Density matrix perturbation theory.
Niklasson, Anders M N; Challacombe, Matt
2004-05-14
An orbital-free quantum perturbation theory is proposed. It gives the response of the density matrix upon variation of the Hamiltonian by quadratically convergent recursions based on perturbed projections. The technique allows treatment of embedded quantum subsystems with a computational cost scaling linearly with the size of the perturbed region, O(N(pert.)), and as O(1) with the total system size. The method allows efficient high order perturbation expansions, as demonstrated with an example involving a 10th order expansion. Density matrix analogs of Wigner's 2n+1 rule are also presented.
Information Theory Density Matrix for a Simple Quantum System.
ERIC Educational Resources Information Center
Titus, William J.
1979-01-01
Derives the density matrix that best describes, according to information theory, a one-dimensional single particle quantum system when the only information available is the values for the linear and quadratic position-momentum moments. (Author/GA)
Transition matrices and orbitals from reduced density matrix theory
Etienne, Thibaud
2015-06-28
In this contribution, we report two different methodologies for characterizing the electronic structure reorganization occurring when a chromophore undergoes an electronic transition. For the first method, we start by setting the theoretical background necessary to the reinterpretation through simple tensor analysis of (i) the transition density matrix and (ii) the natural transition orbitals in the scope of reduced density matrix theory. This novel interpretation is made more clear thanks to a short compendium of the one-particle reduced density matrix theory in a Fock space. The formalism is further applied to two different classes of excited states calculation methods, both requiring a single-determinant reference, that express an excited state as a hole-particle mono-excited configurations expansion, to which particle-hole correlation is coupled (time-dependent Hartree-Fock/time-dependent density functional theory) or not (configuration interaction single/Tamm-Dancoff approximation). For the second methodology presented in this paper, we introduce a novel and complementary concept related to electronic transitions with the canonical transition density matrix and the canonical transition orbitals. Their expression actually reflects the electronic cloud polarisation in the orbital space with a decomposition based on the actual contribution of one-particle excitations from occupied canonical orbitals to virtual ones. This approach validates our novel interpretation of the transition density matrix elements in terms of the Euclidean norm of elementary transition vectors in a linear tensor space. A proper use of these new concepts leads to the conclusion that despite the different principles underlying their construction, they provide two equivalent excited states topological analyses. This connexion is evidenced through simple illustrations of (in)organic dyes electronic transitions analysis.
Spectral density of the correlation matrix of factor models: a random matrix theory approach.
Lillo, F; Mantegna, R N
2005-07-01
We studied the eigenvalue spectral density of the correlation matrix of factor models of multivariate time series. By making use of the random matrix theory, we analytically quantified the effect of statistical uncertainty on the spectral density due to the finiteness of the sample. We considered a broad range of models, ranging from one-factor models to hierarchical multifactor models.
Density Functional Approach and Random Matrix Theory in Proteogenesis
NASA Astrophysics Data System (ADS)
Yamanaka, Masanori
2017-02-01
We study the energy-level statistics of amino acids by random matrix theory. The molecular orbital and the Kohn-Sham orbital energies are calculated using ab initio and density-functional formalisms for 20 different amino acids. To generate statistical data, we performed a multipoint calculation on 10000 molecular structures produced via a molecular dynamics simulation. For the valence orbitals, the energy-level statistics exhibit repulsion, but the universality in the random matrix cannot be determined. For the unoccupied orbitals, the energy-level statistics indicate an intermediate distribution between the Gaussian orthogonal ensemble and the semi-Poisson statistics for all 20 different amino acids. These amino acids are considered to be in a type of critical state.
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.
Matrix product density operators: Renormalization fixed points and boundary theories
NASA Astrophysics Data System (ADS)
Cirac, J. I.; Pérez-García, D.; Schuch, N.; Verstraete, F.
2017-03-01
We consider the tensors generating matrix product states and density operators in a spin chain. For pure states, we revise the renormalization procedure introduced in (Verstraete et al., 2005) and characterize the tensors corresponding to the fixed points. We relate them to the states possessing zero correlation length, saturation of the area law, as well as to those which generate ground states of local and commuting Hamiltonians. For mixed states, we introduce the concept of renormalization fixed points and characterize the corresponding tensors. We also relate them to concepts like finite correlation length, saturation of the area law, as well as to those which generate Gibbs states of local and commuting Hamiltonians. One of the main result of this work is that the resulting fixed points can be associated to the boundary theories of two-dimensional topological states, through the bulk-boundary correspondence introduced in (Cirac et al., 2011).
Efficient perturbation theory to improve the density matrix renormalization group
NASA Astrophysics Data System (ADS)
Tirrito, Emanuele; Ran, Shi-Ju; Ferris, Andrew J.; McCulloch, Ian P.; Lewenstein, Maciej
2017-02-01
The density matrix renormalization group (DMRG) is one of the most powerful numerical methods available for many-body systems. It has been applied to solve many physical problems, including the calculation of ground states and dynamical properties. In this work, we develop a perturbation theory of the DMRG (PT-DMRG) to greatly increase its accuracy in an extremely simple and efficient way. Using the canonical matrix product state (MPS) representation for the ground state of the considered system, a set of orthogonal basis functions {| ψi> } is introduced to describe the perturbations to the ground state obtained by the conventional DMRG. The Schmidt numbers of the MPS that are beyond the bond dimension cutoff are used to define these perturbation terms. The perturbed Hamiltonian is then defined as H˜i j=< ψi| H ̂|ψj> ; its ground state permits us to calculate physical observables with a considerably improved accuracy compared to the original DMRG results. We benchmark the second-order perturbation theory with the help of a one-dimensional Ising chain in a transverse field and the Heisenberg chain, where the precision of the DMRG is shown to be improved O (10 ) times. Furthermore, for moderate L the errors of the DMRG and PT-DMRG both scale linearly with L-1 (with L being the length of the chain). The linear relation between the dimension cutoff of the DMRG and that of the PT-DMRG at the same precision shows a considerable improvement in efficiency, especially for large dimension cutoffs. In the thermodynamic limit we show that the errors of the PT-DMRG scale with √{L-1}. Our work suggests an effective way to define the tangent space of the ground-state MPS, which may shed light on the properties beyond the ground state. This second-order PT-DMRG can be readily generalized to higher orders, as well as applied to models in higher dimensions.
Density Matrix Embedding: A Strong-Coupling Quantum Embedding Theory.
Knizia, Gerald; Chan, Garnet Kin-Lic
2013-03-12
We extend our density matrix embedding theory (DMET) [Phys. Rev. Lett.2012, 109, 186404] from lattice models to the full chemical Hamiltonian. DMET allows the many-body embedding of arbitrary fragments of a quantum system, even when such fragments are open systems and strongly coupled to their environment (e.g., by covalent bonds). In DMET, empirical approaches to strong coupling, such as link atoms or boundary regions, are replaced by a small, rigorous quantum bath designed to reproduce the entanglement between a fragment and its environment. We describe the theory and demonstrate its feasibility in strongly correlated hydrogen ring and grid models; these are not only beyond the scope of traditional embeddings but even challenge conventional quantum chemistry methods themselves. We find that DMET correctly describes the notoriously difficult symmetric dissociation of a 4 × 3 hydrogen atom grid, even when the treated fragments are as small as single hydrogen atoms. We expect that DMET will open up new ways of treating complex strongly coupled, strongly correlated systems in terms of their individual fragments.
Reduced density-matrix functional theory: Correlation and spectroscopy
Di Sabatino, S.; Romaniello, P.; Berger, J. A.; Reining, L.
2015-07-14
In this work, we explore the performance of approximations to electron correlation in reduced density-matrix functional theory (RDMFT) and of approximations to the observables calculated within this theory. Our analysis focuses on the calculation of total energies, occupation numbers, removal/addition energies, and spectral functions. We use the exactly solvable Hubbard dimer at 1/4 and 1/2 fillings as test systems. This allows us to analyze the underlying physics and to elucidate the origin of the observed trends. For comparison, we also report the results of the GW approximation, where the self-energy functional is approximated, but no further hypothesis is made concerning the approximations of the observables. In particular, we focus on the atomic limit, where the two sites of the dimer are pulled apart and electrons localize on either site with equal probability, unless a small perturbation is present: this is the regime of strong electron correlation. In this limit, using the Hubbard dimer at 1/2 filling with or without a spin-symmetry-broken ground state allows us to explore how degeneracies and spin-symmetry breaking are treated in RDMFT. We find that, within the used approximations, neither in RDMFT nor in GW, the signature of strong correlation is present, when looking at the removal/addition energies and spectral function from the spin-singlet ground state, whereas both give the exact result for the spin-symmetry broken case. Moreover, we show how the spectroscopic properties change from one spin structure to the other.
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.
Jordan, Daniel K; Mazziotti, David A
2005-02-22
Two classes of linear-scaling methods to replace diagonalization of the one-particle Hamiltonian matrix in density functional theory are compared to each other. Purification takes a density matrix with the correct eigenfunctions and corrects the occupation numbers; density matrix minimization takes a density matrix with correct occupation numbers and corrects the eigenfunctions by rotating the orbitals. Computational comparisons are performed through modification of the MondoSCF program on water clusters and the protein endothelin. A purification scheme and a density matrix minimization scheme, based on the 1,2-contracted Schrodinger equation [D. A. Mazziotti, J. Chem. Phys. 115, 8305 (2001)] are implemented in large systems.
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).
Performance of the density matrix functional theory in the quantum theory of atoms in molecules.
García-Revilla, Marco; Francisco, E; Costales, A; Martín Pendás, A
2012-02-02
The generalization to arbitrary molecular geometries of the energetic partitioning provided by the atomic virial theorem of the quantum theory of atoms in molecules (QTAIM) leads to an exact and chemically intuitive energy partitioning scheme, the interacting quantum atoms (IQA) approach, that depends on the availability of second-order reduced density matrices (2-RDMs). This work explores the performance of this approach in particular and of the QTAIM in general with approximate 2-RDMs obtained from the density matrix functional theory (DMFT), which rests on the natural expansion (natural orbitals and their corresponding occupation numbers) of the first-order reduced density matrix (1-RDM). A number of these functionals have been implemented in the promolden code and used to perform QTAIM and IQA analyses on several representative molecules and model chemical reactions. Total energies, covalent intra- and interbasin exchange-correlation interactions, as well as localization and delocalization indices have been determined with these functionals from 1-RDMs obtained at different levels of theory. Results are compared to the values computed from the exact 2-RDMs, whenever possible.
NASA Astrophysics Data System (ADS)
Yanai, Takeshi; Kurashige, Yuki; Neuscamman, Eric; Chan, Garnet Kin-Lic
2010-01-01
We describe the joint application of the density matrix renormalization group and canonical transformation theory to multireference quantum chemistry. The density matrix renormalization group provides the ability to describe static correlation in large active spaces, while the canonical transformation theory provides a high-order description of the dynamic correlation effects. We demonstrate the joint theory in two benchmark systems designed to test the dynamic and static correlation capabilities of the methods, namely, (i) total correlation energies in long polyenes and (ii) the isomerization curve of the [Cu2O2]2+ core. The largest complete active spaces and atomic orbital basis sets treated by the joint DMRG-CT theory in these systems correspond to a (24e,24o) active space and 268 atomic orbitals in the polyenes and a (28e,32o) active space and 278 atomic orbitals in [Cu2O2]2+.
The "JK-only" approximation in density matrix functional and wave function theory.
Kollmar, Christian
2004-12-15
Various energy functionals applying the "JK-only" approximation which leads to two-index two-electron integrals instead of four-index two-electron integrals in the electron-electron interaction term of the electronic energy are presented. Numerical results of multiconfiguration self-consistent field calculations for the best possible "JK-only" wave function are compared to those obtained from the pair excitation multiconfiguration self-consistent (PEMCSCF) method and two versions of density matrix functional theory. One of these is derived making explicit use of some necessary conditions for N representability of the second-order density matrix. It is shown that this method models the energy functional based on the best possible "JK-only" wave function with good accuracy. The calculations also indicate that only a minor fraction of the total correlation energy is incorporated by "JK-only" approaches for larger molecules.
Density matrix perturbation theory for magneto-optical response of periodic insulators
NASA Astrophysics Data System (ADS)
Lebedeva, Irina; Tokatly, Ilya; Rubio, Angel
2015-03-01
Density matrix perturbation theory offers an ideal theoretical framework for the description of response of solids to arbitrary electromagnetic fields. In particular, it allows to consider perturbations introduced by uniform electric and magnetic fields under periodic boundary conditions, though the corresponding potentials break the translational invariance of the Hamiltonian. We have implemented the density matrix perturbation theory in the open-source Octopus code on the basis of the efficient Sternheimer approach. The procedures for responses of different order to electromagnetic fields, including electric polarizability, orbital magnetic susceptibility and magneto-optical response, have been developed and tested by comparison with the results for finite systems and for wavefunction-based perturbation theory, which is already available in the code. Additional analysis of the orbital magneto-optical response is performed on the basis of analytical models. Symmetry limitations to observation of the magneto-optical response are discussed. The financial support from the Marie Curie Fellowship PIIF-GA-2012-326435 (RespSpatDisp) is gratefully acknowledged.
2017-01-01
We present a second-order N-electron valence state perturbation theory (NEVPT2) based on a density matrix renormalization group (DMRG) reference wave function that exploits a Cholesky decomposition of the two-electron repulsion integrals (CD-DMRG-NEVPT2). With a parameter-free multireference perturbation theory approach at hand, the latter allows us to efficiently describe static and dynamic correlation in large molecular systems. We demonstrate the applicability of CD-DMRG-NEVPT2 for spin-state energetics of spin-crossover complexes involving calculations with more than 1000 atomic basis functions. We first assess, in a study of a heme model, the accuracy of the strongly and partially contracted variant of CD-DMRG-NEVPT2 before embarking on resolving a controversy about the spin ground state of a cobalt tropocoronand complex. PMID:28094988
Freitag, Leon; Knecht, Stefan; Angeli, Celestino; Reiher, Markus
2017-02-14
We present a second-order N-electron valence state perturbation theory (NEVPT2) based on a density matrix renormalization group (DMRG) reference wave function that exploits a Cholesky decomposition of the two-electron repulsion integrals (CD-DMRG-NEVPT2). With a parameter-free multireference perturbation theory approach at hand, the latter allows us to efficiently describe static and dynamic correlation in large molecular systems. We demonstrate the applicability of CD-DMRG-NEVPT2 for spin-state energetics of spin-crossover complexes involving calculations with more than 1000 atomic basis functions. We first assess, in a study of a heme model, the accuracy of the strongly and partially contracted variant of CD-DMRG-NEVPT2 before embarking on resolving a controversy about the spin ground state of a cobalt tropocoronand complex.
NASA Astrophysics Data System (ADS)
Liang, Wenkel; Isborn, Christine M.; Li, Xiaosong
2009-11-01
The calculation of doubly excited states is one of the major problems plaguing the modern day excited state workhorse methodology of linear response time dependent Hartree-Fock (TDHF) and density function theory (TDDFT). We have previously shown that the use of a resonantly tuned field within real-time TDHF and TDDFT is able to simultaneously excite both the α and β electrons to achieve the two-electron excited states of minimal basis H2 and HeH+ [C. M. Isborn and X. Li, J. Chem. Phys. 129, 204107 (2008)]. We now extend this method to many electron systems with the use of our Car-Parrinello density matrix search (CP-DMS) with a first-principles fictitious mass method for wave function optimization [X. Li, C. L. Moss, W. Liang, and Y. Feng, J. Chem. Phys. 130, 234115 (2009)]. Real-time TDHF/TDDFT is used during the application of the laser field perturbation, driving the electron density toward the doubly excited state. The CP-DMS method then converges the density to the nearest stationary state. We present these stationary state doubly excited state energies and properties at the HF and DFT levels for H2, HeH+, lithium hydride, ethylene, and butadiene.
A Practical Guide to Density Matrix Embedding Theory in Quantum Chemistry.
Wouters, Sebastian; Jiménez-Hoyos, Carlos A; Sun, Qiming; Chan, Garnet K-L
2016-06-14
Density matrix embedding theory (DMET) (Knizia, G.; Chan, G. K.-L. Phys. Rev. Lett. 2012, 109, 186404) provides a theoretical framework to treat finite fragments in the presence of a surrounding molecular or bulk environment, even when there is significant correlation or entanglement between the two. In this work, we give a practically oriented and explicit description of the numerical and theoretical formulation of DMET. We also describe in detail how to perform self-consistent DMET optimizations. We explore different embedding strategies with and without a self-consistency condition in hydrogen rings, beryllium rings, and a sample SN2 reaction. The source code for the calculations in this work can be obtained from https://github.com/sebwouters/qc-dmet .
NASA Astrophysics Data System (ADS)
Putaja, A.; Eich, F. G.; Baldsiefen, T.; Räsänen, E.
2016-03-01
Physically valid and numerically efficient approximations for the exchange and correlation energy are critical for reduced-density-matrix-functional theory to become a widely used method in electronic structure calculations. Here we examine the physical limits of power functionals of the form f (n ,n') =(nn')α for the scaling function in the exchange-correlation energy. To this end we obtain numerically the minimizing momentum distributions for the three- and two-dimensional homogeneous electron gas, respectively. In particular, we examine the limiting values for the power α to yield physically sound solutions that satisfy the Lieb-Oxford lower bound for the exchange-correlation energy and exclude pinned states with the condition n (k )<1 for all wave vectors k . The results refine the constraints previously obtained from trial momentum distributions. We also compute the values for α that yield the exact correlation energy and its kinetic part for both the three- and two-dimensional electron gas. In both systems, narrow regimes of validity and accuracy are found at α ≳0.6 and at rs≳10 for the density parameter, corresponding to relatively low densities.
Nakatani, Naoki; Wouters, Sebastian; Van Neck, Dimitri; Chan, Garnet Kin-Lic
2014-01-14
Linear response theory for the density matrix renormalization group (DMRG-LRT) was first presented in terms of the DMRG renormalization projectors [J. J. Dorando, J. Hachmann, and G. K.-L. Chan, J. Chem. Phys. 130, 184111 (2009)]. Later, with an understanding of the manifold structure of the matrix product state (MPS) ansatz, which lies at the basis of the DMRG algorithm, a way was found to construct the linear response space for general choices of the MPS gauge in terms of the tangent space vectors [J. Haegeman, J. I. Cirac, T. J. Osborne, I. Pižorn, H. Verschelde, and F. Verstraete, Phys. Rev. Lett. 107, 070601 (2011)]. These two developments led to the formulation of the Tamm-Dancoff and random phase approximations (TDA and RPA) for MPS. This work describes how these LRTs may be efficiently implemented through minor modifications of the DMRG sweep algorithm, at a computational cost which scales the same as the ground-state DMRG algorithm. In fact, the mixed canonical MPS form implicit to the DMRG sweep is essential for efficient implementation of the RPA, due to the structure of the second-order tangent space. We present ab initio DMRG-TDA results for excited states of polyenes, the water molecule, and a [2Fe-2S] iron-sulfur cluster.
NASA Astrophysics Data System (ADS)
Nakatani, Naoki; Wouters, Sebastian; Van Neck, Dimitri; Chan, Garnet Kin-Lic
2014-01-01
Linear response theory for the density matrix renormalization group (DMRG-LRT) was first presented in terms of the DMRG renormalization projectors [J. J. Dorando, J. Hachmann, and G. K.-L. Chan, J. Chem. Phys. 130, 184111 (2009)]. Later, with an understanding of the manifold structure of the matrix product state (MPS) ansatz, which lies at the basis of the DMRG algorithm, a way was found to construct the linear response space for general choices of the MPS gauge in terms of the tangent space vectors [J. Haegeman, J. I. Cirac, T. J. Osborne, I. Pižorn, H. Verschelde, and F. Verstraete, Phys. Rev. Lett. 107, 070601 (2011)]. These two developments led to the formulation of the Tamm-Dancoff and random phase approximations (TDA and RPA) for MPS. This work describes how these LRTs may be efficiently implemented through minor modifications of the DMRG sweep algorithm, at a computational cost which scales the same as the ground-state DMRG algorithm. In fact, the mixed canonical MPS form implicit to the DMRG sweep is essential for efficient implementation of the RPA, due to the structure of the second-order tangent space. We present ab initio DMRG-TDA results for excited states of polyenes, the water molecule, and a [2Fe-2S] iron-sulfur cluster.
Computing the Density Matrix in Electronic Structure Theory on Graphics Processing Units.
Cawkwell, M J; Sanville, E J; Mniszewski, S M; Niklasson, Anders M N
2012-11-13
The self-consistent solution of a Schrödinger-like equation for the density matrix is a critical and computationally demanding step in quantum-based models of interatomic bonding. This step was tackled historically via the diagonalization of the Hamiltonian. We have investigated the performance and accuracy of the second-order spectral projection (SP2) algorithm for the computation of the density matrix via a recursive expansion of the Fermi operator in a series of generalized matrix-matrix multiplications. We demonstrate that owing to its simplicity, the SP2 algorithm [Niklasson, A. M. N. Phys. Rev. B2002, 66, 155115] is exceptionally well suited to implementation on graphics processing units (GPUs). The performance in double and single precision arithmetic of a hybrid GPU/central processing unit (CPU) and full GPU implementation of the SP2 algorithm exceed those of a CPU-only implementation of the SP2 algorithm and traditional matrix diagonalization when the dimensions of the matrices exceed about 2000 × 2000. Padding schemes for arrays allocated in the GPU memory that optimize the performance of the CUBLAS implementations of the level 3 BLAS DGEMM and SGEMM subroutines for generalized matrix-matrix multiplications are described in detail. The analysis of the relative performance of the hybrid CPU/GPU and full GPU implementations indicate that the transfer of arrays between the GPU and CPU constitutes only a small fraction of the total computation time. The errors measured in the self-consistent density matrices computed using the SP2 algorithm are generally smaller than those measured in matrices computed via diagonalization. Furthermore, the errors in the density matrices computed using the SP2 algorithm do not exhibit any dependence of system size, whereas the errors increase linearly with the number of orbitals when diagonalization is employed.
Density matrix embedding theory studies of the two-dimensional Hubbard model
NASA Astrophysics Data System (ADS)
Zheng, Bo-Xiao
Density matrix embedding theory (DMET) provides a quantum embedding framework to compute the electronic structure in strongly correlated lattice systems. It has been applied to various model Hamiltonians and ab initio systems. In this talk, I will review the results obtained in the two-dimensional one-band Hubbard model using DMET. Over the last years, we mapped a calibrated ground-state phase diagram of the two-dimensional Hubbard model, concerning magnetic, superconducting and various inhomogeneous phases. Based on the results from this work, as well as the consistent data from other numerical methods, we are able to conclude that many parts of the Hubbard phase diagram is already settled up to an accurate energy scale of 0.001t. Recently, by using large-scale auxiliary-field quantum Monte Carlo (AFQMC) in the impurity problem, we are able to treat much larger embedded clusters at half-filling (and with the constrained path approximation at non-half-filling), which provides a deeper understanding on the finite-size effects of energy and observables in both quantum embedding and finite cluster numerical methods. Finally, we systematically investigated the putative inhomogeneous phases in the underdoped, strong coupling Hubbard model, proposing new inhomogeneous patterns as strong candidates for the ground state. Reference: [1] Bo-Xiao Zheng, Garnet K.-L. Chan, arXiv:1504.01784 [2] J.P.F. Leblanc, Andrey E. Antipov, et al., arXiv:1505.02290 We acknowledge funding from the US Department of Energy, Office of Science, through DE-SC0008624 and DE-SC0010530. This work was also performed as part of the Simons Collaboration on the Many Electron Problem, sponsored by the Simons Foundation.
Adiabatic approximation in time-dependent reduced-density-matrix functional theory
Requist, Ryan; Pankratov, Oleg
2010-04-15
With the aim of describing real-time electron dynamics, we introduce an adiabatic approximation for the equation of motion of the one-body reduced density matrix (one-matrix). The eigenvalues of the one-matrix, which represent the occupation numbers of single-particle orbitals, are obtained from the constrained minimization of the instantaneous ground-state energy functional rather than from their dynamical equations. The performance of the approximation vis-a-vis nonadiabatic effects is assessed in real-time simulations of a two-site Hubbard model. Due to Landau-Zener-type transitions, the system evolves into a nonstationary state with persistent oscillations in the observables. The amplitude of the oscillations displays a strongly nonmonotonic dependence on the strength of the electron-electron interaction and the rate of variation of the external potential. We interpret an associated resonance behavior in the phase of the oscillations in terms of 'scattering' with spectator energy levels. To clarify the motivation for the minimization condition, we derive a sequence of energy functionals E{sub v}{sup (n)}, for which the corresponding sequence of minimizing one-matrices is asymptotic to the exact one-matrix in the adiabatic limit.
High-harmonic spectra from time-dependent two-particle reduced-density-matrix theory
NASA Astrophysics Data System (ADS)
Lackner, Fabian; Březinová, Iva; Sato, Takeshi; Ishikawa, Kenichi L.; Burgdörfer, Joachim
2017-03-01
The ab initio description of the nonlinear response of many-electron systems to strong-laser fields remains a major challenge. In order to address larger systems, alternative methods need to be developed that bypass the exponential scaling with particle number inherent to conventional wave-function-based approaches. In this paper we present a fully three-dimensional implementation of the time-dependent two-particle reduced-density-matrix (TD-2RDM) method for many-electron atoms. We benchmark this approach by a comparison with multiconfigurational time-dependent Hartree-Fock results for the harmonic spectra of beryllium and neon. We show that the TD-2RDM is very well suited to describe the nonlinear atomic response and to reveal the influence of electron-correlation effects.
NASA Astrophysics Data System (ADS)
Oberhofer, Harald; Blumberger, Jochen
2010-12-01
We present a plane wave basis set implementation for the calculation of electronic coupling matrix elements of electron transfer reactions within the framework of constrained density functional theory (CDFT). Following the work of Wu and Van Voorhis [J. Chem. Phys. 125, 164105 (2006)], the diabatic wavefunctions are approximated by the Kohn-Sham determinants obtained from CDFT calculations, and the coupling matrix element calculated by an efficient integration scheme. Our results for intermolecular electron transfer in small systems agree very well with high-level ab initio calculations based on generalized Mulliken-Hush theory, and with previous local basis set CDFT calculations. The effect of thermal fluctuations on the coupling matrix element is demonstrated for intramolecular electron transfer in the tetrathiafulvalene-diquinone (Q-TTF-Q-) anion. Sampling the electronic coupling along density functional based molecular dynamics trajectories, we find that thermal fluctuations, in particular the slow bending motion of the molecule, can lead to changes in the instantaneous electron transfer rate by more than an order of magnitude. The thermal average, ( {< {| {H_ab } |^2 } > } )^{1/2} = 6.7 {mH}, is significantly higher than the value obtained for the minimum energy structure, | {H_ab } | = 3.8 {mH}. While CDFT in combination with generalized gradient approximation (GGA) functionals describes the intermolecular electron transfer in the studied systems well, exact exchange is required for Q-TTF-Q- in order to obtain coupling matrix elements in agreement with experiment (3.9 mH). The implementation presented opens up the possibility to compute electronic coupling matrix elements for extended systems where donor, acceptor, and the environment are treated at the quantum mechanical (QM) level.
Saitow, Masaaki; Kurashige, Yuki; Yanai, Takeshi
2013-07-28
We report development of the multireference configuration interaction (MRCI) method that can use active space scalable to much larger size references than has previously been possible. The recent development of the density matrix renormalization group (DMRG) method in multireference quantum chemistry offers the ability to describe static correlation in a large active space. The present MRCI method provides a critical correction to the DMRG reference by including high-level dynamic correlation through the CI treatment. When the DMRG and MRCI theories are combined (DMRG-MRCI), the full internal contraction of the reference in the MRCI ansatz, including contraction of semi-internal states, plays a central role. However, it is thought to involve formidable complexity because of the presence of the five-particle rank reduced-density matrix (RDM) in the Hamiltonian matrix elements. To address this complexity, we express the Hamiltonian matrix using commutators, which allows the five-particle rank RDM to be canceled out without any approximation. Then we introduce an approximation to the four-particle rank RDM by using a cumulant reconstruction from lower-particle rank RDMs. A computer-aided approach is employed to derive the exceedingly complex equations of the MRCI in tensor-contracted form and to implement them into an efficient parallel computer code. This approach extends to the size-consistency-corrected variants of MRCI, such as the MRCI+Q, MR-ACPF, and MR-AQCC methods. We demonstrate the capability of the DMRG-MRCI method in several benchmark applications, including the evaluation of single-triplet gap of free-base porphyrin using 24 active orbitals.
SivaRanjan, Uppala; Ramachandran, Ramesh
2014-02-07
A quantum-mechanical model integrating the concepts of reduced density matrix and effective Hamiltonians is proposed to explain the multi-spin effects observed in rotational resonance (R{sup 2}) nuclear magnetic resonance (NMR) experiments. Employing this approach, the spin system of interest is described in a reduced subspace inclusive of its coupling to the surroundings. Through suitable model systems, the utility of our theory is demonstrated and verified with simulations emerging from both analytic and numerical methods. The analytic results presented in this article provide an accurate description/interpretation of R{sup 2} experimental results and could serve as a test-bed for distinguishing coherent/incoherent effects in solid-state NMR.
Yan, YiJing
2014-02-07
This work establishes a strongly correlated system-and-bath dynamics theory, the many-dissipaton density operators formalism. It puts forward a quasi-particle picture for environmental influences. This picture unifies the physical descriptions and algebraic treatments on three distinct classes of quantum environments, electron bath, phonon bath, and two-level spin or exciton bath, as their participating in quantum dissipation processes. Dynamical variables for theoretical description are no longer just the reduced density matrix for system, but remarkably also those for quasi-particles of bath. The present theoretical formalism offers efficient and accurate means for the study of steady-state (nonequilibrium and equilibrium) and real-time dynamical properties of both systems and hybridizing environments. It further provides universal evaluations, exact in principle, on various correlation functions, including even those of environmental degrees of freedom in coupling with systems. Induced environmental dynamics could be reflected directly in experimentally measurable quantities, such as Fano resonances and quantum transport current shot noise statistics.
Thorvaldsen, Andreas J; Ruud, Kenneth; Kristensen, Kasper; Jørgensen, Poul; Coriani, Sonia
2008-12-07
A general method is presented for the calculation of molecular properties to arbitrary order at the Kohn-Sham density functional level of theory. The quasienergy and Lagrangian formalisms are combined to derive response functions and their residues by straightforward differentiation of the quasienergy derivative Lagrangian using the elements of the density matrix in the atomic orbital representation as variational parameters. Response functions and response equations are expressed in the atomic orbital basis, allowing recent advances in the field of linear-scaling methodology to be used. Time-dependent and static perturbations are treated on an equal footing, and atomic basis sets that depend on the applied frequency-dependent perturbations may be used, e.g., frequency-dependent London atomic orbitals. The 2n+1 rule may be applied if computationally favorable, but alternative formulations using higher-order perturbed density matrices are also derived. These may be advantageous in order to minimize the number of response equations that needs to be solved, for instance, when one of the perturbations has many components, as is the case for the first-order geometrical derivative of the hyperpolarizability.
NASA Astrophysics Data System (ADS)
Thorvaldsen, Andreas J.; Ruud, Kenneth; Kristensen, Kasper; Jørgensen, Poul; Coriani, Sonia
2008-12-01
A general method is presented for the calculation of molecular properties to arbitrary order at the Kohn-Sham density functional level of theory. The quasienergy and Lagrangian formalisms are combined to derive response functions and their residues by straightforward differentiation of the quasienergy derivative Lagrangian using the elements of the density matrix in the atomic orbital representation as variational parameters. Response functions and response equations are expressed in the atomic orbital basis, allowing recent advances in the field of linear-scaling methodology to be used. Time-dependent and static perturbations are treated on an equal footing, and atomic basis sets that depend on the applied frequency-dependent perturbations may be used, e.g., frequency-dependent London atomic orbitals. The 2n+1 rule may be applied if computationally favorable, but alternative formulations using higher-order perturbed density matrices are also derived. These may be advantageous in order to minimize the number of response equations that needs to be solved, for instance, when one of the perturbations has many components, as is the case for the first-order geometrical derivative of the hyperpolarizability.
