ionosphere. The first mechanism proposed is the ion-plasma instability which arises from the drift of the contaminant with respect to the ambient oxygen ions. The other mechanism proposed is the Ott-Farley instability, which is a result of the ring distribution formed by the 'pick-up' water ions.
Garcia-Aldea, David; Alvarellos, J. E.
2007-11-15
We study two families of approximate nonlocal kinetic-energy functionals that include a full von Weizsaecker functional, and that have nonlocal terms with the mathematical structure of the Thomas-Fermi functional. The functionals recover the exact kinetic energy and the linear response function of a homogeneous electron system. The first family is a generalization of a successful previous nonlocal functional. The second family is proposed in the paper, and is designed to obtain functionals suitable for use in both localized and extended systems. Furthermore, this family has been designed to be evaluated by a single integration in momentum space when a constant reference density is used. The atomic total kinetic energies are in good agreement with the exact calculations. The kinetic-energy density corresponding to each functional has been assessed to control its quality. The results show that, in general, these functionals behave better than both the Thomas-Fermi and all semilocal generalized gradient approximation functionals when describing the kinetic-energy density of atoms, providing a better description of the nonlocal effects of the kinetic energy of electron systems.
Angular Momentum Dependent Orbital Free Density Functional Theory
NASA Astrophysics Data System (ADS)
Ke, Youqi; Libisch, Florian; Xia, Junchao; Wang, Lin-Wang; Carter, Emily A.
2013-03-01
We report a novel and general formalism for linear scaling, angular momentum dependent (AMD) orbital free (OF) density functional theory (DFT) to advance the accuracy and applicability of OFDFT. To introduce angular momentum dependence in OFDFT, we devise a hybrid scheme by partitioning the system into muffin-tin spheres and an interstitial region: the electron density inside the spheres is expressed by a set of Kohn-Sham (KS) DFT derived atom-centered basis functions combined with an on-site density matrix NR. A general OFDFT total energy functional is introduced with a crucial nonlocal energy term ENL which is neglected in conventional implementations of OFDFT. ENL corrects the errors due to the use of approximate kinetic energy density functionals and local pseudopotentials for ion-electron interactions. We approximate ENL to include AMD contributions inside the spheres: as a first step, a linear dependence on the NR is considered with a set of AMD energies ERl.ERlare determined by fitting a small set of bulk properties to KSDFT. We find AMD-OFDFT offers substantial improvements over conventional OFDFT, as we show for various properties of the transition metal Ti and its alloys (TixAl1-x) .
Is Density Functional Theory adequate for quantum transport?
NASA Astrophysics Data System (ADS)
Burke, Kieron
2007-03-01
Density functional calculations for the electronic conductance of single molecules attached to leads are now common. I'll examine the methodology from a rigorous point of view, discussing where it can be expected to work, and where it should fail. When molecules are weakly coupled to leads, local and gradient-corrected approximations fail, as the Kohn-Sham levels are misaligned. In the weak bias regime, XC corrections to the current are missed by the standard methodology. Finally, I will compare and contrast several new methodologies that go beyond the present standard approach of applying the Landauer formula to ground-state DFT. Self-interaction errors in density functional calculations of electronictransport, C. Toher, A. Filippetti, S. Sanvito, and K. Burke, Phys. Rev. Lett. 95, 146402 (2005) The Dramatic Role of the Exchange-Correlation Potential in ab initio Electron Transport Calculations, S-H. Ke, H.U. Baranger, and W. Yang, cond-mat/0609367. Zero-bias molecular electronics: Exchange-correlation corrections to Landauer's formula, M. Koentopp, K. Burke, and F. Evers, Phys. Rev. B Rapid Comm., 73, 121403 (2006). Density Functional Theory of the Electrical Conductivity of Molecular Devices, K. Burke, Roberto Car, and Ralph Gebauer, Phys. Rev. Lett. 94, 146803 (2005). Density functional calculations of nanoscale conductance, Connie Chang, Max Koentopp, Kieron Burke, and Roberto Car, in prep.
Implementation Strategies for Orbital-dependent Density Functionals
NASA Astrophysics Data System (ADS)
Bento, Marsal E.; Vieira, Daniel
2016-12-01
The development of density functional theory (DFT) has been focused primarily on two main pillars: (1) the pursuit of more accurate exchange-correlation (XC) density functionals; (2) the feasibility of computational implementation when dealing with many-body systems. In this context, this work is aimed on using one-dimensional quantum systems as theoretical laboratories to investigate the implementation of orbital functionals (OFs) of density. By definition, OFs are those which depend only implicitly on the density, via an explicit formulation in terms of Kohn-Sham orbitals. Typical examples are the XC functionals arising from the Perdew-Zunger self-interaction correction (PZSIC). Formally, via Kohn-Sham equations, the implementation of OFs must be performed by means of the optimized effective potential method (OEP), which is known by requiring an excessive computational effort even when dealing with few electrons systems. Here, we proceed a systematical investigation aiming to simplify or avoid the OEP procedure, taking as reference the implementation of the PZSIC correction applied to one-dimensional Hubbard chains.
Density functional theory is straying from the path toward the exact functional.
Medvedev, Michael G; Bushmarinov, Ivan S; Sun, Jianwei; Perdew, John P; Lyssenko, Konstantin A
2017-01-06
The theorems at the core of density functional theory (DFT) state that the energy of a many-electron system in its ground state is fully defined by its electron density distribution. This connection is made via the exact functional for the energy, which minimizes at the exact density. For years, DFT development focused on energies, implicitly assuming that functionals producing better energies become better approximations of the exact functional. We examined the other side of the coin: the energy-minimizing electron densities for atomic species, as produced by 128 historical and modern DFT functionals. We found that these densities became closer to the exact ones, reflecting theoretical advances, until the early 2000s, when this trend was reversed by unconstrained functionals sacrificing physical rigor for the flexibility of empirical fitting.
2017-01-01
Recently, exchange-correlation potentials in density functional theory were developed with the goal of providing improved band gaps in solids. Among them, the semilocal potentials are particularly interesting for large systems since they lead to calculations that are much faster than with hybrid functionals or methods like GW. We present an exhaustive comparison of semilocal exchange-correlation potentials for band gap calculations on a large test set of solids, and particular attention is paid to the potential HLE16 proposed by Verma and Truhlar. It is shown that the most accurate potential is the modified Becke–Johnson potential, which, most noticeably, is much more accurate than all other semilocal potentials for strongly correlated systems. This can be attributed to its additional dependence on the kinetic energy density. It is also shown that the modified Becke–Johnson potential is at least as accurate as the hybrid functionals and more reliable for solids with large band gaps. PMID:28402113
Tran, Fabien; Blaha, Peter
2017-05-04
Recently, exchange-correlation potentials in density functional theory were developed with the goal of providing improved band gaps in solids. Among them, the semilocal potentials are particularly interesting for large systems since they lead to calculations that are much faster than with hybrid functionals or methods like GW. We present an exhaustive comparison of semilocal exchange-correlation potentials for band gap calculations on a large test set of solids, and particular attention is paid to the potential HLE16 proposed by Verma and Truhlar. It is shown that the most accurate potential is the modified Becke-Johnson potential, which, most noticeably, is much more accurate than all other semilocal potentials for strongly correlated systems. This can be attributed to its additional dependence on the kinetic energy density. It is also shown that the modified Becke-Johnson potential is at least as accurate as the hybrid functionals and more reliable for solids with large band gaps.
Seo, Dong-Kyun; Weng, Chang'e
2008-08-21
We present how the kinetic energy density (KED) can be interpreted on the basis of the orbital interactions within the Kohn-Sham theory and propose how to utilize a direct space function in chemical bonding analysis, the relative entropy density (RED), which is constructed from the KED, the Thomas-Fermi KED (TF-KED), and the electron density. From the detailed analysis of the KED of wave functions and the TF-KED from the free electron model, it is shown that the RED can reveal the nodal properties of individual wave functions and provide a variationally meaningful way of accumulating chemical bonding information from the wave functions, hence allowing quantitative bonding analysis in direct space. To substantiate the proposal, the RED function has been tested on the tetrahedral network solids, including the group 14 elements and the III-V binary compounds with the zinc blende structure. The direct space maps of the RED quantitatively reflect the trend in metallicity and the polarity of their two-center, two-electron bonds in terms of the absolute values of the RED, the location of the minimum values, and the behavior of the deformation from the spherical symmetry of the atomic RED.
Gonis, A.; Zhang, X. G.; Stocks, G. M.; Nicholson, D. M.
2015-10-23
Density functional theory for the case of general, N-representable densities is reformulated in terms of density functional derivatives of expectation values of operators evaluated with wave functions leading to a density, making no reference to the concept of potential. The developments provide a complete solution of the v-representability problem by establishing a mathematical procedure that determines whether a density is v-representable and in the case of an affirmative answer determines the potential (within an additive constant) as a derivative with respect to the density of a constrained search functional. It also establishes the existence of an energy functional of the density that, for v-representable densities, assumes its minimum value at the density describing the ground state of an interacting many-particle system. The theorems of Hohenberg and Kohn emerge as special cases of the formalism.
Gonis, A.; Zhang, X. G.; Stocks, G. M.; ...
2015-10-23
Density functional theory for the case of general, N-representable densities is reformulated in terms of density functional derivatives of expectation values of operators evaluated with wave functions leading to a density, making no reference to the concept of potential. The developments provide a complete solution of the v-representability problem by establishing a mathematical procedure that determines whether a density is v-representable and in the case of an affirmative answer determines the potential (within an additive constant) as a derivative with respect to the density of a constrained search functional. It also establishes the existence of an energy functional of themore » density that, for v-representable densities, assumes its minimum value at the density describing the ground state of an interacting many-particle system. The theorems of Hohenberg and Kohn emerge as special cases of the formalism.« less
Density functional theory modeling of multilayer "epitaxial" graphene oxide.
Zhou, Si; Bongiorno, Angelo
2014-11-18
CONSPECTUS: Graphene oxide (GO) is a complex material of both fundamental and applied interest. Elucidating the structure of GO is crucial to achieve control over its properties and technological applications. GO is a nonstoichiometric and hygroscopic material with a lamellar structure, and its physical chemical properties depend critically on synthesis procedures and postsynthesis treatments. Numerous efforts are in place to both understand and exploit this versatile layered carbon material. This Account reports on recent density functional theory (DFT) studies of "epitaxial" graphene oxide (hereafter EGO), a type of GO obtained by oxidation of graphene films grown epitaxially on silicon carbide. Here, we rely on selected X-ray photoelectron spectroscopy (XPS), infrared spectroscopy (IR), and X-ray diffraction (XRD) measurements of EGO, and we discuss in great detail how we utilized DFT-based techniques to project out from the experimental data basic atomistic information about the chemistry and structure of these films. This Account provides an example as to how DFT modeling can be used to elucidate complex materials such as GO from a limited set of experimental information. EGO exhibits a uniform layered structure, consisting of a stack of graphene planes hosting predominantly epoxide and hydroxyl groups, and water molecules intercalated between the oxidized carbon layers. Here, we first focus on XPS measurements of EGO, and we use DFT to generate realistic model structures, calculate core-level chemical shifts, and through the comparison with experiment, gain insight on the chemical composition and metastability characteristics of EGO. DFT calculations are then used to devise a simplistic but accurate simulation scheme to study thermodynamic and kinetic stability and to predict the intralayer structure of EGO films aged at room temperature. Our simulations show that aged EGO encompasses layers with nanosized oxidized domains presenting a high concentration of
NASA Astrophysics Data System (ADS)
Manteuffel, V. Mark; Eiblmaier, Martin
2008-05-01
To investigate the role of competitor density in influencing space use patterns of juvenile striped plateau lizards ( Sceloporus virgatus), a density manipulation experiment was conducted within large (800 m 2) field enclosures treated with low (20) and high (60) densities of hatchlings. Enclosures were monitored for 10 months, after which the experiment was replicated. Home range and core area sizes after release of lizards and initial establishment in the fall were significantly reduced in the high-density treatments; fall home range shape, measured as the perimeter-to-area ratio, was significantly reduced in low-density treatments; no significant differences were detected between treatments in core area shape or overlap. During the spring/early summer activity season after the lizard's first winter, no significant differences between density treatments were detected for any of these variables, as enclosure densities had converged between treatments. Individuals in high-density enclosures had increased their space use as competitor density had declined. These results illustrate that competitor density has significant influence on space use by juvenile lizards.
Density Functional Study of Perovskite Superconductor MgCNi3
NASA Astrophysics Data System (ADS)
Kumar, Jagdish; Sharma, Devina; Kumar, Ranjan; Awana, V. P. S.; Ahluwalia, P. K.
2011-12-01
We here report the first principle density functional study of MgCNi3 which crystallize in cubic perovskite structure having critical transition temperature of 8 K. The interesting aspect of this compound is that in normal state it is non magnetic in nature despite conduction electrons in it are derived from partially filled Ni d states, which typically lead to ferromagnetism in metallic Ni and many Ni-based binary alloys. To investigate the detailed microscopic origin of the non magnetic nature we have done density functional based calculations on this compound. The lattice constant is calculated using minimum energy criteria from total energy versus lattice constant plot. By taking the calculated values of lattice constant we have done the precise calculations on the compound using Full Potential Linear Augmented Plane Wave (FP-LAPW) method implemented in ELK code. The electronic density of states is found spin degenerate that corresponds to a non-magnetic ground state. The density of states (DOS) at Fermi level, N(EF) is dominated by Ni-d states. The sharp peak observed just below Fermi level corresponds to van Hove singularity (vHs). The projected density of states (PDOS) suggests a strong hybridization of Ni-3d and C-2p states which is responsible for the observed non magnetic nature of MgCNi3.
Medvedev, Michael G; Bushmarinov, Ivan S; Sun, Jianwei; Perdew, John P; Lyssenko, Konstantin A
2017-05-05
Kepp argues in his Comment, among other concerns, that the atomic densities we have considered are not relevant to molecular bonding. However, this does not change the main conclusion of our study, that unconstrained fitting of flexible functional forms can make a density functional more interpolative but less widely predictive. Copyright © 2017, American Association for the Advancement of Science.
Gillet, Natacha; Berstis, Laura; Wu, Xiaojing; Gajdos, Fruzsina; Heck, Alexander; de la Lande, Aurélien; Blumberger, Jochen; Elstner, Marcus
2016-09-09
In this paper, four methods to calculate charge transfer integrals in the context of bridge-mediated electron transfer are tested. These methods are based on density functional theory (DFT). We consider two perturbative Green's function effective Hamiltonian methods (first, at the DFT level of theory, using localized molecular orbitals; second, applying a tight-binding DFT approach, using fragment orbitals) and two constrained DFT implementations with either plane-wave or local basis sets. To assess the performance of the methods for through-bond (TB)-dominated or through-space (TS)-dominated transfer, different sets of molecules are considered. For through-bond electron transfer (ET), several molecules that were originally synthesized by Paddon-Row and co-workers for the deduction of electronic coupling values from photoemission and electron transmission spectroscopies, are analyzed. The tested methodologies prove to be successful in reproducing experimental data, the exponential distance decay constant and the superbridge effects arising from interference among ET pathways. For through-space ET, dedicated p-stacked systems with heterocyclopentadiene molecules were created and analyzed on the basis of electronic coupling dependence on donor-acceptor distance, structure of the bridge, and ET barrier height. The inexpensive fragment-orbital density functional tight binding (FODFTB) method gives similar results to constrained density functional theory (CDFT) and both reproduce the expected exponential decay of the coupling with donor-acceptor distances and the number of bridging units. Finally, these four approaches appear to give reliable results for both TB and TS ET and present a good alternative to expensive ab initio methodologies for large systems involving long-range charge transfers.
Gillet, Natacha; Berstis, Laura; Wu, Xiaojing; ...
2016-09-09
In this paper, four methods to calculate charge transfer integrals in the context of bridge-mediated electron transfer are tested. These methods are based on density functional theory (DFT). We consider two perturbative Green's function effective Hamiltonian methods (first, at the DFT level of theory, using localized molecular orbitals; second, applying a tight-binding DFT approach, using fragment orbitals) and two constrained DFT implementations with either plane-wave or local basis sets. To assess the performance of the methods for through-bond (TB)-dominated or through-space (TS)-dominated transfer, different sets of molecules are considered. For through-bond electron transfer (ET), several molecules that were originally synthesizedmore » by Paddon-Row and co-workers for the deduction of electronic coupling values from photoemission and electron transmission spectroscopies, are analyzed. The tested methodologies prove to be successful in reproducing experimental data, the exponential distance decay constant and the superbridge effects arising from interference among ET pathways. For through-space ET, dedicated p-stacked systems with heterocyclopentadiene molecules were created and analyzed on the basis of electronic coupling dependence on donor-acceptor distance, structure of the bridge, and ET barrier height. The inexpensive fragment-orbital density functional tight binding (FODFTB) method gives similar results to constrained density functional theory (CDFT) and both reproduce the expected exponential decay of the coupling with donor-acceptor distances and the number of bridging units. Finally, these four approaches appear to give reliable results for both TB and TS ET and present a good alternative to expensive ab initio methodologies for large systems involving long-range charge transfers.« less
Gillet, Natacha; Berstis, Laura; Wu, Xiaojing; Gajdos, Fruzsina; Heck, Alexander; de la Lande, Aurélien; Blumberger, Jochen; Elstner, Marcus
2016-09-09
In this paper, four methods to calculate charge transfer integrals in the context of bridge-mediated electron transfer are tested. These methods are based on density functional theory (DFT). We consider two perturbative Green's function effective Hamiltonian methods (first, at the DFT level of theory, using localized molecular orbitals; second, applying a tight-binding DFT approach, using fragment orbitals) and two constrained DFT implementations with either plane-wave or local basis sets. To assess the performance of the methods for through-bond (TB)-dominated or through-space (TS)-dominated transfer, different sets of molecules are considered. For through-bond electron transfer (ET), several molecules that were originally synthesized by Paddon-Row and co-workers for the deduction of electronic coupling values from photoemission and electron transmission spectroscopies, are analyzed. The tested methodologies prove to be successful in reproducing experimental data, the exponential distance decay constant and the superbridge effects arising from interference among ET pathways. For through-space ET, dedicated p-stacked systems with heterocyclopentadiene molecules were created and analyzed on the basis of electronic coupling dependence on donor-acceptor distance, structure of the bridge, and ET barrier height. The inexpensive fragment-orbital density functional tight binding (FODFTB) method gives similar results to constrained density functional theory (CDFT) and both reproduce the expected exponential decay of the coupling with donor-acceptor distances and the number of bridging units. Finally, these four approaches appear to give reliable results for both TB and TS ET and present a good alternative to expensive ab initio methodologies for large systems involving long-range charge transfers.