Requist, Ryan; Pankratov, Oleg
2011-05-15
We prove that if the two-body terms in the equation of motion for the one-body reduced density matrix are approximated by ground-state functionals, the eigenvalues of the one-body reduced density matrix (occupation numbers) remain constant in time. This deficiency is related to the inability of such an approximation to account for relative phases in the two-body reduced density matrix. We derive an exact differential equation giving the functional dependence of these phases in an interacting Landau-Zener model and study their behavior in short- and long-time regimes. The phases undergo resonances whenever the occupation numbers approach the boundaries of the interval [0,1]. In the long-time regime, the occupation numbers display correlation-induced oscillations and the memory dependence of the functionals assumes a simple form.
NASA Astrophysics Data System (ADS)
Edelman, Alan; Rao, N. Raj
Random matrix theory is now a big subject with applications in many disciplines of science, engineering and finance. This article is a survey specifically oriented towards the needs and interests of a numerical analyst. This survey includes some original material not found anywhere else. We include the important mathematics which is a very modern development, as well as the computational software that is transforming the theory into useful practice.
Random matrix theory within superstatistics.
Abul-Magd, A Y
2005-12-01
We propose a generalization of the random matrix theory following the basic prescription of the recently suggested concept of superstatistics. Spectral characteristics of systems with mixed regular-chaotic dynamics are expressed as weighted averages of the corresponding quantities in the standard theory assuming that the mean level spacing itself is a stochastic variable. We illustrate the method by calculating the level density, the nearest-neighbor-spacing distributions, and the two-level correlation functions for systems in transition from order to chaos. The calculated spacing distribution fits the resonance statistics of random binary networks obtained in a recent numerical experiment.
Lectures on Matrix Field Theory
NASA Astrophysics Data System (ADS)
Ydri, Badis
The subject of matrix field theory involves matrix models, noncommutative geometry, fuzzy physics and noncommutative field theory and their interplay. In these lectures, a lot of emphasis is placed on the matrix formulation of noncommutative and fuzzy spaces, and on the non-perturbative treatment of the corresponding field theories. In particular, the phase structure of noncommutative $\\phi^4$ theory is treated in great detail, and an introduction to noncommutative gauge theory is given.
Palenik, Mark C.; Dunlap, Brett I.
2015-07-28
Despite the fundamental importance of electron density in density functional theory, perturbations are still usually dealt with using Hartree-Fock-like orbital equations known as coupled-perturbed Kohn-Sham (CPKS). As an alternative, we develop a perturbation theory that solves for the perturbed density directly, removing the need for CPKS. This replaces CPKS with a true Hohenberg-Kohn density perturbation theory. In CPKS, the perturbed density is found in the basis of products of occupied and virtual orbitals, which becomes ever more over-complete as the size of the orbital basis set increases. In our method, the perturbation to the density is expanded in terms of a series of density basis functions and found directly. It is possible to solve for the density in such a way that it makes the total energy stationary even if the density basis is incomplete.
NASA Astrophysics Data System (ADS)
van Meer, R.; Gritsenko, O. V.; Baerends, E. J.
2014-01-01
Time dependent density matrix functional theory in its adiabatic linear response formulation delivers exact excitation energies ωα and oscillator strengths fα for two-electron systems if extended to the so-called phase including natural orbital (PINO) theory. The Löwdin-Shull expression for the energy of two-electron systems in terms of the natural orbitals and their phases affords in this case an exact phase-including natural orbital functional (PILS), which is non-primitive (contains other than just J and K integrals). In this paper, the extension of the PILS functional to N-electron systems is investigated. With the example of an elementary primitive NO functional (BBC1) it is shown that current density matrix functional theory ground state functionals, which were designed to produce decent approximations to the total energy, fail to deliver a qualitatively correct structure of the (inverse) response function, due to essential deficiencies in the reconstruction of the two-body reduced density matrix (2RDM). We now deduce essential features of an N-electron functional from a wavefunction Ansatz: The extension of the two-electron Löwdin-Shull wavefunction to the N-electron case informs about the phase information. In this paper, applications of this extended Löwdin-Shull (ELS) functional are considered for the simplest case, ELS(1): one (dissociating) two-electron bond in the field of occupied (including core) orbitals. ELS(1) produces high quality ωα(R) curves along the bond dissociation coordinate R for the molecules LiH, Li2, and BH with the two outer valence electrons correlated. All of these results indicate that response properties are much more sensitive to deficiencies in the reconstruction of the 2RDM than the ground state energy, since derivatives of the functional with respect to both the NOs and the occupation numbers need to be accurate.
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).
Non-Hermitian Euclidean random matrix theory.
Goetschy, A; Skipetrov, S E
2011-07-01
We develop a theory for the eigenvalue density of arbitrary non-Hermitian Euclidean matrices. Closed equations for the resolvent and the eigenvector correlator are derived. The theory is applied to the random Green's matrix relevant to wave propagation in an ensemble of pointlike scattering centers. This opens a new perspective in the study of wave diffusion, Anderson localization, and random lasing.
Schwerdtfeger, Christine A; Mazziotti, David A
2009-06-14
Quantum phase transitions in N-particle systems can be identified and characterized by the movement of the two-particle reduced density matrix (2-RDM) along the boundary of its N-representable convex set as a function of the Hamiltonian parameter controlling the phase transition [G. Gidofalvi and D. A. Mazziotti, Phys. Rev. A 74, 012501 (2006)]. For the one-dimensional transverse Ising model quantum phase transitions as well as their finite-lattice analogs are computed and characterized by the 2-RDM movement with respect to the transverse magnetic field strength g. The definition of a 2-RDM "speed" quantifies the movement of the 2-RDM per unit of g, which reaches its maximum at the critical point of the phase transition. For the infinite lattice the convex set of 2-RDMs and the 2-RDM speed are computed from the exact solution of the 2-RDM in the thermodynamic limit of infinite N [P. Pfeuty, Ann. Phys. 57, 79 (1970)]. For the finite lattices we compute the 2-RDM convex set and its speed by the variational 2-RDM method [D. A. Mazziotti, Phys. Rev. Lett. 93, 213001 (2004)] in which approximate ground-state 2-RDMs are calculated without N-particle wave functions by using constraints, known as N-representability conditions, to restrict the 2-RDMs to represent quantum system of N fermions. Advantages of the method include: (i) rigorous lower bounds on the ground-state energies, (ii) polynomial scaling of the calculation with N, and (iii) independence of the N-representability conditions from a reference wave function, which enables the modeling of multiple quantum phases. Comparing the 2-RDM convex sets for the finite- and infinite-site lattices reveals that the variational 2-RDM method accurately captures the shape of the convex set and the signature of the phase transition in the 2-RDM movement. From the 2-RDM all one- and two-particle expectation values (or order parameters) of the quantum Ising model can also be computed including the pair correlation function, which
Staggered chiral random matrix theory
Osborn, James C.
2011-02-01
We present a random matrix theory for the staggered lattice QCD Dirac operator. The staggered random matrix theory is equivalent to the zero-momentum limit of the staggered chiral Lagrangian and includes all taste breaking terms at their leading order. This is an extension of previous work which only included some of the taste breaking terms. We will also present some results for the taste breaking contributions to the partition function and the Dirac eigenvalues.
NASA Astrophysics Data System (ADS)
Zheng, Bo-Xiao; Kretchmer, Joshua S.; Shi, Hao; Zhang, Shiwei; Chan, Garnet Kin-Lic
2017-01-01
We investigate the cluster size convergence of the energy and observables using two forms of density matrix embedding theory (DMET): the original cluster form (CDMET) and a new formulation motivated by the dynamical cluster approximation (DCA-DMET). Both methods are applied to the half-filled one- and two-dimensional Hubbard models using a sign-problem free auxiliary-field quantum Monte Carlo impurity solver, which allows for the treatment of large impurity clusters of up to 100 sites. While CDMET is more accurate at smaller impurity cluster sizes, DCA-DMET exhibits faster asymptotic convergence towards the thermodynamic limit. We use our two formulations to produce new accurate estimates for the energy and local moment of the two-dimensional Hubbard model for U /t =2 ,4 ,6 . These results compare favorably with the best data available in the literature, and help resolve earlier uncertainties in the moment for U /t =2 .
Kussmann, Jörg; Ochsenfeld, Christian
2007-11-28
A density matrix-based time-dependent self-consistent field (D-TDSCF) method for the calculation of dynamic polarizabilities and first hyperpolarizabilities using the Hartree-Fock and Kohn-Sham density functional theory approaches is presented. The D-TDSCF method allows us to reduce the asymptotic scaling behavior of the computational effort from cubic to linear for systems with a nonvanishing band gap. The linear scaling is achieved by combining a density matrix-based reformulation of the TDSCF equations with linear-scaling schemes for the formation of Fock- or Kohn-Sham-type matrices. In our reformulation only potentially linear-scaling matrices enter the formulation and efficient sparse algebra routines can be employed. Furthermore, the corresponding formulas for the first hyperpolarizabilities are given in terms of zeroth- and first-order one-particle reduced density matrices according to Wigner's (2n+1) rule. The scaling behavior of our method is illustrated for first exemplary calculations with systems of up to 1011 atoms and 8899 basis functions.
Integrable matrix theory: Level statistics.
Scaramazza, Jasen A; Shastry, B Sriram; Yuzbashyan, Emil A
2016-09-01
We study level statistics in ensembles of integrable N×N matrices linear in a real parameter x. The matrix H(x) is considered integrable if it has a prescribed number n>1 of linearly independent commuting partners H^{i}(x) (integrals of motion) [H(x),H^{i}(x)]=0, [H^{i}(x),H^{j}(x)]=0, for all x. In a recent work [Phys. Rev. E 93, 052114 (2016)2470-004510.1103/PhysRevE.93.052114], we developed a basis-independent construction of H(x) for any n from which we derived the probability density function, thereby determining how to choose a typical integrable matrix from the ensemble. Here, we find that typical integrable matrices have Poisson statistics in the N→∞ limit provided n scales at least as logN; otherwise, they exhibit level repulsion. Exceptions to the Poisson case occur at isolated coupling values x=x_{0} or when correlations are introduced between typically independent matrix parameters. However, level statistics cross over to Poisson at O(N^{-0.5}) deviations from these exceptions, indicating that non-Poissonian statistics characterize only subsets of measure zero in the parameter space. Furthermore, we present strong numerical evidence that ensembles of integrable matrices are stationary and ergodic with respect to nearest-neighbor level statistics.
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
Interaction picture density matrix quantum Monte Carlo
Malone, Fionn D. Lee, D. K. K.; Foulkes, W. M. C.; Blunt, N. S.; Shepherd, James J.; Spencer, J. S.
2015-07-28
The recently developed density matrix quantum Monte Carlo (DMQMC) algorithm stochastically samples the N-body thermal density matrix and hence provides access to exact properties of many-particle quantum systems at arbitrary temperatures. We demonstrate that moving to the interaction picture provides substantial benefits when applying DMQMC to interacting fermions. In this first study, we focus on a system of much recent interest: the uniform electron gas in the warm dense regime. The basis set incompleteness error at finite temperature is investigated and extrapolated via a simple Monte Carlo sampling procedure. Finally, we provide benchmark calculations for a four-electron system, comparing our results to previous work where possible.
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.
Measuring Entanglement Spectrum via Density Matrix Exponentiation
NASA Astrophysics Data System (ADS)
Zhu, Guanyu; Seif, Alireza; Pichler, Hannes; Zoller, Peter; Hafezi, Mohammad
Entanglement spectrum (ES), the eigenvalues of the reduced density matrix of a subsystem, serves as a powerful theoretical tool to study many-body systems. For example, the gap and degeneracies of the entanglement spectrum have been used to identify various topological phases. However, the usefulness of such a concept in real experiments has been debated, since it is believed that obtaining the ES requires full state tomography, at a cost which exponentially grows with the systems size. Inspired by a recent density matrix exponentiation technique, we propose a scheme to measure ES by evolving the system with a Hamiltonian that is the subsystem's own reduced density matrix. Such a time evolution can be induced by an ancilla photon that is coupled to multiple qubits at the same time. The phase associated with the time evolution can be detected and converted into ES through either a digital or an analogue scheme. The digital scheme involves a modified quantum phase estimation algorithm based on random time evolution, while the analogue scheme is in the spirit of Ramsey interferometry. Both schemes are not limited by the size of the system, and are especially sensitive to the gap and degeneracies. We also discuss the implementation in cavity/circuit-QED and ion trap systems.
Mazziotti, David A
2016-10-07
A central challenge of physics is the computation of strongly correlated quantum systems. The past ten years have witnessed the development and application of the variational calculation of the two-electron reduced density matrix (2-RDM) without the wave function. In this Letter we present an orders-of-magnitude improvement in the accuracy of 2-RDM calculations without an increase in their computational cost. The advance is based on a low-rank, dual formulation of an important constraint on the 2-RDM, the T2 condition. Calculations are presented for metallic chains and a cadmium-selenide dimer. The low-scaling T2 condition will have significant applications in atomic and molecular, condensed-matter, and nuclear physics.
NASA Astrophysics Data System (ADS)
Mazziotti, David A.
2016-10-01
A central challenge of physics is the computation of strongly correlated quantum systems. The past ten years have witnessed the development and application of the variational calculation of the two-electron reduced density matrix (2-RDM) without the wave function. In this Letter we present an orders-of-magnitude improvement in the accuracy of 2-RDM calculations without an increase in their computational cost. The advance is based on a low-rank, dual formulation of an important constraint on the 2-RDM, the T 2 condition. Calculations are presented for metallic chains and a cadmium-selenide dimer. The low-scaling T 2 condition will have significant applications in atomic and molecular, condensed-matter, and nuclear physics.
Density-orbital embedding theory
Gritsenko, O. V.; Visscher, L.
2010-09-15
In the article density-orbital embedding (DOE) theory is proposed. DOE is based on the concept of density orbital (DO), which is a generalization of the square root of the density for real functions and fractional electron numbers. The basic feature of DOE is the representation of the total supermolecular density {rho}{sub s} as the square of the sum of the DO {phi}{sub a}, which represents the active subsystem A and the square root of the frozen density {rho}{sub f} of the environment F. The correct {rho}{sub s} is obtained with {phi}{sub a} being negative in the regions in which {rho}{sub f} might exceed {rho}{sub s}. This makes it possible to obtain the correct {rho}{sub s} with a broad range of the input frozen densities {rho}{sub f} so that DOE resolves the problem of the frozen-density admissibility of the current frozen-density embedding theory. The DOE Euler equation for the DO {phi}{sub a} is derived with the characteristic embedding potential representing the effect of the environment. The DO square {phi}{sub a}{sup 2} is determined from the orbitals of the effective Kohn-Sham (KS) system. Self-consistent solution of the corresponding one-electron KS equations yields not only {phi}{sub a}{sup 2}, but also the DO {phi}{sub a} itself.
Improved density matrix expansion for spin-unsaturated nuclei
Gebremariam, B.; Bogner, S. K.; Duguet, T.
2010-07-15
A current objective of low-energy nuclear theory is to build nonempirical nuclear energy density functionals (EDFs) from underlying internucleon interactions and many-body perturbation theory (MBPT). The density matrix expansion (DME) of Negele and Vautherin is a convenient method to map highly nonlocal Hartree-Fock expressions into the form of a quasi-local Skyrme functional with density-dependent couplings. In this work, we assess the accuracy of the DME at reproducing the nonlocal exchange (Fock) contribution to the energy. In contrast to the scalar part of the density matrix for which the original formulation of Negele and Vautherin is reasonably accurate, we demonstrate the necessity to reformulate the DME for the vector part of the density matrix, which is needed for an accurate description of spin-unsaturated nuclei. Phase-space-averaging techniques are shown to yield a significant improvement for the vector part of the density matrix compared to the original formulation of Negele and Vautherin. The key to the improved accuracy is to take into account the anisotropy that characterizes the local momentum distribution in the surface region of finite Fermi systems. Optimizing separately the DME for the central, tensor, and spin-orbit contributions to the Fock energy, one reaches a few-percent accuracy over a representative set of semi-magic nuclei. With such an accuracy at hand, one can envision using the corresponding Skyrme-like energy functional as a microscopically constrained starting point around which future phenomenological parametrizations can be built and refined.
NASA Technical Reports Server (NTRS)
Halasinski, Thomas M.; Weisman, Jennifer L.; Lee, Timothy J.; Salama, Farid; Head-Gordon, Martin; Kwak, Dochan (Technical Monitor)
2002-01-01
We present a full experimental and theoretical study of an interesting series of polycyclic aromatic hydrocarbons, the oligorylenes. The absorption spectra of perylene, terrylene and quaterrylene in neutral, cationic and anionic charge states are obtained by matrix-isolation spectroscopy in Ne. The experimental spectra are dominated by a bright state that red shifts with growing molecular size. Excitation energies and state symmetry assignments are supported by calculations using time dependent density functional theory methods. These calculations also provide new insight into the observed trends in oscillator strength and excitation energy for the bright states: the oscillator strength per unit mass of carbon increases along the series.
NASA Astrophysics Data System (ADS)
Hu, Chunping; Sugino, Osamu; Hirai, Hirotoshi; Tateyama, Yoshitaka
2010-12-01
We study the time-dependent density-functional theory formulation of nonadiabatic couplings (NAC’s) to settle problems regarding practical calculations. NAC’s have so far been rigorously formulated on the basis of the density response scheme and expressed using the nuclear derivative of the Hamiltonian, ∂H/∂R, whereby causing the pseudopotential problem. When rewritten using the nuclear derivative operator, ∂/∂R, or the d operator, the formula is found free of the problem and thus provides a working numerical scheme. The d-operator-based formulation also allows us to lay a foundation on the empirical Slater transition-state method and to show an improved way of using the auxiliary excited-state wave-function ansatz, both of which have been utilized in previous works. Evaluation of NAC near either the Jahn-Teller or the Renner-Teller intersection in various molecular systems shows that the values of NAC are much improved over previous calculations when the d-operator formula is implemented in the pseudopotential framework.
Chan, Garnet Kin-Lic; Keselman, Anna; Nakatani, Naoki; Li, Zhendong; White, Steven R
2016-07-07
Current descriptions of the ab initio density matrix renormalization group (DMRG) algorithm use two superficially different languages: an older language of the renormalization group and renormalized operators, and a more recent language of matrix product states and matrix product operators. The same algorithm can appear dramatically different when written in the two different vocabularies. In this work, we carefully describe the translation between the two languages in several contexts. First, we describe how to efficiently implement the ab initio DMRG sweep using a matrix product operator based code, and the equivalence to the original renormalized operator implementation. Next we describe how to implement the general matrix product operator/matrix product state algebra within a pure renormalized operator-based DMRG code. Finally, we discuss two improvements of the ab initio DMRG sweep algorithm motivated by matrix product operator language: Hamiltonian compression, and a sum over operators representation that allows for perfect computational parallelism. The connections and correspondences described here serve to link the future developments with the past and are important in the efficient implementation of continuing advances in ab initio DMRG and related algorithms.
NASA Astrophysics Data System (ADS)
Chan, Garnet Kin-Lic; Keselman, Anna; Nakatani, Naoki; Li, Zhendong; White, Steven R.
2016-07-01
Current descriptions of the ab initio density matrix renormalization group (DMRG) algorithm use two superficially different languages: an older language of the renormalization group and renormalized operators, and a more recent language of matrix product states and matrix product operators. The same algorithm can appear dramatically different when written in the two different vocabularies. In this work, we carefully describe the translation between the two languages in several contexts. First, we describe how to efficiently implement the ab initio DMRG sweep using a matrix product operator based code, and the equivalence to the original renormalized operator implementation. Next we describe how to implement the general matrix product operator/matrix product state algebra within a pure renormalized operator-based DMRG code. Finally, we discuss two improvements of the ab initio DMRG sweep algorithm motivated by matrix product operator language: Hamiltonian compression, and a sum over operators representation that allows for perfect computational parallelism. The connections and correspondences described here serve to link the future developments with the past and are important in the efficient implementation of continuing advances in ab initio DMRG and related algorithms.
A matrix model from string field theory
NASA Astrophysics Data System (ADS)
Zeze, Syoji
2016-09-01
We demonstrate that a Hermitian matrix model can be derived from level truncated open string field theory with Chan-Paton factors. The Hermitian matrix is coupled with a scalar and U(N) vectors which are responsible for the D-brane at the tachyon vacuum. Effective potential for the scalar is evaluated both for finite and large N. Increase of potential height is observed in both cases. The large N matrix integral is identified with a system of N ZZ branes and a ghost FZZT brane.
Two-body density matrix of a normal Fermi fluid
NASA Astrophysics Data System (ADS)
Ristig, M. L.; Clark, J. W.
1990-05-01
The microscopic study of the two-body density matrix ρ2(r1,r2,r'1,r'2) initiated for uniform Bose fluids in an earlier paper is continued for the Fermi case. We present formal results on the structure of the generalized momentum distribution n(p,q)=Σk⁁<Ψ\\|a†k⁁+qa†p⁁-qap⁁ak⁁\\|Ψ>, and its Fourier inverse ρ2(r1,r2,r'1,r2)≡ρ2(r1,r2,r'1), based on a variational ground-state wave function of Jastrow-Slater form. The structural relations are inferred from the cluster expansions of these objects, from the asymptotic condition relating ρ2(r1,r2,r'1) to the particle density and the one-body density matrix ρ1(r1,r'1), and from formal diagrammatic connections with the Bose problem. The two-body density-matrix elements ρ2(r1,r2,r'1) are thereby expressed in closed form in terms of certain sums of irreducible cluster diagrams. Some of these diagram sums are familiar from the analogous theory of the one-body density matrix; all can be evaluated quantitatively by solving a set of Fermi-hypernetted-chain (FHNC) equations. Upon invoking the sequential relation between ρ2(r1,r2,r'1) and ρ1(r1,r'1), the corresponding result for the generalized momentum distribution n(p,q) effects a resolution into contributions from various scattering processes occurring in the many-body medium, specified by form factors that are susceptible to FHNC evaluation. This decomposition is comparable to that derived earlier for the Bose-fluid ground state but is complicated by contributions from exchange scattering and by a dynamically dressed Pauli kinematic correction. Silver has proposed a simple expression for the generalized momentum distribution n(p,q), a function which plays an essential role in his theory of final-state effects in deep-inelastic neutron scattering from the helium liquids. Based on the present microscopic treatment, the quality of Silver's estimate is assessed for the case of normal liquid He3, by evaluating the necessary distribution
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
Random Matrix Theory and Elliptic Curves
2014-11-24
related to the intervals of prime numbers. 15. SUBJECT TERMS EOARD, Random Matrix theory, Riemann Hypothesis, Elliptic Curves 16. SECURITY...range of quantities of fundamental importance in number theory. In the cases of the Riemann zeta function and Dirichlet L-functions, this information...investigation using analytic techniques. As an indication of their significance, two of the Clay Millennium Prize Problems, the Riemann Hypothesis and the
Matrix theory compactifications on twisted tori
NASA Astrophysics Data System (ADS)
Chatzistavrakidis, Athanasios; Jonke, Larisa
2012-05-01
We study compactifications of Matrix theory on twisted tori and noncommutative versions of them. As a first step, we review the construction of multidimensional twisted tori realized as nilmanifolds based on certain nilpotent Lie algebras. Subsequently, matrix compactifications on tori are revisited, and the previously known results are supplemented with a background of a noncommutative torus with nonconstant noncommutativity and an underlying nonassociative structure on its phase space. Next, we turn our attention to three- and six-dimensional twisted tori, and we describe consistent backgrounds of Matrix theory on them by stating and solving the conditions which describe the corresponding compactification. Both commutative and noncommutative solutions are found in all cases. Finally, we comment on the correspondence among the obtained solutions and flux compactifications of 11-dimensional supergravity, as well as on relations among themselves, such as Seiberg-Witten maps and T-duality.
Supergravity Duals of Matrix String Theory
NASA Astrophysics Data System (ADS)
Morales, Jose F.; Samtleben, Henning
2002-08-01
We study holographic duals of type II and heterotic matrix string theories described by warped AdS3 supergravities. By explicitly solving the linearized equations of motion around near horizon D-string geometries, we determine the spectrum of Kaluza-Klein primaries for type I, II supergravities on warped AdS3 × S7. The results match those coming from the dual two-dimensional gauge theories living on the D-string worldvolumes. We briefly discuss the connections with the Script N = (8,8), Script N = (8,0) orbifold superconformal field theories to which type IIB/heterotic matrix strings flow in the infrared. In particular, we associate the dimension (h,bar h) = (3/2,3/2) twisted operator which brings the matrix string theories out from the conformal point (Bbb R8)N/SN with the dilaton profile in the supergravity background. The familiar dictionary between masses and ``scaling'' dimensions of field and operators are modified by the presence of non-trivial warp factors and running dilatons. These modifications are worked out for the general case of domain wall/QFT correspondences between supergravities on warped AdSd+1 × Sq geometries and super Yang-Mills theories with 16 supercharges.
Multivariate and matrix-variate analogues of Maxwell-Boltzmann and Raleigh densities
NASA Astrophysics Data System (ADS)
Mathai, A. M.; Princy, T.
2017-02-01
The Maxwell-Boltzmann and Raleigh densities are basic densities in many problems in Physics. A multivariate analogue and a rectangular matrix-variate analogue of these densities are explored in this article. The results may become useful in extending the usual theories, where these densities for the real scalar variable case occur, to multivariate and matrix variable situations. Various properties are studied and connection to the volumes of parallelotopes determined by p linearly independent random points in Euclidean n-space, n ≥ p, is also established. Structural decompositions of these random determinants and pathway extensions of Maxwell-Boltzmann and Raleigh densities are also considered.
Watching excitons move: the time-dependent transition density matrix
NASA Astrophysics Data System (ADS)
Ullrich, Carsten
2012-02-01
Time-dependent density-functional theory allows one to calculate excitation energies and the associated transition densities in principle exactly. The transition density matrix (TDM) provides additional information on electron-hole localization and coherence of specific excitations of the many-body system. We have extended the TDM concept into the real-time domain in order to visualize the excited-state dynamics in conjugated molecules. The time-dependent TDM is defined as an implicit density functional, and can be approximately obtained from the time-dependent Kohn-Sham orbitals. The quality of this approximation is assessed in simple model systems. A computational scheme for real molecular systems is presented: the time-dependent Kohn-Sham equations are solved with the OCTOPUS code and the time-dependent Kohn-Sham TDM is calculated using a spatial partitioning scheme. The method is applied to show in real time how locally created electron-hole pairs spread out over neighboring conjugated molecular chains. The coupling mechanism, electron-hole coherence, and the possibility of charge separation are discussed.
Hedegård, Erik Donovan Knecht, Stefan; Reiher, Markus; Kielberg, Jesper Skau; Jensen, Hans Jørgen Aagaard
2015-06-14
We present a new hybrid multiconfigurational method based on the concept of range-separation that combines the density matrix renormalization group approach with density functional theory. This new method is designed for the simultaneous description of dynamical and static electron-correlation effects in multiconfigurational electronic structure problems.
Social patterns revealed through random matrix theory
NASA Astrophysics Data System (ADS)
Sarkar, Camellia; Jalan, Sarika
2014-11-01
Despite the tremendous advancements in the field of network theory, very few studies have taken weights in the interactions into consideration that emerge naturally in all real-world systems. Using random matrix analysis of a weighted social network, we demonstrate the profound impact of weights in interactions on emerging structural properties. The analysis reveals that randomness existing in particular time frame affects the decisions of individuals rendering them more freedom of choice in situations of financial security. While the structural organization of networks remains the same throughout all datasets, random matrix theory provides insight into the interaction pattern of individuals of the society in situations of crisis. It has also been contemplated that individual accountability in terms of weighted interactions remains as a key to success unless segregation of tasks comes into play.
Constructing acoustic timefronts using random matrix theory.
Hegewisch, Katherine C; Tomsovic, Steven
2013-10-01
In a recent letter [Hegewisch and Tomsovic, Europhys. Lett. 97, 34002 (2012)], random matrix theory is introduced for long-range acoustic propagation in the ocean. The theory is expressed in terms of unitary propagation matrices that represent the scattering between acoustic modes due to sound speed fluctuations induced by the ocean's internal waves. The scattering exhibits a power-law decay as a function of the differences in mode numbers thereby generating a power-law, banded, random unitary matrix ensemble. This work gives a more complete account of that approach and extends the methods to the construction of an ensemble of acoustic timefronts. The result is a very efficient method for studying the statistical properties of timefronts at various propagation ranges that agrees well with propagation based on the parabolic equation. It helps identify which information about the ocean environment can be deduced from the timefronts and how to connect features of the data to that environmental information. It also makes direct connections to methods used in other disordered waveguide contexts where the use of random matrix theory has a multi-decade history.
Direct Measurement of the Density Matrix of a Quantum System
NASA Astrophysics Data System (ADS)
Thekkadath, G. S.; Giner, L.; Chalich, Y.; Horton, M. J.; Banker, J.; Lundeen, J. S.
2016-09-01
One drawback of conventional quantum state tomography is that it does not readily provide access to single density matrix elements since it requires a global reconstruction. Here, we experimentally demonstrate a scheme that can be used to directly measure individual density matrix elements of general quantum states. The scheme relies on measuring a sequence of three observables, each complementary to the last. The first two measurements are made weak to minimize the disturbance they cause to the state, while the final measurement is strong. We perform this joint measurement on polarized photons in pure and mixed states to directly measure their density matrix. The weak measurements are achieved using two walk-off crystals, each inducing a polarization-dependent spatial shift that couples the spatial and polarization degrees of freedom of the photons. This direct measurement method provides an operational meaning to the density matrix and promises to be especially useful for large dimensional states.
NASA Astrophysics Data System (ADS)
Wouters, Sebastian; Nakatani, Naoki; Van Neck, Dimitri; Chan, Garnet Kin-Lic
2013-08-01
The similarities between Hartree-Fock (HF) theory and the density matrix renormalization group (DMRG) are explored. Both methods can be formulated as the variational optimization of a wave-function Ansatz. Linearization of the time-dependent variational principle near a variational minimum allows to derive the random phase approximation (RPA). We show that the nonredundant parameterization of the matrix product state (MPS) tangent space [J. Haegeman, J. I. Cirac, T. J. Osborne, I. Pižorn, H. Verschelde, and F. Verstraete, Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.107.070601 107, 070601 (2011)] leads to the Thouless theorem for MPS, i.e., an explicit nonredundant parameterization of the entire MPS manifold, starting from a specific MPS reference. Excitation operators are identified, which extends the analogy between HF and DMRG to the Tamm-Dancoff approximation (TDA), the configuration interaction (CI) expansion, and coupled cluster theory. For a small one-dimensional Hubbard chain, we use a CI-MPS Ansatz with single and double excitations to improve on the ground state and to calculate low-lying excitation energies. For a symmetry-broken ground state of this model, we show that RPA-MPS allows to retrieve the Goldstone mode. We also discuss calculations of the RPA-MPS correlation energy. With the long-range quantum chemical Pariser-Parr-Pople Hamiltonian, low-lying TDA-MPS and RPA-MPS excitation energies for polyenes are obtained.
Deconstructing Wigner's density matrix concerning the mind-body question
NASA Astrophysics Data System (ADS)
Brandt, Howard E.
2002-06-01
In honor of the centennial of Eugene Wigner’s birth, a possible interpretation is given of the density matrix appearing in his classic paper, “Remarks on the mind-body question.” It is argued that nearinstantaneous vanishing of the quantum coherences of the reduced density matrix of the measured object would occur either in the case of Wigner’s friend, or in the case of any complex measuring automaton (conscious or not) making the measurement.
Stationary density matrix of a pumped polariton system.
Vera, Carlos Andrés; Cabo, Alejandro; González, Augusto
2009-03-27
The density matrix rho of a model polariton system is obtained numerically from a master equation which takes account of pumping and losses. In the stationary limit, the coherences between eigenstates of the Hamiltonian are 3 orders of magnitude smaller than the occupations, meaning that the stationary density matrix is approximately diagonal in the energy representation. A weakly distorted grand canonical Gibbs distribution fits well the occupations.
Universal shocks in random matrix theory.
Blaizot, Jean-Paul; Nowak, Maciej A
2010-11-01
We link the appearance of universal kernels in random matrix ensembles to the phenomenon of shock formation in some fluid dynamical equations. Such equations are derived from Dyson's random walks after a proper rescaling of the time. In the case of the gaussian unitary ensemble, on which we focus in this paper, we show that the characteristics polynomials and their inverse evolve according to a viscid Burgers equation with an effective "spectral viscosity" ν(s)=1/2N, where N is the size of the matrices. We relate the edge of the spectrum of eigenvalues to the shock that naturally appears in the Burgers equation for appropriate initial conditions, thereby suggesting a connection between the well-known microscopic universality of random matrix theory and the universal properties of the solution of the Burgers equation in the vicinity of a shock.
Matrix product states for gauge field theories.
Buyens, Boye; Haegeman, Jutho; Van Acoleyen, Karel; Verschelde, Henri; Verstraete, Frank
2014-08-29
The matrix product state formalism is used to simulate Hamiltonian lattice gauge theories. To this end, we define matrix product state manifolds which are manifestly gauge invariant. As an application, we study (1+1)-dimensional one flavor quantum electrodynamics, also known as the massive Schwinger model, and are able to determine very accurately the ground-state properties and elementary one-particle excitations in the continuum limit. In particular, a novel particle excitation in the form of a heavy vector boson is uncovered, compatible with the strong coupling expansion in the continuum. We also study full quantum nonequilibrium dynamics by simulating the real-time evolution of the system induced by a quench in the form of a uniform background electric field.
Random matrix techniques in quantum information theory
Collins, Benoît; Nechita, Ion
2016-01-15
The purpose of this review is to present some of the latest developments using random techniques, and in particular, random matrix techniques in quantum information theory. Our review is a blend of a rather exhaustive review and of more detailed examples—coming mainly from research projects in which the authors were involved. We focus on two main topics, random quantum states and random quantum channels. We present results related to entropic quantities, entanglement of typical states, entanglement thresholds, the output set of quantum channels, and violations of the minimum output entropy of random channels.
Schwarzschild Black Holes from Matrix Theory
Banks, T.; Fischler, W.; Klebanov, I.R.; Susskind, L.
1998-01-01
We consider matrix theory compactified on T{sup 3} and show that it correctly describes the properties of Schwarzschild black holes in 7+1 dimensions, including the mass-entropy relation, the Hawking temperature, and the physical size, up to numerical factors of order unity. The most economical description involves setting the cutoff N in the discretized light-cone quantization to be of order the black hole entropy. A crucial ingredient necessary for our work is the recently proposed equation of state for 3+1 dimensional supersymmetric Yang-Mills theory with 16supercharges. We give detailed arguments for the range of validity of this equation following the methods of Horowitz and Polchinski. {copyright} {ital 1998} {ital The American Physical Society}
Exact and approximate many-body dynamics with stochastic one-body density matrix evolution
Lacroix, Denis
2005-06-01
We show that the dynamics of interacting fermions can be exactly replaced by a quantum jump theory in the many-body density matrix space. In this theory, jumps occur between densities formed of pairs of Slater determinants, D{sub ab}= vertical bar {phi}{sub a}><{phi}{sub b} vertical bar, where each state evolves according to the stochastic Schroedinger equation given by O. Juillet and Ph. Chomaz [Phys. Rev. Lett. 88, 142503 (2002)]. A stochastic Liouville-von Neumann equation is derived as well as the associated. Bogolyubov-Born-Green-Kirwood-Yvon hierarchy. Due to the specific form of the many-body density along the path, the presented theory is equivalent to a stochastic theory in one-body density matrix space, in which each density matrix evolves according to its own mean-field augmented by a one-body noise. Guided by the exact reformulation, a stochastic mean-field dynamics valid in the weak coupling approximation is proposed. This theory leads to an approximate treatment of two-body effects similar to the extended time-dependent Hartree-Fock scheme. In this stochastic mean-field dynamics, statistical mixing can be directly considered and jumps occur on a coarse-grained time scale. Accordingly, numerical effort is expected to be significantly reduced for applications.
Information Theory and the Earth's Density Distribution
NASA Technical Reports Server (NTRS)
Rubincam, D. P.
1979-01-01
An argument for using the information theory approach as an inference technique in solid earth geophysics. A spherically symmetric density distribution is derived as an example of the method. A simple model of the earth plus knowledge of its mass and moment of inertia lead to a density distribution which was surprisingly close to the optimum distribution. Future directions for the information theory approach in solid earth geophysics as well as its strengths and weaknesses are discussed.
Information theory and the earth's density distribution
NASA Technical Reports Server (NTRS)
Rubincam, D. P.
1978-01-01
The present paper argues for using the information theory approach as an inference technique in solid earth geophysics. A spherically symmetric density distribution is derived as an example of the method. A simple model of the earth plus knowledge of its mass and moment of inertia leads to a density distribution. Future directions for the information theory approach in solid earth geophysics as well as its strengths and weaknesses are discussed.
Hadronic density of states from string theory.
Pando Zayas, Leopoldo A; Vaman, Diana
2003-09-12
We present an exact calculation of the finite temperature partition function for the hadronic states corresponding to a Penrose-Güven limit of the Maldacena-Nùñez embedding of the N=1 super Yang-Mills (SYM) into string theory. It is established that the theory exhibits a Hagedorn density of states. We propose a semiclassical string approximation to the finite temperature partition function for confining gauge theories admitting a supergravity dual, by performing an expansion around classical solutions characterized by temporal windings. This semiclassical approximation reveals a hadronic energy density of states of a Hagedorn type, with the coefficient determined by the gauge theory string tension as expected for confining theories. We argue that our proposal captures primarily information about states of pure N=1 SYM theory, given that this semiclassical approximation does not entail a projection onto states of large U(1) charge.
The ab-initio density matrix renormalization group in practice
Olivares-Amaya, Roberto; Hu, Weifeng; Sharma, Sandeep; Yang, Jun; Chan, Garnet Kin-Lic; Nakatani, Naoki
2015-01-21
The ab-initio density matrix renormalization group (DMRG) is a tool that can be applied to a wide variety of interesting problems in quantum chemistry. Here, we examine the density matrix renormalization group from the vantage point of the quantum chemistry user. What kinds of problems is the DMRG well-suited to? What are the largest systems that can be treated at practical cost? What sort of accuracies can be obtained, and how do we reason about the computational difficulty in different molecules? By examining a diverse benchmark set of molecules: π-electron systems, benchmark main-group and transition metal dimers, and the Mn-oxo-salen and Fe-porphine organometallic compounds, we provide some answers to these questions, and show how the density matrix renormalization group is used in practice.
NASA Astrophysics Data System (ADS)
March, N. H.
In Hartree-Fock theory, the exchange energy density can be expressed solely in terms of the first-order density matrix. Far from the nucleus of a closed-shell atom, idem potency of the density matrix yields the exchange energy density as the magnitude of the Coulomb energy e2/r times the electron density ρ. Thus two lengths enter the asymptotic form in contrast to ρ-1/3 alone of local-density theory.
Vibrations in Glasses and Random Matrix Theory
NASA Astrophysics Data System (ADS)
Fabian, Jaroslav; Feldman, Joseph L.
1998-03-01
Vibrations in amorphous silicon are analyzed from the perspective of random matrix theory. We use the combination of the Wooten-Winer-Weaire random network and Stillinger-Weber interatomic potential to model the vibrational dynamics of amorphous silicon. By calculating the level-spacing distributions and spectral correlation functions for the vibrations of this model we find that the majority of the vibrations (diffusons--extended non-propagating modes) can be described in terms of random matrices (the corresponding level-spacing distribution corresponds to the Wigner surmise). On the other hand, localized modes, which in our model exist only at the highest frequencies, show no sign of spectral correlation and their level-spacing distribution is a Poisson one.
Random Matrix Theory in molecular dynamics analysis.
Palese, Luigi Leonardo
2015-01-01
It is well known that, in some situations, principal component analysis (PCA) carried out on molecular dynamics data results in the appearance of cosine-shaped low index projections. Because this is reminiscent of the results obtained by performing PCA on a multidimensional Brownian dynamics, it has been suggested that short-time protein dynamics is essentially nothing more than a noisy signal. Here we use Random Matrix Theory to analyze a series of short-time molecular dynamics experiments which are specifically designed to be simulations with high cosine content. We use as a model system the protein apoCox17, a mitochondrial copper chaperone. Spectral analysis on correlation matrices allows to easily differentiate random correlations, simply deriving from the finite length of the process, from non-random signals reflecting the intrinsic system properties. Our results clearly show that protein dynamics is not really Brownian also in presence of the cosine-shaped low index projections on principal axes.
Quantum graphs and random-matrix theory
NASA Astrophysics Data System (ADS)
Pluhař, Z.; Weidenmüller, H. A.
2015-07-01
For simple connected graphs with incommensurate bond lengths and with unitary symmetry we prove the Bohigas-Giannoni-Schmit (BGS) conjecture in its most general form. Using supersymmetry and taking the limit of infinite graph size, we show that the generating function for every (P,Q) correlation function for both closed and open graphs coincides with the corresponding expression of random-matrix theory. We show that the classical Perron-Frobenius operator is bistochastic and possesses a single eigenvalue +1. In the quantum case that implies the existence of a zero (or massless) mode of the effective action. That mode causes universal fluctuation properties. Avoiding the saddle-point approximation we show that for graphs that are classically mixing (i.e. for which the spectrum of the classical Perron-Frobenius operator possesses a finite gap) and that do not carry a special class of bound states, the zero mode dominates in the limit of infinite graph size.
Revisting the Density Matrix Expansion with Regulated Chiral Interactions
NASA Astrophysics Data System (ADS)
Dyhdalo, Alexander; Furnstahl, Richard; Bogner, Scott; Schunck, Nicolas; Navarro Perez, Rodrigo
2016-09-01
The density matrix expansion provides a general way to map microscopic interactions to a local functional. Previous density matrix expansion formulations added unregulated chiral long-range potentials to a Skyrme-type functional, which accounted for the short-range contributions. We implement the expansion with new coordinate space regulators using the regulator cutoff as a tool to adiabatically turn on finite-range pion interactions. We discuss `smoking guns' for correct inclusion of 3-body forces, which are implemented in a normal-ordering prescription, and compare to ab initio calculations.
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.
Auxiliary Density Matrix Methods for Hartree-Fock Exchange Calculations.
Guidon, Manuel; Hutter, Jürg; VandeVondele, Joost
2010-08-10
The calculation of Hartree-Fock exchange (HFX) is computationally demanding for large systems described with high-quality basis sets. In this work, we show that excellent performance and good accuracy can nevertheless be obtained if an auxiliary density matrix is employed for the HFX calculation. Several schemes to derive an auxiliary density matrix from a high-quality density matrix are discussed. Key to the accuracy of the auxiliary density matrix methods (ADMM) is the use of a correction based on standard generalized gradient approximations for HFX. ADMM integrates seamlessly in existing HFX codes and, in particular, can be employed in linear scaling implementations. Demonstrating the performance of the method, the effect of HFX on the structure of liquid water is investigated in detail using Born-Oppenheimer molecular dynamics simulations (300 ps) of a system of 64 molecules. Representative for large systems are calculations on a solvated protein (Rubredoxin), for which ADMM outperforms the corresponding standard HFX implementation by approximately a factor 20.
Communication: Four-component density matrix renormalization group
Knecht, Stefan Reiher, Markus; Legeza, Örs
2014-01-28
We present the first implementation of the relativistic quantum chemical two- and four-component density matrix renormalization group algorithm that includes a variational description of scalar-relativistic effects and spin–orbit coupling. Numerical results based on the four-component Dirac–Coulomb Hamiltonian are presented for the standard reference molecule for correlated relativistic benchmarks: thallium hydride.
Maslow's Implied Matrix: A Clarification of the Need Hierarchy Theory.
ERIC Educational Resources Information Center
Marsh, Edward
1978-01-01
Maslow's need hierarchy theory is restated by means of a matrix arrangement of the constructs within the theory. After consideration of the consequences of this restatement, some significant research is discussed and directions for future research suggested. (Author)
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.
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.
NASA Technical Reports Server (NTRS)
Bhatt, Ramakrishna T.; Kiser, Lames D.
1990-01-01
The room temperature mechanical properties were measured for SiC fiber reinforced reaction-bonded silicon nitride composites (SiC/RBSN) of different densities. The composites consisted of approx. 30 vol percent uniaxially aligned 142 micron diameter SiC fibers (Textron SCS-6) in a reaction-bonded Si3N4 matrix. The composite density was varied by changing the consolidation pressure during RBSN processing and by hot isostatically pressing the SiC/RBSN composites. Results indicate that as the consolidation pressure was increased from 27 to 138 MPa, the average pore size of the nitrided composites decreased from 0.04 to 0.02 microns and the composite density increased from 2.07 to 2.45 gm/cc. Nonetheless, these improvements resulted in only small increases in the first matrix cracking stress, primary elastic modulus, and ultimate tensile strength values of the composites. In contrast, HIP consolidation of SiC/RBSN resulted in a fully dense material whose first matrix cracking stress and elastic modulus were approx. 15 and 50 percent higher, respectively, and ultimate tensile strength values were approx. 40 percent lower than those for unHIPed SiC/RBSN composites. The modulus behavior for all specimens can be explained by simple rule-of-mixture theory. Also, the loss in ultimate strength for the HIPed composites appears to be related to a degradation in fiber strength at the HIP temperature. However, the density effect on matrix fracture strength was much less than would be expected based on typical monolithic Si3N4 behavior, suggesting that composite theory is indeed operating. Possible practical implications of these observations are 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.
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
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.
Localized density matrix minimization and linear-scaling algorithms
NASA Astrophysics Data System (ADS)
Lai, Rongjie; Lu, Jianfeng
2016-06-01
We propose a convex variational approach to compute localized density matrices for both zero temperature and finite temperature cases, by adding an entry-wise ℓ1 regularization to the free energy of the quantum system. Based on the fact that the density matrix decays exponentially away from the diagonal for insulating systems or systems at finite temperature, the proposed ℓ1 regularized variational method provides an effective way to approximate the original quantum system. We provide theoretical analysis of the approximation behavior and also design convergence guaranteed numerical algorithms based on Bregman iteration. More importantly, the ℓ1 regularized system naturally leads to localized density matrices with banded structure, which enables us to develop approximating algorithms to find the localized density matrices with computation cost linearly dependent on the problem size.
Magnesium Matrix Composite Foams-Density, Mechanical Properties, and Applications
2012-07-24
known that the effect of particle-matrix interfacial bonding is much less significant under compression compared to under tension [33,34]. One of the...parameter). Some syntactic foam composites are found to have less than 0.4 g/cc density in Figure 9. These data points belong to foams that contain...syntactic foams containing porosity only inside hollow particles. The yield strength values for various types of MMSFs, including aluminum, titanium , and
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.
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.
Scattering matrix theory for stochastic scalar fields.
Korotkova, Olga; Wolf, Emil
2007-05-01
We consider scattering of stochastic scalar fields on deterministic as well as on random media, occupying a finite domain. The scattering is characterized by a generalized scattering matrix which transforms the angular correlation function of the incident field into the angular correlation function of the scattered field. Within the accuracy of the first Born approximation this matrix can be expressed in a simple manner in terms of the scattering potential of the scatterer. Apart from determining the angular distribution of the spectral intensity of the scattered field, the scattering matrix makes it possible also to determine the changes in the state of coherence of the field produced on scattering.
Derivation of the density matrix of a single photon produced in parametric down-conversion
Kolenderski, Piotr; Wasilewski, Wojciech
2009-07-15
We discuss an effective numerical method of density matrix determination of fiber coupled single photon generated in process of spontaneous parametric down conversion in type I noncollinear configuration. The presented theory has been successfully applied in case of source utilized to demonstrate the experimental characterization of spectral state of single photon, what was reported in Wasilewski, Kolenderski, and Frankowski [Phys. Rev. Lett. 99, 123601 (2007)].
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.
Supersymmetry of Green-Schwarz superstring and matrix string theory
Hyun, Seungjoon; Shin, Hyeonjoon
2001-08-15
We study the dynamics of a Green-Schwarz superstring on the gravitational wave background corresponding to the matrix string theory and the supersymmetry transformation rules of the superstring. The dynamics is obtained in the light-cone formulation and is shown to agree with that derived from matrix string theory. The supersymmetry structure has corrections due to the effect of the background and is identified with that of the low-energy one-loop effective action of matrix string theory in a two superstring background in the weak string coupling limit.
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.
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.
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.
Observational Confirmations of Spiral Density Wave Theory
NASA Astrophysics Data System (ADS)
Kennefick, Julia D.; Kennefick, Daniel; Shameer Abdeen, Mohamed; Berrier, Joel; Davis, Benjamin; Fusco, Michael; Pour Imani, Hamed; Shields, Doug; DMS, SINGS
2017-01-01
Using two techniques to reliably and accurately measure the pitch angles of spiral arms in late-type galaxies, we have compared pitch angles to directly measured black hole masses in local galaxies and demonstrated a strong correlation between them. Using the relation thus established we have developed a pitch angle distribution function of a statistically complete volume limited sample of nearby galaxies and developed a central black hole mass function for nearby spiral galaxies.We have further shown that density wave theory leads us to a three-way correlation between bulge mass, pitch angle, and disk gas density, and have used data from the Galaxy Disk Mass Survey to confirm this possible fundamental plane. Density wave theory also predicts that the pitch angle of spiral arms should change with observed waveband as each waveband is sampling a different stage in stellar population formation and evolution. We present evidence that this is indeed the case using a sample of galaxies from the Spitzer Infrared Nearby Galaxy Survey. Furthermore, the evolved spiral arms cross at the galaxy co-rotation radius. This gives a new method for determining the co-rotation radius of spiral galaxies that is found to agree with those found using previous methods.
Electron correlation in solids via density embedding theory
Bulik, Ireneusz W.; Chen, Weibing; Scuseria, Gustavo E.
2014-08-07
Density matrix embedding theory [G. Knizia and G. K.-L. Chan, Phys. Rev. Lett. 109, 186404 (2012)] and density embedding theory [I. W. Bulik, G. E. Scuseria, and J. Dukelsky, Phys. Rev. B 89, 035140 (2014)] have recently been introduced for model lattice Hamiltonians and molecular systems. In the present work, the formalism is extended to the ab initio description of infinite systems. An appropriate definition of the impurity Hamiltonian for such systems is presented and demonstrated in cases of 1, 2, and 3 dimensions, using coupled cluster theory as the impurity solver. Additionally, we discuss the challenges related to disentanglement of fragment and bath states. The current approach yields results comparable to coupled cluster calculations of infinite systems even when using a single unit cell as the fragment. The theory is formulated in the basis of Wannier functions but it does not require separate localization of unoccupied bands. The embedding scheme presented here is a promising way of employing highly accurate electronic structure methods for extended systems at a fraction of their original computational cost.
Mazziotti, David A.
2005-09-15
The energy and properties of a many-electron atom or molecule may be directly computed from a variational optimization of a two-electron reduced density matrix (2RDM) that is constrained to represent many-electron quantum systems. In this paper we implement a variational 2RDM method with a representability constraint, known as the T{sub 2} condition. The optimization of the 2RDM is performed with a first-order algorithm for semidefinite programming [D. A. Mazziotti, Phys. Rev. Lett. 93, 213001 (2004)] which, because of its lower computational cost in comparison to second-order methods, allows the treatment of larger basis sets. We also derive and implement a spin- and symmetry-adapted formulation of the T{sub 2} condition that significantly decreases the size of the largest block in the T{sub 2} matrix. The T{sub 2} condition, originally derived by Erdahl [Int. J. Quantum Chem. 13, 697 (1978)], was recently applied via a second-order algorithm to atoms and molecules [Z. Zhao et al., J. Chem. Phys. 120, 2095 (2004)]. While these calculations were restricted to molecules at equilibrium geometries in minimal basis sets, we apply the 2RDM method with the T{sub 2} condition to compute the electronic energies of molecules in both minimal and nonminimal basis sets at equilibrium as well as nonequilibrium geometries. Accurate potential energies curves are produced for BH, HF, and N{sub 2}. Results are compared with the 2RDM method without the T{sub 2} condition as well as several wave-function methods.
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.
Development and application of a density dependent matrix ...
Ranging along the Atlantic coast from US Florida to the Maritime Provinces of Canada, the Atlantic killifish (Fundulus heteroclitus) is an important and well-studied model organism for understanding the effects of pollutants and other stressors in estuarine and marine ecosystems. Matrix population models are useful tools for ecological risk assessment because they integrate effects across the life cycle, provide a linkage between endpoints observed in the individual and ecological risk to the population as a whole, and project outcomes for many generations in the future. We developed a density dependent matrix population model for Atlantic killifish by modifying a model developed for fathead minnow (Pimephales promelas) that has proved to be extremely useful, e.g. to incorporate data from laboratory studies and project effects of endocrine disrupting chemicals. We developed a size-structured model (as opposed to one that is based upon developmental stages or age class structure) so that we could readily incorporate output from a Dynamic Energy Budget (DEB) model, currently under development. Due to a lack of sufficient data to accurately define killifish responses to density dependence, we tested a number of scenarios realistic for other fish species in order to demonstrate the outcome of including this ecologically important factor. We applied the model using published data for killifish exposed to dioxin-like compounds, and compared our results to those using
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.
Big bang and big crunch in matrix string theory
Bedford, J.; Ward, J.; Papageorgakis, C.; Rodriguez-Gomez, D.
2007-04-15
Following the holographic description of linear dilaton null cosmologies with a big bang in terms of matrix string theory put forward by Craps, Sethi, and Verlinde, we propose an extended background describing a universe including both big bang and big crunch singularities. This belongs to a class of exact string backgrounds and is perturbative in the string coupling far away from the singularities, both of which can be resolved using matrix string theory. We provide a simple theory capable of describing the complete evolution of this closed universe.
Hermitian one-particle density matrix through a semiclassical gradient expansion
NASA Astrophysics Data System (ADS)
Bencheikh, K.; Räsänen, E.
2016-01-01
We carry out the semiclassical expansion of the one-particle density matrix up to the second order in {{\\hslash }}. We use the method of Grammaticos and Voros based on the Wigner transform of operators. We show that the resulting density matrix is Hermitian and idempotent in contrast with the well-known result of the semiclassical Kirzhnits expansion. Our density matrix leads to the same particle density and kinetic energy density as in the literature, and it satisfies the consistency criterion of the Euler equation. The derived Hermitian density matrix clarifies the ambiguity in the usefulness of gradient expansion approximations and might reignite the development of density functionals with semiclassical methods.
Matrix density effects on the mechanical properties of SiC/RBSN composites
NASA Technical Reports Server (NTRS)
Bhatt, Ramakrishna T.; Kiser, James D.
1990-01-01
The room temperature mechanical properties were measured for SiC fiber reinforced reaction-bonded silicon nitride composites (SiC/RBSN) of different densities. The composites consisted of approx. 30 vol percent uniaxially aligned 142 micron diameter SiC fibers (Textron SCS-6) in a reaction-bonded Si3N4 matrix. The composite density was varied by changing the consolidation pressure during RBSN processing and by hot isostatically pressing the SiC/RBSN composites. Results indicate that as the consolidation pressure was increased from 27 to 138 MPa, the average pore size of the nitrided composites decreased from 0.04 to 0.02 microns and the composite density increased from 2.07 to 2.45 gm/cc. Nonetheless, these improvements resulted in only small increases in the first matrix cracking stress, primary elastic modulus, and ultimate tensile strength values of the composites. In contrast, HIP consolidation of SiC/RBSN resulted in a fully dense material whose first matrix cracking stress and elastic modulus were approx. 15 and 50 percent higher, respectively, and ultimate tensile strength values were approx. 40 percent lower than those for unHIPed SiC/RBSN composites. The modulus behavior for all specimens can be explained by simple rule-of-mixture theory. Also, the loss in ultimate strength for the HIPed composites appears to be related to a degradation in fiber strength at the HIP temperature. However, the density effect on matrix fracture strength was much less than would be expected based on typical monolithic Si3N4 behavior, suggesting that composite theory is indeed operating. Possible practical implications of these observations are discussed.
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.
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).
Fuzzy Field Theory as a Random Matrix Model
NASA Astrophysics Data System (ADS)
Tekel, Juraj
This dissertation considers the theory of scalar fields on fuzzy spaces from the point of view of random matrices. First we define random matrix ensembles, which are natural description of such theory. These ensembles are new and the novel feature is a presence of kinetic term in the probability measure, which couples the random matrix to a set of external matrices and thus breaks the original symmetry. Considering the case of a free field ensemble, which is generalization of a Gaussian matrix ensemble, we develop a technique to compute expectation values of the observables of the theory based on explicit Wick contractions and we write down recursion rules for these. We show that the eigenvalue distribution of the random matrix follows the Wigner semicircle distribution with a rescaled radius. We also compute distributions of the matrix Laplacian of the random matrix given by the new term and demonstrate that the eigenvalues of these two matrices are correlated. We demonstrate the robustness of the method by computing expectation values and distributions for more complicated observables. We then consider the ensemble corresponding to an interacting field theory, with a quartic interaction. We use the same method to compute the distribution of the eigenvalues and show that the presence of the kinetic terms rescales the distribution given by the original theory, which is a polynomially deformed Wigner semicircle. We compute the eigenvalue distribution of the matrix Laplacian and the joint distribution up to second order in the correlation and we show that the correlation between the two changes from the free field case. Finally, as an application of these results, we compute the phase diagram of the fuzzy scalar field theory, we find multiscaling which stabilizes this diagram in the limit of large matrices and compare it with the results obtained numerically and by considering the kinetic part as a perturbation.
Reduced density matrix and order parameters of a topological insulator
NASA Astrophysics Data System (ADS)
Yu, Wing Chi; Li, Yan Chao; Sacramento, P. D.; Lin, Hai-Qing
2016-12-01
It has been recently proposed that the reduced density matrix may be used to derive the order parameter of a condensed matter system. Here we propose order parameters for the phases of a topological insulator, specifically a spinless Su-Schrieffer-Heeger (SSH) model, and consider the effect of short-range interactions. All the derived order parameters and their possible corresponding quantum phases are verified by the entanglement entropy and electronic configuration analysis results. The order parameter appropriate to the topological regions is further proved by calculating the Berry phase under twisted boundary conditions. It is found that the topological nontrivial phase is robust to the introduction of repulsive intersite interactions and can appear in the topological trivial parameter region when appropriate interactions are added.
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.
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.
Are M-atrix theory and Maldacena's conjecture related?
NASA Astrophysics Data System (ADS)
Chepelev, Iouri
1999-05-01
We give arguments in the support of a relation between M-atrix theory and Maldacena's conjecture. M-atrix theory conjecture implies the equivalence of 11-D light-cone supergravity and strongly-coupled (0+1)-D SYM. Maldacena's SUGRA/SYM duality conjecture implies, in the one dimensional SYM case, the equivalence between strongly-coupled (0+1)-D SYM and 11-D supergravity compactified on a spatial circle in the formal Seiberg-Sen limit. Using the classical equivalence between 11-D supergravity on a light-like circle and on a spatial circle in the formal Seiberg-Sen limit, we argue that in the (0+1)-D SYM case, the large-N M-atrix theory in the supergravity regime is equivalent to SUGRA/SYM duality.
Six Decades of Spiral Density Wave Theory
NASA Astrophysics Data System (ADS)
Shu, Frank H.
2016-09-01
The theory of spiral density waves had its origin approximately six decades ago in an attempt to reconcile the winding dilemma of material spiral arms in flattened disk galaxies. We begin with the earliest calculations of linear and nonlinear spiral density waves in disk galaxies, in which the hypothesis of quasi-stationary spiral structure (QSSS) plays a central role. The earliest success was the prediction of the nonlinear compression of the interstellar medium and its embedded magnetic field; the earliest failure, seemingly, was not detecting color gradients associated with the migration of OB stars whose formation is triggered downstream from the spiral shock front. We give the reasons for this apparent failure with an update on the current status of the problem of OB star formation, including its relationship to the feathering substructure of galactic spiral arms. Infrared images can show two-armed, grand design spirals, even when the optical and UV images show flocculent structures. We suggest how the nonlinear response of the interstellar gas, coupled with overlapping subharmonic resonances, might introduce chaotic behavior in the dynamics of the interstellar medium and Population I objects, even though the underlying forces to which they are subject are regular. We then move to a discussion of resonantly forced spiral density waves in a planetary ring and their relationship to the ideas of disk truncation, and the shepherding of narrow rings by satellites orbiting nearby. The back reaction of the rings on the satellites led to the prediction of planet migration in protoplanetary disks, which has had widespread application in the exploding data sets concerning hot Jupiters and extrasolar planetary systems. We then return to the issue of global normal modes in the stellar disk of spiral galaxies and its relationship to the QSSS hypothesis, where the central theoretical concepts involve waves with negative and positive surface densities of energy and angular
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.
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.
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.
Density-matrix formalism for the photoion-electron entanglement in atomic photoionization
Radtke, T.; Fritzsche, S.; Surzhykov, A.
2006-09-15
The density-matrix theory, based on Dirac's relativistic equation, is applied for studying the entanglement between the photoelectron and residual ion in the course of the photoionization of atoms and ions. In particular, emphasis is placed on deriving the final-state density matrix of the overall system 'photoion+electron', including interelectronic effects and the higher multipoles of the radiation field. This final-state density matrix enables one immediately to analyze the change of entanglement as a function of the energy, angle and the polarization of the incoming light. Detailed computations have been carried out for the 5s photoionization of neutral strontium, leading to a photoion in a 5s {sup 2}S J{sub f}=1/2 level. It is found that the photoion-electron entanglement decreases significantly near the ionization threshold and that, in general, it depends on both the photon energy and angle. The possibility to extract photoion-electron pairs with a well-defined degree of entanglement may have far-reaching consequences for quantum information and elsewhere.
Matrix theory interpretation of discrete light cone quantization string worldsheets
Grignani; Orland; Paniak; Semenoff
2000-10-16
We study the null compactification of type-IIA string perturbation theory at finite temperature. We prove a theorem about Riemann surfaces establishing that the moduli spaces of infinite-momentum-frame superstring worldsheets are identical to those of branched-cover instantons in the matrix-string model conjectured to describe M theory. This means that the identification of string degrees of freedom in the matrix model proposed by Dijkgraaf, Verlinde, and Verlinde is correct and that its natural generalization produces the moduli space of Riemann surfaces at all orders in the genus expansion.
Iterative solutions to the steady-state density matrix for optomechanical systems
NASA Astrophysics Data System (ADS)
Nation, P. D.; Johansson, J. R.; Blencowe, M. P.; Rimberg, A. J.
2015-01-01
We present a sparse matrix permutation from graph theory that gives stable incomplete lower-upper preconditioners necessary for iterative solutions to the steady-state density matrix for quantum optomechanical systems. This reordering is efficient, adding little overhead to the computation, and results in a marked reduction in both memory and runtime requirements compared to other solution methods, with performance gains increasing with system size. Either of these benchmarks can be tuned via the preconditioner accuracy and solution tolerance. This reordering optimizes the condition number of the approximate inverse and is the only method found to be stable at large Hilbert space dimensions. This allows for steady-state solutions to otherwise intractable quantum optomechanical systems.
Giesbertz, K J H; Gritsenko, O V; Baerends, E J
2012-03-07
Adiabatic response time-dependent density functional theory (TDDFT) suffers from the restriction to basically an occupied → virtual single excitation formulation. Adiabatic time-dependent density matrix functional theory allows to break away from this restriction. Problematic excitations for TDDFT, viz. bonding-antibonding, double, charge transfer, and higher excitations, are calculated along the bond-dissociation coordinate of the prototype molecules H(2) and HeH(+) using the recently developed adiabatic linear response phase-including (PI) natural orbital theory (PINO). The possibility to systematically increase the scope of the calculation from excitations out of (strongly) occupied into weakly occupied ("virtual") natural orbitals to larger ranges of excitations is explored. The quality of the PINO response calculations is already much improved over TDDFT even when the severest restriction is made, to virtually the size of the TDDFT diagonalization problem (only single excitation out of occupied orbitals plus all diagonal doubles). Further marked improvement is obtained with moderate extension to allow for excitation out of the lumo and lumo+1, which become fractionally occupied in particular at longer distances due to left-right correlation effects. In the second place the interpretation of density matrix response calculations is elucidated. The one-particle reduced density matrix response for an excitation is related to the transition density matrix to the corresponding excited state. The interpretation of the transition density matrix in terms of the familiar excitation character (single excitations, double excitations of various types, etc.) is detailed. The adiabatic PINO theory is shown to successfully resolve the problematic cases of adiabatic TDDFT when it uses a proper PI orbital functional such as the PILS functional.