Gillet, Natacha; Berstis, Laura; Wu, Xiaojing; Gajdos, Fruzsina; Heck, Alexander; de la Lande, Aurélien; Blumberger, Jochen; Elstner, Marcus
2016-10-11
In this article, four methods to calculate charge transfer integrals in the context of bridge-mediated electron transfer are tested. These methods are based on density functional theory (DFT). We consider two perturbative Green's function effective Hamiltonian methods (first, at the DFT level of theory, using localized molecular orbitals; second, applying a tight-binding DFT approach, using fragment orbitals) and two constrained DFT implementations with either plane-wave or local basis sets. To assess the performance of the methods for through-bond (TB)-dominated or through-space (TS)-dominated transfer, different sets of molecules are considered. For through-bond electron transfer (ET), several molecules that were originally synthesized by Paddon-Row and co-workers for the deduction of electronic coupling values from photoemission and electron transmission spectroscopies, are analyzed. The tested methodologies prove to be successful in reproducing experimental data, the exponential distance decay constant and the superbridge effects arising from interference among ET pathways. For through-space ET, dedicated π-stacked systems with heterocyclopentadiene molecules were created and analyzed on the basis of electronic coupling dependence on donor-acceptor distance, structure of the bridge, and ET barrier height. The inexpensive fragment-orbital density functional tight binding (FODFTB) method gives similar results to constrained density functional theory (CDFT) and both reproduce the expected exponential decay of the coupling with donor-acceptor distances and the number of bridging units. These four approaches appear to give reliable results for both TB and TS ET and present a good alternative to expensive ab initio methodologies for large systems involving long-range charge transfers.
g_permute: Permutation-reduced phase space density compaction
NASA Astrophysics Data System (ADS)
Reinhard, F.; Lange, O. F.; Hub, J. S.; Haas, J.; Grubmüller, H.
2009-03-01
Biomolecular processes are governed by free energy changes and thus depend on a fine-tuned interplay between entropy and enthalpy. To calculate accurate values for entropies from simulations is particularly challenging for the solvation shell of proteins, which contributes crucially to the total entropy of solvated proteins, due to the diffusive motion of the solvent molecules. Accordingly, for each frame of a Molecular dynamics (MD) trajectory, our software relabels the solvent molecules, such that the resulting configuration space volume is reduced by a factor of N! with N being the number of solvent molecules. The combinatorial explosion of a naive implementation is here overcome by transforming the task into a linear assignment problem, for which algorithms with complexity O(N) exist. We have shown in previous research that the solvent entropy can be estimated from such a compacted trajectory by established entropy estimation methods. In this paper, we describe the software implementation which also allows applications beyond entropy estimation, such as the permutation of lipids in membrane bilayers. Program summaryProgram title: g_permute Catalogue identifier: AECJ_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AECJ_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GPL No. of lines in distributed program, including test data, etc.: 45 173 No. of bytes in distributed program, including test data, etc.: 2 730 678 Distribution format: tar.gz Programming language: C Computer: PC-compatible running Linux Operating system: Linux RAM: Dependent on the number of solvent molecules, min 12 582 912 bytes Classification: 3, 4.8, 4.9 External routines: liblap (included); From GROMACS-3.3.1: libgmx (not included) Nature of problem: Estimating the entropy of solvent molecules from a molecular dynamics simulation trajectory cannot be performed on ordinary trajectories. Solution method: Compacting
Lei, Youming; Zheng, Fan
2016-12-01
Stochastic chaos induced by diffusion processes, with identical spectral density but different probability density functions (PDFs), is investigated in selected lightly damped Hamiltonian systems. The threshold amplitude of diffusion processes for the onset of chaos is derived by using the stochastic Melnikov method together with a mean-square criterion. Two quasi-Hamiltonian systems, namely, a damped single pendulum and damped Duffing oscillator perturbed by stochastic excitations, are used as illustrative examples. Four different cases of stochastic processes are taking as the driving excitations. It is shown that in such two systems the spectral density of diffusion processes completely determines the threshold amplitude for chaos, regardless of the shape of their PDFs, Gaussian or otherwise. Furthermore, the mean top Lyapunov exponent is employed to verify analytical results. The results obtained by numerical simulations are in accordance with the analytical results. This demonstrates that the stochastic Melnikov method is effective in predicting the onset of chaos in the quasi-Hamiltonian systems.
Numerical Density-to-Potential Inversions in Time-dependent Density Functional Theory
NASA Astrophysics Data System (ADS)
Jensen, Daniel; Inchaustegui, Jean Pierre; Wasserman, Adam
2014-03-01
Time-dependent Density Functional Theory (TDDFT) is a formally exact method for solving the quantum many-body problem. In Kohn-Sham TDDFT, a fictitious noninteracting system is defined that exactly reproduces the time-dependent density of the interacting system. The potential that determines this noninteracting system (the time-dependent Kohn-Sham potential) has been proven to exist under certain restrictions, but finding the exact Kohn-Sham potential for a given density remains challenging. We show that this ill-posed inverse problem requires some form of regularization to produce realistic Kohn-Sham potentials. We explore various forms of regularization and illustrate how they work on simple one-dimensional model systems. We also show how our method can be applied to problems with both particle-in-a-box and periodic boundary conditions subject to oscillating electric fields.
NASA Astrophysics Data System (ADS)
Lei, Youming; Zheng, Fan
2016-12-01
Stochastic chaos induced by diffusion processes, with identical spectral density but different probability density functions (PDFs), is investigated in selected lightly damped Hamiltonian systems. The threshold amplitude of diffusion processes for the onset of chaos is derived by using the stochastic Melnikov method together with a mean-square criterion. Two quasi-Hamiltonian systems, namely, a damped single pendulum and damped Duffing oscillator perturbed by stochastic excitations, are used as illustrative examples. Four different cases of stochastic processes are taking as the driving excitations. It is shown that in such two systems the spectral density of diffusion processes completely determines the threshold amplitude for chaos, regardless of the shape of their PDFs, Gaussian or otherwise. Furthermore, the mean top Lyapunov exponent is employed to verify analytical results. The results obtained by numerical simulations are in accordance with the analytical results. This demonstrates that the stochastic Melnikov method is effective in predicting the onset of chaos in the quasi-Hamiltonian systems.
A Scalable Implementation of Van der Waals Density Functionals
NASA Astrophysics Data System (ADS)
Wu, Jun; Gygi, Francois
2010-03-01
Recently developed Van der Waals density functionals[1] offer the promise to account for weak intermolecular interactions that are not described accurately by local exchange-correlation density functionals. In spite of recent progress [2], the computational cost of such calculations remains high. We present a scalable parallel implementation of the functional proposed by Dion et al.[1]. The method is implemented in the Qbox first-principles simulation code (http://eslab.ucdavis.edu/software/qbox). Application to large molecular systems will be presented. [4pt] [1] M. Dion et al. Phys. Rev. Lett. 92, 246401 (2004).[0pt] [2] G. Roman-Perez and J. M. Soler, Phys. Rev. Lett. 103, 096102 (2009).
Simple spin correction of unrestricted density-functional calculation
NASA Astrophysics Data System (ADS)
Ovchinnikov, Alexander A.; Labanowski, Jan K.
1996-06-01
The unrestricted Hartree-Fock and unrestricted Kohn-Sham calculations generally result in spin-contaminated solutions. Moreover, the energies from these calculations cannot be directly compared with the results of corresponding restricted calculations since the latter yield higher energies due to restrictions imposed on the form of the wave function. We present here a simple method of correcting the mixed spin energies resulting from unrestricted Hartree-Fock or density-functional theory calculations and removing the foreign spin components. The method allows for elimination of higher-multiplet components from the given mixed spin state solution by performing unrestricted calculations at the same fixed geometry for the higher multiplets and the state under consideration. The performance of the method is illustrated with several examples of density-functional calculations of radical species. The current method is also variational in nature and can be further extended in a self-consistent field fashion.
Generalized nuclear Fukui functions in the framework of spin-polarized density-functional theory
Chamorro, E.; Proft, F. de; Geerlings, P.
2005-08-22
An extension of Cohen's nuclear Fukui function is presented in the spin-polarized framework of density-functional theory (SP-DFT). The resulting new nuclear Fukui function indices {phi}{sub N{alpha}} and {phi}{sub S{alpha}} are intended to be the natural descriptors for the responses of the nuclei to changes involving charge transfer at constant multiplicity and also the spin polarization at constant number of electrons. These generalized quantities allow us to gain new insights within a perturbative scheme based on DFT. Calculations of the electronic and nuclear SP-DFT quantities are presented within a Kohn-Sham framework of chemical reactivity for a sample of molecules, including H{sub 2}O, H{sub 2}CO, and some simple nitrenes (NX) and phosphinidenes (PX), with X=H, Li, F, Cl, OH, SH, NH{sub 2}, and PH{sub 2}. Results have been interpreted in terms of chemical bonding in the context of Berlin's theorem, which provides a separation of the molecular space into binding and antibinding regions.
Efficient Computation of Exchange Energy Density with Gaussian Basis Functions.
Liu, Fenglai; Kong, Jing
2017-06-13
Density functional theory (DFT) is widely applied in chemistry and physics. Still it fails to correctly predict quantitatively or even qualitatively for systems with significant nondynamic correlation. Several DFT functionals were proposed in recent years to treat the nondynamic correlation, most of which added the exact exchange energy density as a new variable. This quantity, calculated as Hartree-Fock (HF) exchange energy density, is the computational bottleneck for calculations with these new functionals. We present an implementation of an efficient seminumerical algorithm in this paper as a solution for this computational bottleneck. The method scales quadratically with respect to the molecular size and the basis set size. The scheme, exact for the purpose of computing the HF exchange energy density, is favored for medium-sized basis sets and can be competitive even for large basis sets with efficient grids when compared with our previous approximate resolution-of-identity scheme. It can also be used as a seminumerical integration scheme to compute the HF exchange energy and matrix on a standard atom-centered grid. Calculations on a series of alanine peptides show that for large basis sets the seminumerical scheme becomes competitive to the conventional analytical method and can be about six times faster for aug-cc-pvtz basis. The practicality of the algorithm is demonstrated through a local hybrid self-consistent calculation of the acenes-20 molecule.
Relations among several nuclear and electronic density functional reactivity indexes
NASA Astrophysics Data System (ADS)
Torrent-Sucarrat, Miquel; Luis, Josep M.; Duran, Miquel; Toro-Labbé, Alejandro; Solà, Miquel
2003-11-01
An expansion of the energy functional in terms of the total number of electrons and the normal coordinates within the canonical ensemble is presented. A comparison of this expansion with the expansion of the energy in terms of the total number of electrons and the external potential leads to new relations among common density functional reactivity descriptors. The formulas obtained provide explicit links between important quantities related to the chemical reactivity of a system. In particular, the relation between the nuclear and the electronic Fukui functions is recovered. The connection between the derivatives of the electronic energy and the nuclear repulsion energy with respect to the external potential offers a proof for the "Quantum Chemical le Chatelier Principle." Finally, the nuclear linear response function is defined and the relation of this function with the electronic linear response function is given.
Functional renormalization group in Floquet space
NASA Astrophysics Data System (ADS)
Eissing, Anna Katharina; Meden, Volker; Kennes, Dante Marvin
2016-12-01
We present an extension of the functional renormalization group to Floquet space, which enables us to treat the long time behavior of interacting time periodically driven quantum dots. It is one of its strength that the method is neither bound to small driving amplitudes nor to small driving frequencies, i.e., very general time periodic signals can be considered. It is applied to the interacting resonant level model, a prototype model of a spinless, fermionic quantum dot. The renormalization in several setups with different combinations of time periodic parameters is studied, where the numerical results are complemented by analytic expressions for the renormalization in the limit of small driving amplitude. We show how the driving frequency acts as an infrared cutoff of the underlying renormalization group flow which manifests in novel power laws. We utilize the tunability of the effective reservoir distribution function in a periodically driven onsite energy setup to show how its shape is directly reflected in the renormalization group flow. This allows us to flexibly tune the power-law renormalization generically encountered in quantum dot structures. Finally, an in-phase quantum pump as well as a single parameter pump are investigated in the whole regime of driving frequency, demonstrating that the new power law in the driving frequency is reflected in the mean current of the latter.
Multiphase aluminum equations of state via density functional theory
NASA Astrophysics Data System (ADS)
Sjostrom, Travis; Crockett, Scott; Rudin, Sven
2016-10-01
We have performed density functional theory (DFT) based calculations for aluminum in extreme conditions of both pressure and temperature, up to five times compressed ambient density, and over 1 000 000 K in temperature. In order to cover such a domain, DFT methods including phonon calculations, quantum molecular dynamics, and orbital-free DFT are employed. The results are then used to construct a SESAME equation of state for the aluminum 1100 alloy, encompassing the fcc, hcp, and bcc solid phases as well as the liquid regime. We provide extensive comparison with experiment, and based on this we also provide a slightly modified equation of state for the aluminum 6061 alloy.
Prediction of Dislocation Cores in Aluminum from Density Functional Theory
NASA Astrophysics Data System (ADS)
Woodward, C.; Trinkle, D. R.; Hector, L. G., Jr.; Olmsted, D. L.
2008-02-01
The strain field of isolated screw and edge dislocation cores in aluminum are calculated using density-functional theory and a flexible boundary condition method. Nye tensor density contours and differential displacement fields are used to accurately bound Shockley partial separation distances. Our results of 5 7.5 Å (screw) and 7.0 9.5 Å (edge) eliminate uncertainties resulting from the wide range of previous results based on Peierls-Nabarro and atomistic methods. Favorable agreement of the predicted cores with limited experimental measurements demonstrates the need for quantum mechanical treatment of dislocation cores.
Perspective: Fundamental aspects of time-dependent density functional theory
NASA Astrophysics Data System (ADS)
Maitra, Neepa T.
2016-06-01
In the thirty-two years since the birth of the foundational theorems, time-dependent density functional theory has had a tremendous impact on calculations of electronic spectra and dynamics in chemistry, biology, solid-state physics, and materials science. Alongside the wide-ranging applications, there has been much progress in understanding fundamental aspects of the functionals and the theory itself. This Perspective looks back to some of these developments, reports on some recent progress and current challenges for functionals, and speculates on future directions to improve the accuracy of approximations used in this relatively young theory.
Perspective: Fundamental aspects of time-dependent density functional theory.
Maitra, Neepa T
2016-06-14
In the thirty-two years since the birth of the foundational theorems, time-dependent density functional theory has had a tremendous impact on calculations of electronic spectra and dynamics in chemistry, biology, solid-state physics, and materials science. Alongside the wide-ranging applications, there has been much progress in understanding fundamental aspects of the functionals and the theory itself. This Perspective looks back to some of these developments, reports on some recent progress and current challenges for functionals, and speculates on future directions to improve the accuracy of approximations used in this relatively young theory.
Dispersion corrections to density functionals for water aromatic interactions.
Zimmerli, Urs; Parrinello, Michele; Koumoutsakos, Petros
2004-02-08
We investigate recently published methods for extending density functional theory to the description of long-range dispersive interactions. In all schemes an empirical correction consisting of a C6r(-6) term is introduced that is damped at short range. The coefficient C6 is calculated either from average molecular or atomic polarizabilities. We calculate geometry-dependent interaction energy profiles for the water benzene cluster and compare the results with second-order Møller-Plesset calculations. Our results indicate that the use of the B3LYP functional in combination with an appropriate mixing rule and damping function is recommended for the interaction of water with aromatics.
Density differences for near-Hartree-Fock atomic wave functions
NASA Astrophysics Data System (ADS)
Schmider, Hartmut; Sagar, Robin P.; Smith, Vedene H., Jr.
1994-05-01
The widely used near-Hartree-Fock functions of Clementi and Roetti [At. Data Nucl. Data Tables 14, 177 (1974)] are compared with the newer functions of Bunge et al. [At. Data Nucl. Tables 53, 113 (1993)] by means of different measures of functional distance on the charge density ρ for the atoms He to Xe. The results are correlated with the energy improvement, and an empriical relation between the linear deviation in the first derivative of ρ and the total energy is reported.
Ab initio derivation of model energy density functionals
NASA Astrophysics Data System (ADS)
Dobaczewski, Jacek
2016-08-01
I propose a simple and manageable method that allows for deriving coupling constants of model energy density functionals (EDFs) directly from ab initio calculations performed for finite fermion systems. A proof-of-principle application allows for linking properties of finite nuclei, determined by using the nuclear nonlocal Gogny functional, to the coupling constants of the quasilocal Skyrme functional. The method does not rely on properties of infinite fermion systems but on the ab initio calculations in finite systems. It also allows for quantifying merits of different model EDFs in describing the ab initio results.
Laplacian-level density functionals for the kinetic energy density and exchange-correlation energy
NASA Astrophysics Data System (ADS)
Perdew, John P.; Constantin, Lucian A.
2007-04-01
We construct a Laplacian-level meta-generalized-gradient-approximation (meta-GGA) for the noninteracting (Kohn-Sham orbital) positive kinetic energy density τ of an electronic ground state of density n . This meta-GGA is designed to recover the fourth-order gradient expansion τGE4 in the appropriate slowly varying limit and the von Weizsäcker expression τW=∣∇n∣2/(8n) in the rapidly varying limit. It is constrained to satisfy the rigorous lower bound τW(r)⩽τ(r) . Our meta-GGA is typically a strong improvement over the gradient expansion of τ for atoms, spherical jellium clusters, jellium surfaces, the Airy gas, Hooke’s atom, one-electron Gaussian density, quasi-two-dimensional electron gas, and nonuniformly scaled hydrogen atom. We also construct a Laplacian-level meta-GGA for exchange and correlation by employing our approximate τ in the Tao-Perdew-Staroverov-Scuseria (TPSS) meta-GGA density functional. The Laplacian-level TPSS gives almost the same exchange-correlation enhancement factors and energies as the full TPSS, suggesting that τ and ∇2n carry about the same information beyond that carried by n and ∇n . Our kinetic energy density integrates to an orbital-free kinetic energy functional that is about as accurate as the fourth-order gradient expansion for many real densities (with noticeable improvement in molecular atomization energies), but considerably more accurate for rapidly varying ones.
NASA Astrophysics Data System (ADS)
Zare, Saeed; Alizadeh, M. Mahdi; Schuh, Harald
2017-04-01
Ionosphere is a layer of the upper atmosphere, between the thermosphere and the exosphere, distinguished because it is ionized by solar radiation. As an important part of human living environment, ionosphere affects our modern society in many ways. International broadcasters use this medium to reflect radio signals back toward the Earth. Ionosphere provides long range capabilities for commercial ship-to-shore communications, for trans-oceanic aircraft links, and for military communication and surveillance systems. Space geodetic techniques have turned into a capable tool for studying the ionosphere in the last decades. Up to now, two dimensional (2-D) models of vertical TEC (VTEC) have been widely developed and used by different communities; however, due to the fact that these models provide information about the integral of the whole electron content along the vertical or slant ray path, these maps are not useful when information about the ionosphere at different altitude is required. The aim of this study is to develop three dimensional (3-D) regional model of electron density by using combination of various space geodetic techniques. B-Spline basis functions are used for longitude and latitude variations of the electron density and Chapman profile function for altitude variations. The National Cartographic Center of Iran (NCC) has established a network of one hundred GPS stations: The Iranian Permanent GPS Network for Geodynamics (IPGN). The main task of the GPS stations is to collect and store raw GPS data and send it to Tehran processing center on a daily basis for final processing. The required data for our investigation are ground based measurements of permanent GPS stations over Iran and radio occultation data from Formosat-3/Cosmic for region of interest. We expect to increase accuracy and reliability of final model by integrating different observation techniques.