NASA Astrophysics Data System (ADS)
Giesbertz, K. J. H.; Gritsenko, O. V.; Baerends, E. J.
2012-03-01
Adiabatic response time-dependent density functional theory (TDDFT) suffers from the restriction to basically an occupied → virtual single excitation formulation. Adiabatic time-dependent density matrix functional theory allows to break away from this restriction. Problematic excitations for TDDFT, viz. bonding-antibonding, double, charge transfer, and higher excitations, are calculated along the bond-dissociation coordinate of the prototype molecules H2 and HeH+ using the recently developed adiabatic linear response phase-including (PI) natural orbital theory (PINO). The possibility to systematically increase the scope of the calculation from excitations out of (strongly) occupied into weakly occupied ("virtual") natural orbitals to larger ranges of excitations is explored. The quality of the PINO response calculations is already much improved over TDDFT even when the severest restriction is made, to virtually the size of the TDDFT diagonalization problem (only single excitation out of occupied orbitals plus all diagonal doubles). Further marked improvement is obtained with moderate extension to allow for excitation out of the lumo and lumo+1, which become fractionally occupied in particular at longer distances due to left-right correlation effects. In the second place the interpretation of density matrix response calculations is elucidated. The one-particle reduced density matrix response for an excitation is related to the transition density matrix to the corresponding excited state. The interpretation of the transition density matrix in terms of the familiar excitation character (single excitations, double excitations of various types, etc.) is detailed. The adiabatic PINO theory is shown to successfully resolve the problematic cases of adiabatic TDDFT when it uses a proper PI orbital functional such as the PILS functional.
Perturbation Theory for Parent Hamiltonians of Matrix Product States
NASA Astrophysics Data System (ADS)
Szehr, Oleg; Wolf, Michael M.
2015-05-01
This article investigates the stability of the ground state subspace of a canonical parent Hamiltonian of a Matrix product state against local perturbations. We prove that the spectral gap of such a Hamiltonian remains stable under weak local perturbations even in the thermodynamic limit, where the entire perturbation might not be bounded. Our discussion is based on preceding work by Yarotsky that develops a perturbation theory for relatively bounded quantum perturbations of classical Hamiltonians. We exploit a renormalization procedure, which on large scale transforms the parent Hamiltonian of a Matrix product state into a classical Hamiltonian plus some perturbation. We can thus extend Yarotsky's results to provide a perturbation theory for parent Hamiltonians of Matrix product states and recover some of the findings of the independent contributions (Cirac et al in Phys Rev B 8(11):115108, 2013) and (Michalakis and Pytel in Comm Math Phys 322(2):277-302, 2013).
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.
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.
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.
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).
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
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 matrix reconstruction of a large angular momentum
NASA Astrophysics Data System (ADS)
Klose, Gerd
2001-10-01
A complete description of the quantum state of a physical system is the fundamental knowledge necessary to statistically predict the outcome of measurements. In turning this statement around, Wolfgang Pauli raised already in 1933 the question, whether an unknown quantum state could be uniquely determined by appropriate measurements-a problem that has gained new relevance in recent years. In order to harness the prospects of quantum computing, secure communication, teleportation, and the like, the development of techniques to accurately control and measure quantum states has now become a matter of practical as well as fundamental interest. However, there is no general answer to Pauli's very basic question, and quantum state reconstruction algorithms have been developed and experimentally demonstrated only for a few systems so far. This thesis presents a novel experimental method to measure the unknown and generally mixed quantum state for an angular momentum of arbitrary magnitude. The (2F + 1) x (2F + 1) density matrix describing the quantum state is hereby completely determined from a set of Stern-Gerlach measurements with (4F + 1) different orientations of the quantization axis. This protocol is implemented for laser cooled Cesium atoms in the 6S1/2(F = 4) hyperfine ground state manifold, and is applied to a number of test states prepared by optical pumping and Larmor precession. A comparison of the input and the measured states shows successful reconstructions with fidelities of about 0.95.
Mniszewski, S M; Cawkwell, M J; Wall, M E; Mohd-Yusof, J; Bock, N; Germann, T C; Niklasson, A M N
2015-10-13
We present an algorithm for the calculation of the density matrix that for insulators scales linearly with system size and parallelizes efficiently on multicore, shared memory platforms with small and controllable numerical errors. The algorithm is based on an implementation of the second-order spectral projection (SP2) algorithm [ Niklasson, A. M. N. Phys. Rev. B 2002 , 66 , 155115 ] in sparse matrix algebra with the ELLPACK-R data format. We illustrate the performance of the algorithm within self-consistent tight binding theory by total energy calculations of gas phase poly(ethylene) molecules and periodic liquid water systems containing up to 15,000 atoms on up to 16 CPU cores. We consider algorithm-specific performance aspects, such as local vs nonlocal memory access and the degree of matrix sparsity. Comparisons to sparse matrix algebra implementations using off-the-shelf libraries on multicore CPUs, graphics processing units (GPUs), and the Intel many integrated core (MIC) architecture are also presented. The accuracy and stability of the algorithm are illustrated with long duration Born-Oppenheimer molecular dynamics simulations of 1000 water molecules and a 303 atom Trp cage protein solvated by 2682 water molecules.
NASA Astrophysics Data System (ADS)
Silvi, Pietro; Calarco, Tommaso; Morigi, Giovanna; Montangero, Simone
2014-03-01
Ions of the same charge inside confining potentials can form crystalline structures which can be controlled by means of the ion density and of the external trap parameters. In particular, a linear chain of trapped ions exhibits a transition to a zigzag equilibrium configuration, which is controlled by the strength of the transverse confinement. Studying this phase transition in the quantum regime is a challenging problem, even when employing numerical methods to simulate microscopically quantum many-body systems. Here we present a compact analytical treatment to map the original long-range problem into a short-range quantum field theory on a lattice. We provide a complete numerical architecture, based on the density matrix renormalization group, to address the effective quantum ϕ4 model. This technique is instrumental in giving a complete characterization of the phase diagram, as well as pinpointing the universality class of the criticality.
Random matrix theory and portfolio optimization in Moroccan stock exchange
NASA Astrophysics Data System (ADS)
El Alaoui, Marwane
2015-09-01
In this work, we use random matrix theory to analyze eigenvalues and see if there is a presence of pertinent information by using Marčenko-Pastur distribution. Thus, we study cross-correlation among stocks of Casablanca Stock Exchange. Moreover, we clean correlation matrix from noisy elements to see if the gap between predicted risk and realized risk would be reduced. We also analyze eigenvectors components distributions and their degree of deviations by computing the inverse participation ratio. This analysis is a way to understand the correlation structure among stocks of Casablanca Stock Exchange portfolio.
The origin of linear scaling Fock matrix calculation with density prescreening
Mitin, Alexander V.
2015-12-31
A theorem was proven, which reads that the number of nonzero two-electron integrals scales linearly with respect to the number of basis functions for large molecular systems. This permits to show that linear scaling property of the Fock matrix calculation with using density prescreening arises due to linear scaling properties of the number of nonzero two-electron integrals and the number of leading matrix elements of density matrix. This property is reinforced by employing the density prescreening technique. The use of the density difference prescreening further improves the linear scaling property of the Fock matrix calculation method. As a result, the linear scaling regime of the Fock matrix calculation can begin from the number of basis functions of 2000–3000 in dependence on the basis function type in molecular calculations. It was also shown that the conventional algorithm of Fock matrix calculation from stored nonzero two-electron integrals with density prescreening possesses linear scaling property.
Random matrix theory for portfolio optimization: a stability approach
NASA Astrophysics Data System (ADS)
Sharifi, S.; Crane, M.; Shamaie, A.; Ruskin, H.
2004-04-01
We apply random matrix theory (RMT) to an empirically measured financial correlation matrix, C, and show that this matrix contains a large amount of noise. In order to determine the sensitivity of the spectral properties of a random matrix to noise, we simulate a set of data and add different volumes of random noise. Having ascertained that the eigenspectrum is independent of the standard deviation of added noise, we use RMT to determine the noise percentage in a correlation matrix based on real data from S&P500. Eigenvalue and eigenvector analyses are applied and the experimental results for each of them are presented to identify qualitatively and quantitatively different spectral properties of the empirical correlation matrix to a random counterpart. Finally, we attempt to separate the noisy part from the non-noisy part of C. We apply an existing technique to cleaning C and then discuss its associated problems. We propose a technique of filtering C that has many advantages, from the stability point of view, over the existing method of cleaning.
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.
Stoitsov, M. V.; Kortelainen, Erno M; Bogner, S. K.; Duguet, T.; Furnstahl, R. J.; Gebremariam, B.; Schunck, N.
2010-01-01
In a recent series of papers, Gebremariam, Bogner, and Duguet derived a microscopically-based nuclear energy density functional by applying the Density Matrix Expansion (DME) to the Hartree-Fock energy obtained from chiral effective field theory (EFT) two- and three-nucleon interactions. Due to the structure of the chiral interactions, each coupling in the DME functional is given as the sum of a coupling constant arising from zero-range contact interactions and a coupling function of the density arising from the finite-range pion exchanges. Since the contact contributions have essentially the same structure as those entering empirical Skyrme functionals, a microscopically guided Skyrme phenomenology has been suggested in which the contact terms in the DME functional are released for optimization to finite-density observables to capture short-range correlation energy contributions from beyond Hartree-Fock. The present paper is the first attempt to assess the ability of the newly suggested DME functional, which has a much richer set of density dependencies than traditional Skyrme functionals, to generate sensible and stable results for nuclear applications. The results of the first proof-of-principle calculations are given, and numerous practical issues related to the implementation of the new functional in existing Skyrme codes are discussed. Using a restricted singular value decomposition (SVD) optimization procedure, it is found that the new DME functional gives numerically stable results and exhibits a small but systematic reduction in {chi}^{2} compared to standard Skyrme functionals, thus justifying its suitability for future global optimizations and large-scale calculations.
Stoitsov, M.; Kortelainen, M.; Schunck, N.; Bogner, S. K.; Gebremariam, B.; Duguet, T.
2010-11-15
In a recent series of articles, Gebremariam, Bogner, and Duguet derived a microscopically based nuclear energy density functional by applying the density matrix expansion (DME) to the Hartree-Fock energy obtained from chiral effective field theory two- and three-nucleon interactions. Owing to the structure of the chiral interactions, each coupling in the DME functional is given as the sum of a coupling constant arising from zero-range contact interactions and a coupling function of the density arising from the finite-range pion exchanges. Because the contact contributions have essentially the same structure as those entering empirical Skyrme functionals, a microscopically guided Skyrme phenomenology has been suggested in which the contact terms in the DME functional are released for optimization to finite-density observables to capture short-range correlation energy contributions from beyond Hartree-Fock. The present article is the first attempt to assess the ability of the newly suggested DME functional, which has a much richer set of density dependencies than traditional Skyrme functionals, to generate sensible and stable results for nuclear applications. The results of the first proof-of-principle calculations are given, and numerous practical issues related to the implementation of the new functional in existing Skyrme codes are discussed. Using a restricted singular value decomposition optimization procedure, it is found that the new DME functional gives numerically stable results and exhibits a small but systematic reduction of our test {chi}{sup 2} function compared to standard Skyrme functionals, thus justifying its suitability for future global optimizations and large-scale calculations.
Eigenvalue density of linear stochastic dynamical systems: A random matrix approach
NASA Astrophysics Data System (ADS)
Adhikari, S.; Pastur, L.; Lytova, A.; Du Bois, J.
2012-02-01
Eigenvalue problems play an important role in the dynamic analysis of engineering systems modeled using the theory of linear structural mechanics. When uncertainties are considered, the eigenvalue problem becomes a random eigenvalue problem. In this paper the density of the eigenvalues of a discretized continuous system with uncertainty is discussed by considering the model where the system matrices are the Wishart random matrices. An analytical expression involving the Stieltjes transform is derived for the density of the eigenvalues when the dimension of the corresponding random matrix becomes asymptotically large. The mean matrices and the dispersion parameters associated with the mass and stiffness matrices are necessary to obtain the density of the eigenvalues in the frameworks of the proposed approach. The applicability of a simple eigenvalue density function, known as the Marenko-Pastur (MP) density, is investigated. The analytical results are demonstrated by numerical examples involving a plate and the tail boom of a helicopter with uncertain properties. The new results are validated using an experiment on a vibrating plate with randomly attached spring-mass oscillators where 100 nominally identical samples are physically created and individually tested within a laboratory framework.
Nonextensive random matrix theory approach to mixed regular-chaotic dynamics.
Abul-Magd, A Y
2005-06-01
We apply Tsallis' q -indexed entropy to formulate a nonextensive random matrix theory, which may be suitable for systems with mixed regular-chaotic dynamics. The joint distribution of the matrix elements is given by folding the corresponding quantity in the conventional random matrix theory by a distribution of the inverse matrix-element variance. It keeps the basis invariance of the standard theory but violates the independence of the matrix elements. We consider the subextensive regime of q more than unity in which the transition from the Wigner to the Poisson statistics is expected to start. We calculate the level density for different values of the entropic index. Our results are consistent with an analogous calculation by Tsallis and collaborators. We calculate the spacing distribution for mixed systems with and without time-reversal symmetry. Comparing the result of calculation to a numerical experiment shows that the proposed nonextensive model provides a satisfactory description for the initial stage of the transition from chaos towards the Poisson statistics.
Enumeration of RNA complexes via random matrix theory.
Andersen, Jørgen E; Chekhov, Leonid O; Penner, Robert C; Reidys, Christian M; Sułkowski, Piotr
2013-04-01
In the present article, we review a derivation of the numbers of RNA complexes of an arbitrary topology. These numbers are encoded in the free energy of the Hermitian matrix model with potential V(x)=x2/2-stx/(1-tx), where s and t are respective generating parameters for the number of RNA molecules and hydrogen bonds in a given complex. The free energies of this matrix model are computed using the so-called topological recursion, which is a powerful new formalism arising from random matrix theory. These numbers of RNA complexes also have profound meaning in mathematics: they provide the number of chord diagrams of fixed genus with specified numbers of backbones and chords as well as the number of cells in Riemann's moduli spaces for bordered surfaces of fixed topological type.
Failure of random matrix theory to correctly describe quantum dynamics.
Kottos, T; Cohen, D
2001-12-01
Consider a classically chaotic system that is described by a Hamiltonian H(0). At t=0 the Hamiltonian undergoes a sudden change (H)0-->H. We consider the quantum-mechanical spreading of the evolving energy distribution, and argue that it cannot be analyzed using a conventional random-matrix theory (RMT) approach. Conventional RMT can be trusted only to the extent that it gives trivial results that are implied by first-order perturbation theory. Nonperturbative effects are sensitive to the underlying classical dynamics, and therefore the Planck's over 2 pi-->0 behavior for effective RMT models is strikingly different from the correct semiclassical limit.
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…
Matrix models and stochastic growth in Donaldson-Thomas theory
NASA Astrophysics Data System (ADS)
Szabo, Richard J.; Tierz, Miguel
2012-10-01
We show that the partition functions which enumerate Donaldson-Thomas invariants of local toric Calabi-Yau threefolds without compact divisors can be expressed in terms of specializations of the Schur measure. We also discuss the relevance of the Hall-Littlewood and Jack measures in the context of BPS state counting and study the partition functions at arbitrary points of the Kähler moduli space. This rewriting in terms of symmetric functions leads to a unitary one-matrix model representation for Donaldson-Thomas theory. We describe explicitly how this result is related to the unitary matrix model description of Chern-Simons gauge theory. This representation is used to show that the generating functions for Donaldson-Thomas invariants are related to tau-functions of the integrable Toda and Toeplitz lattice hierarchies. The matrix model also leads to an interpretation of Donaldson-Thomas theory in terms of non-intersecting paths in the lock-step model of vicious walkers. We further show that these generating functions can be interpreted as normalization constants of a corner growth/last-passage stochastic model.
Matrix models and stochastic growth in Donaldson-Thomas theory
Szabo, Richard J.; Tierz, Miguel
2012-10-15
We show that the partition functions which enumerate Donaldson-Thomas invariants of local toric Calabi-Yau threefolds without compact divisors can be expressed in terms of specializations of the Schur measure. We also discuss the relevance of the Hall-Littlewood and Jack measures in the context of BPS state counting and study the partition functions at arbitrary points of the Kaehler moduli space. This rewriting in terms of symmetric functions leads to a unitary one-matrix model representation for Donaldson-Thomas theory. We describe explicitly how this result is related to the unitary matrix model description of Chern-Simons gauge theory. This representation is used to show that the generating functions for Donaldson-Thomas invariants are related to tau-functions of the integrable Toda and Toeplitz lattice hierarchies. The matrix model also leads to an interpretation of Donaldson-Thomas theory in terms of non-intersecting paths in the lock-step model of vicious walkers. We further show that these generating functions can be interpreted as normalization constants of a corner growth/last-passage stochastic model.
Yang, Weitao; Mori-Sánchez, Paula; Cohen, Aron J
2013-09-14
The exact conditions for density functionals and density matrix functionals in terms of fractional charges and fractional spins are known, and their violation in commonly used functionals has been shown to be the root of many major failures in practical applications. However, approximate functionals are designed for physical systems with integer charges and spins, not in terms of the fractional variables. Here we develop a general framework for extending approximate density functionals and many-electron theory to fractional-charge and fractional-spin systems. Our development allows for the fractional extension of any approximate theory that is a functional of G(0), the one-electron Green's function of the non-interacting reference system. The extension to fractional charge and fractional spin systems is based on the ensemble average of the basic variable, G(0). We demonstrate the fractional extension for the following theories: (1) any explicit functional of the one-electron density, such as the local density approximation and generalized gradient approximations; (2) any explicit functional of the one-electron density matrix of the non-interacting reference system, such as the exact exchange functional (or Hartree-Fock theory) and hybrid functionals; (3) many-body perturbation theory; and (4) random-phase approximations. A general rule for such an extension has also been derived through scaling the orbitals and should be useful for functionals where the link to the Green's function is not obvious. The development thus enables the examination of approximate theories against known exact conditions on the fractional variables and the analysis of their failures in chemical and physical applications in terms of violations of exact conditions of the energy functionals. The present work should facilitate the calculation of chemical potentials and fundamental bandgaps with approximate functionals and many-electron theories through the energy derivatives with respect to the
Energy density matrix formalism for interacting quantum systems: a quantum Monte Carlo study
Krogel, Jaron T; Kim, Jeongnim; Reboredo, Fernando A
2014-01-01
We develop an energy density matrix that parallels the one-body reduced density matrix (1RDM) for many-body quantum systems. Just as the density matrix gives access to the number density and occupation numbers, the energy density matrix yields the energy density and orbital occupation energies. The eigenvectors of the matrix provide a natural orbital partitioning of the energy density while the eigenvalues comprise a single particle energy spectrum obeying a total energy sum rule. For mean-field systems the energy density matrix recovers the exact spectrum. When correlation becomes important, the occupation energies resemble quasiparticle energies in some respects. We explore the occupation energy spectrum for the finite 3D homogeneous electron gas in the metallic regime and an isolated oxygen atom with ground state quantum Monte Carlo techniques imple- mented in the QMCPACK simulation code. The occupation energy spectrum for the homogeneous electron gas can be described by an effective mass below the Fermi level. Above the Fermi level evanescent behavior in the occupation energies is observed in similar fashion to the occupation numbers of the 1RDM. A direct comparison with total energy differences demonstrates a quantita- tive connection between the occupation energies and electron addition and removal energies for the electron gas. For the oxygen atom, the association between the ground state occupation energies and particle addition and removal energies becomes only qualitative. The energy density matrix provides a new avenue for describing energetics with quantum Monte Carlo methods which have traditionally been limited to total energies.
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.
Metal-insulator transition in disordered systems from the one-body density matrix
NASA Astrophysics Data System (ADS)
Olsen, Thomas; Resta, Raffaele; Souza, Ivo
2017-01-01
The insulating state of matter can be probed by means of a ground state geometrical marker, which is closely related to the modern theory of polarization (based on a Berry phase). In the present work we show that this marker can be applied to determine the metal-insulator transition in disordered systems. In particular, for noninteracting systems the geometrical marker can be obtained from the configurational average of the norm-squared one-body density matrix, which can be calculated within open as well as periodic boundary conditions. This is in sharp contrast to a classification based on the static conductivity, which is only sensible within periodic boundary conditions. We exemplify the method by considering a simple lattice model, known to have a metal-insulator transition as a function of the disorder strength, and demonstrate that the transition point can be obtained accurately from the one-body density matrix. The approach has a general ab initio formulation and could in principle be applied to realistic disordered materials by standard electronic structure methods.
Linear-response time-dependent density-functional theory with pairing fields.
Peng, Degao; van Aggelen, Helen; Yang, Yang; Yang, Weitao
2014-05-14
Recent development in particle-particle random phase approximation (pp-RPA) broadens the perspective on ground state correlation energies [H. van Aggelen, Y. Yang, and W. Yang, Phys. Rev. A 88, 030501 (2013), Y. Yang, H. van Aggelen, S. N. Steinmann, D. Peng, and W. Yang, J. Chem. Phys. 139, 174110 (2013); D. Peng, S. N. Steinmann, H. van Aggelen, and W. Yang, J. Chem. Phys. 139, 104112 (2013)] and N ± 2 excitation energies [Y. Yang, H. van Aggelen, and W. Yang, J. Chem. Phys. 139, 224105 (2013)]. So far Hartree-Fock and approximated density-functional orbitals have been utilized to evaluate the pp-RPA equation. In this paper, to further explore the fundamentals and the potential use of pairing matrix dependent functionals, we present the linear-response time-dependent density-functional theory with pairing fields with both adiabatic and frequency-dependent kernels. This theory is related to the density-functional theory and time-dependent density-functional theory for superconductors, but is applied to normal non-superconducting systems for our purpose. Due to the lack of the proof of the one-to-one mapping between the pairing matrix and the pairing field for time-dependent systems, the linear-response theory is established based on the representability assumption of the pairing matrix. The linear response theory justifies the use of approximated density-functionals in the pp-RPA equation. This work sets the fundamentals for future density-functional development to enhance the description of ground state correlation energies and N ± 2 excitation energies.
Quasi-degenerate perturbation theory using matrix product states
Sharma, Sandeep Jeanmairet, Guillaume; Alavi, Ali
2016-01-21
In this work, we generalize the recently proposed matrix product state perturbation theory (MPSPT) for calculating energies of excited states using quasi-degenerate (QD) perturbation theory. Our formulation uses the Kirtman-Certain-Hirschfelder canonical Van Vleck perturbation theory, which gives Hermitian effective Hamiltonians at each order, and also allows one to make use of Wigner’s 2n + 1 rule. Further, our formulation satisfies Granovsky’s requirement of model space invariance which is important for obtaining smooth potential energy curves. Thus, when we use MPSPT with the Dyall Hamiltonian, we obtain a model space invariant version of quasi-degenerate n-electron valence state perturbation theory (NEVPT), a property that the usual formulation of QD-NEVPT2 based on a multipartitioning technique lacked. We use our method on the benchmark problems of bond breaking of LiF which shows ionic to covalent curve crossing and the twist around the double bond of ethylene where significant valence-Rydberg mixing occurs in the excited states. In accordance with our previous work, we find that multi-reference linearized coupled cluster theory is more accurate than other multi-reference theories of similar cost.
Release behaviour of clozapine matrix pellets based on percolation theory.
Aguilar-de-Leyva, Angela; Sharkawi, Tahmer; Bataille, Bernard; Baylac, Gilles; Caraballo, Isidoro
2011-02-14
The release behaviour of clozapine matrix pellets was studied in order to investigate if it is possible to explain it applying the concepts of percolation theory, previously used in the understanding of the release process of inert and hydrophilic matrix tablets. Thirteen batches of pellets with different proportions of clozapine/microcrystalline cellulose (MCC)/hydroxypropylmethyl cellulose (HPMC) and different clozapine particle size fractions were prepared by extrusion-spheronisation and the release profiles were studied. It has been observed that the distance to the excipient (HPMC) percolation threshold is important to control the release rate. Furthermore, the drug percolation threshold has a big influence in these systems. Batches very close to the drug percolation threshold, show a clear effect of the drug particle size in the release rate. However, this effect is much less evident when there is a bigger distance to the drug percolation threshold, so the release behaviour of clozapine matrix pellets is possible to be explained based on the percolation theory.
Exploring multicollinearity using a random matrix theory approach.
Feher, Kristen; Whelan, James; Müller, Samuel
2012-01-01
Clustering of gene expression data is often done with the latent aim of dimension reduction, by finding groups of genes that have a common response to potentially unknown stimuli. However, what is poorly understood to date is the behaviour of a low dimensional signal embedded in high dimensions. This paper introduces a multicollinear model which is based on random matrix theory results, and shows potential for the characterisation of a gene cluster's correlation matrix. This model projects a one dimensional signal into many dimensions and is based on the spiked covariance model, but rather characterises the behaviour of the corresponding correlation matrix. The eigenspectrum of the correlation matrix is empirically examined by simulation, under the addition of noise to the original signal. The simulation results are then used to propose a dimension estimation procedure of clusters from data. Moreover, the simulation results warn against considering pairwise correlations in isolation, as the model provides a mechanism whereby a pair of genes with `low' correlation may simply be due to the interaction of high dimension and noise. Instead, collective information about all the variables is given by the eigenspectrum.
Random matrix theory and fund of funds portfolio optimisation
NASA Astrophysics Data System (ADS)
Conlon, T.; Ruskin, H. J.; Crane, M.
2007-08-01
The proprietary nature of Hedge Fund investing means that it is common practise for managers to release minimal information about their returns. The construction of a fund of hedge funds portfolio requires a correlation matrix which often has to be estimated using a relatively small sample of monthly returns data which induces noise. In this paper, random matrix theory (RMT) is applied to a cross-correlation matrix C, constructed using hedge fund returns data. The analysis reveals a number of eigenvalues that deviate from the spectrum suggested by RMT. The components of the deviating eigenvectors are found to correspond to distinct groups of strategies that are applied by hedge fund managers. The inverse participation ratio is used to quantify the number of components that participate in each eigenvector. Finally, the correlation matrix is cleaned by separating the noisy part from the non-noisy part of C. This technique is found to greatly reduce the difference between the predicted and realised risk of a portfolio, leading to an improved risk profile for a fund of hedge funds.
S-Matrix Theory of Ultrafast Optical Phenomena in Semiconductors
NASA Astrophysics Data System (ADS)
Kuznetsov, Alex V.
1997-08-01
A formalism for describing optical and transport properties of semiconductors excited by ultrashort laser pulses is presented. In contrast to existing theories, the quantum dynamics is described in terms of appropriately generalized single-particle wavefunctions (S-matrix) instead of the ensemble-averaged observables such as distribution functions. TheS-matrix is an operator that relates Heisenberg second quantization operators at finite times to their values in a vacuum state prior to excitation. The explicit form of theS-matrix is given by a perturbative expansion whose terms contain pairs of creation and annihilation operators. The coefficients of the expansion are found using a specially developed diagram technique for Coulomb systems. The first (c-number) term of this expansion is formed from single-electron wavefunctions in an optically excited noninteracting system. In real space, these wavefunctions are well-defined wavepackets whose properties can be investigated analytically. Linear and nonlinear ultrafast optical phenomena are controlled by overlap between conduction and valence band wavepackets. Specific cases of noninteracting electrons, coherent interactions leading to excitonic effects, and the incoherent scattering in the Born approximation are analysed within theS-matrix approach.
Assessing modularity using a random matrix theory approach.
Feher, Kristen; Whelan, James; Müller, Samuel
2011-09-26
Random matrix theory (RMT) is well suited to describing the emergent properties of systems with complex interactions amongst their constituents through their eigenvalue spectrums. Some RMT results are applied to the problem of clustering high dimensional biological data with complex dependence structure amongst the variables. It will be shown that a gene relevance or correlation network can be constructed by choosing a correlation threshold in a principled way, such that it corresponds to a block diagonal structure in the correlation matrix, if such a structure exists. The structure is then found using community detection algorithms, but with parameter choice guided by RMT predictions. The resulting clustering is compared to a variety of hierarchical clustering outputs and is found to the most generalised result, in that it captures all the features found by the other considered methods.
The variational two-electron reduced-density-matrix method for extended systems
NASA Astrophysics Data System (ADS)
Rubin, Nicholas C.
In this thesis we develop the variational two-electron reduced-density-matrix method for extended systems. Extended systems are represented in two ways: i) lattice models describing the dominant valence electronic structure with periodic boundaries to account for their extended nature and ii) a crystalline-orbital basis built from atomic orbitals using the generalization of molecular orbital theory to polymers. The first part of this thesis (Ch. 3--4) examines the performance of the variational 2-RDM method on lattice systems with tunable electron correlation. The first of these systems is the classic Hubbard model with linear and ladder lattice topologies. Because electron correlation functions, such as charge- and spin-ordering, are linear functions of the 2-RDM, the difference in electronic structure between one- and quasi-one-dimensional systems is accurately characterized. The second model contains only two-body interactions and is unique among typical spin models in that it does not have a mean-field reference wave function. The ground state wave functions from all Hamiltonians in the model have the same 1-electron reduced density matrix; consequently, one-electron theories are largely inapplicable. The superconducting eta-pairing ground states make the model a unique tool for demonstrating the necessary N-representability in highly correlated environments. The second part of this thesis (Ch. 5--6) develops a formalism for modeling materials by solving the full Schrodinger equation. Crystalline-orbital Hartree-Fock provides a set of orbitals and integral tensors for the variational 2-RDM method. We demonstrate that time-reversal symmetry, which is implicitly included in position space electronic structure calculations, must be explicitly included as an N-representability constraint on the 2-RDM when using a momentum space basis. The necessity of these equality constraints is demonstrated by the accurate recovery of the binding energy of two polymers and the
Edgar, Lowell T.; Hoying, James B.; Weiss, Jeffrey A.
2015-01-01
Mechanical interactions during angiogenesis, i.e., traction applied by neovessels to the extracellular matrix and the corresponding deformation, are important regulators of growth and neovascularization. We have previously designed, implemented, and validated a coupled model of angiogenesis in which a discrete microvessel growth model interacts with a continuous finite element mesh through the application of local remodeling sprout stresses (Edgar et al. in Biomech Model Mechanobiol, 2014). However, the initial implementation of this framework does not take matrix density into account when determined these remodeling stresses and is therefore insufficient for the study of angiogenesis within heterogeneous matrix environments such as those found in vivo. The objective of this study was to implement sensitivity to matrix density in the active stress generation within AngioFE in order to allow the study of angiogenic growth within a heterogeneous density environment. We accomplished this by scaling active sprout stresses relative to local matrix density using a scaling factor previously determined from experimental data. We then exercised the new functionality of the model by simulating angiogenesis within four different scenarios: homogeneous density, a narrow gap model, and matrix density gradient, and a construct subjected to repeated loading/unloading and preconditioning. These numerical experiments predicted heterogeneous matrix density in the initially homogeneous case, the closure and alignment of microvessels along a low-density gap, the formation of a unique cap-like structure during angiogenesis within a density gradient, and the alignment of microvessels in the absence of applied load due to preconditioning. The result of these in silico investigations demonstrate how matrix heterogeneity affects neovascularization and matrix deformation and provides a platform for studying angiogenesis in complicated and multi-faceted mechanical environments that
Daubechies wavelets for linear scaling density functional theory.
Mohr, Stephan; Ratcliff, Laura E; Boulanger, Paul; Genovese, Luigi; Caliste, Damien; Deutsch, Thierry; Goedecker, Stefan
2014-05-28
We demonstrate that Daubechies wavelets can be used to construct a minimal set of optimized localized adaptively contracted basis functions in which the Kohn-Sham orbitals can be represented with an arbitrarily high, controllable precision. Ground state energies and the forces acting on the ions can be calculated in this basis with the same accuracy as if they were calculated directly in a Daubechies wavelets basis, provided that the amplitude of these adaptively contracted basis functions is sufficiently small on the surface of the localization region, which is guaranteed by the optimization procedure described in this work. This approach reduces the computational costs of density functional theory calculations, and can be combined with sparse matrix algebra to obtain linear scaling with respect to the number of electrons in the system. Calculations on systems of 10,000 atoms or more thus become feasible in a systematic basis set with moderate computational resources. Further computational savings can be achieved by exploiting the similarity of the adaptively contracted basis functions for closely related environments, e.g., in geometry optimizations or combined calculations of neutral and charged systems.
Extracting electron transfer coupling elements from constrained density functional theory
NASA Astrophysics Data System (ADS)
Wu, Qin; Van Voorhis, Troy
2006-10-01
Constrained density functional theory (DFT) is a useful tool for studying electron transfer (ET) reactions. It can straightforwardly construct the charge-localized diabatic states and give a direct measure of the inner-sphere reorganization energy. In this work, a method is presented for calculating the electronic coupling matrix element (Hab) based on constrained DFT. This method completely avoids the use of ground-state DFT energies because they are known to irrationally predict fractional electron transfer in many cases. Instead it makes use of the constrained DFT energies and the Kohn-Sham wave functions for the diabatic states in a careful way. Test calculations on the Zn2+ and the benzene-Cl atom systems show that the new prescription yields reasonable agreement with the standard generalized Mulliken-Hush method. We then proceed to produce the diabatic and adiabatic potential energy curves along the reaction pathway for intervalence ET in the tetrathiafulvalene-diquinone (Q-TTF-Q) anion. While the unconstrained DFT curve has no reaction barrier and gives Hab≈17kcal /mol, which qualitatively disagrees with experimental results, the Hab calculated from constrained DFT is about 3kcal /mol and the generated ground state has a barrier height of 1.70kcal/mol, successfully predicting (Q-TTF-Q)- to be a class II mixed-valence compound.
Random Matrix Theory Approach to Chaotic Coherent Perfect Absorbers.
Li, Huanan; Suwunnarat, Suwun; Fleischmann, Ragnar; Schanz, Holger; Kottos, Tsampikos
2017-01-27
We employ random matrix theory in order to investigate coherent perfect absorption (CPA) in lossy systems with complex internal dynamics. The loss strength γ_{CPA} and energy E_{CPA}, for which a CPA occurs, are expressed in terms of the eigenmodes of the isolated cavity-thus carrying over the information about the chaotic nature of the target-and their coupling to a finite number of scattering channels. Our results are tested against numerical calculations using complex networks of resonators and chaotic graphs as CPA cavities.
Wigner surmise for mixed symmetry classes in random matrix theory.
Schierenberg, Sebastian; Bruckmann, Falk; Wettig, Tilo
2012-06-01
We consider the nearest-neighbor spacing distributions of mixed random matrix ensembles interpolating between different symmetry classes or between integrable and nonintegrable systems. We derive analytical formulas for the spacing distributions of 2×2 or 4×4 matrices and show numerically that they provide very good approximations for those of random matrices with large dimension. This generalizes the Wigner surmise, which is valid for pure ensembles that are recovered as limits of the mixed ensembles. We show how the coupling parameters of small and large matrices must be matched depending on the local eigenvalue density.
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.
Particle diagrams and embedded many-body random matrix theory.
Small, R A; Müller, S
2014-07-01
We present a method which uses Feynman-like diagrams to calculate the statistical quantities of embedded many-body random matrix problems. The method provides a promising alternative to existing techniques and offers many important simplifications. We use it here to find the fourth, sixth, and eighth moments of the level density of an m-body system with k fermions or bosons interacting through a random Hermitian potential (k ≤ m) in the limit where the number of possible single-particle states is taken to infinity. All share the same transition, starting immediately after 2k = m, from moments arising from a semicircular level density to Gaussian moments. The results also reveal a striking feature; the domain of the 2nth moment is naturally divided into n subdomains specified by the points 2k = m,3 k = m,...,nk = m.
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.
Nonlinear density wave theory for the spiral structure of galaxies.
Kondoh, S; Teramoto, R; Yoshida, Z
2000-05-01
The theory of nonlinear waves for plasmas has been applied to the analysis of the density wave theory of galaxies which are many-body systems of gravity. A nonlinear Schrödinger equation has been derived by applying the reductive perturbation method on the fluid equations that describe the behavior of infinitesimally thin disk galaxies. Their spiral arms are characterized by a soliton and explained as a pattern of a propagating nonlinear density wave.
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.
Density perturbations in general modified gravitational theories
De Felice, Antonio; Tsujikawa, Shinji; Mukohyama, Shinji
2010-07-15
We derive the equations of linear cosmological perturbations for the general Lagrangian density f(R,{phi},X)/2+L{sub c}, where R is a Ricci scalar, {phi} is a scalar field, and X=-{partial_derivative}{sup {mu}{phi}{partial_derivative}}{sub {mu}{phi}/}2 is a field kinetic energy. We take into account a nonlinear self-interaction term L{sub c}={xi}({phi}) {open_square}{phi}({partial_derivative}{sup {mu}{phi}{partial_derivative}}{sub {mu}{phi}}) recently studied in the context of ''Galileon'' cosmology, which keeps the field equations at second order. Taking into account a scalar-field mass explicitly, the equations of matter density perturbations and gravitational potentials are obtained under a quasistatic approximation on subhorizon scales. We also derive conditions for the avoidance of ghosts and Laplacian instabilities associated with propagation speeds. Our analysis includes most of modified gravity models of dark energy proposed in literature; and thus it is convenient to test the viability of such models from both theoretical and observational points of view.
Random matrix theory analysis of cross correlations in financial markets.
Utsugi, Akihiko; Ino, Kazusumi; Oshikawa, Masaki
2004-08-01
We confirm universal behaviors such as eigenvalue distribution and spacings predicted by random matrix theory (RMT) for the cross correlation matrix of the daily stock prices of Tokyo Stock Exchange from 1993 to 2001, which have been reported for New York Stock Exchange in previous studies. It is shown that the random part of the eigenvalue distribution of the cross correlation matrix is stable even when deterministic correlations are present. Some deviations in the small eigenvalue statistics outside the bounds of the universality class of RMT are not completely explained with the deterministic correlations as proposed in previous studies. We study the effect of randomness on deterministic correlations and find that randomness causes a repulsion between deterministic eigenvalues and the random eigenvalues. This is interpreted as a reminiscent of "level repulsion" in RMT and explains some deviations from the previous studies observed in the market data. We also study correlated groups of issues in these markets and propose a refined method to identify correlated groups based on RMT. Some characteristic differences between properties of Tokyo Stock Exchange and New York Stock Exchange are found.
Density matrix of radiation of a black hole with a fluctuating horizon
NASA Astrophysics Data System (ADS)
Iofa, Mikhail Z.
2016-09-01
The density matrix of Hawking radiation is calculated in the model of a black hole with a fluctuating horizon. Quantum fluctuations smear the classical horizon of a black hole and modify the density matrix of radiation producing the off-diagonal elements. The off-diagonal elements may store information on correlations between the radiation and the black hole. The smeared density matrix was constructed by convolution of the density matrix calculated with the instantaneous horizon with the Gaussian distribution over the instantaneous horizons. The distribution has the extremum at the classical radius of the black hole and the width of order of the Planck length. Calculations were performed in the model of a black hole formed by the thin collapsing shell which follows a trajectory that is a solution of the matching equations connecting the interior and exterior geometries.
Andrews, Lester
2004-02-20
Metal hydrides are of considerable importance in chemical synthesis as intermediates in catalytic hydrogenation reactions. Transition metal atoms react with dihydrogen to produce metal dihydrides or dihydrogen complexes and these may be trapped in solid matrix samples for infrared spectroscopic study. The MH(2) or M(H(2)) molecules so formed react further to form higher MH(4), (H(2))MH(2), or M(H(2))(2), and MH(6), (H(2))(2)MH(2), or M(H(2))(3) hydrides or complexes depending on the metal. In this critical review these transition metal and dihydrogen reaction products are surveyed for Groups 3 though 12 and the contrasting behaviour in Groups 6 and 10 is discussed. Minimum energy structures and vibrational frequencies predicted by Density Functional Theory agree with the experimental results, strongly supporting the identification of novel binary transition metal hydride species, which the matrix-isolation method is well-suited to investigate. 104 references are cited.
Technology Transfer Automated Retrieval System (TEKTRAN)
Ecological edge effects are sensitive to landscape context. In particular, edge effects can be altered by matrix type and by the presence of other nearby edges. We experimentally altered patch configurations in an African savanna to determine how edge density and matrix type influence edge effect de...
Cohomological gauge theory, quiver matrix models and Donaldson-Thomas theory
NASA Astrophysics Data System (ADS)
Cirafici, Michele; Sinkovics, Annamaria; Szabo, Richard J.
2009-03-01
We study the relation between Donaldson-Thomas theory of Calabi-Yau threefolds and a six-dimensional topological Yang-Mills theory. Our main example is the topological U(N) gauge theory on flat space in its Coulomb branch. To evaluate its partition function we use equivariant localization techniques on its noncommutative deformation. As a result the gauge theory localizes on noncommutative instantons which can be classified in terms of N-coloured three-dimensional Young diagrams. We give to these noncommutative instantons a geometrical description in terms of certain stable framed coherent sheaves on projective space by using a higher-dimensional generalization of the ADHM formalism. From this formalism we construct a topological matrix quantum mechanics which computes an index of BPS states and provides an alternative approach to the six-dimensional gauge theory.
Overlap Dirac operator at nonzero chemical potential and random matrix theory.
Bloch, Jacques; Wettig, Tilo
2006-07-07
We show how to introduce a quark chemical potential in the overlap Dirac operator. The resulting operator satisfies a Ginsparg-Wilson relation and has exact zero modes. It is no longer gamma5 Hermitian, but its nonreal eigenvalues still occur in pairs. We compute the spectral density of the operator on the lattice and show that, for small eigenvalues, the data agree with analytical predictions of non-Hermitian chiral random matrix theory for both trivial and nontrivial topology. We also explain an observed change in the number of zero modes as a function of chemical potential.
NASA Astrophysics Data System (ADS)
Jain, Shekhar; Dominik, Aleksandra; Chapman, Walter G.
2007-12-01
A density functional theory based on Wertheim's first order perturbation theory is developed for inhomogeneous complex fluids. The theory is derived along similar lines as interfacial statistical associating fluid theory [S. Tripathi and W. G. Chapman, J. Chem. Phys. 122, 094506 (2005)]. However, the derivation is more general and applies broadly to a range of systems, retaining the simplicity of a segment density based theory. Furthermore, the theory gives the exact density profile for ideal chains in an external field. The general avail of the theory has been demonstrated by applying the theory to lipids near surfaces, lipid bilayers, and copolymer thin films. The theoretical results show excellent agreement with the results from molecular simulations.
NASA Astrophysics Data System (ADS)
Li, Yonghui; Ullrich, Carsten
2013-03-01
The time-dependent transition density matrix (TDM) is a useful tool to visualize and interpret the induced charges and electron-hole coherences of excitonic processes in large molecules. Combined with time-dependent density functional theory on a real-space grid (as implemented in the octopus code), the TDM is a computationally viable visualization tool for optical excitation processes in molecules. It provides real-time maps of particles and holes which gives information on excitations, in particular those that have charge-transfer character, that cannot be obtained from the density alone. Some illustration of the TDM and comparison with standard density difference plots will be shown for photoexcited organic donor-acceptor molecules. This work is supported by NSF Grant DMR-1005651
SCDM-k: Localized orbitals for solids via selected columns of the density matrix
NASA Astrophysics Data System (ADS)
Damle, Anil; Lin, Lin; Ying, Lexing
2017-04-01
The recently developed selected columns of the density matrix (SCDM) method (Damle et al. 2015, [16]) is a simple, robust, efficient and highly parallelizable method for constructing localized orbitals from a set of delocalized Kohn-Sham orbitals for insulators and semiconductors with Γ point sampling of the Brillouin zone. In this work we generalize the SCDM method to Kohn-Sham density functional theory calculations with k-point sampling of the Brillouin zone, which is needed for more general electronic structure calculations for solids. We demonstrate that our new method, called SCDM-k, is by construction gauge independent and a natural way to describe localized orbitals. SCDM-k computes localized orbitals without the use of an optimization procedure, and thus does not suffer from the possibility of being trapped in a local minimum. Furthermore, the computational complexity of using SCDM-k to construct orthogonal and localized orbitals scales as O (Nlog N) where N is the total number of k-points in the Brillouin zone. SCDM-k is therefore efficient even when a large number of k-points are used for Brillouin zone sampling. We demonstrate the numerical performance of SCDM-k using systems with model potentials in two and three dimensions.
NASA Astrophysics Data System (ADS)
Todoroki, Akira; Omagari, Kazuomi
Carbon Fiber Reinforced Plastic (CFRP) laminates are adopted for fuel tank structures of next generation space rockets or automobiles. Matrix cracks may cause fuel leak or trigger fatigue damage. A monitoring system of the matrix crack density is required. The authors have developed an electrical resistance change method for the monitoring of delamination cracks in CFRP laminates. Reinforcement fibers are used as a self-sensing system. In the present study, the electric potential method is adopted for matrix crack density monitoring. Finite element analysis (FEA) was performed to investigate the possibility of monitoring matrix crack density using multiple electrodes mounted on a single surface of a specimen. The FEA reveals the matrix crack density increases electrical resistance for a target segment between electrodes. Experimental confirmation was also performed using cross-ply laminates. Eight electrodes were mounted on a single surface of a specimen using silver paste after polishing of the specimen surface with sandpaper. The two outermost electrodes applied electrical current, and the inner electrodes measured electric voltage changes. The slope of electrical resistance during reloading is revealed to be an appropriate index for the detection of matrix crack density.
Matrix operator theory of radiative transfer. I - Rayleigh scattering.
NASA Technical Reports Server (NTRS)
Plass, G. N.; Kattawar, G. W.; Catchings, F. E.
1973-01-01
An entirely rigorous method for the solution of the equations for radiative transfer based on the matrix operator theory is reviewed. The advantages of the present method are: (1) all orders of the reflection and transmission matrices are calculated at once; (2) layers of any thickness may be combined, so that a realistic model of the atmosphere can be developed from any arbitrary number of layers, each with different properties and thicknesses; (3) calculations can readily be made for large optical depths and with highly anisotropic phase functions; (4) results are obtained for any desired value of the surface albedo including the value unity and for a large number of polar and azimuthal angles; (5) all fundamental equations can be interpreted immediately in terms of the physical interactions appropriate to the problem; and (6) both upward and downward radiance can be calculated at interior points from relatively simple expressions.
Collective field theory of a singular supersymmetric matrix model
de Mello Koch, R.; Rodrigues, J.P.
1995-05-15
The supersymmetric collective field theory with the potential {ital v}{prime}({ital x})={omega}{ital x}{minus}{eta}/{ital x} is studied. Consistency with supersymmetry enforces a two band solution. A supersymmetric classical configuration is found, and interpreted in terms of the density of zeroes of certain Laguerre polynomials. The spectrum of the model is then studied and is seen to correspond to a massless scalar and a Majorana fermion. The {ital x} space eigenfunctions are constructed and expressed in terms of Chebyshev polynomials. Higher order interactions are also discussed.
Cleaning large correlation matrices: Tools from Random Matrix Theory
NASA Astrophysics Data System (ADS)
Bun, Joël; Bouchaud, Jean-Philippe; Potters, Marc
2017-01-01
This review covers recent results concerning the estimation of large covariance matrices using tools from Random Matrix Theory (RMT). We introduce several RMT methods and analytical techniques, such as the Replica formalism and Free Probability, with an emphasis on the Marčenko-Pastur equation that provides information on the resolvent of multiplicatively corrupted noisy matrices. Special care is devoted to the statistics of the eigenvectors of the empirical correlation matrix, which turn out to be crucial for many applications. We show in particular how these results can be used to build consistent "Rotationally Invariant" estimators (RIE) for large correlation matrices when there is no prior on the structure of the underlying process. The last part of this review is dedicated to some real-world applications within financial markets as a case in point. We establish empirically the efficacy of the RIE framework, which is found to be superior in this case to all previously proposed methods. The case of additively (rather than multiplicatively) corrupted noisy matrices is also dealt with in a special Appendix. Several open problems and interesting technical developments are discussed throughout the paper.
Construct order parameters from the reduced density matrix spectra
Gu, Shi-Jian; Yu, Wing Chi; Lin, Hai-Qing
2013-09-15
In this paper, we try to establish a connection between a quantum information concept, i.e., the mutual information, and the conventional order parameter in condensed matter physics. We show that non-vanishing mutual information between two subsystems separated by a long distance means the existence of long-range orders in the system. By analyzing the spectra of the reduced density matrices that are used to calculate the mutual information, we show how to derive the local order operators that identify various ordered phases in condensed matter physics. -- Highlights: •Discussed the relation between long-range order and the mutual information (MI). •Pointed out how to check the existence of long-range order from MI. •Proposed a scheme to derive the diagonal and off-diagonal order parameter. •Gave three examples to show the effectiveness of the scheme.
Gaussian point processes and two-by-two random matrix theory.
Nieminen, John M
2007-10-01
The statistics of the multidimensional Gaussian point process are discussed in connection with the spacing statistics of eigenvalues of 2x2 random matrices. We consider the three-dimensional Gaussian point process when two of the coordinates of a point are randomly chosen from a Gaussian distribution having a mean of zero and a variance of sigma;{2}=1 but the third coordinate is chosen from a Gaussian distribution having a variance in the range of 0< or =sigma_{3};{2}< or =1 . The probability density function associated with a random point being at a distance r from the origin is shown to be closely related to the nearest-neighbor spacing distribution of eigenvalues coming from an ensemble of 2x2 matrices defined by the French-Kota-Pandey-Mehta two-matrix model of random matrix theory. An elementary explanation of this result is given.
Internal rotations of aromatic polyamides: a density functional theory study
NASA Astrophysics Data System (ADS)
Nishikawa, Joe; Imase, Tatsuya; Koike, Masao; Fukuda, Kaoru; Tokita, Masatoshi; Watanabe, Junji; Kawauchi, Susumu
2005-05-01
Internal rotations of benzanilide ( BA) and 4-(4'-aminobenzamido)benzoic acid ( AA) were investigated by density functional theory (DFT) calculations. B3LYP/6-31G* optimization for both BA and AA structures gives non-planar trans structures as the most stable conformers with lower energy of 4.60 and 5.08 kcal/mol than cis ones, respectively. The amide bond and aniline moiety are found to be coplanar in transBA, while in trans phenyl benzoate ( PB) the ester bond and benzoyl moiety are coplanar. The relaxed potential energy surface (PES) scans were then carried out with rotations of three single bonds, i.e. amide bond and both adjacent bonds. The discontinuous point is found on the relaxed PES for the amide bond rotation. This indicates that inversion of a pyramidal amino group is involved with the amide bond rotation. Therefore, two transition states (TSs) arise for rotation around the amide bond. Two TS structures ( TS-1 and TS-2) were optimized for both BA and AA, and their activation energies were estimated as 14.34 kcal/mol ( TS-1) and 16.27 kcal/mol ( TS-2) for BA, and 12.20 kcal/mol ( TS-1) for AA, respectively. The TS-2 structure for AA failed to be optimized. The activation energy for the amide bond rotation, which is larger than that of 7.90 kcal/mol for PB, as well as the coplanarity in aromatic amide is ascribed to the partial double bond character of amide bond. This is also confirmed by the Wiberg bond index (bond order). The chain persistence length for poly(4-benzamide) was estimated by the rotation matrix formalism using the calculated structural parameters of transAA. The estimated value of 1131 Å is longer than our previously calculated value of corresponding aromatic polyester, 364 Å for poly( p-hydroxybenzoic acid) [T. Imase, S. Kawauchi, J. Watanabe, Macromol. Theory Simul. 10 (2001) 434].
A Surrogate Measure of Cortical Bone Matrix Density by Long T2-Suppressed MRI
Seifert, Alan C.; Li, Cheng; Wehrli, Suzanne L.; Wehrli, Felix W.
2015-01-01
Magnetic resonance has the potential to image and quantify two pools of water within bone: free water within the Haversian pore system (transverse relaxation time, T2 > 1 ms), and water hydrogen-bonded to matrix collagen (T2 ~ 300–400 µs). While total bone water concentration quantified by MRI has been shown to scale with porosity, greater insight into bone matrix density and porosity may be gained by relaxation-based separation of bound and pore water fractions. The objective of this study was to evaluate a recently developed surrogate measurement for matrix density, single adiabatic inversion recovery (SIR) zero echo-time (ZTE) MRI, in human bone. Specimens of tibial cortical bone from 15 donors (27–97 y/o, eight female and seven male) were examined at 9.4T field strength using two methods: (1) 1H ZTE MRI, to capture total 1H signal, and (2) 1H SIR-ZTE MRI, to selectively image matrix-associated 1H signal. Total water, bone matrix, and bone mineral densities were also quantified gravimetrically, and porosity was measured by micro-CT. ZTE apparent total water 1H concentration was 32.7±3.2 M (range: 28.5–40.3 M), and was correlated positively with porosity (R2 = 0.80) and negatively with matrix and mineral densities (R2 = 0.90 and 0.82, respectively). SIR-ZTE apparent bound water 1H concentration was 32.9±3.9 M (range: 24.4–39.8 M), and its correlations were opposite to those of apparent total water: negative with porosity (R2 = 0.73) and positive with matrix density (R2 = 0.74) and mineral density (R2 = 0.72). Porosity was strongly correlated with gravimetric matrix density (R2 = 0.91, negative) and total water density (R2 = 0.92, positive). The strong correlations of SIR-ZTE-derived apparent bound water 1H concentration with ground-truth measurements suggest that this quantitative solid-state MRI method provides a nondestructive surrogate measure of bone matrix density. PMID:26085307
Lipid Bilayer Phase Transition: Density Measurements and Theory
Nagle, J. F.
1973-01-01
The overall change of density for dipalmitoyl lecithin bilayers agrees with a general order-disorder theory and yields about seven gauche rotations per molecule for the biologically relevant high-temperature phase. The shape of the curve of density against temperature is similar to the result of an exact calculation on a specific model, which gives a 3/2-order phase transition. PMID:4519637
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.
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.
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.
Berkolaiko, Gregory; Kuipers, Jack
2012-04-01
Electronic transport through chaotic quantum dots exhibits universal, system-independent properties, consistent with random-matrix theory. The quantum transport can also be rooted, via the semiclassical approximation, in sums over the classical scattering trajectories. Correlations between such trajectories can be organized diagrammatically and have been shown to yield universal answers for some observables. Here, we develop the general combinatorial treatment of the semiclassical diagrams, through a connection to factorizations of permutations. We show agreement between the semiclassical and random matrix approaches to the moments of the transmission eigenvalues. The result is valid for all moments to all orders of the expansion in inverse channel number for all three main symmetry classes (with and without time-reversal symmetry and spin-orbit interaction) and extends to nonlinear statistics. This finally explains the applicability of random-matrix theory to chaotic quantum transport in terms of the underlying dynamics as well as providing semiclassical access to the probability density of the transmission eigenvalues.
Smallwood, D.O.
1995-08-07
It is shown that the usual method for computing the coherence functions (ordinary, partial, and multiple) for a general multiple-input/multiple-output problem can be expressed as a modified form of Cholesky decomposition of the cross spectral density matrix of the inputs and outputs. The modified form of Cholesky decomposition used is G{sub zz} = LCL{prime}, where G is the cross spectral density matrix of inputs and outputs, L is a lower; triangular matrix with ones on the diagonal, and C is a diagonal matrix, and the symbol {prime} denotes the conjugate transpose. If a diagonal element of C is zero, the off diagonal elements in the corresponding column of L are set to zero. It is shown that the results can be equivalently obtained using singular value decomposition (SVD) of G{sub zz}. The formulation as a SVD problem suggests a way to order the inputs when a natural physical order of the inputs is absent.
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.
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.
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.
Self consistent theories of superfluid density and collective modes in BCS-BEC
NASA Astrophysics Data System (ADS)
Boyack, Rufus; Anderson, Brandon; Wu, Chien-Te; Levin, Kathryn
Establishing fully self consistent and sum rule compatible response functions in strongly correlated Fermi superfluids has been a historically challenging subject. In this talk, we present recent progress pertaining to response functions in many-body Fermi systems. We note that even in strict BCS theory, the textbook derivation of density and current response functions in the gradient expansion breaks certain conservation laws such as the compressibility sum rule. To include additional contributions that preserve all expected conservation laws, we show how to exploit Ward identities within two different t-matrix schemes. In this way we address the density-density response (including collective modes) and the superfluid density. Finally, we characterize approximations made in the literature where some consistency requirements have been dropped.
Nonequilibrium density-matrix description of steady-state quantum transport.
Dhar, Abhishek; Saito, Keiji; Hänggi, Peter
2012-01-01
With this work we investigate the stationary nonequilibrium density matrix of current carrying nonequilibrium steady states of in-between quantum systems that are connected to reservoirs. We describe the analytical procedure to obtain the explicit result for the reduced density matrix of quantum transport when the system, the connecting reservoirs, and the system-reservoir interactions are described by quadratic Hamiltonians. Our procedure is detailed for both electronic transport described by the tight-binding Hamiltonian and for phonon transport described by harmonic Hamiltonians. For the special case of weak system-reservoir couplings, a more detailed description of the steady-state density matrix is obtained. Several paradigm transport setups for interelectrode electron transport and low-dimensional phonon heat flux are elucidated.
Effective field theory for plasmas at all temperatures and densities
NASA Astrophysics Data System (ADS)
Braaten, Eric
1993-05-01
The solution of the plasmon problem and the subsequent development of an effective field-theory approach to ultrarelativistic plasmas are reviewed. The effective Lagrangians that summarize collective effects in ultrarelativistic quark-gluon and electron-photon plasmas are presented. A generalization that describes an electromagnetic plasma at all temperatures and densities is proposed.
Parkhomenko, A I; Shalagin, Anatolii M
2011-11-30
Using the eikonal approximation, we have calculated effective collision frequencies in density-matrix kinetic equations describing nonlinear effects in the wings of spectral lines. We have established the relation between the probabilities of absorption and stimulated emission and the characteristics of the radiation and elementary scattering event. The example of the power interaction potential shows that quantum mechanical calculation of the collision frequencies in the eikonal approximation and previously known spectral line wing theory give similar results for the probability of radiation absorption.
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.
Matrix sublimation method for the formation of high-density amorphous ice
NASA Astrophysics Data System (ADS)
Kouchi, A.; Hama, T.; Kimura, Y.; Hidaka, H.; Escribano, R.; Watanabe, N.
2016-08-01
A novel method for the formation of amorphous ice involving matrix sublimation has been developed. A CO-rich CO:H2O mixed ice was deposited at 8-10 K under ultra-high vacuum condition, which was then allowed to warm. After the sublimation of matrix CO at 35 K, amorphous ice remained. The amorphous ice formed exhibits a highly porous microscale texture; however, it also rather exhibits a density similar to that of high-density amorphous ice formed under high pressure. Furthermore, unlike conventional vapor-deposited amorphous ice, the amorphous ice is stable up to 140 K, where it transforms directly to cubic ice Ic.
Edgar, Lowell T.; Underwood, Clayton J.; Guilkey, James E.; Hoying, James B.; Weiss, Jeffrey A.
2014-01-01
Angiogenesis is regulated by the local microenvironment, including the mechanical interactions between neovessel sprouts and the extracellular matrix (ECM). However, the mechanisms controlling the relationship of mechanical and biophysical properties of the ECM to neovessel growth during sprouting angiogenesis are just beginning to be understood. In this research, we characterized the relationship between matrix density and microvascular topology in an in vitro 3D organ culture model of sprouting angiogenesis. We used these results to design and calibrate a computational growth model to demonstrate how changes in individual neovessel behavior produce the changes in vascular topology that were observed experimentally. Vascularized gels with higher collagen densities produced neovasculatures with shorter vessel lengths, less branch points, and reduced network interconnectivity. The computational model was able to predict these experimental results by scaling the rates of neovessel growth and branching according to local matrix density. As a final demonstration of utility of the modeling framework, we used our growth model to predict several scenarios of practical interest that could not be investigated experimentally using the organ culture model. Increasing the density of the ECM significantly reduced angiogenesis and network formation within a 3D organ culture model of angiogenesis. Increasing the density of the matrix increases the stiffness of the ECM, changing how neovessels are able to deform and remodel their surroundings. The computational framework outlined in this study was capable of predicting this observed experimental behavior by adjusting neovessel growth rate and branching probability according to local ECM density, demonstrating that altering the stiffness of the ECM via increasing matrix density affects neovessel behavior, thereby regulated vascular topology during angiogenesis. PMID:24465500
Remarks on time-dependent [current]-density functional theory for open quantum systems.
Yuen-Zhou, Joel; Aspuru-Guzik, Alán
2013-08-14
Time-dependent [current]-density functional theory for open quantum systems (OQS) has emerged as a formalism that can incorporate dissipative effects in the dynamics of many-body quantum systems. Here, we review and clarify some formal aspects of these theories that have been recently questioned in the literature. In particular, we provide theoretical support for the following conclusions: (1) contrary to what we and others had stated before, within the master equation framework, there is in fact a one-to-one mapping between vector potentials and current densities for fixed initial state, particle-particle interaction, and memory kernel; (2) regardless of the first conclusion, all of our recently suggested Kohn-Sham (KS) schemes to reproduce the current and particle densities of the original OQS, and in particular, the use of a KS closed driven system, remains formally valid; (3) the Lindblad master equation maintains the positivity of the density matrix regardless of the time-dependence of the Hamiltonian or the dissipation operators; (4) within the stochastic Schrödinger equation picture, a one-to-one mapping from stochastic vector potential to stochastic current density for individual trajectories has not been proven so far, except in the case where the vector potential is the same for every member of the ensemble, in which case, it reduces to the Lindblad master equation picture; (5) master equations may violate certain desired properties of the density matrix, such as positivity, but they remain as one of the most useful constructs to study OQS when the environment is not easily incorporated explicitly in the calculation. The conclusions support our previous work as formally rigorous, offer new insights into it, and provide a common ground to discuss related theories.
How Fast Can Networks Synchronize? A Random Matrix Theory Approach
NASA Astrophysics Data System (ADS)
Timme, Marc; Wolf, Fred; Geisel, Theo
2004-03-01
Pulse-coupled oscillators constitute a paradigmatic class of dynamical systems interacting on networks because they model a variety of biological systems including flashing fireflies and chirping crickets as well as pacemaker cells of the heart and neural networks. Synchronization is one of the most simple and most prevailing kinds of collective dynamics on such networks. Here we study collective synchronization [1] of pulse-coupled oscillators interacting on asymmetric random networks. Using random matrix theory we analytically determine the speed of synchronization in such networks in dependence on the dynamical and network parameters [2]. The speed of synchronization increases with increasing coupling strengths. Surprisingly, however, it stays finite even for infinitely strong interactions. The results indicate that the speed of synchronization is limited by the connectivity of the network. We discuss the relevance of our findings to general equilibration processes on complex networks. [5mm] [1] M. Timme, F. Wolf, T. Geisel, Phys. Rev. Lett. 89:258701 (2002). [2] M. Timme, F. Wolf, T. Geisel, cond-mat/0306512 (2003).
Random matrix theory filters and currency portfolio optimisation
NASA Astrophysics Data System (ADS)
Daly, J.; Crane, M.; Ruskin, H. J.
2010-04-01
Random matrix theory (RMT) filters have recently been shown to improve the optimisation of financial portfolios. This paper studies the effect of three RMT filters on realised portfolio risk, using bootstrap analysis and out-of-sample testing. We considered the case of a foreign exchange and commodity portfolio, weighted towards foreign exchange, and consisting of 39 assets. This was intended to test the limits of RMT filtering, which is more obviously applicable to portfolios with larger numbers of assets. We considered both equally and exponentially weighted covariance matrices, and observed that, despite the small number of assets involved, RMT filters reduced risk in a way that was consistent with a much larger S&P 500 portfolio. The exponential weightings indicated showed good consistency with the value suggested by Riskmetrics, in contrast to previous results involving stocks. This decay factor, along with the low number of past moves preferred in the filtered, equally weighted case, displayed a trend towards models which were reactive to recent market changes. On testing portfolios with fewer assets, RMT filtering provided less or no overall risk reduction. In particular, no long term out-of-sample risk reduction was observed for a portfolio consisting of 15 major currencies and commodities.
Advances in random matrix theory, zeta functions, and sphere packing.