Probability density function model equation for particle charging in a homogeneous dusty plasma.
Pandya, R V; Mashayek, F
2001-09-01
In this paper, we use the direct interaction approximation (DIA) to obtain an approximate integrodifferential equation for the probability density function (PDF) of charge (q) on dust particles in homogeneous dusty plasma. The DIA is used to solve the closure problem which appears in the PDF equation due to the interactions between the phase space density of plasma particles and the phase space density of dust particles. The equation simplifies to a differential form under the condition when the fluctuations in phase space density for plasma particles change very rapidly in time and is correlated for very short times. The result is a Fokker-Planck type equation with extra terms having third and fourth order differentials in q, which account for the discrete nature of distribution of plasma particles and the interaction between fluctuations. Approximate macroscopic equations for the time evolution of the average charge and the higher order moments of the fluctuations in charge on the dust particles are obtained from the differential PDF equation. These equations are computed, in the case of a Maxwellian plasma, to show the effect of density fluctuations of plasma particles on the statistics of dust charge.
Husowitz, B; Talanquer, V
2007-02-07
Density functional theory is used to explore the solvation properties of a spherical solute immersed in a supercritical diatomic fluid. The solute is modeled as a hard core Yukawa particle surrounded by a diatomic Lennard-Jones fluid represented by two fused tangent spheres using an interaction site approximation. The authors' approach is particularly suitable for thoroughly exploring the effect of different interaction parameters, such as solute-solvent interaction strength and range, solvent-solvent long-range interactions, and particle size, on the local solvent structure and the solvation free energy under supercritical conditions. Their results indicate that the behavior of the local coordination number in homonuclear diatomic fluids follows trends similar to those reported in previous studies for monatomic fluids. The local density augmentation is particularly sensitive to changes in solute size and is affected to a lesser degree by variations in the solute-solvent interaction strength and range. The associated solvation free energies exhibit a nonmonotonous behavior as a function of density for systems with weak solute-solvent interactions. The authors' results suggest that solute-solvent interaction anisotropies have a major influence on the nature and extent of local solvent density inhomogeneities and on the value of the solvation free energies in supercritical solutions of heteronuclear molecules.
NASA Astrophysics Data System (ADS)
Baker, Thomas E.; Wagner, Lucas O.; Stoudenmire, E. Miles; White, Steven R.; Burke, Kieron
2014-03-01
Kohn-Sham Density Functional Theory (DFT) is a mathematically exact method that requires approximation to the exchange correlation energy which may exclude features seen in experiment or provide inadequate estimates. Meanwhile, we may use Density Matrix Renormalization Group (DMRG), a numerical method which can accurately treat strongly correlated electrons in one dimension, to find exact DFT quantities such as the Kohn-Sham potential. We use DMRG in one dimension as a benchmark to test new functionals. Further, recommendations for calculations in two and three dimensional systems are discussed as well as computational proof of principles. We graciously acknowledge the support of the Department of Energy (DE-SC0008696). L.O.W. also thanks the Korean Global Research Network Grant (No. NRF-2010-220-C00017).
The force distribution probability function for simple fluids by density functional theory.
Rickayzen, G; Heyes, D M
2013-02-28
Classical density functional theory (DFT) is used to derive a formula for the probability density distribution function, P(F), and probability distribution function, W(F), for simple fluids, where F is the net force on a particle. The final formula for P(F) ∝ exp(-AF(2)), where A depends on the fluid density, the temperature, and the Fourier transform of the pair potential. The form of the DFT theory used is only applicable to bounded potential fluids. When combined with the hypernetted chain closure of the Ornstein-Zernike equation, the DFT theory for W(F) agrees with molecular dynamics computer simulations for the Gaussian and bounded soft sphere at high density. The Gaussian form for P(F) is still accurate at lower densities (but not too low density) for the two potentials, but with a smaller value for the constant, A, than that predicted by the DFT theory.
Differential spectra and phase space densities of trapped electrons at Jupiter
NASA Technical Reports Server (NTRS)
Mcilwain, C. E.; Fillius, R. W.
1975-01-01
Using Pioneer 10 data, differential spectra and phase-space densities have been constructed for trapped electrons at Jupiter. These quantities should assist in calculating synchrotron radiation from these particles and in evaluating the diffusion mechanisms that accelerate the particles. Absorption by the moons Io and Europa is evident, and injection by Io is demonstrated by a density peak in phase space, which demands a local source. There is also a rapid decrease in density between the moons, which could call for either a local loss mechanism or nonlocal losses fed by diffusion.
Steady-State Density Functional Theory for Finite Bias Conductances.
Stefanucci, G; Kurth, S
2015-12-09
In the framework of density functional theory, a formalism to describe electronic transport in the steady state is proposed which uses the density on the junction and the steady current as basic variables. We prove that, in a finite window around zero bias, there is a one-to-one map between the basic variables and both local potential on as well as bias across the junction. The resulting Kohn-Sham system features two exchange-correlation (xc) potentials, a local xc potential, and an xc contribution to the bias. For weakly coupled junctions the xc potentials exhibit steps in the density-current plane which are shown to be crucial to describe the Coulomb blockade diamonds. At small currents these steps emerge as the equilibrium xc discontinuity bifurcates. The formalism is applied to a model benzene junction, finding perfect agreement with the orthodox theory of Coulomb blockade.
SURFACE SYMMETRY ENERGY OF NUCLEAR ENERGY DENSITY FUNCTIONALS
Nikolov, N; Schunck, N; Nazarewicz, W; Bender, M; Pei, J
2010-12-20
We study the bulk deformation properties of the Skyrme nuclear energy density functionals. Following simple arguments based on the leptodermous expansion and liquid drop model, we apply the nuclear density functional theory to assess the role of the surface symmetry energy in nuclei. To this end, we validate the commonly used functional parametrizations against the data on excitation energies of superdeformed band-heads in Hg and Pb isotopes, and fission isomers in actinide nuclei. After subtracting shell effects, the results of our self-consistent calculations are consistent with macroscopic arguments and indicate that experimental data on strongly deformed configurations in neutron-rich nuclei are essential for optimizing future nuclear energy density functionals. The resulting survey provides a useful benchmark for further theoretical improvements. Unlike in nuclei close to the stability valley, whose macroscopic deformability hangs on the balance of surface and Coulomb terms, the deformability of neutron-rich nuclei strongly depends on the surface-symmetry energy; hence, its proper determination is crucial for the stability of deformed phases of the neutron-rich matter and description of fission rates for r-process nucleosynthesis.
Differentiable but exact formulation of density-functional theory.
Kvaal, Simen; Ekström, Ulf; Teale, Andrew M; Helgaker, Trygve
2014-05-14
The universal density functional F of density-functional theory is a complicated and ill-behaved function of the density-in particular, F is not differentiable, making many formal manipulations more complicated. While F has been well characterized in terms of convex analysis as forming a conjugate pair (E, F) with the ground-state energy E via the Hohenberg-Kohn and Lieb variation principles, F is nondifferentiable and subdifferentiable only on a small (but dense) subset of its domain. In this article, we apply a tool from convex analysis, Moreau-Yosida regularization, to construct, for any ε > 0, pairs of conjugate functionals ((ε)E, (ε)F) that converge to (E, F) pointwise everywhere as ε → 0(+), and such that (ε)F is (Fréchet) differentiable. For technical reasons, we limit our attention to molecular electronic systems in a finite but large box. It is noteworthy that no information is lost in the Moreau-Yosida regularization: the physical ground-state energy E(v) is exactly recoverable from the regularized ground-state energy (ε)E(v) in a simple way. All concepts and results pertaining to the original (E, F) pair have direct counterparts in results for ((ε)E, (ε)F). The Moreau-Yosida regularization therefore allows for an exact, differentiable formulation of density-functional theory. In particular, taking advantage of the differentiability of (ε)F, a rigorous formulation of Kohn-Sham theory is presented that does not suffer from the noninteracting representability problem in standard Kohn-Sham theory.
Density versus spin-density functional in DFT+U and DFT+DMFT
NASA Astrophysics Data System (ADS)
Park, Hyowon; Millis, Andrew; Marianetti, Chris
2015-03-01
The construction of multi-variable effective action theories such as DFT+U and DFT+DMFT requires the choice of a local subspace of correlated orbitals and an additional variable being either the charge density or spin density. This talk examines the differences between using charge-only and spin-dependent exchange-correlation functionals with the aim of providing guidance for constructing more sophisticated beyond-density functional theories. The widely used spin-dependent approximations to the exchange-correlation functional are found to lead to a large and in some cases unphysical effective exchange coupling within the correlated subspace. Additionally, the differences between Wannier and Projector based definitions of the correlated orbitals are examined, and only small differences are found provided that the orbitals are orthonormal and strongly localized. These results are documented in the context of the rare earth nickelates. This work is supported under the Grant DOE-ER-046169 and under the FAME grant, one of six centers of STARnet, a Semiconductor Research Corporation program sponsored by MARCO and DARPA.
Functional responses: a question of alternative prey and predator density.
Tschanz, Britta; Bersier, Louis-Felix; Bacher, Sven
2007-05-01
Throughout the study of ecology, there has been a growing realization that indirect effects among species cause complexity in food webs. Understanding and predicting the behavior of ecosystems consequently depends on our ability to identify indirect effects and their mechanisms. The present study experimentally investigates indirect interactions arising between two prey species that share a common predator. In a natural field experiment, we introduced different densities of mealworms (Tenebrio molitor), an alternative prey, to a previously studied predator-prey system in which paper wasps (Polistes dominulus) preyed on shield beetle larvae (Cassida rubiginosa). We tested if alternative prey affects predation on the first prey (i.e., the predator-dependent functional response of paper wasps) by modifying either interference among predators or the effective number of predators foraging on shield beetles. Presence of mealworms significantly reduced the effective number of predators, whereas predator interference was not affected. In this way, the experimentally introduced alternative prey altered the wasps' functional response and thereby indirectly influenced C. rubiginosa density. In all prey-density combinations offered, paper wasps constantly preferred T. molitor. This led to an asymmetrical, indirect interaction between both prey species: an increase in mealworm density significantly relaxed predation on C. rubiginosa, whereas an increase in C. rubiginosa density intensified predation on mealworms. Such asymmetrical outcomes of a fixed food preference can significantly affect the population dynamics of the species involved. In spite of the repeated finding of a Type III functional response in this system, our experiment did not reveal switching behavior in paper wasps. The variety of mechanisms underlying direct and indirect interactions within our study system exemplifies the importance of incorporating alternative prey when investigating the impact of a
Density Functional Theory for Steady-State Nonequilibrium Molecular Junctions
Liu, Shuanglong; Nurbawono, Argo; Zhang, Chun
2015-01-01
We present a density functional theory (DFT) for steady-state nonequilibrium quantum systems such as molecular junctions under a finite bias. Based on the steady-state nonequilibrium statistics that maps nonequilibrium to an effective equilibrium, we show that ground-state DFT (GS-DFT) is not applicable in this case and two densities, the total electron density and the density of current-carrying electrons, are needed to uniquely determine the properties of the corresponding nonequilibrium system. A self-consistent mean-field approach based on two densities is then derived. The theory is implemented into SIESTA computational package and applied to study nonequilibrium electronic/transport properties of a realistic carbon-nanotube (CNT)/Benzene junction. Results obtained from our steady-state DFT (SS-DFT) are compared with those of conventional GS-DFT based transport calculations. We show that SS-DFT yields energetically more stable nonequilibrium steady state, predicts significantly lower electric current, and is able to produce correct electronic structures in local equilibrium under a limiting case. PMID:26472080
Bond energy decomposition analysis for subsystem density functional theory
NASA Astrophysics Data System (ADS)
Beyhan, S. Maya; Götz, Andreas W.; Visscher, Lucas
2013-03-01
We employed an explicit expression for the dispersion (D) energy in conjunction with Kohn-Sham (KS) density functional theory and frozen-density embedding (FDE) to calculate interaction energies between DNA base pairs and a selected set of amino acid pairs in the hydrophobic core of a small protein Rubredoxin. We use this data to assess the accuracy of an FDE-D approach for the calculation of intermolecular interactions. To better analyze the calculated interaction energies we furthermore propose a new energy decomposition scheme that is similar to the well-known KS bond formation analysis [F. M. Bickelhaupt and E. J. Baerends, Rev. Comput. Chem. 15, 1 (2000), 10.1002/9780470125922.ch1], but differs in the electron densities used to define the bond energy. The individual subsystem electron densities of the FDE approach sum to the total electron density which makes it possible to define bond energies in terms of promotion energies and an explicit interaction energy. We show that for the systems considered only a few freeze-and-thaw cycles suffice to reach convergence in these individual bond energy components, illustrating the potential of FDE-D as an efficient method to calculate intermolecular interactions.
Bond energy decomposition analysis for subsystem density functional theory.
Beyhan, S Maya; Götz, Andreas W; Visscher, Lucas
2013-03-07
We employed an explicit expression for the dispersion (D) energy in conjunction with Kohn-Sham (KS) density functional theory and frozen-density embedding (FDE) to calculate interaction energies between DNA base pairs and a selected set of amino acid pairs in the hydrophobic core of a small protein Rubredoxin. We use this data to assess the accuracy of an FDE-D approach for the calculation of intermolecular interactions. To better analyze the calculated interaction energies we furthermore propose a new energy decomposition scheme that is similar to the well-known KS bond formation analysis [F. M. Bickelhaupt and E. J. Baerends, Rev. Comput. Chem. 15, 1 (2000)], but differs in the electron densities used to define the bond energy. The individual subsystem electron densities of the FDE approach sum to the total electron density which makes it possible to define bond energies in terms of promotion energies and an explicit interaction energy. We show that for the systems considered only a few freeze-and-thaw cycles suffice to reach convergence in these individual bond energy components, illustrating the potential of FDE-D as an efficient method to calculate intermolecular interactions.
Predator density and the functional responses of coral reef fish
NASA Astrophysics Data System (ADS)
Stier, A. C.; White, J. W.
2014-03-01
Predation is a key process driving coral reef fish population dynamics, with higher per capita prey mortality rates on reefs with more predators. Reef predators often forage together, and at high densities, they may either cooperate or antagonize one another, thereby causing prey mortality rates to be substantially higher or lower than one would expect if predators did not interact. However, we have a limited mechanistic understanding of how prey mortality rates change with predator densities. We re-analyzed a previously published observational dataset to investigate how the foraging response of the coney grouper ( Cephalopholis fulva) feeding on the bluehead wrasse ( Thalassoma bifasciatum) changed with shifts in predator and prey densities. Using a model-selection approach, we found that per-predator feeding rates were most consistent with a functional response that declines as predator density increases, suggesting either antagonistic interactions among predators or a shared antipredator behavioral response by the prey. Our findings suggest that variation in predator density (natural or anthropogenic) may have substantial consequences for coral reef fish population dynamics.
Open-system Kohn-Sham density functional theory.
Zhou, Yongxi; Ernzerhof, Matthias
2012-03-07
A simple model for electron transport through molecules is provided by the source-sink potential (SSP) method [F. Goyer, M. Ernzerhof, and M. Zhuang, J. Chem. Phys. 126, 144104 (2007)]. In SSP, the boundary conditions of having an incoming and outgoing electron current are enforced through complex potentials that are added to the Hamiltonian. Depending on the sign of the imaginary part of the potentials, current density is generated or absorbed. In this way, a finite system can be used to model infinite molecular electronic devices. The SSP has originally been developed for the Hückel method and subsequently it has been extended [F. Goyer and M. Ernzerhof, J. Chem. Phys. 134, 174101 (2011)] to the Hubbard model. Here we present a step towards its generalization for first-principles electronic structure theory methods. In particular, drawing on our earlier work, we discuss a new generalized density functional theory for complex non-Hermitian Hamiltonians. This theory enables us to combine SSP and Kohn-Sham theory to obtain a method for the description of open systems that exchange current density with their environment. Similarly, the Hartree-Fock method is extended to the realm of non-Hermitian, SSP containing Hamiltonians. As a proof of principle, we present the first applications of complex-density functional theory (CODFT) as well as non-Hermitian Hartree-Fock theory to electron transport through molecules. © 2012 American Institute of Physics
Dynamical density functional theory for colloidal dispersions including hydrodynamic interactions
NASA Astrophysics Data System (ADS)
Rex, M.; Löwen, H.
2009-02-01
A dynamical density functional theory (DDFT) for translational Brownian dynamics is derived which includes hydrodynamic interactions. The theory reduces to the simple Brownian DDFT proposed by Marconi and Tarazona (U. Marini Bettolo Marconi and P. Tarazona, J. Chem. Phys. 110, 8032 (1999); J. Phys.: Condens. Matter 12, A413 (2000)) when hydrodynamic interactions are neglected. The derivation is based on Smoluchowski’s equation for the time evolution of the probability density with pairwise hydrodynamic interactions. The theory is applied to hard-sphere colloids in an oscillating spherical optical trap which switches periodically in time from a stable confining to an unstable potential. Rosenfeld’s fundamental measure theory for the equilibrium density functional is used and hydrodynamics are incorporated on the Rotne-Prager level. The results for the time-dependent density profiles are compared to extensive Brownian dynamics simulations which are performed on the same Rotne-Prager level and excellent agreement is obtained. It is further found that hydrodynamic interactions damp and slow the dynamics of the confined colloid cluster in comparison to the same situation with neglected hydrodynamic interactions.
Precise effective masses from density functional perturbation theory
NASA Astrophysics Data System (ADS)
Laflamme Janssen, J.; Gillet, Y.; Poncé, S.; Martin, A.; Torrent, M.; Gonze, X.
2016-05-01
The knowledge of effective masses is a key ingredient to analyze numerous properties of semiconductors, like carrier mobilities, (magneto)transport properties, or band extrema characteristics yielding carrier densities and density of states. Currently, these masses are usually calculated using finite-difference estimation of density functional theory (DFT) electronic band curvatures. However, finite differences require an additional convergence study and are prone to numerical noise. Moreover, the concept of effective mass breaks down at degenerate band extrema. We assess the former limitation by developing a method that allows to obtain the Hessian of DFT bands directly, using density functional perturbation theory. Then, we solve the latter issue by adapting the concept of "transport equivalent effective mass" to the k .p ̂ framework. The numerical noise inherent to finite-difference methods is thus eliminated, along with the associated convergence study. The resulting method is therefore more general, more robust, and simpler to use, which makes it especially appropriate for high-throughput computing. After validating the developed techniques, we apply them to the study of silicon, graphane, and arsenic. The formalism is implemented into the abinit software and supports the norm-conserving pseudopotential approach, the projector augmented-wave method, and the inclusion of spin-orbit coupling. The derived expressions also apply to the ultrasoft pseudopotential method.
Nonparametric maximum likelihood estimation of probability densities by penalty function methods
NASA Technical Reports Server (NTRS)
Demontricher, G. F.; Tapia, R. A.; Thompson, J. R.
1974-01-01
When it is known a priori exactly to which finite dimensional manifold the probability density function gives rise to a set of samples, the parametric maximum likelihood estimation procedure leads to poor estimates and is unstable; while the nonparametric maximum likelihood procedure is undefined. A very general theory of maximum penalized likelihood estimation which should avoid many of these difficulties is presented. It is demonstrated that each reproducing kernel Hilbert space leads, in a very natural way, to a maximum penalized likelihood estimator and that a well-known class of reproducing kernel Hilbert spaces gives polynomial splines as the nonparametric maximum penalized likelihood estimates.