Hales, T C; Sarnak, P; Pugh, M C
2000-11-21
Over four hundred years ago, Sir Walter Raleigh asked his mathematical assistant to find formulas for the number of cannonballs in regularly stacked piles. These investigations aroused the curiosity of the astronomer Johannes Kepler and led to a problem that has gone centuries without a solution: why is the familiar cannonball stack the most efficient arrangement possible? Here we discuss the solution that Hales found in 1998. Almost every part of the 282-page proof relies on long computer verifications. Random matrix theory was developed by physicists to describe the spectra of complex nuclei. In particular, the statistical fluctuations of the eigenvalues ("the energy levels") follow certain universal laws based on symmetry types. We describe these and then discuss the remarkable appearance of these laws for zeros of the Riemann zeta function (which is the generating function for prime numbers and is the last special function from the last century that is not understood today.) Explaining this phenomenon is a central problem. These topics are distinct, so we present them separately with their own introductory remarks.
Advances in random matrix theory, zeta functions, and sphere packing
Hales, T. C.; Sarnak, P.; Pugh, M. C.
2000-01-01
Over four hundred years ago, Sir Walter Raleigh asked his mathematical assistant to find formulas for the number of cannonballs in regularly stacked piles. These investigations aroused the curiosity of the astronomer Johannes Kepler and led to a problem that has gone centuries without a solution: why is the familiar cannonball stack the most efficient arrangement possible? Here we discuss the solution that Hales found in 1998. Almost every part of the 282-page proof relies on long computer verifications. Random matrix theory was developed by physicists to describe the spectra of complex nuclei. In particular, the statistical fluctuations of the eigenvalues (“the energy levels”) follow certain universal laws based on symmetry types. We describe these and then discuss the remarkable appearance of these laws for zeros of the Riemann zeta function (which is the generating function for prime numbers and is the last special function from the last century that is not understood today.) Explaining this phenomenon is a central problem. These topics are distinct, so we present them separately with their own introductory remarks. PMID:11058156
Juxtaposing density matrix and classical path-based wave packet dynamics
Aghtar, Mortaza; Liebers, Jörg; Strümpfer, Johan; Schulten, Klaus; Kleinekathöfer, Ulrich
2012-01-01
In many physical, chemical, and biological systems energy and charge transfer processes are of utmost importance. To determine the influence of the environment on these transport processes, equilibrium molecular dynamics simulations become more and more popular. From these simulations, one usually determines the thermal fluctuations of certain energy gaps, which are then either used to perform ensemble-averaged wave packet simulations, also called Ehrenfest dynamics, or to employ a density matrix approach via spectral densities. These two approaches are analyzed through energy gap fluctuations that are generated to correspond to a predetermined spectral density. Subsequently, density matrix and wave packet simulations are compared through population dynamics and absorption spectra for different parameter regimes. Furthermore, a previously proposed approach to enforce the correct long-time behavior in the wave packet simulations is probed and an improvement is proposed. PMID:22697524
Closed String S-matrix Elements in Open String Field Theory
NASA Astrophysics Data System (ADS)
Garousi, Mohammad R.; Maktabdaran, G. R.
2005-03-01
We study the S-matrix elements of the gauge invariant operators corresponding to on-shell closed strings, in open string field theory. In particular, we calculate the tree level S-matrix element of two arbitrary closed strings, and the S-matrix element of one closed string and two open strings. By mapping the world-sheet of these amplitudes to the upper half z-plane, and by evaluating explicitly the correlators in the ghost part, we show that these S-matrix elements are exactly identical to the corresponding disk level S-matrix elements in perturbative string theory.
Goodwin, D L; Kuprov, Ilya
2015-08-28
Auxiliary matrix exponential method is used to derive simple and numerically efficient general expressions for the following, historically rather cumbersome, and hard to compute, theoretical methods: (1) average Hamiltonian theory following interaction representation transformations; (2) Bloch-Redfield-Wangsness theory of nuclear and electron relaxation; (3) gradient ascent pulse engineering version of quantum optimal control theory. In the context of spin dynamics, the auxiliary matrix exponential method is more efficient than methods based on matrix factorizations and also exhibits more favourable complexity scaling with the dimension of the Hamiltonian matrix.
Goodwin, D. L.; Kuprov, Ilya
2015-08-28
Auxiliary matrix exponential method is used to derive simple and numerically efficient general expressions for the following, historically rather cumbersome, and hard to compute, theoretical methods: (1) average Hamiltonian theory following interaction representation transformations; (2) Bloch-Redfield-Wangsness theory of nuclear and electron relaxation; (3) gradient ascent pulse engineering version of quantum optimal control theory. In the context of spin dynamics, the auxiliary matrix exponential method is more efficient than methods based on matrix factorizations and also exhibits more favourable complexity scaling with the dimension of the Hamiltonian matrix.
Kinetic equations for a density matrix describing nonlinear effects in spectral line wings
Parkhomenko, A. I. Shalagin, A. M.
2011-11-15
Kinetic quantum equations are derived for a density matrix with collision integrals describing nonlinear effects in spectra line wings. These equations take into account the earlier established inequality of the spectral densities of Einstein coefficients for absorption and stimulated radiation emission by a two-level quantum system in the far wing of a spectral line in the case of frequent collisions. The relationship of the absorption and stimulated emission probabilities with the characteristics of radiation and an elementary scattering event is found.
Density functional theory and simulations of colloidal triangular prisms.
Marechal, Matthieu; Dussi, Simone; Dijkstra, Marjolein
2017-03-28
Nanopolyhedra form a versatile toolbox to investigate the effect of particle shape on self-assembly. Here we consider rod-like triangular prisms to gauge the effect of the cross section of the rods on liquid crystal phase behavior. We also take this opportunity to implement and test a previously proposed version of fundamental measure density functional theory (0D-FMT). Additionally, we perform Monte Carlocomputer simulations and we employ a simpler Onsager theory with a Parsons-Lee correction. Surprisingly and disappointingly, 0D-FMT does not perform better than the Tarazona and Rosenfeld's version of fundamental measure theory (TR-FMT). Both versions of FMT perform somewhat better than the Parsons-Lee theory. In addition, we find that the stability regime of the smectic phase is larger for triangular prisms than for spherocylinders and square prisms.
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.
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.
Mechanical behavior of Fiber Reinforced SiC/RBSN Ceramic Matrix Composites: Theory and Experiment
1991-01-01
AD-A235 926 NASA AVSCOM Technical Memorandum 103688 Technical Report 91-C-004 Mechanical Behavior of Fiber Reinforced SiC/RBSN Ceramic Matrix Composites : Theory... CERAMIC MATRIX COMPOSITES : THEORY AND EXPERIMENT Abhisak Chulya* Department of Civil Engineering Cleveland State University Cleveland, Ohio 44115...tough and sufficiently stable continuous fiber- reinforced ceramic matrix composites (CMC) which can survive in oxidizing environ- ments at temperatures
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 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
Wen, Xiaotong; Rangarajan, Govindan; Ding, Mingzhou
2013-08-28
Granger causality is increasingly being applied to multi-electrode neurophysiological and functional imaging data to characterize directional interactions between neurons and brain regions. For a multivariate dataset, one might be interested in different subsets of the recorded neurons or brain regions. According to the current estimation framework, for each subset, one conducts a separate autoregressive model fitting process, introducing the potential for unwanted variability and uncertainty. In this paper, we propose a multivariate framework for estimating Granger causality. It is based on spectral density matrix factorization and offers the advantage that the estimation of such a matrix needs to be done only once for the entire multivariate dataset. For any subset of recorded data, Granger causality can be calculated through factorizing the appropriate submatrix of the overall spectral density matrix.
Sensitivity of the NMR density matrix to pulse sequence parameters: a simplified analytic approach.
Momot, Konstantin I; Takegoshi, K
2012-08-01
We present a formalism for the analysis of sensitivity of nuclear magnetic resonance pulse sequences to variations of pulse sequence parameters, such as radiofrequency pulses, gradient pulses or evolution delays. The formalism enables the calculation of compact, analytic expressions for the derivatives of the density matrix and the observed signal with respect to the parameters varied. The analysis is based on two constructs computed in the course of modified density-matrix simulations: the error interrogation operators and error commutators. The approach presented is consequently named the Error Commutator Formalism (ECF). It is used to evaluate the sensitivity of the density matrix to parameter variation based on the simulations carried out for the ideal parameters, obviating the need for finite-difference calculations of signal errors. The ECF analysis therefore carries a computational cost comparable to a single density-matrix or product-operator simulation. Its application is illustrated using a number of examples from basic NMR spectroscopy. We show that the strength of the ECF is its ability to provide analytic insights into the propagation of errors through pulse sequences and the behaviour of signal errors under phase cycling. Furthermore, the approach is algorithmic and easily amenable to implementation in the form of a programming code. It is envisaged that it could be incorporated into standard NMR product-operator simulation packages.
Collagen Matrix Density Drives the Metabolic Shift in Breast Cancer Cells.
Morris, Brett A; Burkel, Brian; Ponik, Suzanne M; Fan, Jing; Condeelis, John S; Aguirre-Ghiso, Julio A; Castracane, James; Denu, John M; Keely, Patricia J
2016-11-01
Increased breast density attributed to collagen I deposition is associated with a 4-6 fold increased risk of developing breast cancer. Here, we assessed cellular metabolic reprogramming of mammary carcinoma cells in response to increased collagen matrix density using an in vitro 3D model. Our initial observations demonstrated changes in functional metabolism in both normal mammary epithelial cells and mammary carcinoma cells in response to changes in matrix density. Further, mammary carcinoma cells grown in high density collagen matrices displayed decreased oxygen consumption and glucose metabolism via the tricarboxylic acid (TCA) cycle compared to cells cultured in low density matrices. Despite decreased glucose entry into the TCA cycle, levels of glucose uptake, cell viability, and ROS were not different between high and low density matrices. Interestingly, under high density conditions the contribution of glutamine as a fuel source to drive the TCA cycle was significantly enhanced. These alterations in functional metabolism mirrored significant changes in the expression of metabolic genes involved in glycolysis, oxidative phosphorylation, and the serine synthesis pathway. This study highlights the broad importance of the collagen microenvironment to cellular expression profiles, and shows that changes in density of the collagen microenvironment can modulate metabolic shifts of cancer cells.
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.
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.
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.
Giesbertz, K. J. H.; Gritsenko, O. V.; Baerends, E. J.
2014-05-14
Recently, we have demonstrated that the problems finding a suitable adiabatic approximation in time-dependent one-body reduced density matrix functional theory can be remedied by introducing an additional degree of freedom to describe the system: the phase of the natural orbitals [K. J. H. Giesbertz, O. V. Gritsenko, and E. J. Baerends, Phys. Rev. Lett. 105, 013002 (2010); K. J. H. Giesbertz, O. V. Gritsenko, and E. J. Baerends, J. Chem. Phys. 133, 174119 (2010)]. In this article we will show in detail how the frequency-dependent response equations give the proper static limit (ω → 0), including the perturbation in the chemical potential, which is required in static response theory to ensure the correct number of particles. Additionally we show results for the polarizability for H{sub 2} and compare the performance of two different two-electron functionals: the phase-including Löwdin–Shull functional and the density matrix form of the Löwdin–Shull functional.
NASA Astrophysics Data System (ADS)
Sharma, Sandeep; Alavi, Ali
2015-09-01
We propose a multireference linearized coupled cluster theory using matrix product states (MPSs-LCC) which provides remarkably accurate ground-state energies, at a computational cost that has the same scaling as multireference configuration interaction singles and doubles, for a wide variety of electronic Hamiltonians. These range from first-row dimers at equilibrium and stretched geometries to highly multireference systems such as the chromium dimer and lattice models such as periodic two-dimensional 1-band and 3-band Hubbard models. The MPS-LCC theory shows a speed up of several orders of magnitude over the usual Density Matrix Renormalization Group (DMRG) algorithm while delivering energies in excellent agreement with converged DMRG calculations. Also, in all the benchmark calculations presented here, MPS-LCC outperformed the commonly used multi-reference quantum chemistry methods in some cases giving energies in excess of an order of magnitude more accurate. As a size-extensive method that can treat large active spaces, MPS-LCC opens up the use of multireference quantum chemical techniques in strongly correlated ab initio Hamiltonians, including two- and three-dimensional solids.
Sharma, Sandeep; Alavi, Ali
2015-09-14
We propose a multireference linearized coupled cluster theory using matrix product states (MPSs-LCC) which provides remarkably accurate ground-state energies, at a computational cost that has the same scaling as multireference configuration interaction singles and doubles, for a wide variety of electronic Hamiltonians. These range from first-row dimers at equilibrium and stretched geometries to highly multireference systems such as the chromium dimer and lattice models such as periodic two-dimensional 1-band and 3-band Hubbard models. The MPS-LCC theory shows a speed up of several orders of magnitude over the usual Density Matrix Renormalization Group (DMRG) algorithm while delivering energies in excellent agreement with converged DMRG calculations. Also, in all the benchmark calculations presented here, MPS-LCC outperformed the commonly used multi-reference quantum chemistry methods in some cases giving energies in excess of an order of magnitude more accurate. As a size-extensive method that can treat large active spaces, MPS-LCC opens up the use of multireference quantum chemical techniques in strongly correlated ab initio Hamiltonians, including two- and three-dimensional solids.
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.
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.
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.
Bhuyan, M.; Panda, R. N.; Routray, T. R.; Patra, S. K.
2010-12-15
In the framework of relativistic mean field (RMF) theory, we have calculated the density distribution of protons and neutrons for {sup 40,42,44,48}Ca with NL3 and G2 parameter sets. The microscopic proton-nucleus optical potentials for p+{sup 40,42,44,48}Ca systems are evaluated from the Dirac nucleon-nucleon scattering amplitude and the density of the target nucleus using relativistic-Love-Franey and McNeil-Ray-Wallace parametrizations. We have estimated the scattering observables, such as the elastic differential scattering cross section, analyzing power and the spin observables with the relativistic impulse approximation (RIA). The results have been compared with the experimental data for a few selective cases and we find that the use of density as well as the scattering matrix parametrizations are crucial for the theoretical prediction.
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.
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.
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 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.
Richter, Marten Knorr, Andreas
2010-04-15
Time convolution less density matrix theory (TCL) is a powerful and well established tool to investigate strong system-bath coupling for linear optical spectra. We show that TCL equations can be generalised to the nonlinear optical response up to a chosen order in the optical field. This goal is achieved via an time convolution less perturbation scheme for the reduced density matrices of the electronic system. In our approach, the most important results are the inclusion of a electron-phonon coupling non-diagonal in the electronic states and memory effects of the bath: First, the considered model system is introduced. Second, the time evolution of the statistical operator is expanded with respect to the external optical field. This expansion is the starting point to explain how a TCL theory can treat the response up to in a certain order in the external field. Third, new TCL equations, including bath memory effects, are derived and the problem of information loss in the reduced density matrix is analysed. For this purpose, new dimensions are added to the reduced statistical operator to compensate lack of information in comparison with the full statistical operator. The theory is benchmarked with a two level system and applied to a three level system including non-diagonal phonon coupling. In our analysis of pump-probe experiments, the bath memory is influenced by the system state occupied between pump and probe pulse. In particular, the memory of the bath influences the dephasing process of electronic coherences developing during the time interval between pump and probe pulses.
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.
An information theory approach to the density of the earth
NASA Technical Reports Server (NTRS)
Graber, M. A.
1977-01-01
Information theory can develop a technique which takes experimentally determined numbers and produces a uniquely specified best density model satisfying those numbers. A model was generated using five numerical parameters: the mass of the earth, its moment of inertia, three zero-node torsional normal modes (L = 2, 8, 26). In order to determine the stability of the solution, six additional densities were generated, in each of which the period of one of the three normal modes was increased or decreased by one standard deviation. The superposition of the seven models is shown. It indicates that current knowledge of the torsional modes is sufficient to specify the density in the upper mantle but that the lower mantle and core will require smaller standard deviations before they can be accurately specified.
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.
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.
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.
Novaes, Marcel
2015-06-15
We consider the statistics of time delay in a chaotic cavity having M open channels, in the absence of time-reversal invariance. In the random matrix theory approach, we compute the average value of polynomial functions of the time delay matrix Q = − iħS{sup †}dS/dE, where S is the scattering matrix. Our results do not assume M to be large. In a companion paper, we develop a semiclassical approximation to S-matrix correlation functions, from which the statistics of Q can also be derived. Together, these papers contribute to establishing the conjectured equivalence between the random matrix and the semiclassical approaches.
Local density approximation in site-occupation embedding theory
NASA Astrophysics Data System (ADS)
Senjean, Bruno; Tsuchiizu, Masahisa; Robert, Vincent; Fromager, Emmanuel
2017-01-01
Site-occupation embedding theory (SOET) is a density-functional theory (DFT)-based method which aims at modelling strongly correlated electrons. It is in principle exact and applicable to model and quantum chemical Hamiltonians. The theory is presented here for the Hubbard Hamiltonian. In contrast to conventional DFT approaches, the site (or orbital) occupations are deduced in SOET from a partially-interacting system consisting of one (or more) impurity site(s) and non-interacting bath sites. The correlation energy of the bath is then treated implicitly by means of a site-occupation functional. In this work, we propose a simple impurity-occupation functional approximation based on the two-level (2L) Hubbard model which is referred to as two-level impurity local density approximation (2L-ILDA). Results obtained on a prototypical uniform 8-site Hubbard ring are promising. The extension of the method to larger systems and more sophisticated model Hamiltonians is currently in progress.
Density functional theory and phytochemical study of 8-hydroxyisodiospyrin
NASA Astrophysics Data System (ADS)
Ullah, Zakir; Ata-ur-Rahman; Fazl-i-Sattar; Rauf, Abdur; Yaseen, Muhammad; Hassan, Waseem; Tariq, Muhammad; Ayub, Khurshid; Tahir, Asif Ali; Ullah, Habib
2015-09-01
Comprehensive theoretical and experimental studies of a natural product, 8-hydroxyisodiospyrin (HDO) have been carried out. Based on the correlation of experimental and theoretical data, an appropriate computational model was developed for obtaining the electronic, spectroscopic, and thermodynamic parameters of HDO. First of all, the exact structure of HDO is confirmed from the nice correlation of theory and experiment, prior to determination of its electroactive nature. Hybrid density functional theory (DFT) is employed for all theoretical simulations. The experimental and predicted IR and UV-vis spectra [B3LYP/6-31+G(d,p) level of theory] have excellent correlation. Inter-molecular non-covalent interaction of HDO with different gases such as NH3, CO2, CO, H2O is investigated through geometrical counterpoise (gCP) i.e., B3LYP-gCP-D3/6-31G∗ method. Furthermore, the inter-molecular interaction is also supported by geometrical parameters, electronic properties, thermodynamic parameters and charge analysis. All these characterizations have corroborated each other and confirmed the electroactive nature (non-covalent interaction ability) of HDO for the studied gases. Electronic properties such as Ionization Potential (IP), Electron Affinities (EA), electrostatic potential (ESP), density of states (DOS), HOMO, LUMO, and band gap of HDO have been estimated for the first time theoretically.
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.
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.
Theory of melting at high pressures: Amending density functional theory with quantum Monte Carlo
Shulenburger, L.; Desjarlais, M. P.; Mattsson, T. R.
2014-10-01
We present an improved first-principles description of melting under pressure based on thermodynamic integration comparing Density Functional Theory (DFT) and quantum Monte Carlo (QMC) treatments of the system. The method is applied to address the longstanding discrepancy between density functional theory (DFT) calculations and diamond anvil cell (DAC) experiments on the melting curve of xenon, a noble gas solid where van der Waals binding is challenging for traditional DFT methods. The calculations show excellent agreement with data below 20 GPa and that the high-pressure melt curve is well described by a Lindemann behavior up to at least 80 GPa, a finding in stark contrast to DAC data.
NASA Astrophysics Data System (ADS)
Nemes, Csaba; Barcza, Gergely; Nagy, Zoltán; Legeza, Örs; Szolgay, Péter
2014-06-01
In the numerical analysis of strongly correlated quantum lattice models one of the leading algorithms developed to balance the size of the effective Hilbert space and the accuracy of the simulation is the density matrix renormalization group (DMRG) algorithm, in which the run-time is dominated by the iterative diagonalization of the Hamilton operator. As the most time-dominant step of the diagonalization can be expressed as a list of dense matrix operations, the DMRG is an appealing candidate to fully utilize the computing power residing in novel kilo-processor architectures. In the paper a smart hybrid CPU-GPU implementation is presented, which exploits the power of both CPU and GPU and tolerates problems exceeding the GPU memory size. Furthermore, a new CUDA kernel has been designed for asymmetric matrix-vector multiplication to accelerate the rest of the diagonalization. Besides the evaluation of the GPU implementation, the practical limits of an FPGA implementation are also discussed.
Roemelt, Michael
2015-07-28
Spin Orbit Coupling (SOC) is introduced to molecular ab initio density matrix renormalization group (DMRG) calculations. In the presented scheme, one first approximates the electronic ground state and a number of excited states of the Born-Oppenheimer (BO) Hamiltonian with the aid of the DMRG algorithm. Owing to the spin-adaptation of the algorithm, the total spin S is a good quantum number for these states. After the non-relativistic DMRG calculation is finished, all magnetic sublevels of the calculated states are constructed explicitly, and the SOC operator is expanded in the resulting basis. To this end, spin orbit coupled energies and wavefunctions are obtained as eigenvalues and eigenfunctions of the full Hamiltonian matrix which is composed of the SOC operator matrix and the BO Hamiltonian matrix. This treatment corresponds to a quasi-degenerate perturbation theory approach and can be regarded as the molecular equivalent to atomic Russell-Saunders coupling. For the evaluation of SOC matrix elements, the full Breit-Pauli SOC Hamiltonian is approximated by the widely used spin-orbit mean field operator. This operator allows for an efficient use of the second quantized triplet replacement operators that are readily generated during the non-relativistic DMRG algorithm, together with the Wigner-Eckart theorem. With a set of spin-orbit coupled wavefunctions at hand, the molecular g-tensors are calculated following the scheme proposed by Gerloch and McMeeking. It interprets the effective molecular g-values as the slope of the energy difference between the lowest Kramers pair with respect to the strength of the applied magnetic field. Test calculations on a chemically relevant Mo complex demonstrate the capabilities of the presented method.
NASA Astrophysics Data System (ADS)
Roemelt, Michael
2015-07-01
Spin Orbit Coupling (SOC) is introduced to molecular ab initio density matrix renormalization group (DMRG) calculations. In the presented scheme, one first approximates the electronic ground state and a number of excited states of the Born-Oppenheimer (BO) Hamiltonian with the aid of the DMRG algorithm. Owing to the spin-adaptation of the algorithm, the total spin S is a good quantum number for these states. After the non-relativistic DMRG calculation is finished, all magnetic sublevels of the calculated states are constructed explicitly, and the SOC operator is expanded in the resulting basis. To this end, spin orbit coupled energies and wavefunctions are obtained as eigenvalues and eigenfunctions of the full Hamiltonian matrix which is composed of the SOC operator matrix and the BO Hamiltonian matrix. This treatment corresponds to a quasi-degenerate perturbation theory approach and can be regarded as the molecular equivalent to atomic Russell-Saunders coupling. For the evaluation of SOC matrix elements, the full Breit-Pauli SOC Hamiltonian is approximated by the widely used spin-orbit mean field operator. This operator allows for an efficient use of the second quantized triplet replacement operators that are readily generated during the non-relativistic DMRG algorithm, together with the Wigner-Eckart theorem. With a set of spin-orbit coupled wavefunctions at hand, the molecular g-tensors are calculated following the scheme proposed by Gerloch and McMeeking. It interprets the effective molecular g-values as the slope of the energy difference between the lowest Kramers pair with respect to the strength of the applied magnetic field. Test calculations on a chemically relevant Mo complex demonstrate the capabilities of the presented method.
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.
Ghosh, Soumen; Sonnenberger, Andrew L; Hoyer, Chad E; Truhlar, Donald G; Gagliardi, Laura
2015-08-11
The correct description of charge transfer in ground and excited states is very important for molecular interactions, photochemistry, electrochemistry, and charge transport, but it is very challenging for Kohn-Sham (KS) density functional theory (DFT). KS-DFT exchange-correlation functionals without nonlocal exchange fail to describe both ground- and excited-state charge transfer properly. We have recently proposed a theory called multiconfiguration pair-density functional theory (MC-PDFT), which is based on a combination of multiconfiguration wave function theory with a new type of density functional called an on-top density functional. Here we have used MC-PDFT to study challenging ground- and excited-state charge-transfer processes by using on-top density functionals obtained by translating KS exchange-correlation functionals. For ground-state charge transfer, MC-PDFT performs better than either the PBE exchange-correlation functional or CASPT2 wave function theory. For excited-state charge transfer, MC-PDFT (unlike KS-DFT) shows qualitatively correct behavior at long-range with great improvement in predicted excitation energies.
Testing the density matrix expansion against ab initio calculations of trapped neutron drops
Bogner, S. K.; Hergert, H.; Furnstahl, R. J.; Kortelainen, Erno M; Stoitsov, M. V.; Maris, Pieter; Vary, J. P.
2011-01-01
Microscopic input to a universal nuclear energy density functional can be provided through the density matrix expansion (DME), which has recently been revived and improved. Several DME implementation strategies are tested for neutron drop systems in harmonic traps by comparing to Hartree-Fock (HF) and ab initio no-core full configuration (NCFC) calculations with a model interaction (Minnesota potential). The new DME with exact treatment of Hartree contributions is found to best reproduce HF results and supplementing the functional with fit Skyrme-like contact terms shows systematic improvement toward the full NCFC results.
Huo, Pengfei; Coker, David F
2012-12-14
Powerful approximate methods for propagating the density matrix of complex systems that are conveniently described in terms of electronic subsystem states and nuclear degrees of freedom have recently been developed that involve linearizing the density matrix propagator in the difference between the forward and backward paths of the nuclear degrees of freedom while keeping the interference effects between the different forward and backward paths of the electronic subsystem described in terms of the mapping Hamiltonian formalism and semi-classical mechanics. Here we demonstrate that different approaches to developing the linearized approximation to the density matrix propagator can yield a mean-field like approximate propagator in which the nuclear variables evolve classically subject to Ehrenfest-like forces that involve an average over quantum subsystem states, and by adopting an alternative approach to linearizing we obtain an algorithm that involves classical like nuclear dynamics influenced by a quantum subsystem state dependent force reminiscent of trajectory surface hopping methods. We show how these different short time approximations can be implemented iteratively to achieve accurate, stable long time propagation and explore their implementation in different representations. The merits of the different approximate quantum dynamics methods that are thus consistently derived from the density matrix propagator starting point and different partial linearization approximations are explored in various model system studies of multi-state scattering problems and dissipative non-adiabatic relaxation in condensed phase environments that demonstrate the capabilities of these different types of approximations for treating non-adiabatic electronic relaxation, bifurcation of nuclear distributions, and the passage from nonequilibrium coherent dynamics at short times to long time thermal equilibration in the presence of a model dissipative environment.
Uncertainty Quantification and Propagation in Nuclear Density Functional Theory
Schunck, N; McDonnell, J D; Higdon, D; Sarich, J; Wild, S M
2015-03-17
Nuclear density functional theory (DFT) is one of the main theoretical tools used to study the properties of heavy and superheavy elements, or to describe the structure of nuclei far from stability. While on-going eff orts seek to better root nuclear DFT in the theory of nuclear forces, energy functionals remain semi-phenomenological constructions that depend on a set of parameters adjusted to experimental data in fi nite nuclei. In this paper, we review recent eff orts to quantify the related uncertainties, and propagate them to model predictions. In particular, we cover the topics of parameter estimation for inverse problems, statistical analysis of model uncertainties and Bayesian inference methods. Illustrative examples are taken from the literature.
Time-dependent density functional theory for quantum transport.
Zheng, Xiao; Chen, GuanHua; Mo, Yan; Koo, SiuKong; Tian, Heng; Yam, ChiYung; Yan, YiJing
2010-09-21
Based on our earlier works [X. Zheng et al., Phys. Rev. B 75, 195127 (2007); J. S. Jin et al., J. Chem. Phys. 128, 234703 (2008)], we propose a rigorous and numerically convenient approach to simulate time-dependent quantum transport from first-principles. The proposed approach combines time-dependent density functional theory with quantum dissipation theory, and results in a useful tool for studying transient dynamics of electronic systems. Within the proposed exact theoretical framework, we construct a number of practical schemes for simulating realistic systems such as nanoscopic electronic devices. Computational cost of each scheme is analyzed, with the expected level of accuracy discussed. As a demonstration, a simulation based on the adiabatic wide-band limit approximation scheme is carried out to characterize the transient current response of a carbon nanotube based electronic device under time-dependent external voltages.
Descriptions of carbon isotopes within the energy density functional theory
Ismail, Atef; Cheong, Lee Yen; Yahya, Noorhana; Tammam, M.
2014-10-24
Within the energy density functional (EDF) theory, the structure properties of Carbon isotopes are systematically studied. The shell model calculations are done for both even-A and odd-A nuclei, to study the structure of rich-neutron Carbon isotopes. The EDF theory indicates the single-neutron halo structures in {sup 15}C, {sup 17}C and {sup 19}C, and the two-neutron halo structures in {sup 16}C and {sup 22}C nuclei. It is also found that close to the neutron drip-line, there exist amazing increase in the neutron radii and decrease on the binding energies BE, which are tightly related with the blocking effect and correspondingly the blocking effect plays a significant role in the shell model configurations.
Density functional theory for inhomogeneous associating chain fluids.
Bryk, P; Sokołowski, S; Pizio, O
2006-07-14
We propose a nonlocal density functional theory for associating chain molecules. The chains are modeled as tangent spheres, which interact via Lennard-Jones (12,6) attractive interactions. A selected segment contains additional, short-ranged, highly directional interaction sites. The theory incorporates an accurate treatment of the chain molecules via the intramolecular potential formalism and should accurately describe systems with strongly varying external fields, e.g., attractive walls. Within our approach we investigate the structure of the liquid-vapor interface and capillary condensation of a simple model of associating chains with only one associating site placed on the first segment. In general, the properties of inhomogeneous associating chains depend on the association energy. Similar to the bulk systems we find the behavior of associating chains of a given length to be in between that for the nonassociating chains of the same length and that for the nonassociating chains twice as large.
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.
Accurate van der Waals coefficients from density functional theory
Tao, Jianmin; Perdew, John P.; Ruzsinszky, Adrienn
2012-01-01
The van der Waals interaction is a weak, long-range correlation, arising from quantum electronic charge fluctuations. This interaction affects many properties of materials. A simple and yet accurate estimate of this effect will facilitate computer simulation of complex molecular materials and drug design. Here we develop a fast approach for accurate evaluation of dynamic multipole polarizabilities and van der Waals (vdW) coefficients of all orders from the electron density and static multipole polarizabilities of each atom or other spherical object, without empirical fitting. Our dynamic polarizabilities (dipole, quadrupole, octupole, etc.) are exact in the zero- and high-frequency limits, and exact at all frequencies for a metallic sphere of uniform density. Our theory predicts dynamic multipole polarizabilities in excellent agreement with more expensive many-body methods, and yields therefrom vdW coefficients C6, C8, C10 for atom pairs with a mean absolute relative error of only 3%. PMID:22205765
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.
Estimation of probability densities using scale-free field theories.
Kinney, Justin B
2014-07-01
The question of how best to estimate a continuous probability density from finite data is an intriguing open problem at the interface of statistics and physics. Previous work has argued that this problem can be addressed in a natural way using methods from statistical field theory. Here I describe results that allow this field-theoretic approach to be rapidly and deterministically computed in low dimensions, making it practical for use in day-to-day data analysis. Importantly, this approach does not impose a privileged length scale for smoothness of the inferred probability density, but rather learns a natural length scale from the data due to the tradeoff between goodness of fit and an Occam factor. Open source software implementing this method in one and two dimensions is provided.
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.
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.
Estimation of probability densities using scale-free field theories
NASA Astrophysics Data System (ADS)
Kinney, Justin B.
2014-07-01
The question of how best to estimate a continuous probability density from finite data is an intriguing open problem at the interface of statistics and physics. Previous work has argued that this problem can be addressed in a natural way using methods from statistical field theory. Here I describe results that allow this field-theoretic approach to be rapidly and deterministically computed in low dimensions, making it practical for use in day-to-day data analysis. Importantly, this approach does not impose a privileged length scale for smoothness of the inferred probability density, but rather learns a natural length scale from the data due to the tradeoff between goodness of fit and an Occam factor. Open source software implementing this method in one and two dimensions is provided.