Scrutinizing "Invisible" astatine: A challenge for modern density functionals.
Sergentu, Dumitru-Claudiu; David, Grégoire; Montavon, Gilles; Maurice, Rémi; Galland, Nicolas
2016-06-05
The main-group 6p elements did not receive much attention in the development of recent density functionals. In many cases it is still difficult to choose among the modern ones a relevant functional for various applications. Here, we illustrate the case of astatine species (At, Z = 85) and we report the first, and quite complete, benchmark study on several properties concerning such species. Insights on geometries, transition energies and thermodynamic properties of a set of 19 astatine species, for which reference experimental or theoretical data has been reported, are obtained with relativistic (two-component) density functional theory calculations. An extensive set of widely used functionals is employed. The hybrid meta-generalized gradient approximation (meta-GGA) PW6B95 functional is overall the best choice. It is worth noting that the range-separated HSE06 functional as well as the old and very popular B3LYP and PBE0 hybrid-GGAs appear to perform quite well too. Moreover, we found that astatine chemistry in solution can accurately be predicted using implicit solvent models, provided that specific parameters are used to build At cavities. © 2016 Wiley Periodicals, Inc. © 2016 Wiley Periodicals, Inc.
Density-Dependent Spacing Behaviour and Activity Budget in Pregnant, Domestic Goats (Capra hircus)
Vas, Judit; Andersen, Inger Lise
2015-01-01
Very little is known about the spacing behaviour in social groups of domestic goats (Capra hircus) in the farm environment. In this experiment, we studied interindividual distances, movement patterns and activity budgets in pregnant goats housed at three different densities. Norwegian dairy goats were kept in stable social groups of six animals throughout pregnancy at 1, 2 or 3 m2 per individual and their spacing behaviours (i.e. distance travelled, nearest and furthest neighbour distance) and activity budgets (e.g. resting, feeding, social activities) were monitored. Observations were made in the first, second and last thirds of pregnancy in the mornings, at noon and in the afternoons of each of these phases (4.5 hours per observation period). The findings show that goats held at animal densities of 2 and 3 m2 moved longer distances when they had more space per animal and kept larger nearest and furthest neighbour distances when compared to the 1 m2 per animal density. Less feeding activity was observed at the high animal density compared to the medium and low density treatments. The phase of gestation also had an impact on almost all behavioural variables. Closer to parturition, animals moved further distances and the increase in nearest and furthest neighbour distance was more pronounced at the lower animal densities. During the last period of gestation, goats spent less time feeding and more on resting, social behaviours and engaging in other various activities. Our data suggest that more space per goat is needed for goats closer to parturition than in the early gestation phase. We concluded that in goats spacing behaviour is density-dependent and changes with stages of pregnancy and activities. Finally, the lower density allowed animals to express individual preferences regarding spacing behaviour which is important in ensuring good welfare in a farming situation. PMID:26657240
Density-Dependent Spacing Behaviour and Activity Budget in Pregnant, Domestic Goats (Capra hircus).
Vas, Judit; Andersen, Inger Lise
2015-01-01
Very little is known about the spacing behaviour in social groups of domestic goats (Capra hircus) in the farm environment. In this experiment, we studied interindividual distances, movement patterns and activity budgets in pregnant goats housed at three different densities. Norwegian dairy goats were kept in stable social groups of six animals throughout pregnancy at 1, 2 or 3 m2 per individual and their spacing behaviours (i.e., distance travelled, nearest and furthest neighbour distance) and activity budgets (e.g., resting, feeding, social activities) were monitored. Observations were made in the first, second and last thirds of pregnancy in the mornings, at noon and in the afternoons of each of these phases (4.5 hours per observation period). The findings show that goats held at animal densities of 2 and 3 m2 moved longer distances when they had more space per animal and kept larger nearest and furthest neighbour distances when compared to the 1 m2 per animal density. Less feeding activity was observed at the high animal density compared to the medium and low density treatments. The phase of gestation also had an impact on almost all behavioural variables. Closer to parturition, animals moved further distances and the increase in nearest and furthest neighbour distance was more pronounced at the lower animal densities. During the last period of gestation, goats spent less time feeding and more on resting, social behaviours and engaging in other various activities. Our data suggest that more space per goat is needed for goats closer to parturition than in the early gestation phase. We concluded that in goats spacing behaviour is density-dependent and changes with stages of pregnancy and activities. Finally, the lower density allowed animals to express individual preferences regarding spacing behaviour which is important in ensuring good welfare in a farming situation.
What Density Functional Theory could do for Quantum Information
NASA Astrophysics Data System (ADS)
Mattsson, Ann
2015-03-01
The Hohenberg-Kohn theorem of Density Functional Theory (DFT), and extensions thereof, tells us that all properties of a system of electrons can be determined through their density, which uniquely determines the many-body wave-function. Given access to the appropriate, universal, functionals of the density we would, in theory, be able to determine all observables of any electronic system, without explicit reference to the wave-function. On the other hand, the wave-function is at the core of Quantum Information (QI), with the wave-function of a set of qubits being the central computational resource in a quantum computer. While there is seemingly little overlap between DFT and QI, reliance upon observables form a key connection. Though the time-evolution of the wave-function and associated phase information is fundamental to quantum computation, the initial and final states of a quantum computer are characterized by observables of the system. While observables can be extracted directly from a system's wave-function, DFT tells us that we may be able to intuit a method for extracting them from its density. In this talk, I will review the fundamentals of DFT and how these principles connect to the world of QI. This will range from DFT's utility in the engineering of physical qubits, to the possibility of using it to efficiently (but approximately) simulate Hamiltonians at the logical level. The apparent paradox of describing algorithms based on the quantum mechanical many-body wave-function with a DFT-like theory based on observables will remain a focus throughout. The ultimate goal of this talk is to initiate a dialog about what DFT could do for QI, in theory and in practice. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.
Modeling of nanoscale liquid mixture transport by density functional hydrodynamics
NASA Astrophysics Data System (ADS)
Dinariev, Oleg Yu.; Evseev, Nikolay V.
2017-06-01
Modeling of multiphase compositional hydrodynamics at nanoscale is performed by means of density functional hydrodynamics (DFH). DFH is the method based on density functional theory and continuum mechanics. This method has been developed by the authors over 20 years and used for modeling in various multiphase hydrodynamic applications. In this paper, DFH was further extended to encompass phenomena inherent in liquids at nanoscale. The new DFH extension is based on the introduction of external potentials for chemical components. These potentials are localized in the vicinity of solid surfaces and take account of the van der Waals forces. A set of numerical examples, including disjoining pressure, film precursors, anomalous rheology, liquid in contact with heterogeneous surface, capillary condensation, and forward and reverse osmosis, is presented to demonstrate modeling capabilities.
Nonequilibrium Anderson model made simple with density functional theory
NASA Astrophysics Data System (ADS)
Kurth, S.; Stefanucci, G.
2016-12-01
The single-impurity Anderson model is studied within the i-DFT framework, a recently proposed extension of density functional theory (DFT) for the description of electron transport in the steady state. i-DFT is designed to give both the steady current and density at the impurity, and it requires the knowledge of the exchange-correlation (xc) bias and on-site potential (gate). In this work we construct an approximation for both quantities which is accurate in a wide range of temperatures, gates, and biases, thus providing a simple and unifying framework to calculate the differential conductance at negligible computational cost in different regimes. Our results mark a substantial advance for DFT and may inform the construction of functionals applicable to other correlated systems.
Excitations and benchmark ensemble density functional theory for two electrons
Pribram-Jones, Aurora; Burke, Kieron; Yang, Zeng-hui; Ullrich, Carsten A.; Trail, John R.; Needs, Richard J.
2014-05-14
A new method for extracting ensemble Kohn-Sham potentials from accurate excited state densities is applied to a variety of two-electron systems, exploring the behavior of exact ensemble density functional theory. The issue of separating the Hartree energy and the choice of degenerate eigenstates is explored. A new approximation, spin eigenstate Hartree-exchange, is derived. Exact conditions that are proven include the signs of the correlation energy components and the asymptotic behavior of the potential for small weights of the excited states. Many energy components are given as a function of the weights for two electrons in a one-dimensional flat box, in a box with a large barrier to create charge transfer excitations, in a three-dimensional harmonic well (Hooke's atom), and for the He atom singlet-triplet ensemble, singlet-triplet-singlet ensemble, and triplet bi-ensemble.
Density-Functional Theory of the Fractional Quantum Hall Effect.
Zhao, Jianyun; Thakurathi, Manisha; Jain, Manish; Sen, Diptiman; Jain, J K
2017-05-12
A conceptual difficulty in formulating the density-functional theory of the fractional quantum Hall effect is that while in the standard approach the Kohn-Sham orbitals are either fully occupied or unoccupied, the physics of the fractional quantum Hall effect calls for fractionally occupied Kohn-Sham orbitals. This has necessitated averaging over an ensemble of Slater determinants to obtain meaningful results. We develop an alternative approach in which we express and minimize the grand canonical potential in terms of the composite fermion variables. This provides a natural resolution of the fractional-occupation problem because the fully occupied orbitals of composite fermions automatically correspond to fractionally occupied orbitals of electrons. We demonstrate the quantitative validity of our approach by evaluating the density profile of fractional Hall edge as a function of temperature and the distance from the delta dopant layer and showing that it reproduces edge reconstruction in the expected parameter region.
Covariant density functional theory: The role of the pion
Lalazissis, G. A.; Karatzikos, S.; Serra, M.; Otsuka, T.; Ring, P.
2009-10-15
We investigate the role of the pion in covariant density functional theory. Starting from conventional relativistic mean field (RMF) theory with a nonlinear coupling of the {sigma} meson and without exchange terms we add pions with a pseudovector coupling to the nucleons in relativistic Hartree-Fock approximation. In order to take into account the change of the pion field in the nuclear medium the effective coupling constant of the pion is treated as a free parameter. It is found that the inclusion of the pion to this sort of density functionals does not destroy the overall description of the bulk properties by RMF. On the other hand, the noncentral contribution of the pion (tensor coupling) does have effects on single particle energies and on binding energies of certain nuclei.
Analyzing the financial crisis using the entropy density function
NASA Astrophysics Data System (ADS)
Oh, Gabjin; Kim, Ho-yong; Ahn, Seok-Won; Kwak, Wooseop
2015-02-01
The risk that is created by nonlinear interactions among subjects in economic systems is assumed to increase during an abnormal state of a financial market. Nevertheless, investigating the systemic risk in financial markets following the global financial crisis is not sufficient. In this paper, we analyze the entropy density function in the return time series for several financial markets, such as the S&P500, KOSPI, and DAX indices, from October 2002 to December 2011 and analyze the variability in the entropy value over time. We find that the entropy density function of the S&P500 index during the subprime crisis exhibits a significant decrease compared to that in other periods, whereas the other markets, such as those in Germany and Korea, exhibit no significant decrease during the market crisis. These findings demonstrate that the S&P500 index generated a regular pattern in the return time series during the financial crisis.
Neutrinoless double-beta decay in covariant density functional theory
Ring, P.; Yao, J. M.; Song, L. S.; Hagino, K.; Meng, J.
2015-10-15
We use covariant density functional theory beyond mean field in order to describe neutrinoless double-beta decay in a fully relativistic way. The dynamic effects of particle-number and angular-momentum conservations as well as shape fluctuations of quadrupole character are taken into account within the generator coordinate method for both initial and final nuclei. The calculations are based on the full relativistic transition operator. The nuclear matrix elements (NME’s) for a large number of possible transitions are investigated. The results are compared with various non-relativistic calculations, in particular also with the density functional theory based on the Gogny force. We find that the non-relativistic approximation is justified and that the total NME’s can be well approximated by the pure axial-vector coupling term. This corresponds to a considerable reduction of the computational effort.
Accelerating Density Functional Calculations with Graphics Processing Unit.
Yasuda, Koji
2008-08-01
An algorithm is presented for graphics processing units (GPUs), which execute single-precision arithmetic much faster than commodity microprocessors (CPUs), to calculate the exchange-correlation term in ab initio density functional calculations. The algorithm was implemented and applied to two molecules, taxol and valinomycin. The errors in the total energies were about 10(-5) a.u., which is accurate enough for practical usage. If the exchange-correlation term is split into a simple analytic model potential and the correction to it, and only the latter is calculated with the GPU, the energy error is decreased by an order of magnitude. The resulting time to compute the exchange-correlation term is smaller than it is on the latest CPU by a factor of 10, indicating that a GPU running the proposed algorithm accelerates the density functional calculation considerably.
Exact probability-density function for phase-measurement interferometry
NASA Astrophysics Data System (ADS)
Ho, Keang-Po; Kahn, Joseph M.
1995-09-01
Conventional analyses of the accuracy of phase-measurement interferometry derive a figure of merit that is either a variance or a signal-to-noise ratio. We derive the probability-density function of the phase-measurement output, so that the measurement confidence interval can be determined. We include both laser phase noise and additive Gaussian noise, and we consider both unmodulated interferometers and those employing phase or frequency modulation. For both unmodulated and modulated interferometers the confidence interval can be obtained by numerical integration of the probability-density function. For the modulated interferometer we derive a series summation for the confidence interval. For both unmodulated and modulated interferometers we derive approximate analytical expressions for the confidence interval, which we show to be extremely accurate at high signal-to-noise ratios.
Resveratrol preserves cerebrovascular density and cognitive function in aging mice.
Oomen, Charlotte A; Farkas, Eszter; Roman, Viktor; van der Beek, Eline M; Luiten, Paul G M; Meerlo, Peter
2009-01-01
Resveratrol, a natural polyphenol abundant in grapes and red wine, has been reported to exert numerous beneficial health effects. Among others, acute neuroprotective effects of resveratrol have been described in several models of neurodegeneration, both in vitro and in vivo. In the present study we examined the neuroprotective effects of long-term dietary supplementation with resveratrol in mice on behavioral, neurochemical and cerebrovascular level. We report a preserved cognitive function in resveratrol-treated aging mice, as shown by an enhanced acquisition of a spatial Y-maze task. This was paralleled by a higher microvascular density and a lower number of microvascular abnormalities in comparison to aging non-treated control animals. We found no effects of resveratrol supplementation on cholinergic cell number or fiber density. The present findings support the hypothesis that resveratrol exerts beneficial effects on the brain by maintaining cerebrovascular health. Via this mechanism resveratrol can contribute to the preservation of cognitive function during aging.
Density-Functional Theory of the Fractional Quantum Hall Effect
NASA Astrophysics Data System (ADS)
Zhao, Jianyun; Thakurathi, Manisha; Jain, Manish; Sen, Diptiman; Jain, J. K.
2017-05-01
A conceptual difficulty in formulating the density-functional theory of the fractional quantum Hall effect is that while in the standard approach the Kohn-Sham orbitals are either fully occupied or unoccupied, the physics of the fractional quantum Hall effect calls for fractionally occupied Kohn-Sham orbitals. This has necessitated averaging over an ensemble of Slater determinants to obtain meaningful results. We develop an alternative approach in which we express and minimize the grand canonical potential in terms of the composite fermion variables. This provides a natural resolution of the fractional-occupation problem because the fully occupied orbitals of composite fermions automatically correspond to fractionally occupied orbitals of electrons. We demonstrate the quantitative validity of our approach by evaluating the density profile of fractional Hall edge as a function of temperature and the distance from the delta dopant layer and showing that it reproduces edge reconstruction in the expected parameter region.
Autoionization in time-dependent density-functional theory
NASA Astrophysics Data System (ADS)
Kapoor, V.
2016-06-01
We compute the exact exchange-correlation potential of the time-dependent density-functional theory (TDDFT) for the correlated process of autoionization. The potential develops barriers which regulate the autoionization rate. TDDFT employing known and practicable exchange-correlation potentials does not capture any autoionization dynamics. Approximate exchange-correlation potentials capturing such dynamics would necessarily require memory effects and are unlikely to be developed, as will be illustrated.
Density functional theory across chemistry, physics and biology
van Mourik, Tanja; Bühl, Michael; Gaigeot, Marie-Pierre
2014-01-01
The past decades have seen density functional theory (DFT) evolve from a rising star in computational quantum chemistry to one of its major players. This Theme Issue, which comes half a century after the publication of the Hohenberg–Kohn theorems that laid the foundations of modern DFT, reviews progress and challenges in present-day DFT research. Rather than trying to be comprehensive, this Theme Issue attempts to give a flavour of selected aspects of DFT. PMID:24516181
Association between lung function and airway wall density
NASA Astrophysics Data System (ADS)
Leader, J. Ken; Zheng, Bin; Fuhrman, Carl R.; Tedrow, John; Park, Sang C.; Tan, Jun; Pu, Jiantao; Drescher, John M.; Gur, David; Sciurba, Frank C.
2009-02-01
Computed tomography (CT) examination is often used to quantify the relation between lung function and airway remodeling in chronic obstructive pulmonary disease (COPD). In this preliminary study, we examined the association between lung function and airway wall computed attenuation ("density") in 200 COPD screening subjects. Percent predicted FVC (FVC%), percent predicted FEV1 (FEV1%), and the ratio of FEV1 to FVC as a percentage (FEV1/FVC%) were measured post-bronchodilator. The apical bronchus of the right upper lobe was manually selected from CT examinations for evaluation. Total airway area, lumen area, wall area, lumen perimeter and wall area as fraction of the total airway area were computed. Mean HU (meanHU) and maximum HU (maxHU) values were computed across pixels assigned membership in the wall and with a HU value greater than -550. The Pearson correlation coefficients (PCC) between FVC%, FEV1%, and FEV1/FVC% and meanHU were -0.221 (p = 0.002), -0.175 (p = 0.014), and -0.110 (p = 0.123), respectively. The PCCs for maxHU were only significant for FVC%. The correlations between lung function and the airway morphometry parameters were slightly stronger compared to airway wall density. MeanHU was significantly correlated with wall area (PCC = 0.720), airway area (0.498) and wall area percent (0.611). This preliminary work demonstrates that airway wall density is associated with lung function. Although the correlations in our study were weaker than a recent study, airway wall density initially appears to be an important parameter in quantitative CT analysis of COPD.
Finite-size instabilities in nuclear energy density functionals
Hellemans, V.; Heenen, P.-H.; Bender, M.
2012-10-20
The systematic lack of convergence of self-consistent mean-field calculations with certain parameterizations of the Skyrme energy density functional has been attributed to the appearance of finite-size instabilities. In this contribution, we investigate what happens at the instability associated with the C{sub 0}{sup {Delta}s}s{sub 0} Dot-Operator {Delta}s{sub 0} term in a high-spin state of the superdeformed band in {sup 194}Hg.
Excitons in Time-Dependent Density-Functional Theory.
Ullrich, Carsten A; Yang, Zeng-hui
2016-01-01
This chapter gives an overview of the description of the optical and dielectric properties of bulk insulators and semiconductors in time-dependent density-functional theory (TDDFT), with an emphasis on excitons. We review the linear-response formalism for periodic solids, discuss excitonic exchange-correlation kernels, calculate exciton binding energies for various materials, and compare the treatment of excitons with TDDFT and with the Bethe-Salpeter equation.
Ferromagnetic elements by epitaxial growth: A density functional prediction
NASA Astrophysics Data System (ADS)
Schönecker, Stephan; Richter, Manuel; Koepernik, Klaus; Eschrig, Helmut
2012-01-01
The periodic table contains only six natural elements with a ferromagnetic ground state. For example, the metal uranium, which is magnetically ordered in many compounds, is paramagnetic in all its known elemental bulk phases. Also, the iron-group elements ruthenium and osmium are known to be bulk paramagnets. We predict by means of density functional calculations that epitaxial growth of uranium, ruthenium, or osmium on suitable substrates may allow stabilization of bulklike films with tetragonal structures showing ferromagnetic order.
Probability Density Function Method for Langevin Equations with Colored Noise
Wang, Peng; Tartakovsky, Alexandre M.; Tartakovsky, Daniel M.
2013-04-05
We present a novel method to derive closed-form, computable PDF equations for Langevin systems with colored noise. The derived equations govern the dynamics of joint or marginal probability density functions (PDFs) of state variables, and rely on a so-called Large-Eddy-Diffusivity (LED) closure. We demonstrate the accuracy of the proposed PDF method for linear and nonlinear Langevin equations, describing the classical Brownian displacement and dispersion in porous media.
Density functional theory across chemistry, physics and biology.
van Mourik, Tanja; Bühl, Michael; Gaigeot, Marie-Pierre
2014-03-13
The past decades have seen density functional theory (DFT) evolve from a rising star in computational quantum chemistry to one of its major players. This Theme Issue, which comes half a century after the publication of the Hohenberg-Kohn theorems that laid the foundations of modern DFT, reviews progress and challenges in present-day DFT research. Rather than trying to be comprehensive, this Theme Issue attempts to give a flavour of selected aspects of DFT.
Archer, A J
2009-01-07
In recent years, a number of dynamical density functional theories (DDFTs) have been developed for describing the dynamics of the one-body density of both colloidal and atomic fluids. In the colloidal case, the particles are assumed to have stochastic equations of motion and theories exist for both the case when the particle motion is overdamped and also in the regime where inertial effects are relevant. In this paper, we extend the theory and explore the connections between the microscopic DDFT and the equations of motion from continuum fluid mechanics. In particular, starting from the Kramers equation, which governs the dynamics of the phase space probability distribution function for the system, we show that one may obtain an approximate DDFT that is a generalization of the Euler equation. This DDFT is capable of describing the dynamics of the fluid density profile down to the scale of the individual particles. As with previous DDFTs, the dynamical equations require as input the Helmholtz free energy functional from equilibrium density functional theory (DFT). For an equilibrium system, the theory predicts the same fluid one-body density profile as one would obtain from DFT. Making further approximations, we show that the theory may be used to obtain the mode coupling theory that is widely used for describing the transition from a liquid to a glassy state.
Plato: A localised orbital based density functional theory code
NASA Astrophysics Data System (ADS)
Kenny, S. D.; Horsfield, A. P.
2009-12-01
The Plato package allows both orthogonal and non-orthogonal tight-binding as well as density functional theory (DFT) calculations to be performed within a single framework. The package also provides extensive tools for analysing the results of simulations as well as a number of tools for creating input files. The code is based upon the ideas first discussed in Sankey and Niklewski (1989) [1] with extensions to allow high-quality DFT calculations to be performed. DFT calculations can utilise either the local density approximation or the generalised gradient approximation. Basis sets from minimal basis through to ones containing multiple radial functions per angular momenta and polarisation functions can be used. Illustrations of how the package has been employed are given along with instructions for its utilisation. Program summaryProgram title: Plato Catalogue identifier: AEFC_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEFC_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 219 974 No. of bytes in distributed program, including test data, etc.: 1 821 493 Distribution format: tar.gz Programming language: C/MPI and PERL Computer: Apple Macintosh, PC, Unix machines Operating system: Unix, Linux and Mac OS X Has the code been vectorised or parallelised?: Yes, up to 256 processors tested RAM: Up to 2 Gbytes per processor Classification: 7.3 External routines: LAPACK, BLAS and optionally ScaLAPACK, BLACS, PBLAS, FFTW Nature of problem: Density functional theory study of electronic structure and total energies of molecules, crystals and surfaces. Solution method: Localised orbital based density functional theory. Restrictions: Tight-binding and density functional theory only, no exact exchange. Unusual features: Both atom centred and uniform meshes available
Probability density functions for hyperbolic and isodiachronic locations.
Spiesberger, John L; Wahlberg, Magnus
2002-12-01
Animal locations are sometimes estimated with hyperbolic techniques by estimating the difference in distances of their sounds between pairs of receivers. Each pair specifies the animal's location to a hyperboloid because the speed of sound is assumed to be spatially homogeneous. Sufficient numbers of intersecting hyperboloids specify the location. A nonlinear method is developed for computing probability density functions for location. The method incorporates a priori probability density functions for the receiver locations, the speed of sound, winds, and the errors in the differences in travel time. The traditional linear approximation method overestimates bounds for probability density functions by one or two orders of magnitude compared with the more accurate nonlinear method. The nonlinear method incorporates a generalization of hyperbolic methods because the average speed of sound is allowed to vary between different receivers and the source. The resulting "isodiachronic" surface is the locus of points on which the difference in travel time is constant. Isodiachronic locations yield correct location errors in situations where hyperbolic methods yield incorrect results, particularly when the speed of propagation varies significantly between a source and different receivers.
Chemical reactivity in the framework of pair density functional theories.
Otero, Nicolás; Mandado, Marcos
2012-05-15
Chemical reactivity descriptors are derived within the framework of the pair density functional theory. These indices provide valuable information about bonding rearrangements and activating mechanisms upon electrophilic or nucleophilic reactions. Indices derived and tested in this work represent nonlocal counterparts of the local reactivity indices derived in the context of conceptual density functional theory (CDFT) and frequently used in reactivity studies; the Fukui function, the local softness and the dual descriptor. In this work, we show how these nonlocal indices provide a quantum chemical basis to explain the success of qualitative resonance models in chemical reactivity predictions. Also, local information is implicitly contained as CDFT indices are obtained by simple integration. As illustrative examples, we have considered in this work the Markovnikov's rule, the reactivity of enolate anion, the nucleophilic conjugate addition to α,β-unsaturated compounds and the electrophilic aromatic substitution of benzene derivatives. The densities used in this work were obtained with Hartree-Fock, Kohn-Sham DFT, and singles and doubles configuration interaction (CISD) approaches.
Density functional wavelet calculation of solid state systems
NASA Astrophysics Data System (ADS)
Daykov, I. P.; Engeness, T. D.; Arias, T. A.
2001-03-01
We present, to our knowledge, the first all-electron wavelet calculations of the electronic structure of solids within density functional theory. To make these calculations competitive with traditional approaches, we employ recent developments in algorithms for multiresolution analysis (MRA) which speed density functional calculations by three to four orders of magnitude[1,2]. MRA provides a fully systematic, integrated treatment of core and valence electrons and is ideal for exploring the limits of the accuracy of density functional theory in the calculation of EELS spectra, which involve matrix elements between the core and valence states. We shall present results for EELS spectra as well as the resolution of technical issues which arise in carrying out solid-state calculations within a wavelet-like basis. [1] ``Multiscale computation with interpolating wavelets,'' by Ross A. Lippert, T.A. Arias and Alan Edelman, Journal of Computational Physics, 140:2, 278--310 (1 March 1998). Preprint: http://xxx.lanl.gov/abs/cond-mat/9805283 . [2] ``Multiresolution analysis of electronic structure: semicardinal and wavelet bases,'' T.A. Arias, Reviews of Modern Physics 71:1, 267--311 (January 1999). Preprint: http://xxx.lanl.gov/abs/cond-mat/9805262 .
Density functional theories of surface interactions in salt solutions.
Forsman, Jan
2009-02-14
Most current density functional theories rely upon the presence of hard cores, also between ions of like charge. These hard cores should in principle reflect exchange repulsion. However, by the way in which these theories are formulated, the hard cores effectively determine the range of ion-ion correlations. This is because the mutual repulsion between like-charged ions is truncated below the corresponding hard sphere diameter. In most relevant applications, at least those related to ion correlations and surface forces in colloidal dispersions, exchange repulsion between like-charged ions is unimportant. This can easily be demonstrated by simulations. Unfortunately, the hard cores can in practice serve as fitting parameters in calculations with traditional density functional theory. In this work, we present alternative density functional theories to describe aqueous salt solutions. In these approaches, an approximation of the relevant "Coulomb hole" that results from correlations between like-charged ions is calculated for the system under study. Hence, our theories are completely free from fitting parameters, and the results are appropriately insensitive to the exchange repulsion acting between ions of like charge. The theories are evaluated by comparing predictions with simulation data, with an emphasis on ion correlations and surface interactions.
NASA Astrophysics Data System (ADS)
Khan, Shehryar; Kubica-Misztal, Aleksandra; Kruk, Danuta; Kowalewski, Jozef; Odelius, Michael
2015-01-01
The zero-field splitting (ZFS) of the electronic ground state in paramagnetic ions is a sensitive probe of the variations in the electronic and molecular structure with an impact on fields ranging from fundamental physical chemistry to medical applications. A detailed analysis of the ZFS in a series of symmetric Gd(III) complexes is presented in order to establish the applicability and accuracy of computational methods using multiconfigurational complete-active-space self-consistent field wave functions and of density functional theory calculations. The various computational schemes are then applied to larger complexes Gd(III)DOTA(H2O)-, Gd(III)DTPA(H2O)2-, and Gd(III)(H2O)83+ in order to analyze how the theoretical results compare to experimentally derived parameters. In contrast to approximations based on density functional theory, the multiconfigurational methods produce results for the ZFS of Gd(III) complexes on the correct order of magnitude.
Linear Scaling Density Functional Calculations with Gaussian Orbitals
NASA Technical Reports Server (NTRS)
Scuseria, Gustavo E.
1999-01-01
Recent advances in linear scaling algorithms that circumvent the computational bottlenecks of large-scale electronic structure simulations make it possible to carry out density functional calculations with Gaussian orbitals on molecules containing more than 1000 atoms and 15000 basis functions using current workstations and personal computers. This paper discusses the recent theoretical developments that have led to these advances and demonstrates in a series of benchmark calculations the present capabilities of state-of-the-art computational quantum chemistry programs for the prediction of molecular structure and properties.
Atomistic force field for alumina fit to density functional theory
Sarsam, Joanne; Finnis, Michael W.; Tangney, Paul
2013-11-28
We present a force field for bulk alumina (Al{sub 2}O{sub 3}), which has been parametrized by fitting the energies, forces, and stresses of a large database of reference configurations to those calculated with density functional theory (DFT). We use a functional form that is simpler and computationally more efficient than some existing models of alumina parametrized by a similar technique. Nevertheless, we demonstrate an accuracy of our potential that is comparable to those existing models and to DFT. We present calculations of crystal structures and energies, elastic constants, phonon spectra, thermal expansion, and point defect formation energies.
Conformational Analysis of Thioether Musks Using Density Functional Theory
Setzer, William N.
2009-01-01
A conformational analysis of nine macrocyclic thioether musks has been carried out using molecular mechanics (MMFF), density functional theory (DFT) using both B3LYP and M06 functionals, as well as Hartree-Fock and post-Hartree-Fock (MP2) ab initio methods. 6-Thia-, 10-thia- and 4-methyl-5-thia-14-tetradecananolide, 4-thia-, 7-thia-, 11-thia- and 12-thia-15-pentadecanolide and 6-thia- and 12-thia-16-hexadecanolide were modeled. Unfortunately, there was little agreement between the computational methods at the levels of theory used in this study. PMID:20111690
Surface regulated arsenenes as Dirac materials: From density functional calculations
NASA Astrophysics Data System (ADS)
Yuan, Junhui; Xie, Qingxing; Yu, Niannian; Wang, Jiafu
2017-02-01
Using first principle calculations based on density functional theory (DFT), we have systematically investigated the structure stability and electronic properties of chemically decorated arsenenes, AsX (X = CN, NC, NCO, NCS and NCSe). Phonon dispersion and formation energy analysis reveal that all the five chemically decorated buckled arsenenes are energetically favorable and could be synthesized. Our study shows that wide-bandgap arsenene would turn into Dirac materials when functionalized by -X (X = CN, NC, NCO, NCS and NCSe) groups, rendering new promises in next generation high-performance electronic devices.
Advances in time-dependent current-density functional theory
NASA Astrophysics Data System (ADS)
Berger, Arjan
In this work we solve the problem of the gauge dependence of molecular magnetic properties (magnetizabilities, circular dichroism) using time-dependent current-density functional theory [1]. We also present a new functional that accurately describes the optical absorption spectra of insulators, semiconductors and metals [2] N. Raimbault, P.L. de Boeij, P. Romaniello, and J.A. Berger Phys. Rev. Lett. 114, 066404 (2015) J.A. Berger, Phys. Rev. Lett. 115, 137402 (2015) This study has been partially supported through the Grant NEXT No. ANR-10-LABX-0037 in the framework of the Programme des Investissements d'Avenir.
Ambient mass density effects on the International Space Station (ISS) microgravity experiments
NASA Technical Reports Server (NTRS)
Smith, O. E.; Adelfang, S. I.; Smith, R. E.
1996-01-01
The Marshall engineering thermosphere model was specified by NASA to be used in the design, development and testing phases of the International Space Station (ISS). The mass density is the atmospheric parameter which most affects the ISS. Under simplifying assumptions, the critical ambient neutral density required to produce one micro-g on the ISS is estimated using an atmospheric drag acceleration equation. Examples are presented for the critical density versus altitude, and for the critical density that is exceeded at least once a month and once per orbit during periods of low and high solar activity. An analysis of the ISS orbital decay is presented.
Density functional theory and chromium: Insights from the dimers
Würdemann, Rolf; Kristoffersen, Henrik H.; Moseler, Michael; Walter, Michael
2015-03-28
The binding in small Cr clusters is re-investigated, where the correct description of the dimer in three charge states is used as criterion to assign the most suitable density functional theory approximation. The difficulty in chromium arises from the subtle interplay between energy gain from hybridization and energetic cost due to exchange between s and d based molecular orbitals. Variations in published bond lengths and binding energies are shown to arise from insufficient numerical representation of electron density and Kohn-Sham wave-functions. The best functional performance is found for gradient corrected (GGA) functionals and meta-GGAs, where we find severe differences between functionals from the same family due to the importance of exchange. Only the “best fit” from Bayesian error estimation is able to predict the correct energetics for all three charge states unambiguously. With this knowledge, we predict small bond-lengths to be exclusively present in Cr{sub 2} and Cr{sub 2}{sup −}. Already for the dimer cation, solely long bond-lengths appear, similar to what is found in the trimer and in chromium bulk.
Many-body theory and Energy Density Functionals
NASA Astrophysics Data System (ADS)
Baldo, M.
2016-07-01
In this paper a method is first presented to construct an Energy Density Functional on a microscopic basis. The approach is based on the Kohn-Sham method, where one introduces explicitly the Nuclear Matter Equation of State, which can be obtained by an accurate many-body calculation. In this way it connects the functional to the bare nucleon-nucleon interaction. It is shown that the resulting functional can be performing as the best Gogny force functional. In the second part of the paper it is shown how one can go beyond the mean-field level and the difficulty that can appear. The method is based on the particle-vibration coupling scheme and a formalism is presented that can handle the correct use of the vibrational degrees of freedom within a microscopic approach.
Current density partitioning in time-dependent current density functional theory
Mosquera, Martín A.; Wasserman, Adam
2014-05-14
We adapt time-dependent current density functional theory to allow for a fragment-based solution of the many-electron problem of molecules in the presence of time-dependent electric and magnetic fields. Regarding a molecule as a set of non-interacting subsystems that individually evolve under the influence of an auxiliary external electromagnetic vector-scalar potential pair, the partition 4-potential, we show that there are one-to-one mappings between this auxiliary potential, a sharply-defined set of fragment current densities, and the total current density of the system. The partition electromagnetic (EM) 4-potential is expressed in terms of the real EM 4-potential of the system and a gluing EM 4-potential that accounts for exchange-correlation effects and mutual interaction forces between fragments that are required to yield the correct electron dynamics. We prove the zero-force theorem for the fragmented system, establish a variational formulation in terms of action functionals, and provide a simple illustration for a charged particle in a ring.
Franco-Pérez, Marco E-mail: ayers@mcmaster.ca E-mail: avela@cinvestav.mx; Ayers, Paul W. E-mail: ayers@mcmaster.ca E-mail: avela@cinvestav.mx; Gázquez, José L. E-mail: ayers@mcmaster.ca E-mail: avela@cinvestav.mx; Vela, Alberto E-mail: ayers@mcmaster.ca E-mail: avela@cinvestav.mx
2015-12-28
We explore the local and nonlocal response functions of the grand canonical potential density functional at nonzero temperature. In analogy to the zero-temperature treatment, local (e.g., the average electron density and the local softness) and nonlocal (e.g., the softness kernel) intrinsic response functions are defined as partial derivatives of the grand canonical potential with respect to its thermodynamic variables (i.e., the chemical potential of the electron reservoir and the external potential generated by the atomic nuclei). To define the local and nonlocal response functions of the electron density (e.g., the Fukui function, the linear density response function, and the dual descriptor), we differentiate with respect to the average electron number and the external potential. The well-known mathematical relationships between the intrinsic response functions and the electron-density responses are generalized to nonzero temperature, and we prove that in the zero-temperature limit, our results recover well-known identities from the density functional theory of chemical reactivity. Specific working equations and numerical results are provided for the 3-state ensemble model.
Franco-Pérez, Marco; Ayers, Paul W; Gázquez, José L; Vela, Alberto
2015-12-28
We explore the local and nonlocal response functions of the grand canonical potential density functional at nonzero temperature. In analogy to the zero-temperature treatment, local (e.g., the average electron density and the local softness) and nonlocal (e.g., the softness kernel) intrinsic response functions are defined as partial derivatives of the grand canonical potential with respect to its thermodynamic variables (i.e., the chemical potential of the electron reservoir and the external potential generated by the atomic nuclei). To define the local and nonlocal response functions of the electron density (e.g., the Fukui function, the linear density response function, and the dual descriptor), we differentiate with respect to the average electron number and the external potential. The well-known mathematical relationships between the intrinsic response functions and the electron-density responses are generalized to nonzero temperature, and we prove that in the zero-temperature limit, our results recover well-known identities from the density functional theory of chemical reactivity. Specific working equations and numerical results are provided for the 3-state ensemble model.
Berkane, K.; Bencheikh, K.
2005-08-15
For first-principles density functional theory of a many fermion system, the determination of the kinetic energy functional is important. We consider N independent fermions with spatially varying effective mass in two dimensions, we derive the corresponding kinetic energy density using the ({Dirac_h}/2{pi}) semiclassical approach. Our result reduces, as expected, to the one obtained in the literature for a constant effective mass. We examine the analytical expressions of the position dependent effective mass terms in the kinetic energy density functional with respect to the dimensionality d=1,2,3 of the space.