Benchmark Study of Density Cumulant Functional Theory: Thermochemistry and Kinetics.
Copan, Andreas V; Sokolov, Alexander Yu; Schaefer, Henry F
2014-06-10
We present an extensive benchmark study of density cumulant functional theory (DCFT) for thermochemistry and kinetics of closed- and open-shell molecules. The performance of DCFT methods (DC-06, DC-12, ODC-06, and ODC-12) is compared to that of coupled-electron pair methods (CEPA0 and OCEPA0) and coupled-cluster theory (CCSD and CCSD(T)) for the description of noncovalent interactions (A24 database), barrier heights of hydrogen-transfer reactions (HTBH38), radical stabilization energies (RSE30), adiabatic ionization energies (AIE), and covalent bond stretching in diatomic molecules. Our results indicate that out of four DCFT methods the ODC-12 method is the most reliable and accurate DCFT formulation to date. Compared to CCSD, ODC-12 shows superior results for all benchmark tests employed in our study. With respect to coupled-pair theories, ODC-12 outperforms CEPA0 and shows similar accuracy to the orbital-optimized CEPA0 variant (OCEPA0) for systems at equilibrium geometries. For covalent bond stretching, ODC-12 is found to be more reliable than OCEPA0. For the RSE30 and AIE data sets, ODC-12 shows competitive performance with CCSD(T). In addition to benchmark results, we report new reference values for the RSE30 data set computed using coupled cluster theory with up to perturbative quadruple excitations.
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.
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.
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.
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.
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.
Augmented Lagrangian Method for Constrained Nuclear Density Functiional Theory
Staszczak, A.; Stoitsov, Mario; Baran, Andrzej K; Nazarewicz, Witold
2010-01-01
The augmented Lagrangian 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 multidimensional energy surfaces in the space of collective coordinates that are needed to, e.g., determine fission pathways and saddle points; it improves accuracy of computed derivatives with respect to collective variables that are used to determine collective inertia and is well adapted to supercomputer applications.
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.
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.
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.
Superfluid density in the slave-boson theory
NASA Astrophysics Data System (ADS)
Zhong, Yin; Lu, Han-Tao; Luo, Hong-Gang
2016-02-01
Despite of the success of the slave-boson theory in capturing qualitative physics of high-temperature superconductors like cuprates, it fails to reproduce the correct temperature-dependent behavior of superfluid density, let alone the independence of the linear temperature term on doping in the underdoped regimes of hole-doped cuprate, a common experimental observation in different cuprates. It remains puzzling up to now in spite of intensive theoretical efforts. For electron-doped case, even qualitative treatment is not reported at present time. Here we revisit these problems and provide an alternative superfluid density formulation by using the London relation instead of employing the paramagnetic current-current correlation function. The obtained formula, on the one hand, provides the correct temperature-dependent behavior of the superfluid density in the whole temperature regime, on the other hand, makes the doping dependence of the linear temperature term substantially weaken and a possible interpretation for its independence on doping is proposed. As an application, electron-doped cuprate is studied, whose result qualitatively agrees with existing experiments and successfully explains the origin of d- to anisotropic s-wave transition across the optimal doping. Our result remedies some failures of the slave-boson theory as employed to calculate superfluid density in cuprates and may be useful in the understanding of the related physics in other strongly correlated systems, e.g. Na x CoO2· yH2O and certain iron-based superconductors with dominating local magnetic exchange interaction.
NASA Astrophysics Data System (ADS)
Saini, Anshul; Stojkovic, Dejan
2016-09-01
We study time-dependent Hawking-like radiation as seen by an infalling observer during gravitational collapse of a thin shell. We calculate the occupation number of particles of which the frequencies are measured in the proper time of an infalling observer in Eddington-Finkelstein coordinates. We solve the equations for the whole process from the beginning of the collapse till the moment when the collapsing shell reaches zero radius. The radiation distribution is not thermal in the whole frequency regime, but it is approximately thermal for the wavelengths of the order of the Schwarzschild radius of the collapsing shell. After the Schwarzschild radius is crossed, the temperature increases without limits as the singularity is approached. We also calculate the density matrix associated with this radiation. It turns out that the off-diagonal correlation terms to the diagonal Hawking leading-order terms are very important. While the trace of the diagonal (Hawking) density matrix squared decreases during the evolution, the trace of the total density matrix squared remains unity at all times and all frequencies.
Matrix formulation of the surface-enhanced Raman optical activity theory
NASA Astrophysics Data System (ADS)
Bouř, Petr
2007-04-01
The surface-enhanced Raman optical activity theory [J. Chem. Phys.125, 124704 (2006)] is formulated in a matrix form, which makes the formalism simpler and allows to extend it for more complicated colloid and molecular systems.
Cui, Ganglong; Fang, Weihai; Yang, Weitao
2010-01-14
Time-dependent density functional theory (TDDFT) has broad application in the study of electronic response, excitation and transport. To extend such application to large and complex systems, we develop a reformulation of TDDFT equations in terms of non-orthogonal localized molecular orbitals (NOLMOs). NOLMO is the most localized representation of electronic degrees of freedom and has been used in ground state calculations. In atomic orbital (AO) representation, the sparsity of NOLMO is transferred to the coefficient matrix of molecular orbitals (MOs). Its novel use in TDDFT here leads to a very simple form of time propagation equations which can be solved with linear-scaling effort. We have tested the method for several long-chain saturated and conjugated molecular systems within the self-consistent charge density-functional tight-binding method (SCC-DFTB) and demonstrated its accuracy. This opens up pathways for TDDFT applications to large bio- and nano-systems.
Linear-scaling density functional theory using the projector augmented wave method
NASA Astrophysics Data System (ADS)
Hine, Nicholas D. M.
2017-01-01
Quantum mechanical simulation of realistic models of nanostructured systems, such as nanocrystals and crystalline interfaces, demands computational methods combining high-accuracy with low-order scaling with system size. Blöchl’s projector augmented wave (PAW) approach enables all-electron (AE) calculations with the efficiency and systematic accuracy of plane-wave pseudopotential calculations. Meanwhile, linear-scaling (LS) approaches to density functional theory (DFT) allow for simulation of thousands of atoms in feasible computational effort. This article describes an adaptation of PAW for use in the LS-DFT framework provided by the ONETEP LS-DFT package. ONETEP uses optimisation of the density matrix through in situ-optimised local orbitals rather than the direct calculation of eigenstates as in traditional PAW approaches. The method is shown to be comparably accurate to both PAW and AE approaches and to exhibit improved convergence properties compared to norm-conserving pseudopotential methods.
Quark Physics without Quarks: A Review of Recent Developments in S-Matrix Theory.
ERIC Educational Resources Information Center
Capra, Fritjof
1979-01-01
Reviews the developments in S-matrix theory over the past five years which have made it possible to derive results characteristic of quark models without any need to postulate the existence of physical quarks. In the new approach, the quark patterns emerge as a consequence of combining the general S-matrix principles with the concept of order.…
Hydrogel core flexible matrix composite (H-FMC) actuators: theory and preliminary modelling
NASA Astrophysics Data System (ADS)
Dicker, M. P. M.; Weaver, P. M.; Rossiter, J. M.; Bond, I. P.
2014-09-01
The underlying theory of a new actuator concept based on hydrogel core flexible matrix composites (H-FMC) is presented. The key principle that underlines the H-FMC actuator operation is that the three-dimensional swelling of a hydrogel is partially constrained in order to improve the amount of useful work done. The partial constraint is applied to the hydrogel by a flexible matrix composite (FMC) that minimizes the hydrogel's volume expansion while swelling. This constraint serves to maximize the fixed charge density and resulting osmotic pressure, the driving force behind actuation. In addition, for certain FMC fibre orientations the Poisson's ratio of the anisotropic FMC laminate converts previously unused hydrogel swelling in the radial and circumferential directions into useful axial strains. The potential benefit of the H-FMC concept to hydrogel actuator performance is shown through comparison of force-stroke curves and evaluation of improvements in useful actuation work. The model used to achieve this couples chemical and electrical components, represented with the Nernst-Plank and Poisson equations, as well as a linear elastic mechanical material model, encompassing limited geometric nonlinearities. It is found that improvements in useful actuation work in the order of 1500% over bare hydrogel performance are achieved by the H-FMC concept. A parametric study is also undertaken to determine the effect of various FMC design parameters on actuator free strain and blocking stress. A comparison to other actuator concepts is also included.
The Moduli Space and M(Atrix) Theory of 9d N=1 Backgrounds of M/String Theory
Aharony, Ofer; Komargodski, Zohar; Patir, Assaf; /Weizmann Inst.
2007-03-21
We discuss the moduli space of nine dimensional N = 1 supersymmetric compactifications of M theory/string theory with reduced rank (rank 10 or rank 2), exhibiting how all the different theories (including M theory compactified on a Klein bottle and on a Moebius strip, the Dabholkar-Park background, CHL strings and asymmetric orbifolds of type II strings on a circle) fit together, and what are the weakly coupled descriptions in different regions of the moduli space. We argue that there are two disconnected components in the moduli space of theories with rank 2. We analyze in detail the limits of the M theory compactifications on a Klein bottle and on a Moebius strip which naively give type IIA string theory with an uncharged orientifold 8-plane carrying discrete RR flux. In order to consistently describe these limits we conjecture that this orientifold non-perturbatively splits into a D8-brane and an orientifold plane of charge (-1) which sits at infinite coupling. We construct the M(atrix) theory for M theory on a Klein bottle (and the theories related to it), which is given by a 2 + 1 dimensional gauge theory with a varying gauge coupling compactified on a cylinder with specific boundary conditions. We also clarify the construction of the M(atrix) theory for backgrounds of rank 18, including the heterotic string on a circle.
Aspects of renormalization in finite-density field theory
Fitzpatrick, A. Liam; Torroba, Gonzalo; Wang, Huajia
2015-05-26
We study the renormalization of the Fermi surface coupled to a massless boson near three spatial dimensions. For this, we set up a Wilsonian RG with independent decimation procedures for bosons and fermions, where the four-fermion interaction “Landau parameters” run already at tree level. Our explicit one-loop analysis resolves previously found obstacles in the renormalization of finite-density field theory, including logarithmic divergences in nonlocal interactions and the appearance of multilogarithms. The key aspects of the RG are the above tree-level running, and a UV-IR mixing between virtual bosons and fermions at the quantum level, which is responsible for the renormalization of the Fermi velocity. We apply this approach to the renormalization of 2 k F singularities, and to Fermi surface instabilities in a companion paper, showing how multilogarithms are properly renormalized. We end with some comments on the renormalization of finite-density field theory with the inclusion of Landau damping of the boson.
Analytic second derivatives from auxiliary density perturbation theory.
Delgado-Venegas, Rogelio Isaac; Mejía-Rodríguez, Daniel; Flores-Moreno, Roberto; Calaminici, Patrizia; Köster, Andreas M
2016-12-14
The working equations for the calculation of analytic second energy derivatives in the framework of auxiliary density functional theory (ADFT) are presented. The needed perturbations are calculated with auxiliary density perturbation theory (ADPT) which is extended to perturbation dependent basis and auxiliary functions sets. The obtained ADPT equation systems are solved with the Eirola-Nevanlinna algorithm. The newly developed analytic second ADFT energy derivative approach was implemented in deMon2k and validated with respect to the corresponding finite difference approach by calculating the harmonic frequencies of small molecules. Good agreement between these two methodologies is found. To analyze the scaling of the new analytic second ADFT energy derivatives with respect to the number of processors in parallel runs, the harmonic frequencies of the carbon fullerene C240 are calculated with varying numbers of processors. Fair scaling up to 720 processors was found. As showcase applications, symmetry unrestricted optimization and frequency analyses of icosahedral carbon fullerenes with up to 960 atoms are presented.
Direct Neutron Capture Calculations with Covariant Density Functional Theory Inputs
NASA Astrophysics Data System (ADS)
Zhang, Shi-Sheng; Peng, Jin-Peng; Smith, Michael S.; Arbanas, Goran; Kozub, Ray L.
2014-09-01
Predictions of direct neutron capture are of vital importance for simulations of nucleosynthesis in supernovae, merging neutron stars, and other astrophysical environments. We calculate the direct capture cross sections for E1 transitions using nuclear structure information from a covariant density functional theory as input for the FRESCO coupled-channels reaction code. We find good agreement of our predictions with experimental cross section data on the double closed-shell targets 16O, 48Ca, and 90Zr, and the exotic nucleus 36S. Extensions of the technique for unstable nuclei and for large-scale calculations will be discussed. Predictions of direct neutron capture are of vital importance for simulations of nucleosynthesis in supernovae, merging neutron stars, and other astrophysical environments. We calculate the direct capture cross sections for E1 transitions using nuclear structure information from a covariant density functional theory as input for the FRESCO coupled-channels reaction code. We find good agreement of our predictions with experimental cross section data on the double closed-shell targets 16O, 48Ca, and 90Zr, and the exotic nucleus 36S. Extensions of the technique for unstable nuclei and for large-scale calculations will be discussed. Supported by the U.S. Dept. of Energy, Office of Nuclear Physics.
Guidez, Emilie B; Gordon, Mark S
2015-03-12
The modeling of dispersion interactions in density functional theory (DFT) is commonly performed using an energy correction that involves empirically fitted parameters for all atom pairs of the system investigated. In this study, the first-principles-derived dispersion energy from the effective fragment potential (EFP) method is implemented for the density functional theory (DFT-D(EFP)) and Hartree-Fock (HF-D(EFP)) energies. Overall, DFT-D(EFP) performs similarly to the semiempirical DFT-D corrections for the test cases investigated in this work. HF-D(EFP) tends to underestimate binding energies and overestimate intermolecular equilibrium distances, relative to coupled cluster theory, most likely due to incomplete accounting for electron correlation. Overall, this first-principles dispersion correction yields results that are in good agreement with coupled-cluster calculations at a low computational cost.
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."
NASA Astrophysics Data System (ADS)
Ruggenthaler, Michael; Flick, Johannes; Pellegrini, Camilla; Appel, Heiko; Tokatly, Ilya V.; Rubio, Angel
2014-07-01
In this work, we give a comprehensive derivation of an exact and numerically feasible method to perform ab initio calculations of quantum particles interacting with a quantized electromagnetic field. We present a hierarchy of density-functional-type theories that describe the interaction of charged particles with photons and introduce the appropriate Kohn-Sham schemes. We show how the evolution of a system described by quantum electrodynamics in Coulomb gauge is uniquely determined by its initial state and two reduced quantities. These two fundamental observables, the polarization of the Dirac field and the vector potential of the photon field, can be calculated by solving two coupled, nonlinear evolution equations without the need to explicitly determine the (numerically infeasible) many-body wave function of the coupled quantum system. To find reliable approximations to the implicit functionals, we present the appropriate Kohn-Sham construction. In the nonrelativistic limit, this density-functional-type theory of quantum electrodynamics reduces to the density-functional reformulation of the Pauli-Fierz Hamiltonian, which is based on the current density of the electrons and the vector potential of the photon field. By making further approximations, e.g., restricting the allowed modes of the photon field, we derive further density-functional-type theories of coupled matter-photon systems for the corresponding approximate Hamiltonians. In the limit of only two sites and one mode we deduce the appropriate effective theory for the two-site Hubbard model coupled to one photonic mode. This model system is used to illustrate the basic ideas of a density-functional reformulation in great detail and we present the exact Kohn-Sham potentials for our coupled matter-photon model system.
Density hysteresis of heavy water confined in a nanoporous silica matrix
Zhang, Yang; Faraone, Antonio; Kamitakahara, William; Liu, Kao-Hsiang; Mou, Chung-Yuan; Leao, Juscelino B; Chang, Sung C; Chen, Sow-hsin H
2011-01-01
A neutron scattering technique was developed to measure the density of heavy water confined in a nanoporous silica matrix in a temperature-pressure range, from 300 to 130 K and from 1 to 2,900 bars, where bulk water will crystalize. We observed a prominent hysteresis phenomenon in the measured density profiles between warming and cooling scans above 1,000 bars. We inter- pret this hysteresis phenomenon as support (although not a proof) of the hypothetical existence of a first-order liquid liquid phase transition of water that would exist in the macroscopic system if crystallization could be avoided in the relevant phase region. Moreover, the density data we obtained for the confined heavy water under these conditions are valuable to large communities in biology and earth and planetary sciences interested in phenomena in which nanometer-sized water layers are involved.
Density hysteresis of heavy water confined in a nanoporous silica matrix
Zhang, Yang; Faraone, Antonio; Kamitakahara, William A.; Liu, Kao-Hsiang; Mou, Chung-Yuan; Leão, Juscelino B.; Chang, Sung; Chen, Sow-Hsin
2011-01-01
A neutron scattering technique was developed to measure the density of heavy water confined in a nanoporous silica matrix in a temperature-pressure range, from 300 to 130 K and from 1 to 2,900 bars, where bulk water will crystalize. We observed a prominent hysteresis phenomenon in the measured density profiles between warming and cooling scans above 1,000 bars. We interpret this hysteresis phenomenon as support (although not a proof) of the hypothetical existence of a first-order liquid–liquid phase transition of water that would exist in the macroscopic system if crystallization could be avoided in the relevant phase region. Moreover, the density data we obtained for the confined heavy water under these conditions are valuable to large communities in biology and earth and planetary sciences interested in phenomena in which nanometer-sized water layers are involved. PMID:21746898
Characterization of Phase Transition in Heisenberg Fluids from Density Functional Theory
NASA Astrophysics Data System (ADS)
Li, Liang-Sheng; Li, Li; Chen, Xiao-Song
2009-02-01
The phase transition of Heisenberg fluid has been investigated with the density functional theory in mean-field approximation (MF). The matrix of the second derivatives of the grand canonical potential Ω with respect to the particle density fluctuations and the magnetization fluctuations has been investigated and diagonalized. The smallest eigenvalue being 0 signalizes the phase instability and the related eigenvector characterizes this phase transition. We find a Curie line where the order parameter is pure magnetization and a spinodal where the order parameter is a mixture of particle density and magnetization. Along the spinodal, the character of phase instability changes continuously from predominant condensation to predominant ferromagnetic phase transition with the decrease of total density. The spinodal meets the Curie line at the critical endpoint with the reduced density ρ* = ρσ3 = 0.224 and the reduced temperature T* = kT/in = 1.87 (σ is the diameter of Heisenberg hard sphere and in is the coupling constant).
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.
A generalization of random matrix theory and its application to statistical physics
NASA Astrophysics Data System (ADS)
Wang, Duan; Zhang, Xin; Horvatic, Davor; Podobnik, Boris; Eugene Stanley, H.
2017-02-01
To study the statistical structure of crosscorrelations in empirical data, we generalize random matrix theory and propose a new method of cross-correlation analysis, known as autoregressive random matrix theory (ARRMT). ARRMT takes into account the influence of auto-correlations in the study of cross-correlations in multiple time series. We first analytically and numerically determine how auto-correlations affect the eigenvalue distribution of the correlation matrix. Then we introduce ARRMT with a detailed procedure of how to implement the method. Finally, we illustrate the method using two examples taken from inflation rates for air pressure data for 95 US cities.
A generalization of random matrix theory and its application to statistical physics.
Wang, Duan; Zhang, Xin; Horvatic, Davor; Podobnik, Boris; Eugene Stanley, H
2017-02-01
To study the statistical structure of crosscorrelations in empirical data, we generalize random matrix theory and propose a new method of cross-correlation analysis, known as autoregressive random matrix theory (ARRMT). ARRMT takes into account the influence of auto-correlations in the study of cross-correlations in multiple time series. We first analytically and numerically determine how auto-correlations affect the eigenvalue distribution of the correlation matrix. Then we introduce ARRMT with a detailed procedure of how to implement the method. Finally, we illustrate the method using two examples taken from inflation rates for air pressure data for 95 US cities.
Chan, Garnet Kin-Lic; Van Voorhis, Troy
2005-05-22
We describe the theory and implementation of two extensions to the density-matrix renormalization-group (DMRG) algorithm in quantum chemistry: (i) to work with an underlying nonorthogonal one-particle basis (using a biorthogonal formulation) and (ii) to use non-Hermitian and complex operators and complex wave functions, which occur naturally in biorthogonal formulations. Using these developments, we carry out ground-state calculations on ethene, butadiene, and hexatriene, in a polarized atomic-orbital basis. The description of correlation in these systems using a localized nonorthogonal basis is improved over molecular-orbital DMRG calculations, and comparable to or better than coupled-cluster calculations, although we encountered numerical problems associated with non-Hermiticity. We believe that the non-Hermitian DMRG algorithm may further become useful in conjunction with other non-Hermitian Hamiltonians, for example, similarity-transformed coupled-cluster Hamiltonians.
Extending the range of real time density matrix renormalization group simulations
NASA Astrophysics Data System (ADS)
Kennes, D. M.; Karrasch, C.
2016-03-01
We discuss a few simple modifications to time-dependent density matrix renormalization group (DMRG) algorithms which allow to access larger time scales. We specifically aim at beginners and present practical aspects of how to implement these modifications within any standard matrix product state (MPS) based formulation of the method. Most importantly, we show how to 'combine' the Schrödinger and Heisenberg time evolutions of arbitrary pure states | ψ > and operators A in the evaluation of ψ(t) = < ψ | A(t) | ψ > . This includes quantum quenches. The generalization to (non-)thermal mixed state dynamics ρ(t) =Tr [ ρA(t) ] induced by an initial density matrix ρ is straightforward. In the context of linear response (ground state or finite temperature T > 0) correlation functions, one can extend the simulation time by a factor of two by 'exploiting time translation invariance', which is efficiently implementable within MPS DMRG. We present a simple analytic argument for why a recently-introduced disentangler succeeds in reducing the effort of time-dependent simulations at T > 0. Finally, we advocate the python programming language as an elegant option for beginners to set up a DMRG code.
Controlled-surface-wettability-based fabrication of hydrogel substrates with matrix tethering density variations
NASA Astrophysics Data System (ADS)
Rahman, Md. Mahmudur; Lee, Donghee; Bhagirath, Divya; Zhao, Xiangshan; Band, Vimla; Ryu, Sangjin
2014-03-01
It is widely accepted that cells behave differently responding to the stiffness of extracellular matrix (ECM). Such observations were made by culturing cells on hydrogel substrates of tunable stiffness. However, it was recently proposed that cells actually sense how strongly they are tethered to ECM, not the local stiffness of ECM. To investigate the hypothesis, we develop constant-stiffness hydrogel substrates with varying matrix tethering density (the number of anchoring sites between the gel and the ECM protein molecules). We fabricate polyacrylamide gel of static stiffness and conjugate ECM proteins to the gel using a cross-linker. When treating the gel with the cross-linker, we control positioning of cross-linker solutions with different concentrations using superhydrophobic barriers on glass, functionalize the gel by pressing it to the aligned cross-linker solutions, and conjugate an ECM protein of constant concentration to the gel. We expect that the gel will be functionalized to different degrees depending on the concentration distribution of the cross-linker and thus the gel will have variations of matrix tethering density even with constant ECM protein concentration. We acknowledge support from Bioengineering for Human Health grant of UNL-UNMC.
NASA Astrophysics Data System (ADS)
Micha, David A.
This contribution deals with two approaches for localized phenomena in excited many-atom systems. The first approach develops a quantum quasi-classical treatment for the density operator, including all atoms. It is based on a partial Wigner representation and is illustrated with applications to photodissociation of NaI, and to light emission of excited Li interacting with a He cluster. This second application describes the direct dynamics with a time-dependent electronic density matrix, expanded in a basis set of atomic functions. It shows that such an approach can deal with electronically excited many-atom systems involving tens of quantum states and hundreds of classical variables. The second approach makes use of the reduced density operator description for a system in a medium. This allows for dissipative dynamics, which can be instantaneous or delayed. An application is presented for femtosecond photodesorption using a Markovian dissipation and construction of the density operator from density amplitudes, for CO/Cu(001). A second application of a reduced density operator has been made to vibrational relaxation of adsorbates, solving integrodifferential equations to compare delayed, instantaneous, and Markovian dissipation. It is concluded that delayed dissipation is needed at short times and that a Markovian treatment is suitable for the interpretation of cross-sectional measurements that involve long-term dynamics.
Cluster density functional theory for lattice models based on the theory of Möbius functions
NASA Astrophysics Data System (ADS)
Lafuente, Luis; Cuesta, José A.
2005-08-01
Rosenfeld's fundamental-measure theory for lattice models is given a rigorous formulation in terms of the theory of Möbius functions of partially ordered sets. The free-energy density functional is expressed as an expansion in a finite set of lattice clusters. This set is endowed with a partial order, so that the coefficients of the cluster expansion are connected to its Möbius function. Because of this, it is rigorously proven that a unique such expansion exists for any lattice model. The low-density analysis of the free-energy functional motivates a redefinition of the basic clusters (zero-dimensional cavities) which guarantees a correct zero-density limit of the pair and triplet direct correlation functions. This new definition extends Rosenfeld's theory to lattice models with any kind of short-range interaction (repulsive or attractive, hard or soft, one or multicomponent ...). Finally, a proof is given that these functionals have a consistent dimensional reduction, i.e. the functional for dimension d' can be obtained from that for dimension d (d' < d) if the latter is evaluated at a density profile confined to a d'-dimensional subset.
Spin Matrix theory: a quantum mechanical model of the AdS/CFT correspondence
NASA Astrophysics Data System (ADS)
Harmark, Troels; Orselli, Marta
2014-11-01
We introduce a new quantum mechanical theory called Spin Matrix theory (SMT). The theory is interacting with a single coupling constant g and is based on a Hilbert space of harmonic oscillators with a spin index taking values in a Lie (super)algebra representation as well as matrix indices for the adjoint representation of U( N). We show that SMT describes super-Yang-Mills theory (SYM) near zero-temperature critical points in the grand canonical phase diagram. Equivalently, SMT arises from non-relativistic limits of SYM. Even though SMT is a non-relativistic quantum mechanical theory it contains a variety of phases mimicking the AdS/CFT correspondence. Moreover, the g → ∞ limit of SMT can be mapped to the supersymmetric sector of string theory on AdS5 × S 5. We study SU(2) SMT in detail. At large N and low temperatures it is a theory of spin chains that for small g resembles planar gauge theory and for large g a non-relativistic string theory. When raising the temperature a partial deconfinement transition occurs due to finite- N effects. For sufficiently high temperatures the partially deconfined phase has a classical regime. We find a matrix model description of this regime at any coupling g. Setting g = 0 it is a theory of N 2 + 1 harmonic oscillators while for large g it becomes 2 N harmonic oscillators.
Vibrational spectroscopy and density functional theory study of 4-mercaptophenol
NASA Astrophysics Data System (ADS)
Li, Ran; Ji, Wei; Chen, Lei; Lv, Haiming; Cheng, Jianbo; Zhao, Bing
2014-03-01
In this paper, 4-mercaptophenol (4-MPH) was designed as a model molecule for theoretical and experimental studies of the molecule structure. Density functional theory (DFT) calculations have been performed to predict the IR and Raman spectra for the molecule. In addition, Fourier transform infrared (FTIR) and Raman spectra of the compound have been obtained experimentally. All FTIR and Raman bands of the compound obtained experimentally were assigned based on the modeling results obtained at the B3LYP/6-311 + G** level. Our calculated vibrational frequencies are in good agreement with the experimental vales. The molecular electrostatic potential surface calculation was performed and the result suggested that the 4-MPH has two hydrogen bond donors and three hydrogen bond acceptors. HOMO-LUMO gap was also obtained theoretically at B3LYP/6-311 + G** level.
Machine-learned approximations to Density Functional Theory Hamiltonians
NASA Astrophysics Data System (ADS)
Hegde, Ganesh; Bowen, R. Chris
2017-02-01
Large scale Density Functional Theory (DFT) based electronic structure calculations are highly time consuming and scale poorly with system size. While semi-empirical approximations to DFT result in a reduction in computational time versus ab initio DFT, creating such approximations involves significant manual intervention and is highly inefficient for high-throughput electronic structure screening calculations. In this letter, we propose the use of machine-learning for prediction of DFT Hamiltonians. Using suitable representations of atomic neighborhoods and Kernel Ridge Regression, we show that an accurate and transferable prediction of DFT Hamiltonians for a variety of material environments can be achieved. Electronic structure properties such as ballistic transmission and band structure computed using predicted Hamiltonians compare accurately with their DFT counterparts. The method is independent of the specifics of the DFT basis or material system used and can easily be automated and scaled for predicting Hamiltonians of any material system of interest.
The photochemistry of transition metal complexes using density functional theory.
Garino, Claudio; Salassa, Luca
2013-07-28
The use of density functional theory (DFT) and time-dependent DFT (TD-DFT) to study the photochemistry of metal complexes is becoming increasingly important among chemists. Computational methods provide unique information on the electronic nature of excited states and their atomic structure, integrating spectroscopy observations on transient species and excited-state dynamics. In this contribution, we present an overview on photochemically active transition metal complexes investigated by DFT. In particular, we discuss a representative range of systems studied up to now, which include CO- and NO-releasing inorganic and organometallic complexes, haem and haem-like complexes dissociating small diatomic molecules, photoactive anti-cancer Pt and Ru complexes, Ru polypyridyls and diphosphino Pt derivatives.
Machine-learned approximations to Density Functional Theory Hamiltonians.
Hegde, Ganesh; Bowen, R Chris
2017-02-15
Large scale Density Functional Theory (DFT) based electronic structure calculations are highly time consuming and scale poorly with system size. While semi-empirical approximations to DFT result in a reduction in computational time versus ab initio DFT, creating such approximations involves significant manual intervention and is highly inefficient for high-throughput electronic structure screening calculations. In this letter, we propose the use of machine-learning for prediction of DFT Hamiltonians. Using suitable representations of atomic neighborhoods and Kernel Ridge Regression, we show that an accurate and transferable prediction of DFT Hamiltonians for a variety of material environments can be achieved. Electronic structure properties such as ballistic transmission and band structure computed using predicted Hamiltonians compare accurately with their DFT counterparts. The method is independent of the specifics of the DFT basis or material system used and can easily be automated and scaled for predicting Hamiltonians of any material system of interest.
Self-consistent polarization density functional theory: Application to Argon
Maerzke, Katie A.; Murdachaew, Garold; Mundy, Christopher J.; Schenter, Gregory K.; Siepmann, J. I.
2009-03-12
We present a comprehensive set of results for argon, a case study in weak interactions, using the selfconsistent polarization density functional theory (SCP-DFT). With minimal parameterization, SCPDFT is found is give excellent results for the dimer interaction energy, the second virial coefficient, the liquid structure, and the lattice constant and cohesion energy of the face-centered cubic (fcc) crystal compared to both accurate theoretical and experimental benchmarks. Thus, SCP-DFT holds promise as a fast, efficient, and accurate method for performing ab initio dynamics that include additional polarization and dispersion interactions for large, complex systems involving solvation and bond breaking. This work was supported by the U.S. Department of Energy's (DOE) Office of Basic Energy Sciences, Chemical Sciences program. The Pacific Northwest National Laboratory is operated by Battelle for DOE.
Nitrotyrosine adsorption on defective graphene: A density functional theory study
NASA Astrophysics Data System (ADS)
Majidi, R.; Karami, A. R.
2015-06-01
We have applied density functional theory to study adsorption of nitrotyrosine on perfect and defective graphene sheets. The graphene sheets with Stone-Wales (SW) defect, pentagon-nonagon (5-9) single vacancy, and pentagon-octagon-pentagon (5-8-5) double vacancy were considered. The calculations of adsorption energy showed that nitrotyrosine presents a more strong interaction with defective graphene rather than with perfect graphene sheet. The order of interaction strength is: SW>5-9>5-8-5>perfect graphene. It is found that the electronic properties of perfect and defective graphene are sensitive to the presence of nitrotyrosine. Hence, graphene sheets can be considered as a good sensor for detection of nitrotyrosine molecule which is observed in connection with several human disorders, such as Parkinson's and Alzheimer's disease.