Self-similar space-time evolution of an initial density discontinuity
Rekaa, V. L.; Pécseli, H. L.; Trulsen, J. K.
2013-07-15
The space-time evolution of an initial step-like plasma density variation is studied. We give particular attention to formulate the problem in a way that opens for the possibility of realizing the conditions experimentally. After a short transient time interval of the order of the electron plasma period, the solution is self-similar as illustrated by a video where the space-time evolution is reduced to be a function of the ratio x/t. Solutions of this form are usually found for problems without characteristic length and time scales, in our case the quasi-neutral limit. By introducing ion collisions with neutrals into the numerical analysis, we introduce a length scale, the collisional mean free path. We study the breakdown of the self-similarity of the solution as the mean free path is made shorter than the system length. Analytical results are presented for charge exchange collisions, demonstrating a short time collisionless evolution with an ensuing long time diffusive relaxation of the initial perturbation. For large times, we find a diffusion equation as the limiting analytical form for a charge-exchange collisional plasma, with a diffusion coefficient defined as the square of the ion sound speed divided by the (constant) ion collision frequency. The ion-neutral collision frequency acts as a parameter that allows a collisionless result to be obtained in one limit, while the solution of a diffusion equation is recovered in the opposite limit of large collision frequencies.
Generation of time histories with a specified auto spectral density and probability density function
Smallwood, D.O.
1996-08-01
It is recognized that some dynamic and noise environments are characterized by time histories which are not Gaussian. An example is high intensity acoustic noise. Another example is some transportation vibration. A better simulation of these environments can be generated if a zero mean non-Gaussian time history can be reproduced with a specified auto (or power) spectral density (ASD or PSD) and a specified probability density function (pdf). After the required time history is synthesized, the waveform can be used for simulation purposes. For example, modem waveform reproduction techniques can be used to reproduce the waveform on electrodynamic or electrohydraulic shakers. Or the waveforms can be used in digital simulations. A method is presented for the generation of realizations of zero mean non-Gaussian random time histories with a specified ASD, and pdf. First a Gaussian time history with the specified auto (or power) spectral density (ASD) is generated. A monotonic nonlinear function relating the Gaussian waveform to the desired realization is then established based on the Cumulative Distribution Function (CDF) of the desired waveform and the known CDF of a Gaussian waveform. The established function is used to transform the Gaussian waveform to a realization of the desired waveform. Since the transformation preserves the zero-crossings and peaks of the original Gaussian waveform, and does not introduce any substantial discontinuities, the ASD is not substantially changed. Several methods are available to generate a realization of a Gaussian distributed waveform with a known ASD. The method of Smallwood and Paez (1993) is an example. However, the generation of random noise with a specified ASD but with a non-Gaussian distribution is less well known.
Differentiable but exact formulation of density-functional theory
Kvaal, Simen Ekström, Ulf; Helgaker, Trygve; Teale, Andrew M.
2014-05-14
The universal density functional F of density-functional theory is a complicated and ill-behaved function of the density—in particular, F is not differentiable, making many formal manipulations more complicated. While F has been well characterized in terms of convex analysis as forming a conjugate pair (E, F) with the ground-state energy E via the Hohenberg–Kohn and Lieb variation principles, F is nondifferentiable and subdifferentiable only on a small (but dense) subset of its domain. In this article, we apply a tool from convex analysis, Moreau–Yosida regularization, to construct, for any ε > 0, pairs of conjugate functionals ({sup ε}E, {sup ε}F) that converge to (E, F) pointwise everywhere as ε → 0{sup +}, and such that {sup ε}F is (Fréchet) differentiable. For technical reasons, we limit our attention to molecular electronic systems in a finite but large box. It is noteworthy that no information is lost in the Moreau–Yosida regularization: the physical ground-state energy E(v) is exactly recoverable from the regularized ground-state energy {sup ε}E(v) in a simple way. All concepts and results pertaining to the original (E, F) pair have direct counterparts in results for ({sup ε}E, {sup ε}F). The Moreau–Yosida regularization therefore allows for an exact, differentiable formulation of density-functional theory. In particular, taking advantage of the differentiability of {sup ε}F, a rigorous formulation of Kohn–Sham theory is presented that does not suffer from the noninteracting representability problem in standard Kohn–Sham theory.
Orbital nodal surfaces: Topological challenges for density functionals
NASA Astrophysics Data System (ADS)
Aschebrock, Thilo; Armiento, Rickard; Kümmel, Stephan
2017-06-01
Nodal surfaces of orbitals, in particular of the highest occupied one, play a special role in Kohn-Sham density-functional theory. The exact Kohn-Sham exchange potential, for example, shows a protruding ridge along such nodal surfaces, leading to the counterintuitive feature of a potential that goes to different asymptotic limits in different directions. We show here that nodal surfaces can heavily affect the potential of semilocal density-functional approximations. For the functional derivatives of the Armiento-Kümmel (AK13) [Phys. Rev. Lett. 111, 036402 (2013), 10.1103/PhysRevLett.111.036402] and Becke88 [Phys. Rev. A 38, 3098 (1988), 10.1103/PhysRevA.38.3098] energy functionals, i.e., the corresponding semilocal exchange potentials, as well as the Becke-Johnson [J. Chem. Phys. 124, 221101 (2006), 10.1063/1.2213970] and van Leeuwen-Baerends (LB94) [Phys. Rev. A 49, 2421 (1994), 10.1103/PhysRevA.49.2421] model potentials, we explicitly demonstrate exponential divergences in the vicinity of nodal surfaces. We further point out that many other semilocal potentials have similar features. Such divergences pose a challenge for the convergence of numerical solutions of the Kohn-Sham equations. We prove that for exchange functionals of the generalized gradient approximation (GGA) form, enforcing correct asymptotic behavior of the potential or energy density necessarily leads to irregular behavior on or near orbital nodal surfaces. We formulate constraints on the GGA exchange enhancement factor for avoiding such divergences.
Differentiable but exact formulation of density-functional theory
NASA Astrophysics Data System (ADS)
Kvaal, Simen; Ekström, Ulf; Teale, Andrew M.; Helgaker, Trygve
2014-05-01
The universal density functional F of density-functional theory is a complicated and ill-behaved function of the density—in particular, F is not differentiable, making many formal manipulations more complicated. While F has been well characterized in terms of convex analysis as forming a conjugate pair (E, F) with the ground-state energy E via the Hohenberg-Kohn and Lieb variation principles, F is nondifferentiable and subdifferentiable only on a small (but dense) subset of its domain. In this article, we apply a tool from convex analysis, Moreau-Yosida regularization, to construct, for any ɛ > 0, pairs of conjugate functionals (ɛE, ɛF) that converge to (E, F) pointwise everywhere as ɛ → 0+, and such that ɛF is (Fréchet) differentiable. For technical reasons, we limit our attention to molecular electronic systems in a finite but large box. It is noteworthy that no information is lost in the Moreau-Yosida regularization: the physical ground-state energy E(v) is exactly recoverable from the regularized ground-state energy ɛE(v) in a simple way. All concepts and results pertaining to the original (E, F) pair have direct counterparts in results for (ɛE, ɛF). The Moreau-Yosida regularization therefore allows for an exact, differentiable formulation of density-functional theory. In particular, taking advantage of the differentiability of ɛF, a rigorous formulation of Kohn-Sham theory is presented that does not suffer from the noninteracting representability problem in standard Kohn-Sham theory.
Time-dependent Partition Density-functional Theory
NASA Astrophysics Data System (ADS)
Mosquera, Martin; Wasserman, Adam
2012-02-01
We present an extension of time-dependent density functional theory that allows to partition the time-dependent external potential in terms of localized molecular fragment potentials. As a consequence, localized time-dependent densities arise for each molecular fragment. To enforce the condition that the sum of fragments must add up to the exact total density, a new quantity termed ``time-dependent partition potential'' is introduced. The Runge-Gross theorem is employed to show that there is a quasi one-to-one correspondence between the partition potential and the electronic density. The corresponding quantum-mechanical actions are derived by using the van Leeuwen's action and are used to derive a decomposition of the partition potential which allows for practical approximations. Linear response formulas are deduced to obtain the transition energies, and an approximation is suggested to obtain localized excitations in large molecular systems. Finally, numerical illustration of our theory is shown for one-dimensional fermions under the influence of a laser field.
Nonadiabatic electron dynamics in time-dependent density-functional theory
NASA Astrophysics Data System (ADS)
Ullrich, C. A.; Tokatly, I. V.
2006-06-01
Time-dependent density-functional theory (TDDFT) treats dynamical exchange and correlation (xc) via a single-particle potential, Vxc(r,t) , defined as a nonlocal functional of the density n(r',t') . The popular adiabatic local-density approximation (ALDA) for Vxc(r,t) uses only densities at the same space-time point (r,t) . To go beyond the ALDA, two local approximations have been proposed based on quantum hydrodynamics and elasticity theory: (a) using the current as the basic variable (C-TDDFT) [G. Vignale, C. A. Ullrich, and S. Conti, Phys. Rev. Lett. 79, 4847 (1997)], (b) working in a comoving Lagrangian reference frame (L-TDDFT) [I. V. Tokatly, Phys. Rev. B 71, 165105 (2005)]. In this paper we illustrate, compare, and analyze both nonadiabatic theories for simple time-dependent model densities in the linear and nonlinear regime, for a broad range of time and frequency scales. C- and L-TDDFT are identical in certain limits, but, in general, exhibit qualitative and quantitative differences in their respective treatment of elastic and dissipative electron dynamics. In situations where the electronic density rapidly undergoes large deformations, it is found that nonadiabatic effects can become significant, causing the ALDA to break down.
Density-dependence of functional spiking networks in vitro
Ham, Michael I; Gintautuas, Vadas; Rodriguez, Marko A; Bettencourt, Luis M A; Bennett, Ryan; Santa Maria, Cara L
2008-01-01
During development, the mammalian brain differentiates into specialized regions with unique functional abilities. While many factors contribute to this functional specialization, we explore the effect neuronal density can have on neuronal interactions. Two types of networks, dense (50,000 neurons and glia support cells) and sparse (12,000 neurons and glia support cells), are studied. A competitive first response model is applied to construct activation graphs that represent pairwise neuronal interactions. By observing the evolution of these graphs during development in vitro we observe that dense networks form activation connections earlier than sparse networks, and that link-!llltropy analysis of the resulting dense activation graphs reveals that balanced directional connections dominate. Information theoretic measures reveal in addition that early functional information interactions (of order 3) are synergetic in both dense and sparse networks. However, during development in vitro, such interactions become redundant in dense, but not sparse networks. Large values of activation graph link-entropy correlate strongly with redundant ensembles observed in the dense networks. Results demonstrate differences between dense and sparse networks in terms of informational groups, pairwise relationships, and activation graphs. These differences suggest that variations in cell density may result in different functional specialization of nervous system tissue also in vivo.
Downlink Probability Density Functions for EOS-McMurdo Sound
NASA Technical Reports Server (NTRS)
Christopher, P.; Jackson, A. H.
1996-01-01
The visibility times and communication link dynamics for the Earth Observations Satellite (EOS)-McMurdo Sound direct downlinks have been studied. The 16 day EOS periodicity may be shown with the Goddard Trajectory Determination System (GTDS) and the entire 16 day period should be simulated for representative link statistics. We desire many attributes of the downlink, however, and a faster orbital determination method is desirable. We use the method of osculating elements for speed and accuracy in simulating the EOS orbit. The accuracy of the method of osculating elements is demonstrated by closely reproducing the observed 16 day Landsat periodicity. An autocorrelation function method is used to show the correlation spike at 16 days. The entire 16 day record of passes over McMurdo Sound is then used to generate statistics for innage time, outage time, elevation angle, antenna angle rates, and propagation loss. The levation angle probability density function is compared with 1967 analytic approximation which has been used for medium to high altitude satellites. One practical result of this comparison is seen to be the rare occurrence of zenith passes. The new result is functionally different than the earlier result, with a heavy emphasis on low elevation angles. EOS is one of a large class of sun synchronous satellites which may be downlinked to McMurdo Sound. We examine delay statistics for an entire group of sun synchronous satellites ranging from 400 km to 1000 km altitude. Outage probability density function results are presented three dimensionally.
Bone mineral density and functional measures in patients with arthrogryposis.
Spencer, Hillard T; Bowen, Richard E; Caputo, Kimberly; Green, Terri A; Lawrence, John F
2010-01-01
Patients with arthrogryposis often report decreased ambulation and physical activity. Given that skeletal mineralisation is responsive to force, we identified the need to characterize bone mineral density and functional measures in this population, and conducted a cross-sectional study to establish a reference for future investigations. Thirty consecutive patients aged 5 to 18 years with either the diagnosis of amyoplasia or nonsyndromic arthrogryposis with predominantly lower extremity involvement underwent bone densitometry testing, and lumbar spine Z-scores were calculated against an age and sex-matched control population as is customary in children. Pediatric outcomes data collection instrument (PODCI) and functional independence measure for Children (WeeFIM) assessment forms were completed. Mean Z-scores, PODCI, and WeeFIM scores were calculated. Statistical analysis was performed to compare lumbar spine Z-scores between patients divided by ambulatory status and to correlate WeeFIM and PODCI scores. Mean lumbar spine Z-score was -0.47, with 73% of Z-scores being <0. Mean Z-score among nonambulators or home ambulators was -1.05, as compared to a mean Z-score among limited and unlimited community ambulators of -0.14 with a trend toward significance (P=0.10), and a dose-response relationship between higher bone density and increasing ambulatory function. Mean WeeFIM self-care and mobility quotient scores were 67.5/100 and 70.9/100, respectively. PODCI normative scores were decreased for upper extremity (10/50), transfer/basic mobility (-17/50), and sports/physical function (4/50), but normal in pain/comfort (45/50) and happiness (49/50). A linear relationship was noted between functional ambulation level and WeeFIM quotient and PODCI normative scores. There was good correlation between WeeFIM mobility and PODCI transfers and basic mobility standardised scores (R=0.86). This is the first study to measure bone mineral density in children with arthrogryposis, and
Stochastic Time-Dependent Current-Density Functional Theory
NASA Astrophysics Data System (ADS)
D'Agosta, Roberto
2008-03-01
Static and dynamical density functional methods have been applied with a certain degree of success to a variety of closed quantum mechanical systems, i.e., systems that can be described via a Hamiltonian dynamics. However, the relevance of open quantum systems - those coupled to external environments, e.g., baths or reservoirs - cannot be overestimated. To investigate open quantum systems with DFT methods we have introduced a new theory, we have named Stochastic Time-Dependent Current Density Functional theory (S-TDCDFT) [1]: starting from a suitable description of the system dynamics via a stochastic Schrödinger equation [2], we have proven that given an initial quantum state and the coupling between the system and the environment, there is a one-to-one correspondence between the ensemble-averaged current density and the external vector potential applied to the system.In this talk, I will introduce the stochastic formalism needed for the description of open quantum systems, discuss in details the theorem of Stochastic TD-CDFT, and provide few examples of its applicability like the dissipative dynamics of excited systems, quantum-measurement theory and other applications relevant to charge and energy transport in nanoscale systems.[1] M. Di Ventra and R. D'Agosta, Physical Review Letters 98, 226403 (2007)[2] N.G. van Kampen, Stochastic processes in Physics and Chemistry, (North Holland, 2001), 2nd ed.
Density functional calculation of transition metal adatom adsorption on graphene.
Mao, Yuliang; Yuan, Jianmei; Zhong, Jianxin
2008-03-19
The functionalization of graphene (a single graphite layer) by the addition of transition metal atoms of Mn, Fe and Co to its surface has been investigated computationally using density functional theory. In the calculation, the graphene surface supercell was constructed from a single layer of graphite (0001) surface separated by vertical vacuum layers 2 nm thick. We found that the center of the hexagonal ring formed by carbon from graphene is the most stable site for Mn, Fe, Co to stay after optimization. The calculated spin-polarized band structures of the graphene encapsulating the Mn adatom indicate that the conduction bands are modified and move down due to the coupling between the Mn atom and graphene. For Fe adsorbed on the graphene surface, it is semi-half-metallic, and the spin polarization P is found to be 100%. The system of Co adatom on graphene exhibits metallic electronic structure due to the density of states (DOS) peak at the band center with both majority and minority spins. Local density of states analyses indicate a larger promotion of 4s electrons into the 3d state in Fe and Co, resulting in lower local moments compared to an Mn adatom on the graphite surface.
Density functional theory for inhomogeneous ring polymeric fluids.
Jiang, Jian; Xu, Xiaofei; Cao, Dapeng
2012-10-01
The modeling of ring polymers remains a challenge in classical density functional theory (DFT) due to the difficulty in solving the direct bond connectivity of the ring architecture without free ends. By considering the feature that all of the segments in a ring are equivalent, we give an algorithm to solve the integral of direct bond connectivity for ideal ring polymers, and therefore propose a DFT for inhomogeneous ring polymers, where the excess free energy functional is extended from an equation of state (EOS). This EOS exhibits better agreement than other EOSs for the compressibility factors, compared to Monte Carlo data. Importantly, the DFT satisfactorily reproduces the data of the configurational-bias Monte Carlo (CBMC) simulations for ring polymers. The local density profiles from the DFT show that the bead density of inhomogeneous ring fluids is independent of ring size, which is also confirmed by the CBMC simulations. Interestingly, the behavior of solvation force for ring polymers is quite similar to that of the polymers with infinite chain length.
Density functional theory: Its origins, rise to prominence, and future
NASA Astrophysics Data System (ADS)
Jones, R. O.
2015-07-01
In little more than 20 years, the number of applications of the density functional (DF) formalism in chemistry and materials science has grown in an astonishing fashion. The number of publications alone shows that DF calculations make up a huge success story, and many younger colleagues are surprised to learn that the widespread application of density functional methods, particularly in chemistry, began only after 1990. This is indeed unexpected, because the origins are usually traced to the papers of Hohenberg, Kohn, and Sham more than a quarter of a century earlier. The DF formalism, its applications, and prospects were reviewed for this journal in 1989. About the same time, the combination of DF calculations with molecular dynamics promised to provide an efficient way to study structures and reactions in molecules and extended systems. This paper reviews the development of density-related methods back to the early years of quantum mechanics and follows the breakthrough in their application after 1990. The two examples from biochemistry and materials science are among the many current applications that were simply far beyond expectations in 1990. The reasons why—50 years after its modern formulation and after two decades of rapid expansion—some of the most cited practitioners in the field are concerned about its future are discussed.
NASA Astrophysics Data System (ADS)
Higuchi, Katsuhiko; Niwa, Hiroyasu; Higuchi, Masahiko
2017-10-01
We present the current-density functional theory for the superconductor immersed in the magnetic field. The order parameter of the superconducting state, transverse component of the paramagnetic current-density, and electron density are chosen as basic variables that uniquely determine the equilibrium properties of the system. In order to construct this theory, the development of the approximate form of the exchange-correlation (xc) energy functional is indispensable as well as the derivation of the effective single-particle equation which makes it possible to reproduce the equilibrium densities mentioned above. The rigorous expression of the xc-energy functional is derived using the technique of the coupling-constant integration. Furthermore, the approximate form of the xc energy functional is proposed such that the energy gap resulting from the effective single-particle equation is consistent with the attractive interaction energy of the system.
Massively parallel density functional calculations for thousands of atoms: KKRnano
NASA Astrophysics Data System (ADS)
Thiess, A.; Zeller, R.; Bolten, M.; Dederichs, P. H.; Blügel, S.
2012-06-01
Applications of existing precise electronic-structure methods based on density functional theory are typically limited to the treatment of about 1000 inequivalent atoms, which leaves unresolved many open questions in material science, e.g., on complex defects, interfaces, dislocations, and nanostructures. KKRnano is a new massively parallel linear scaling all-electron density functional algorithm in the framework of the Korringa-Kohn-Rostoker (KKR) Green's-function method. We conceptualized, developed, and optimized KKRnano for large-scale applications of many thousands of atoms without compromising on the precision of a full-potential all-electron method, i.e., it is a method without any shape approximation of the charge density or potential. A key element of the new method is the iterative solution of the sparse linear Dyson equation, which we parallelized atom by atom, across energy points in the complex plane and for each spin degree of freedom using the message passing interface standard, followed by a lower-level OpenMP parallelization. This hybrid four-level parallelization allows for an efficient use of up to 100000 processors on the latest generation of supercomputers. The iterative solution of the Dyson equation is significantly accelerated, employing preconditioning techniques making use of coarse-graining principles expressed in a block-circulant preconditioner. In this paper, we will describe the important elements of this new algorithm, focusing on the parallelization and preconditioning and showing scaling results for NiPd alloys up to 8192 atoms and 65536 processors. At the end, we present an order-N algorithm for large-scale simulations of metallic systems, making use of the nearsighted principle of the KKR Green's-function approach by introducing a truncation of the electron scattering to a local cluster of atoms, the size of which is determined by the requested accuracy. By exploiting this algorithm, we show linear scaling calculations of more
Visualization of high-density 3D graphs using nonlinear visual space transformations
NASA Astrophysics Data System (ADS)
Hao, Ming C.; Dayal, Umeshwar; Garg, Pankaj; Machiraju, Vijay
2002-03-01
The real world data distribution is seldom uniform. Clutter and sparsity commonly occur in visualization. Often, clutter results in overplotting, in which certain data items are not visible because other data items occlude them. Sparsity results in the inefficient use of the available display space. Common mechanisms to overcome this include reducing the amount of information displayed or using multiple representations with a varying amount of detail. This paper describes out experiments on Non-Linear Visual Space Transformations (NLVST). NLVST encompasses several innovative techniques: (1) employing a histogram for calculating the density of data distribution; (2) mapping the raw data values to a non-linear scale for stretching a high-density area; (3) tightening the sparse area to save the display space; (4) employing different color ranges of values on a non-linear scale according to the local density. We have applied NLVST to several web applications: market basket analysis, transactions observation, and IT search behavior analysis.
Simplified Computation for Nonparametric Windows Method of Probability Density Function Estimation.
Joshi, Niranjan; Kadir, Timor; Brady, Michael
2011-08-01
Recently, Kadir and Brady proposed a method for estimating probability density functions (PDFs) for digital signals which they call the Nonparametric (NP) Windows method. The method involves constructing a continuous space representation of the discrete space and sampled signal by using a suitable interpolation method. NP Windows requires only a small number of observed signal samples to estimate the PDF and is completely data driven. In this short paper, we first develop analytical formulae to obtain the NP Windows PDF estimates for 1D, 2D, and 3D signals, for different interpolation methods. We then show that the original procedure to calculate the PDF estimate can be significantly simplified and made computationally more efficient by a judicious choice of the frame of reference. We have also outlined specific algorithmic details of the procedures enabling quick implementation. Our reformulation of the original concept has directly demonstrated a close link between the NP Windows method and the Kernel Density Estimator.
Predictors of immune function in space flight
NASA Astrophysics Data System (ADS)
Shearer, William T.; Zhang, Shaojie; Reuben, James M.; Lee, Bang-Ning; Butel, Janet S.
2007-02-01
Of all of the environmental conditions of space flight that might have an adverse effect upon human immunity and the incidence of infection, space radiation stands out as the single-most important threat. As important as this would be on humans engaged in long and deep space flight, it obviously is not possible to plan Earth-bound radiation and infection studies in humans. Therefore, we propose to develop a murine model that could predict the adverse effects of space flight radiation and reactivation of latent virus infection for humans. Recent observations on the effects of gamma and latent virus infection demonstrate latent virus reactivation and loss of T cell mediated immune responses in a murine model. We conclude that using this small animal method of quantitating the amounts of radiation and latent virus infection and resulting alterations in immune responses, it may be possible to predict the degree of immunosuppression in interplanetary space travel for humans. Moreover, this model could be extended to include other space flight conditions, such as microgravity, sleep deprivation, and isolation, to obtain a more complete assessment of space flight risks for humans.
Nuclear chiral and magnetic rotation in covariant density functional theory
NASA Astrophysics Data System (ADS)
Meng, Jie; Zhao, Pengwei
2016-05-01
Excitations of chiral rotation observed in triaxial nuclei and magnetic and/or antimagnetic rotations (AMR) seen in near-spherical nuclei have attracted a lot of attention. Unlike conventional rotation in well-deformed or superdeformed nuclei, here the rotational axis is not necessary coinciding with any principal axis of the nuclear density distribution. Thus, tilted axis cranking (TAC) is mandatory to describe these excitations self-consistently in the framework of covariant density functional theory (CDFT). We will briefly introduce the formalism of TAC-CDFT and its application for magnetic and AMR phenomena. Configuration-fixed CDFT and its predictions for nuclear chiral configurations and for favorable triaxial deformation parameters are also presented, and the discoveries of the multiple chiral doublets in 133Ce and 103Rh are discussed.
Formaldehyde adsorption on carbon nanotubes fragment by density functional theory
NASA Astrophysics Data System (ADS)
Chen, D.; Yuan, Yong J.
2017-07-01
The interaction between formaldehyde (HCOH) and pristine single-walled carbon nanotube (SWCNT) fragment was investigated by density functional theory (DFT) to evaluate the detection of HCOH. The simulation results demonstrated less adsorption on surface of SWCNT and doped CNTs, while a HCOH molecule tended to be chemisorbed to the C atom located on SWCNT’s edge positions with larger binding energy of 1.742 eV and smaller binding distance of 1.351 Å. Furthermore, charge transfer and density of states study indicated that the electronic properties changed evidently in the most stable HCOH-SWCNT system, and were mainly around the Fermi level. More importantly, the adsorption of HCOH affected the electronic conductance of SWCNT. It is expected that the results could provide a useful theoretical guidance for the investigation of molecular films interface bonding and design of HCOH sensing devices.
Applications of large-scale density functional theory in biology
NASA Astrophysics Data System (ADS)
Cole, Daniel J.; Hine, Nicholas D. M.
2016-10-01
Density functional theory (DFT) has become a routine tool for the computation of electronic structure in the physics, materials and chemistry fields. Yet the application of traditional DFT to problems in the biological sciences is hindered, to a large extent, by the unfavourable scaling of the computational effort with system size. Here, we review some of the major software and functionality advances that enable insightful electronic structure calculations to be performed on systems comprising many thousands of atoms. We describe some of the early applications of large-scale DFT to the computation of the electronic properties and structure of biomolecules, as well as to paradigmatic problems in enzymology, metalloproteins, photosynthesis and computer-aided drug design. With this review, we hope to demonstrate that first principles modelling of biological structure-function relationships are approaching a reality.
Time-dependent density functional theory for open quantum systems
NASA Astrophysics Data System (ADS)
Tempel, David; Aspuru-Guzik, Alan
2012-02-01
We present the extension of time-dependent density functional theory (TDDFT) to the realm of open quantum systems (OQS). OQS-TDDFT allows a first principles description of electronic systems undergoing non-unitary dynamics due to coupling with a bath, such as that arising from molecular vibrations, solvent degrees of freedom or photon modes of the electromagnetic field. We first prove extensions of the Runge-Gross and van Leeuwen theorems to OQS-TDDFT, which rigorously establish it as a formally exact theory. We then discuss development of approximate OQS-TDDFT functionals, exact conditions on these functionals, as well as future challenges. Finally, we will discuss the application of OQS-TDDFT in obtaining broadened absorption spectra.
Nonlocal van der Waals density functional made simple and efficient
NASA Astrophysics Data System (ADS)
Sabatini, Riccardo; Gorni, Tommaso; de Gironcoli, Stefano
2013-01-01
We present a simple revision of the VV10 nonlocal density functional by Vydrov and Van Voorhis [J. Chem. Phys.JCPSA60021-960610.1063/1.3521275 133, 244103 (2010)] for dispersion interactions. Unlike the original functional our modification allows nonlocal correlation energy and its derivatives to be efficiently evaluated in a plane wave framework along the lines pioneered by Román-Pérez and Soler [Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.103.096102 103, 096102 (2009)]. Our revised functional maintains the outstanding precision of the original VV10 in noncovalently bound complexes and performs well in representative covalent, ionic, and metallic solids.
Density functional theory based simulations of silicon nanowire field effect transistors
Shin, Mincheol Jeong, Woo Jin; Lee, Jaehyun
2016-04-21
First-principles density functional theory (DFT) based, atomistic, self-consistent device simulations are performed for realistically sized Si nanowire field effect transistors (NW FETs) having tens of thousands of atoms. Through mode space transformation, DFT Hamiltonian and overlap matrices are reduced in size from a few thousands to around one hundred. Ultra-efficient quantum-mechanical transport calculations in the non-equilibrium Green's function formalism in a non-orthogonal basis are therefore made possible. The n-type and p-type Si NW FETs are simulated and found to exhibit similar device performance in the nanoscale regime.
De Laender, Frederik; Taub, Frieda B; Janssen, Colin R
2011-12-01
Understanding whether and to what extent ecosystem functions respond to chemicals is a major challenge in environmental toxicology. The available data gathered by ecosystem-level experiments (micro- and mesocosms) often describe the responses of taxa densities to stress. However, whether these responses are proportional to the responses of associated ecosystem functions to stress is unclear. By combining a carbon budget modeling technique with data from a standardized microcosm experiment with a known community composition, we quantified three ecosystem functions (net primary production [NPP], net mesozooplankton production [NZP], and net bacterial production [NBP]) at three Cu concentrations, with a control. Changes of these ecosystem functions with increasing chemical concentrations were not always proportional to the Cu effects on the densities of the contributing functional groups. For example, Cu treatments decreased mesozooplankton density by 100-fold and increased phytoplankton density 10- to 100-fold while increasing NZP and leaving NPP unaltered. However, in contrast, Cu affected microzooplankton and the associated function (NBP) in a comparable way. We illustrate that differences in the response of phytoplankton/mesozooplankton densities and the associated ecosystem functions to stress occur because functional rates (e.g., photosynthesis rates/ingestion rates) vary among Cu treatments and in time. These variations could be explained by food web ecology but not by direct Cu effects, indicating that ecology may be a useful basis for understanding environmental effects of stressors.
A method to estimate plant density and plant spacing heterogeneity: application to wheat crops.
Liu, Shouyang; Baret, Fred; Allard, Denis; Jin, Xiuliang; Andrieu, Bruno; Burger, Philippe; Hemmerlé, Matthieu; Comar, Alexis
2017-01-01
Plant density and its non-uniformity drive the competition among plants as well as with weeds. They need thus to be estimated with small uncertainties accuracy. An optimal sampling method is proposed to estimate the plant density in wheat crops from plant counting and reach a given precision. Three experiments were conducted in 2014 resulting in 14 plots across varied sowing density, cultivars and environmental conditions. The coordinates of the plants along the row were measured over RGB high resolution images taken from the ground level. Results show that the spacing between consecutive plants along the row direction are independent and follow a gamma distribution under the varied conditions experienced. A gamma count model was then derived to define the optimal sample size required to estimate plant density for a given precision. Results suggest that measuring the length of segments containing 90 plants will achieve a precision better than 10%, independently from the plant density. This approach appears more efficient than the usual method based on fixed length segments where the number of plants are counted: the optimal length for a given precision on the density estimation will depend on the actual plant density. The gamma count model parameters may also be used to quantify the heterogeneity of plant spacing along the row by exploiting the variability between replicated samples. Results show that to achieve a 10% precision on the estimates of the 2 parameters of the gamma model, 200 elementary samples corresponding to the spacing between 2 consecutive plants should be measured. This method provides an optimal sampling strategy to estimate the plant density and quantify the plant spacing heterogeneity along the row.
NASA Astrophysics Data System (ADS)
Pretorius, M.
2014-07-01
I will present estimates of the space densities of both non-magnetic and magnetic cataclysmic variables (CVs), based on X-ray flux-limited samples. The measurements can be used to address several questions relevant to the evolution of CVs and to the makeup of Galactic X-ray source populations. I will discuss the implications of these results for the high predicted space density of non-magnetic CVs, the evolutionary relationship between intermediate polars and polars, the fraction of CVs with strongly magnetic white dwarfs, and for the contribution of magnetic CVs to Galactic populations of hard X-ray sources.
Progress at the interface of wave-function and density-functional theories
Gidopoulos, Nikitas I.
2011-04-15
The Kohn-Sham (KS) potential of density-functional theory (DFT) emerges as the minimizing effective potential in a variational scheme that does not involve fixing the unknown single-electron density. Using Rayleigh Schroedinger (RS) perturbation theory (PT), we construct ab initio approximations for the energy difference, the minimization of which determines the KS potential directly - thereby bypassing DFT's traditional algorithm to search for the density that minimizes the total energy. From second-order RS PT, we obtain variationally stable energy differences to be minimized, solving the severe problem of variational collapse of orbital-dependent exchange-correlation functionals based on second-order RS PT.
Graphene oxide and adsorption of chloroform: A density functional study
NASA Astrophysics Data System (ADS)
Kuisma, Elena; Hansson, C. Fredrik; Lindberg, Th. Benjamin; Gillberg, Christoffer A.; Idh, Sebastian; Schröder, Elsebeth
2016-05-01
Chlorinated hydrocarbon compounds are of environmental concerns, since they are toxic to humans and other mammals, and are widespread, and exposure is hard to avoid. Understanding and improving methods to reduce the amount of the substances are important. We present an atomic-scale calculational study of the adsorption of chlorine-based substance chloroform (CHCl3) on graphene oxide, as a step in estimating the capacity of graphene oxide for filtering out such substances, e.g., from drinking water. The calculations are based on density functional theory, and the recently developed consistent-exchange functional for the van der Waals density-functional method is employed. We obtain values of the chloroform adsorption energy varying from roughly 0.2 to 0.4 eV per molecule. This is comparable to previously found results for chloroform adsorbed directly on clean graphene, using similar calculations. In a wet environment, like filters for drinking water, the graphene will not stay clean and will likely oxidize, and thus adsorption onto graphene oxide, rather than clean graphene, is a more relevant process to study.
INTERACTIVE VISUALIZATION OF PROBABILITY AND CUMULATIVE DENSITY FUNCTIONS
Potter, Kristin; Kirby, Robert M.; Xiu, Dongbin; Johnson, Chris R.
2013-01-01
The probability density function (PDF), and its corresponding cumulative density function (CDF), provide direct statistical insight into the characterization of a random process or field. Typically displayed as a histogram, one can infer probabilities of the occurrence of particular events. When examining a field over some two-dimensional domain in which at each point a PDF of the function values is available, it is challenging to assess the global (stochastic) features present within the field. In this paper, we present a visualization system that allows the user to examine two-dimensional data sets in which PDF (or CDF) information is available at any position within the domain. The tool provides a contour display showing the normed difference between the PDFs and an ansatz PDF selected by the user and, furthermore, allows the user to interactively examine the PDF at any particular position. Canonical examples of the tool are provided to help guide the reader into the mapping of stochastic information to visual cues along with a description of the use of the tool for examining data generated from an uncertainty quantification exercise accomplished within the field of electrophysiology. PMID:23543120
NASA Astrophysics Data System (ADS)
Ellison, James A.; Heinemann, Klaus
2007-10-01
A class of orbital motions with volume preserving flows and with vector fields periodic in the “time” parameter θ is defined. Spin motion coupled to the orbital dynamics is then defined, resulting in a class of spin-orbit motions which are important for storage rings. Phase space densities and polarization fields are introduced. It is important, in the context of storage rings, to understand the behavior of periodic polarization fields and phase space densities. Due to the 2π time periodicity of the spin-orbit equations of motion the polarization field, taken at a sequence of increasing time values θ,θ+2π,θ+4π,…, gives a sequence of polarization fields, called the stroboscopic sequence. We show, by using the Birkhoff ergodic theorem, that under very general conditions the Cesàro averages of that sequence converge almost everywhere on phase space to a polarization field which is 2π-periodic in time. This fulfills the main aim of this paper in that it demonstrates that the tracking algorithm for stroboscopic averaging, encoded in the program SPRINT and used in the study of spin motion in storage rings, is mathematically well-founded. The machinery developed is also shown to work for the stroboscopic average of phase space densities associated with the orbital dynamics. This yields a large family of periodic phase space densities and, as an example, a quite detailed analysis of the so-called betatron motion in a storage ring is presented.
Two functions of the density matrix and their relation to the chemical bond
NASA Astrophysics Data System (ADS)
Schmider, Hartmut L.; Becke, Axel D.
2002-02-01
We examine and compare two previously introduced functions of the one-particle density matrix that are suitable to represent its off-diagonal structure in a condensed form and that have illustrative connections to the nature of the chemical bond. One of them, the Localized-Orbital Locator (LOL) [J. Molec. Struct. (THEOCHEM) 527, 51 (2000)], is based only on the noninteracting kinetic-energy density τ and the charge density ρ at a point, and gives an intuitive measure of the relative speed of electrons in its vicinity. Alternatively, LOL focuses on regions that are dominated by single localized orbitals. The other one, the Parity Function P [J. Chem. Phys. 105, 11134 (1996)], is a section through the Wigner phase-space function at zero momentum, and contains information about the phase of the interference of atomiclike orbital contributions from bound centers. In this paper, we discuss the way in which these functions condense information in the density matrix, and illustrate on a variety of examples of unusual chemical bonds how they can help to understand the nature of "covalence."
Relativistic cosmology number densities and the luminosity function
NASA Astrophysics Data System (ADS)
Iribarrem, A. S.; Lopes, A. R.; Ribeiro, M. B.; Stoeger, W. R.
2012-03-01
Aims: This paper studies the connection between the relativistic number density of galaxies down the past light cone in a Friedmann-Lemaître-Robertson-Walker spacetime with non-vanishing cosmological constant and the galaxy luminosity function (LF) data. It extends the redshift range of previous results presented in Albani et al. (2007, ApJ, 657, 760), where the galaxy distribution was studied out to z = 1. Observational inhomogeneities were detected at this range. This research also searches for LF evolution in the context of the framework advanced by Ribeiro and Stoeger (2003, ApJ, 592, 1), further developing the theory linking relativistic cosmology theory and LF data. Methods: Selection functions are obtained using the Schechter parameters and redshift parametrization of the galaxy LF obtained from an I-band selected dataset of the FORS deep field galaxy survey in the redshift range 0.5 ≤ z ≤ 5.0 for its blue bands and 0.75 ≤ z ≤ 3.0 for its red ones. Differential number counts, densities and other related observables are obtained, and then used with the calculated selection functions to study the empirical radial distribution of the galaxies in a fully relativistic framework. Results: The redshift range of the dataset used in this work, which is up to five times larger than the one used in previous studies, shows an increased relevance of the relativistic effects of expansion when compared to the evolution of the LF at the higher redshifts. The results also agree with the preliminary ones presented in Albani et al., suggesting a power-law behavior of relativistic densities at high redshifts when they are defined in terms of the luminosity distance.
Harris-type van der Waals density functional scheme
NASA Astrophysics Data System (ADS)
Berland, Kristian; Londero, Elisa; Schröder, Elsebeth; Hyldgaard, Per
2013-07-01
Biomolecular systems that involve thousands of atoms are difficult to address with standard density functional theory (DFT) calculations. With the development of sparse-matter methods such as the van der Waals density functional (vdW-DF) method [M. Dion , Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.92.246401 92, 246401 (2004)], it is now possible to include the dispersive forces in DFT which are necessary to describe the cohesion and behavior of these systems. vdW-DF implementations can be as efficient as those for traditional DFT. Yet, the computational costs of self-consistently determining the electron wave functions and hence the kinetic-energy repulsion still limit the scope of sparse-matter DFT. We propose to speed up sparse-matter calculations by using the Harris scheme [J. Harris, Phys. Rev. BPRBMDO1098-012110.1103/PhysRevB.31.1770 31, 1770 (1985)]; that is, we propose to perform electronic relaxations only for separated fragments (molecules) and use a superposition of fragment densities as a starting point to obtain the total energy non-self-consistently. We evaluate the feasibility of this approach for an adaption of the Harris scheme for non-self-consistent vdW-DF (sfd-vdW-DF). We study four molecular dimers with varying degrees of polarity and find that the sfd scheme accurately reproduces standard non-self-consistent vdW-DF for van der Waals dominated systems but is less accurate for those dominated by polar interactions. Results for the S22 set of typical organic molecular dimers are promising.
Electron response in van der Waals density functionals
NASA Astrophysics Data System (ADS)
Hyldgaard, Per
2013-03-01
There is significant interest in density functional theory (DFT) of dispersive or van der Waals (vdW) interactions and in DFT studies of sparse systems where vdW forces contribute to the cohesion and behavior. The Rutgers-Chalmers van der Waals density functional (vdW-DF) method [PRL 92, 246401 (2004); PRB 76, 125112 (2007)] is a nonempirical approach to calculate vdW bonding and for DFT characterizations of sparse matter. The vdW-DF framework is defined by a single exchange-correlation density functional that rests on a plasmon-type description for both semilocal components and for a parameter-free evaluation of nonlocal correlation. My talk summarizes a set of vdW-DF studies that seeks to map and analyze details in the vdW-DF electron-response nature. The purpose is in part to extract consequences that can facilitate an experiment-theory comparison that goes beyond binding geometries and energies. The aim is also to seek implications that can help develop the vdW-DF framework. I present an analysis of the relative importance of morphology, screening (image-plane formation), and collective effects in the vdW-DF description of molecular systems. In addition, I compare vdW-DF results with Cu(111) experiments that tests the electron-response behavior in terms of adsorption-induced band shifts, the form of the overall light-molecule physisorption potential, and the corrugation in the kinetic-energy repulsion of molecules at surfaces. Overall, the vdW-DF studies suggest the importance of benchmarking vdW methods across different length scales and by exploring the variation that arise when related structures have a different balance between exchange repulsion and vdW attraction.
Density Functional Theory Investigation of Sodium Azide at High Pressure
NASA Astrophysics Data System (ADS)
Steele, Brad; Landerville, Aaron; Oleynik, Ivan
2013-03-01
Sodium azide is intriguing because it could potentially be used as a precursor to a high-nitrogen energetic material. Furthermore, recent absorption and Raman spectroscopic results have shown that novel nitrogen structures may indeed be attainable from sodium azide. First-principles density functional theory calculations were performed to characterize possible novel crystalline structures of sodium azide including their atomic structure, vibrational properties, Raman spectra, and equation of state up to 90 GPa. Calculated Raman peaks and intensities show good agreement with experiment.
Density Functional Theory Investigation of Sodium Azide at High Pressure
NASA Astrophysics Data System (ADS)
Steele, Brad; Landerville, Aaron; Oleynik, Ivan
2013-06-01
Sodium azide is being investigated as a potential precursor to a high-nitrogen content energetic material. Changes in the experimentally measured raman spectra under compression and high temperature indicate that a structural change may have taken place. Accurate mode assignments of new peaks arising in the raman spectra have been inconclusive. In this work, the first order raman spectra of sodium azide's alpha and beta phases are calculated using Density Function Pertubation Theory (DFPT) under compression and expansion. Normal mode assignments are made and compared to experiment. In addition, the equation of state of both phases is obtained up to 90 GPa.
Dynamical density functional theory with hydrodynamic interactions in confined geometries
NASA Astrophysics Data System (ADS)
Goddard, B. D.; Nold, A.; Kalliadasis, S.
2016-12-01
We study the dynamics of colloidal fluids in both unconfined geometries and when confined by a hard wall. Under minimal assumptions, we derive a dynamical density functional theory (DDFT) which includes hydrodynamic interactions (HI; bath-mediated forces). By using an efficient numerical scheme based on pseudospectral methods for integro-differential equations, we demonstrate its excellent agreement with the full underlying Langevin equations for systems of hard disks in partial confinement. We further use the derived DDFT formalism to elucidate the crucial effects of HI in confined systems.
Probability Density Function at the 3D Anderson Transition
NASA Astrophysics Data System (ADS)
Rodriguez, Alberto; Vasquez, Louella J.; Roemer, Rudolf
2009-03-01
The probability density function (PDF) for the wavefunction amplitudes is studied at the metal-insulator transition of the 3D Anderson model, for very large systems up to L^3=240^3. The implications of the multifractal nature of the state upon the PDF are presented in detail. A formal expression between the PDF and the singularity spectrum f(α) is given. The PDF can be easily used to carry out a numerical multifractal analysis and it appears as a valid alternative to the more usual approach based on the scaling law of the general inverse participation rations.
Determining Ionospheric Irregularity Spectral Density Function from Japan GEONET
NASA Astrophysics Data System (ADS)
Lay, E. H.; Light, M. E.; Parker, P. A.; Carrano, C. S.; Haaser, R. A.
2015-12-01
Japan's GEONET GPS network is the densest GPS monitoring network in the world, with 1200+ receivers over the area of Japan. Measuring and calibrating the integrated total electron content (TEC) from each station has been done in many cases to provide detailed maps of ionospheric disturbances over Japan. We use TEC measurements from Japan's GEONET array to determine an empirically derived description of the 2-dimensional scale sizes of spatial irregularities above Japan. The contributions from various scale sizes will be included in a statistical description for the irregularity spectral density (ISD) function. We will compare the statistics of the spatial irregularities between calm and moderately scintillated conditions.
Relativistic Energy Density Functionals: Exotic modes of excitation
Vretenar, D.; Paar, N.; Marketin, T.
2008-11-11
The framework of relativistic energy density functionals has been applied to the description of a variety of nuclear structure phenomena, not only in spherical and deformed nuclei along the valley of {beta}-stability, but also in exotic systems with extreme isospin values and close to the particle drip-lines. Dynamical aspects of exotic nuclear structure have been investigated with the relativistic quasiparticle random-phase approximation. We present results for the evolution of low-lying dipole (pygmy) strength in neutron-rich nuclei, and charged-current neutrino-nucleus cross sections.
Density Functional Study of the structural properties in Tamoxifen
NASA Astrophysics Data System (ADS)
de Coss-Martinez, Romeo; Tapia, Jorge A.; Quijano-Quiñones, Ramiro F.; Canto, Gabriel I.
2013-03-01
Using the density functional theory, we have studied the structural properties of Tamoxifen. The calculations were performed with two methodological approaches, which were implemented in SIESTA and Spartan codes. For SIESTA, we considerate a linear combination of atomic orbitals method, using pseudopotentials and the van der Waals approximation for the exchange-correlation potential. Here we analyzed and compared the atomic structure between our results and other theoretical study. We found differences in the bond lengths between the results, that could be attributed to code approaches in each one. This work was supported under Grant FOMIX 2011-09 N: 170297 of Ph.D. A. Tapia.
Quantification of Uncertainties in Nuclear Density Functional Theory
NASA Astrophysics Data System (ADS)
Schunck, N.; McDonnell, J. D.; Higdon, D.; Sarich, J.; Wild, S.
2015-01-01
Reliable predictions of nuclear properties are needed as much to answer fundamental science questions as in applications such as reactor physics or data evaluation. Nuclear density functional theory is currently the only microscopic, global approach to nuclear structure that is applicable throughout the nuclear chart. In the past few years, a lot of effort has been devoted to setting up a general methodology to assess theoretical uncertainties in nuclear DFT calculations. In this paper, we summarize some of the recent progress in this direction. Most of the new material discussed here will be be published in separate articles.
Quantification of Uncertainties in Nuclear Density Functional Theory
Schunck, N.; McDonnell, J.D.; Higdon, D.; Sarich, J.; Wild, S.
2015-01-15
Reliable predictions of nuclear properties are needed as much to answer fundamental science questions as in applications such as reactor physics or data evaluation. Nuclear density functional theory is currently the only microscopic, global approach to nuclear structure that is applicable throughout the nuclear chart. In the past few years, a lot of effort has been devoted to setting up a general methodology to assess theoretical uncertainties in nuclear DFT calculations. In this paper, we summarize some of the recent progress in this direction. Most of the new material discussed here will be be published in separate articles.
Application of Density Functional Theory to Systems Containing Metal Atoms
NASA Technical Reports Server (NTRS)
Bauschlicher, Charles W., Jr.
2006-01-01
The accuracy of density functional theory (DFT) for problems involving metal atoms is considered. The DFT results are compared with experiment as well as results obtained using the coupled cluster approach. The comparisons include geometries, frequencies, and bond energies. The systems considered include MO2, M(OH)+n, MNO+, and MCO+2. The DFT works well for frequencies and geometries, even in case with symmetry breaking; however, some examples have been found where the symmetry breaking is quite severe and the DFT methods do not work well. The calculation of bond energies is more difficult and examples of successes as well as failures of DFT will be given.
Continuation of probability density functions using a generalized Lyapunov approach
NASA Astrophysics Data System (ADS)
Baars, S.; Viebahn, J. P.; Mulder, T. E.; Kuehn, C.; Wubs, F. W.; Dijkstra, H. A.
2017-05-01
Techniques from numerical bifurcation theory are very useful to study transitions between steady fluid flow patterns and the instabilities involved. Here, we provide computational methodology to use parameter continuation in determining probability density functions of systems of stochastic partial differential equations near fixed points, under a small noise approximation. Key innovation is the efficient solution of a generalized Lyapunov equation using an iterative method involving low-rank approximations. We apply and illustrate the capabilities of the method using a problem in physical oceanography, i.e. the occurrence of multiple steady states of the Atlantic Ocean circulation.
Classical density functional study of wetting transitions on nanopatterned surfaces
NASA Astrophysics Data System (ADS)
Yatsyshin, P.; Parry, A. O.; Rascón, C.; Kalliadasis, S.
2017-03-01
Even simple fluids on simple substrates can exhibit very rich surface phase behaviour. To illustrate this, we consider fluid adsorption on a planar wall chemically patterned with a deep stripe of a different material. In this system, two phase transitions compete: unbending and pre-wetting. Using microscopic density-functional theory, we show that, for thin stripes, the lines of these two phase transitions may merge, leading to a new two-dimensional-like wetting transition occurring along the walls. The influence of intermolecular forces and interfacial fluctuations on this phase transition and at complete pre-wetting are considered in detail.
DENSITY-FUNCTIONAL STUDY OF Zr-BASED ACTINIDE ALLOYS
Landa, A; Soderlind, P; Turchi, P; Vitos, L; Ruban, A
2008-06-26
Density-functional formalism is applied to study the phase equilibria in the U-Zr system. The obtained ground-state properties of the {gamma} (bcc) and {delta} (C32) phases are in good agreement with experimental data. The decomposition curve for the {gamma}-based U-Zr solutions is calculated. We argue that stabilization of the {delta}-UZr{sub 2} phase relative to the {alpha}-Zr (hcp) structure is due to an increase of the Zr d-band occupancy that occurs when U is alloyed with Zr.
Application of Density Functional Theory to Systems Containing Metal Atoms
NASA Technical Reports Server (NTRS)
Bauschlicher, Charles W., Jr.
2006-01-01
The accuracy of density functional theory (DFT) for problems involving metal atoms is considered. The DFT results are compared with experiment as well as results obtained using the coupled cluster approach. The comparisons include geometries, frequencies, and bond energies. The systems considered include MO2, M(OH)+n, MNO+, and MCO+2. The DFT works well for frequencies and geometries, even in case with symmetry breaking; however, some examples have been found where the symmetry breaking is quite severe and the DFT methods do not work well. The calculation of bond energies is more difficult and examples of successes as well as failures of DFT will be given.
Density functional theory for hydrogen storage materials: successes and opportunities
NASA Astrophysics Data System (ADS)
Hector, L. G., Jr.; Herbst, J. F.
2008-02-01
Solid state systems for hydrogen storage continue to be the focus of considerable international research, driven to a large extent by technological demands, especially for mobile applications. Density functional theory (DFT) has become a valuable tool in this effort. It has greatly expanded our understanding of the properties of known hydrides, including electronic structure, hydrogen bonding character, enthalpy of formation, elastic behavior, and vibrational energetics. Moreover, DFT holds substantial promise for guiding the discovery of new materials. In this paper we discuss, within the context of results from our own work, some successes and a few shortcomings of state-of-the-art DFT as applied to hydrogen storage materials.
Atomic volumes and polarizabilities in density-functional theory.
Kannemann, Felix O; Becke, Axel D
2012-01-21
Becke and Johnson introduced an ad hoc definition of atomic volume [J. Chem. Phys. 124, 014204 (2006)] in order to obtain atom-in-molecule polarizabilities from free-atom polarizabilities in their nonempirical exchange-hole dipole moment model of dispersion interactions. Here we explore the dependence of Becke-Johnson atomic volumes on basis sets and density-functional approximations and provide reference data for all atoms H-Lr. A persuasive theoretical foundation for the Becke-Johnson definition is also provided.
Nuclear clustering in the energy density functional approach
Ebran, J.-P.; Khan, E.; Nikšić, T.; Vretenar, D.
2015-10-15
Nuclear Energy Density Functionals (EDFs) are a microscopic tool of choice extensively used over the whole chart to successfully describe the properties of atomic nuclei ensuing from their quantum liquid nature. In the last decade, they also have proved their ability to deal with the cluster phenomenon, shedding a new light on its fundamental understanding by treating on an equal footing both quantum liquid and cluster aspects of nuclei. Such a unified microscopic description based on nucleonic degrees of freedom enables to tackle the question pertaining to the origin of the cluster phenomenon and emphasizes intrinsic mechanisms leading to the emergence of clusters in nuclei.
Lithium adsorption on graphite from density functional theory calculations.
Valencia, Felipe; Romero, Aldo H; Ancilotto, Francesco; Silvestrelli, Pier Luigi
2006-08-03
The structural, energetic, and electronic properties of the Li/graphite system are studied through density functional theory (DFT) calculations using both the local spin density approximation (LSDA), and the gradient-corrected Perdew-Burke-Ernzerhof (PBE) approximation to the exchange-correlation energy. The calculations were performed using plane waves basis, and the electron-core interactions are described using pseudopotentials. We consider a disperse phase of the adsorbate comprising one Li atom for each 16 graphite surface cells, in a slab geometry. The close contact between the Li nucleus and the graphene plane results in a relatively large binding energy (larger than 1.1 eV). A detailed analysis of the electronic charge distribution, density difference distribution, and band structures indicates that one valence electron is entirely transferred from the atom to the surface, which gives rise to a strong interaction between the resulting lithium ion and the cloud of pi electrons in the substrate. We show that it is possible to explain the differences in the binding of Li, Na, and K adatoms on graphite considering the properties of the corresponding cation/aromatic complexes.
NASA Technical Reports Server (NTRS)
Misra, Ajay K.
1988-01-01
Liquid densities were determined for a number of fluoride salt mixtures suitable for heat storage in space power applications, using a procedure that consisted of measuring the loss of weight of an inert bob in the melt. The density apparatus was calibrated with pure LiF and NaF at different temperatures. Density data for safe binary and ternary fluoride salt eutectics and congruently melting intermediate compounds are presented. In addition, a comparison was made between the volumetric heat storage capacity of different salt mixtures.
NASA Technical Reports Server (NTRS)
Misra, Ajay K.
1988-01-01
Liquid densities were determined for a number of fluoride salt mixtures suitable for heat storage in space power applications, using a procedure that consisted of measuring the loss of weight of an inert bob in the melt. The density apparatus was calibrated with pure LiF and NaF at different temperatures. Density data for safe binary and ternary fluoride salt eutectics and congruently melting intermediate compounds are presented. In addition, a comparison was made between the volumetric heat storage capacity of different salt mixtures.
NASA Astrophysics Data System (ADS)
Harbola, Manoj; Myneni, Hemanadhan; Shamim, Md.
2014-03-01
The modified local spin density functional and the related local potential for excited-states are tested by employing the ionization potential theorem. The functional is constructed by splitting k-space. Since its functional derivative cannot be obtained easily, the corresponding potential is given by analogy to its ground-state counterpart. Further, to calculate the highest occupied orbital energy ɛmax accurately, the potential is corrected for its asymptotic behavior by employing the van Leeuwen-Barends correction to it. The highest occupied orbital energy ɛmax thus obtained is then compared with the ΔSCF ionization energy calculated using the excited-state functional. It is shown that the two match quite accurately, demonstrating thereby that our approach of constructing excited-state functional is on sound footing.
Ab initio molecular dynamics using hybrid density functionals.
Guidon, Manuel; Schiffmann, Florian; Hutter, Jürg; VandeVondele, Joost
2008-06-07
Ab initio molecular dynamics simulations with hybrid density functionals have so far found little application due to their computational cost. In this work, an implementation of the Hartree-Fock exchange is presented that is specifically targeted at ab initio molecular dynamics simulations of medium sized systems. We demonstrate that our implementation, which is available as part of the CP2K/Quickstep program, is robust and efficient. Several prescreening techniques lead to a linear scaling cost for integral evaluation and storage. Integral compression techniques allow for in-core calculations on systems containing several thousand basis functions. The massively parallel implementation respects integral symmetry and scales up to hundreds of CPUs using a dynamic load balancing scheme. A time-reversible multiple time step scheme, exploiting the difference in computational efficiency between hybrid and local functionals, brings further time savings. With extensive simulations of liquid water, we demonstrate the ability to perform, for several tens of picoseconds, ab initio molecular dynamics based on hybrid functionals of systems in the condensed phase containing a few thousand Gaussian basis functions.