Density functional theory studies of HCOOH decomposition on Pd(111)
NASA Astrophysics Data System (ADS)
Scaranto, Jessica; Mavrikakis, Manos
2016-08-01
The investigation of formic acid (HCOOH) decomposition on transition metal surfaces is important to derive useful insights for vapor phase catalysis involving HCOOH and for the development of direct HCOOH fuel cells (DFAFC). Here we present the results obtained from periodic, self-consistent, density functional theory (DFT-GGA) calculations for the elementary steps involved in the gas-phase decomposition of HCOOH on Pd(111). Accordingly, we analyzed the minimum energy paths for HCOOH dehydrogenation to CO2 + H2 and dehydration to CO + H2O through the carboxyl (COOH) and formate (HCOO) intermediates. Our results suggest that HCOO formation is easier than COOH formation, but HCOO decomposition is more difficult than COOH decomposition, in particular in the presence of co-adsorbed O and OH species. Therefore, both paths may contribute to HCOOH decomposition. CO formation goes mainly through COOH decomposition.
Machine-learned approximations to Density Functional Theory Hamiltonians
Hegde, Ganesh; Bowen, R. Chris
2017-01-01
Large scale Density Functional Theory (DFT) based electronic structure calculations are highly time consuming and scale poorly with system size. While semi-empirical approximations to DFT result in a reduction in computational time versus ab initio DFT, creating such approximations involves significant manual intervention and is highly inefficient for high-throughput electronic structure screening calculations. In this letter, we propose the use of machine-learning for prediction of DFT Hamiltonians. Using suitable representations of atomic neighborhoods and Kernel Ridge Regression, we show that an accurate and transferable prediction of DFT Hamiltonians for a variety of material environments can be achieved. Electronic structure properties such as ballistic transmission and band structure computed using predicted Hamiltonians compare accurately with their DFT counterparts. The method is independent of the specifics of the DFT basis or material system used and can easily be automated and scaled for predicting Hamiltonians of any material system of interest. PMID:28198471
Reproducibility in density functional theory calculations of solids.
Lejaeghere, Kurt; Bihlmayer, Gustav; Björkman, Torbjörn; Blaha, Peter; Blügel, Stefan; Blum, Volker; Caliste, Damien; Castelli, Ivano E; Clark, Stewart J; Dal Corso, Andrea; de Gironcoli, Stefano; Deutsch, Thierry; Dewhurst, John Kay; Di Marco, Igor; Draxl, Claudia; Dułak, Marcin; Eriksson, Olle; Flores-Livas, José A; Garrity, Kevin F; Genovese, Luigi; Giannozzi, Paolo; Giantomassi, Matteo; Goedecker, Stefan; Gonze, Xavier; Grånäs, Oscar; Gross, E K U; Gulans, Andris; Gygi, François; Hamann, D R; Hasnip, Phil J; Holzwarth, N A W; Iuşan, Diana; Jochym, Dominik B; Jollet, François; Jones, Daniel; Kresse, Georg; Koepernik, Klaus; Küçükbenli, Emine; Kvashnin, Yaroslav O; Locht, Inka L M; Lubeck, Sven; Marsman, Martijn; Marzari, Nicola; Nitzsche, Ulrike; Nordström, Lars; Ozaki, Taisuke; Paulatto, Lorenzo; Pickard, Chris J; Poelmans, Ward; Probert, Matt I J; Refson, Keith; Richter, Manuel; Rignanese, Gian-Marco; Saha, Santanu; Scheffler, Matthias; Schlipf, Martin; Schwarz, Karlheinz; Sharma, Sangeeta; Tavazza, Francesca; Thunström, Patrik; Tkatchenko, Alexandre; Torrent, Marc; Vanderbilt, David; van Setten, Michiel J; Van Speybroeck, Veronique; Wills, John M; Yates, Jonathan R; Zhang, Guo-Xu; Cottenier, Stefaan
2016-03-25
The widespread popularity of density functional theory has given rise to an extensive range of dedicated codes for predicting molecular and crystalline properties. However, each code implements the formalism in a different way, raising questions about the reproducibility of such predictions. We report the results of a community-wide effort that compared 15 solid-state codes, using 40 different potentials or basis set types, to assess the quality of the Perdew-Burke-Ernzerhof equations of state for 71 elemental crystals. We conclude that predictions from recent codes and pseudopotentials agree very well, with pairwise differences that are comparable to those between different high-precision experiments. Older methods, however, have less precise agreement. Our benchmark provides a framework for users and developers to document the precision of new applications and methodological improvements.
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.
A numerical efficient way to minimize classical density functional theory.
Edelmann, Markus; Roth, Roland
2016-02-21
The minimization of the functional of the grand potential within the framework of classical density functional theory in three spatial dimensions can be numerically very demanding. The Picard iteration, that is often employed, is very simple and robust but can be rather slow. While a number of different algorithms for optimization problems have been suggested, there is still great need for additional strategies. Here, we present an approach based on the limited memory Broyden algorithm that is efficient and relatively simple to implement. We demonstrate the performance of this algorithm with the minimization of an inhomogeneous bulk structure of a fluid with competing interactions. For the problems we studied, we find that the presented algorithm improves performance by roughly a factor of three.
NASA Technical Reports Server (NTRS)
Arenburg, R. T.; Reddy, J. N.
1991-01-01
The micromechanical constitutive theory is used to examine the nonlinear behavior of continuous-fiber-reinforced metal-matrix composite structures. Effective lamina constitutive relations based on the Abouli micromechanics theory are presented. The inelastic matrix behavior is modeled by the unified viscoplasticity theory of Bodner and Partom. The laminate constitutive relations are incorporated into a first-order deformation plate theory. The resulting boundary value problem is solved by utilizing the finite element method. Attention is also given to computational aspects of the numerical solution, including the temporal integration of the inelastic strains and the spatial integration of bending moments. Numerical results the nonlinear response of metal matrix composites subjected to extensional and bending loads are presented.
McMahon, Suzanne; Amirjalayer, Saeed; Buma, Wybren J; Halpin, Yvonne; Long, Conor; Rooney, A Denise; Woutersen, Sander; Pryce, Mary T
2015-09-21
The photophysics and photochemistry of [(CO)5MC(OMe)Me] (M = Cr or W) were investigated using picosecond time-resolved infrared spectroscopy (M = Cr or W), low-temperature matrix isolation techniques (M = Cr), and time-dependent density functional calculations (M = Cr or W). These studies provide unambiguous evidence for the photochemical formation of a long-lived, 18-electron metallaketene species capable of acting as a synthetically useful intermediate. For the Cr complex, an intermediate metallacyclopropanone singlet excited state was detected on the reaction path to the metallaketene species. This metallacyclopropanone excited state species has a lifetime of less than 100 ps and a characteristic bridging carbonyl band at 1770 cm(-1). The tungsten ketene species was also detected but in contrast to the chromium system, this forms directly from a low-lying triplet excited state. The electrochemical release of CO showed a greater efficiency for the chromium complex when compared to the tungsten.
Density Induced Phase Transitions in the Schwinger Model: A Study with Matrix Product States
NASA Astrophysics Data System (ADS)
Bañuls, Mari Carmen; Cichy, Krzysztof; Cirac, J. Ignacio; Jansen, Karl; Kühn, Stefan
2017-02-01
We numerically study the zero temperature phase structure of the multiflavor Schwinger model at nonzero chemical potential. Using matrix product states, we reproduce analytical results for the phase structure for two flavors in the massless case and extend the computation to the massive case, where no analytical predictions are available. Our calculations allow us to locate phase transitions in the mass-chemical potential plane with great precision and provide a concrete example of tensor networks overcoming the sign problem in a lattice gauge theory calculation.
NASA Astrophysics Data System (ADS)
Mendoza-Arenas, J. J.; Franco, R.; Silva-Valencia, J.
2010-01-01
We analyze the one-dimensional Kondo necklace model, at zero temperature, with an anisotropy parameter η in the interaction of the conduction chain, by means of the density matrix renormalization group. We calculate the energy gap and estimate the quantum critical points that separate a Kondo singlet state from an antiferromagnetic state, assuming a Kosterlitz-Thouless tendency. We also observe the correlation functions and the structure factors that support our critical points. The resulting phase diagram is presented and compared to that reported previously using Lanczos calculations. It is shown that the quantum critical points vary very slowly with η , but when η approaches zero, they drop abruptly.
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.
Analysis of NMR self-diffusion measurements by a density matrix calculation
NASA Astrophysics Data System (ADS)
Stepišnik, J.
1981-04-01
The density matrix formalism with the Magnus expansion of the time evolution operator is used to study the nmr response in a pulsed magnetic field gradient (mfg) spin-echo experiment. The results show that the spin-echo cannot only measure the self-diffusion coefficient but can determine the spectrum of the single-particle velocity autocorrelation function as well. The proper combination of rf and mfg pulse sequences are proposed for measuring self-diffusion in spin systems with strong dipolar coupling where the classical method fails.
Highly linear high-density vector quantiser and vector-matrix multiplier
NASA Astrophysics Data System (ADS)
Pedroni, V. A.
1994-06-01
Simplicity is a key factor in the development of high-density systems. The authors discuss a balanced, four-quadrant, fully-analogue vector-matrix multiplier (VMM) and a vector quantiser (VQ) which require very small silicon area for their implementations, while presenting high linearity, a totally flexible input dynamic range, a symmetric power consumption behaviour, and are inherently suitable for parallel operation. The circuits require only four transistors per synapse in the VMM and two in the VQ, plus two (small) refresh transistors.
Theory of melting at high pressures: Amending density functional theory with quantum Monte Carlo
Shulenburger, L.; Desjarlais, M. P.; Mattsson, T. R.
2014-10-01
We present an improved first-principles description of melting under pressure based on thermodynamic integration comparing Density Functional Theory (DFT) and quantum Monte Carlo (QMC) treatments of the system. The method is applied to address the longstanding discrepancy between density functional theory (DFT) calculations and diamond anvil cell (DAC) experiments on the melting curve of xenon, a noble gas solid where van der Waals binding is challenging for traditional DFT methods. The calculations show excellent agreement with data below 20 GPa and that the high-pressure melt curve is well described by a Lindemann behavior up to at least 80 GPa, amore » finding in stark contrast to DAC data.« less
Density Functional Theory Study on Interaction between Catechin and Thymine
NASA Astrophysics Data System (ADS)
Cai, Wan-fei; Zheng, Yan; Li, Lai-cai; Tian, An-min
2012-12-01
The interacting patterns and mechanism of the catechin and thymine have been investigated with the density functional theory Becke's three-parameter nonlocal exchange functional and the Lee, Yang, and Parr nonlocal correlation functional (B3LYP) method by 6-31+G* basis set. Thirteen stable structures for the catechin-thymine complexes have been found which form two hydrogen bonds at least. The vibrational frequencies are also studied at the same level to analyze these complexes. The results indicated that catechin interacted with thymine by three different hydrogen bonds as N—H···O, C—H···O, O—H···O and the complexes are mainly stabilized by the hydrogen bonding interactions. Theories of atoms in molecules and natural bond orbital have been adopted to investigate the hydrogen bonds involved in all systems. The interaction energies of all complexes have been corrected for basis set superposition error, which are from -18.15 kJ/mol to -32.99 kJ/mol. The results showed that the hydrogen bonding contribute to the interaction energies dominantly. The corresponding bonds stretching motions in all complexes are red-shifted relative to that of the monomer, which is in agreement with experimental results.
Metallophilic interactions from dispersion-corrected density-functional theory
Otero-de-la-Roza, Alberto Mallory, Joel D.; Johnson, Erin R.
2014-05-14
In this article, we present the first comprehensive study of metallophilic (aurophilic) interactions using dispersion-corrected density-functional theory. Dispersion interactions (an essential component of metallophilicity) are treated using the exchange-hole dipole moment (XDM) model. By comparing against coupled-cluster benchmark calculations on simple dimers, we show that LC-ωPBE-XDM is a viable functional to study interactions between closed-shell transition metals and that it performs uniformly better than second-order Møller-Plesset theory, the basic computational technique used in previous works. We apply LC-ωPBE-XDM to address several open questions regarding metallophilicity, such as the interplay between dispersion and relativistic effects, the interaction strength along group 11, the additivity of homo- and hetero-metallophilic effects, the stability of [E(AuPH{sub 3}){sub 4}]{sup +} cations (E = N, P, As, Sb), and the role of metallophilic effects in crystal packing. We find that relativistic effects explain the prevalence of aurophilicity not by stabilizing metal-metal contacts, but by preventing gold from forming ionic structures involving bridge anions (which are otherwise common for Ag and Cu) as a result of the increased electron affinity of the metal. Dispersion effects are less important than previously assumed and their stabilization contribution is relatively independent of the metal.
Particle-vibration coupling within covariant density functional theory
Litvinova, E.; Ring, P.; Tselyaev, V.
2007-06-15
Covariant density functional theory, which has so far been applied only within the framework of static and time-dependent mean-field theory, is extended to include particle-vibration coupling (PVC) in a consistent way. Starting from a conventional energy functional, we calculate the low-lying collective vibrations in the relativistic random phase approximation (RRPA) and construct an energy-dependent self-energy for the Dyson equation. The resulting Bethe-Salpeter equation in the particle-hole (p-h) channel is solved in the time blocking approximation (TBA). No additional parameters are used, and double counting is avoided by a proper subtraction method. The same energy functional, i.e., the same set of coupling constants, generates the Dirac-Hartree single-particle spectrum, the static part of the residual p-h interaction, and the particle-phonon coupling vertices. Therefore, a fully consistent description of nuclear excited states is developed. This method is applied for an investigation of damping phenomena in the spherical nuclei with closed shells {sup 208}Pb and {sup 132}Sn. Since the phonon coupling terms enrich the RRPA spectrum with a multitude of p-hxphonon components, a noticeable fragmentation of the giant resonances is found, which is in full agreement with experimental data and with results of the semiphenomenological nonrelativistic approach.
Molecular acidity: A quantitative conceptual density functional theory description.
Liu, Shubin; Schauer, Cynthia K; Pedersen, Lee G
2009-10-28
Accurate predictions of molecular acidity using ab initio and density functional approaches are still a daunting task. Using electronic and reactivity properties, one can quantitatively estimate pKa values of acids. In a recent paper [S. B. Liu and L. G. Pedersen, J. Phys. Chem. A 113, 3648 (2009)], we employed the molecular electrostatic potential (MEP) on the nucleus and the sum of valence natural atomic orbital (NAO) energies for the purpose. In this work, we reformulate these relationships on the basis of conceptual density functional theory and compare the results with those from the thermodynamic cycle method. We show that MEP and NAO properties of the dissociating proton of an acid should satisfy the same relationships with experimental pKa data. We employ 27 main groups and first to third row transition metal-water complexes as illustrative examples to numerically verify the validity of these strong linear correlations. Results also show that the accuracy of our approach and that of the conventional method through the thermodynamic cycle are statistically similar.
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.
Nuclear charge radii: density functional theory meets Bayesian neural networks
NASA Astrophysics Data System (ADS)
Utama, R.; Chen, Wei-Chia; Piekarewicz, J.
2016-11-01
The distribution of electric charge in atomic nuclei is fundamental to our understanding of the complex nuclear dynamics and a quintessential observable to validate nuclear structure models. The aim of this study is to explore a novel approach that combines sophisticated models of nuclear structure with Bayesian neural networks (BNN) to generate predictions for the charge radii of thousands of nuclei throughout the nuclear chart. A class of relativistic energy density functionals is used to provide robust predictions for nuclear charge radii. In turn, these predictions are refined through Bayesian learning for a neural network that is trained using residuals between theoretical predictions and the experimental data. Although predictions obtained with density functional theory provide a fairly good description of experiment, our results show significant improvement (better than 40%) after BNN refinement. Moreover, these improved results for nuclear charge radii are supplemented with theoretical error bars. We have successfully demonstrated the ability of the BNN approach to significantly increase the accuracy of nuclear models in the predictions of nuclear charge radii. However, as many before us, we failed to uncover the underlying physics behind the intriguing behavior of charge radii along the calcium isotopic chain.
Nuclear structure and dynamics with density functional theory
NASA Astrophysics Data System (ADS)
Stetcu, Ionel
2015-10-01
Even in the absence of ab initio methods capable of tackling heavy nuclei without restrictions, one can obtain an ab initio description of ground-state properties by means of the density functional theory (DFT), and its extension to superfluid systems in its local variant, the superfluid local density approximation (SLDA). Information about the properties of excited states can be obtained in the same framework by using an extension to the time-dependent (TD) phenomena. Unlike other approaches in which the nuclear structure information is used as a separate input into reaction models, the TD approach treats on the same footing the nuclear structure and dynamics, and is well suited to provide more reliable description for a large number of processes involving heavy nuclei, from the nuclear response to electroweak probes, to nuclear reactions, such as neutron-induced reactions, or nuclear fusion and fission. Such processes, sometimes part of integrated nuclear systems, have important applications in astrophysics, energy production, global security, etc. In this talk, I will present the simulation of a simple reaction, that is the Coulomb excitation of a 238U nucleus, and discuss the application of the TD-DFT formalism to the description of induced fission. I gratefully acknowledge partial support of the U.S. Department of Energy through an Early Career Award of the LANL/LDRD Program.
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.
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.
Density-matrix based determination of low-energy model Hamiltonians from ab initio wavefunctions.
Changlani, Hitesh J; Zheng, Huihuo; Wagner, Lucas K
2015-09-14
We propose a way of obtaining effective low energy Hubbard-like model Hamiltonians from ab initio quantum Monte Carlo calculations for molecular and extended systems. The Hamiltonian parameters are fit to best match the ab initio two-body density matrices and energies of the ground and excited states, and thus we refer to the method as ab initio density matrix based downfolding. For benzene (a finite system), we find good agreement with experimentally available energy gaps without using any experimental inputs. For graphene, a two dimensional solid (extended system) with periodic boundary conditions, we find the effective on-site Hubbard U(∗)/t to be 1.3 ± 0.2, comparable to a recent estimate based on the constrained random phase approximation. For molecules, such parameterizations enable calculation of excited states that are usually not accessible within ground state approaches. For solids, the effective Hamiltonian enables large-scale calculations using techniques designed for lattice models.
An investigation of theories of failure for ceramic matrix composites
NASA Technical Reports Server (NTRS)
Hemann, John H.
1995-01-01
This final report is comprised of the abstract of a masters thesis research grant. The abstract of the thesis, 'An Investigation of Acoustic Emission Techniques for the Discrimination of Damage Mechanisms in Ceramic Matrix Composites', is as follows: In order to further advance the understanding of the mechanical behavior of ceramic matrix composites (CMS's), acoustic emission (AE) techniques were implemented to monitor and identify damage mechanisms in CMC's under tensile loading. In addition to real-time AE monitoring techniques, a data acquisition system was developed and implemented in order to capture AE waveforms resulting from stress-induced damage. Waveforms were inspected for multiple events, separated in distinct events, and then analyzed to determine waveform characteristics in the time and frequency domains. Waveform characteristics included peak amplitude, event duration, MARSE, energy, and dominant and centroidal frequency. In addition to conventional methods for determining a damage discrimination criteria, a study of the distribution and correlation of the waveform characteristics criteria and a study of the distribution and correlation of the waveform characteristics were performed to aid in the determination of a damage discrimination criteria. The damage discrimination criteria was tested for 'uniqueness', i.e., the effectiveness of the criteria to identify and monitor damage independent of the stress-strain relationship. Insitu radiography was used to substantiate the damage accumulation. A simulation test was also performed over the loading history to study the changes in the waveform characteristics of the system response from a constant excitation. This thesis demonstrates the use of waveform analysis to study the AE activity resulting from stress-induced damage in CMC's in conjunction with other nondestructive evaluation techniques to investigate the mechanical behavior of CMC's.
Derivation of dynamical density functional theory using the projection operator technique.
Español, Pep; Löwen, Hartmut
2009-12-28
Density functional theory is a particular case of a general theory of conjugate variables that serves as the basis of the projection operator technique. By using this technique we derive a general dynamical version of density functional theory which involves a generalized diffusion tensor. The diffusion tensor is given by a Green-Kubo expression. For Brownian dynamics of dilute colloidal suspensions, the standard dynamical density functional theory is recovered.
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
Low excitations of 16O using generalized density matrix random phase approximation GDRPA
NASA Astrophysics Data System (ADS)
Taqi, Ali H.; Radhi, R. A.; Hussein, Adil M.
2014-07-01
The random phase approximation (RPA) equations based on the generalized density matrix (GDM), the so-called GDRPA are reformulated in a more compact matrix form, which renders the method especially suitable for realistic nuclear structure calculations. The GDRPA Hamiltonian is expressed in terms of the one-body particle-particle (pp) and hole-hole (hh) density matrices, and the nuclear force contributes not only in the particle-hole (ph) channel, as in normal ph-RPA, but also in the pp and hh channels. The Hamiltonian is diagonalized iteratively starting from initial guess values and the iterating process is carried out until self-consistency is achieved. The calculation in the model space 1p, 1d and 2s using Warburton and Brown interaction WBP is performed for 16O. The GDRPA in the ph shell model calculations is tested, by comparing the energy eigenvalues and the electron scattering form factors with the results of the normal RPA and with the available experimental data.
Leptogenesis with heavy neutrino flavours: from density matrix to Boltzmann equations
Blanchet, Steve; Bari, Pasquale Di; Jones, David A.; Marzola, Luca E-mail: pdb1d08@soton.ac.uk E-mail: daj1g08@soton.ac.uk
2013-01-01
Leptogenesis with heavy neutrino flavours is discussed within a density matrix formalism. We write the density matrix equation, describing the generation of the matter-antimatter asymmetry, for an arbitrary choice of the right-handed (RH) neutrino masses. For hierarchical RH neutrino masses lying in the fully flavoured regimes, this reduces to multiple-stage Boltzmann equations. In this case we recover and extend results previously derived within a quantum state collapse description. We confirm the generic existence of phantom terms. However, taking into account the effect of gauge interactions, we show that they are washed out at the production with a wash-out rate that is halved compared to that one acting on the total asymmetry. In the N{sub 1}-dominated scenario they cancel without contributing to the final baryon asymmetry. In other scenarios they do not in general and they have to be taken into account. We also confirm that there is a (orthogonal) component in the asymmetry produced by the heavier RH neutrinos which completely escapes the washout from the lighter RH neutrinos and show that phantom terms additionally contribute to it. The other (parallel) component is washed out with the usual exponential factor, even for weak washout. Finally, as an illustration, we study the two RH neutrino model in the light of the above findings, showing that phantom terms can contribute to the final asymmetry also in this case.
Leptogenesis with heavy neutrino flavours: from density matrix to Boltzmann equations
NASA Astrophysics Data System (ADS)
Blanchet, Steve; Di Bari, Pasquale; Jones, David A.; Marzola, Luca
2013-01-01
Leptogenesis with heavy neutrino flavours is discussed within a density matrix formalism. We write the density matrix equation, describing the generation of the matter-antimatter asymmetry, for an arbitrary choice of the right-handed (RH) neutrino masses. For hierarchical RH neutrino masses lying in the fully flavoured regimes, this reduces to multiple-stage Boltzmann equations. In this case we recover and extend results previously derived within a quantum state collapse description. We confirm the generic existence of phantom terms. However, taking into account the effect of gauge interactions, we show that they are washed out at the production with a wash-out rate that is halved compared to that one acting on the total asymmetry. In the N1-dominated scenario they cancel without contributing to the final baryon asymmetry. In other scenarios they do not in general and they have to be taken into account. We also confirm that there is a (orthogonal) component in the asymmetry produced by the heavier RH neutrinos which completely escapes the washout from the lighter RH neutrinos and show that phantom terms additionally contribute to it. The other (parallel) component is washed out with the usual exponential factor, even for weak washout. Finally, as an illustration, we study the two RH neutrino model in the light of the above findings, showing that phantom terms can contribute to the final asymmetry also in this case.
The reduced density matrix method and the role of three-index representability conditions
NASA Astrophysics Data System (ADS)
Braams, Bastiaan J.; Zhao, Zhengji; Fukuda, Mituhiro; Overton, Michael L.; Percus, Jerome K.
2004-03-01
The variational approach for electronic structure based on the two-body reduced density matrix is studied, incorporating two representability conditions beyond the previously used P, Q and G conditions. The additional conditions (called T1 and T2 here) are implicit in work of R. M. Erdahl and extend the well-known three-index diagonal conditions also known as the Weinhold-Wilson inequalities. Calculations of the ground state energy and the dipole moment are reported for 47 different systems, in each case using an STO-6G basis set and comparing with Hartree-Fock, SDCI, BD(T), CCSD(T) and full CI calculations [2]. It is found that the use of the T1 and T2 conditions gives a significant improvement over just the P, Q and G conditions, and provides in all cases that we have studied more accurate results than the other mentioned approximations. [1] R. M. Erdahl, Int. J. Quantum Chem. 13, 697--718 (1978). [2] Zhengji Zhao, Bastiaan J. Braams, Mituhiro Fukuda, Michael L. Overton and Jerome K. Percus: "The reduced density matrix method and the role of three-index representability conditions". Accepted for publication in Journal of Chemical Physics.
Quantum Monte Carlo with density matrix: potential energy curve derived properties.
Bonfim, Víctor S; Borges, Nádia M; Martins, João B L; Gargano, Ricardo; Politi, José Roberto Dos S
2017-04-01
In this work, we used diffusion quantum Monte Carlo with density matrix (d-DMC) and variational quantum Monte Carlo (d-VMC) to determine the potential energy curve (PEC) and obtain the spectroscopic constants of H2 molecule in the ground state, in order to evaluate the capability of these methods to provide an accurate PEC description. These quantum Monte Carlo methods build with density matrix are new approaches to conventional quantum Monte Carlo methods based on wave function formed by product of α and β determinants. To investigate the robustness of d-DMC, we performed calculations with two different basis sets and analyzed the influence of the size of these sets on results. To the best of our knowledge, this is the first study that shows the dissociation energy and rotational constant obtained from d-QMC. We found that the quality of PEC described by the d-DMC is essentially coincident with the most accurate results available in the literature, regardless of the complexity of basis set employed.
Influence matrix program for aerodynamic lifting surface theory. [in subsonic flows
NASA Technical Reports Server (NTRS)
Medan, R. T.; Ray, K. S.
1973-01-01
A users manual is described for a USA FORTRAN 4 computer program which computes an aerodynamic influence matrix and is one of several computer programs used to analyze lifting, thin wings in steady, subsonic flow according to a kernel function method lifting surface theory. The most significant features of the program are that it can treat unsymmetrical wings, control points can be placed on the leading and/or trailing edges, and a stable, efficient algorithm is used to compute the influence matrix.
Lu, Zhang-Hui; Jiang, Ling; Xu, Qiang
2009-07-21
Laser-ablated tantalum and niobium atoms react with CO and N(2) mixtures in excess neon to produce carbonyl metal dinitrogen complexes, NNMCO (M = Ta, Nb), (NN)(2)TaCO, and NNTa(CO)(2), as well as metal carbonyls and dinitrogen complexes. These carbonylmetal dinitrogen complexes are characterized using infrared spectroscopy on the basis of the results of the isotopic substitution and mixed isotopic splitting patterns. Density functional theory calculations have been performed on these novel species. The good agreement between the experimental and calculated vibrational frequencies, relative absorption intensities, and isotopic shifts supports the identification of these species from the matrix infrared spectra. Natural bond orbital analysis and plausible reaction mechanisms for the formation of the products are discussed.
An efficient state-specific scheme of time-dependent density functional theory
NASA Astrophysics Data System (ADS)
Chiba, Mahito; Tsuneda, Takao; Hirao, Kimihiko
2006-03-01
A state-specific scheme for time-dependent density functional theory (SS-TDDFT) based on the Davidson algorithm is presented. SS-TDDFT is a method devised for speeding up TDDFT calculations by screening transitions that contribute to a specific excitation. By applying this method to calculations of the low-lying excitation energies of test molecules (N 2, CO, H 2CO, C 2H 4 and C 6H 6), water clusters and polyenes, we found that SS-TDDFT accurately reproduced the excitation energies of standard TDDFT while drastically reducing the rank of the TDDFT response matrix without loss of accuracy. We have thus formulated TDDFT that works more efficiently and economically for memory storage.
Shamloo, Amir; Mohammadaliha, Negar; Heilshorn, Sarah C; Bauer, Amy L
2016-04-01
A thorough understanding of determining factors in angiogenesis is a necessary step to control the development of new blood vessels. Extracellular matrix density is known to have a significant influence on cellular behaviors and consequently can regulate vessel formation. The utilization of experimental platforms in combination with numerical models can be a powerful method to explore the mechanisms of new capillary sprout formation. In this study, using an integrative method, the interplay between the matrix density and angiogenesis was investigated. Owing the fact that the extracellular matrix density is a global parameter that can affect other parameters such as pore size, stiffness, cell-matrix adhesion and cross-linking, deeper understanding of the most important biomechanical or biochemical properties of the ECM causing changes in sprout morphogenesis is crucial. Here, we implemented both computational and experimental methods to analyze the mechanisms responsible for the influence of ECM density on the sprout formation that is difficult to be investigated comprehensively using each of these single methods. For this purpose, we first utilized an innovative approach to quantify the correspondence of the simulated collagen fibril density to the collagen density in the experimental part. Comparing the results of the experimental study and computational model led to some considerable achievements. First, we verified the results of the computational model using the experimental results. Then, we reported parameters such as the ratio of proliferating cells to migrating cells that was difficult to obtain from experimental study. Finally, this integrative system led to gain an understanding of the possible mechanisms responsible for the effect of ECM density on angiogenesis. The results showed that stable and long sprouts were observed at an intermediate collagen matrix density of 1.2 and 1.9 mg/ml due to a balance between the number of migrating and proliferating
Understanding density functional theory (DFT) and completing it in practice
Bagayoko, Diola
2014-12-15
We review some salient points in the derivation of density functional theory (DFT) and of the local density approximation (LDA) of it. We then articulate an understanding of DFT and LDA that seems to be ignored in the literature. We note the well-established failures of many DFT and LDA calculations to reproduce the measured energy gaps of finite systems and band gaps of semiconductors and insulators. We then illustrate significant differences between the results from self consistent calculations using single trial basis sets and those from computations following the Bagayoko, Zhao, and Williams (BZW) method, as enhanced by Ekuma and Franklin (BZW-EF). Unlike the former, the latter calculations verifiably attain the absolute minima of the occupied energies, as required by DFT. These minima are one of the reasons for the agreement between their results and corresponding, experimental ones for the band gap and a host of other properties. Further, we note predictions of DFT BZW-EF calculations that have been confirmed by experiment. Our subsequent description of the BZW-EF method ends with the application of the Rayleigh theorem in the selection, among the several calculations the method requires, of the one whose results have a full, physics content ascribed to DFT. This application of the Rayleigh theorem adds to or completes DFT, in practice, to preserve the physical content of unoccupied, low energy levels. Discussions, including implications of the method, and a short conclusion follow the description of the method. The successive augmentation of the basis set in the BZW-EF method, needed for the application of the Rayleigh theorem, is also necessary in the search for the absolute minima of the occupied energies, in practice.
Random matrix theory for mixed regular-chaotic dynamics in the super-extensive regime
El-Hady, A. Abd; Abul-Magd, A. Y.
2011-10-27
We apply Tsallis's q-indexed nonextensive entropy to formulate a random matrix theory (RMT), which may be suitable for systems with mixed regular-chaotic dynamics. We consider the super-extensive regime of q<1. We obtain analytical expressions for the level-spacing distributions, which are strictly valid for 2 X2 random-matrix ensembles, as usually done in the standard RMT. We compare the results with spacing distributions, numerically calculated for random matrix ensembles describing a harmonic oscillator perturbed by Gaussian orthogonal and unitary ensembles.
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
NASA Astrophysics Data System (ADS)
Nakatani, Naoki; Guo, Sheng
2017-03-01
This paper describes an interface between the density matrix renormalization group (DMRG) method and the complete active-space self-consistent field (CASSCF) method and its analytical gradient, as well as an extension to the second-order perturbation theory (CASPT2) method. This interfacing allows large active-space multi-reference computations to be easily performed. The interface and its extension are both implemented in terms of reduced density matrices (RDMs) which can be efficiently computed via the DMRG sweep algorithm. We also present benchmark results showing that, in practice, the DMRG-CASSCF calculations scale with active-space size in a polynomial manner in the case of quasi-1D systems. Geometry optimization of a binuclear iron-sulfur cluster using the DMRG-CASSCF analytical gradient is demonstrated, indicating that the inclusion of the valence p-orbitals of sulfur and double-shell d-orbitals of iron lead to non-negligible changes in the geometry compared to the results of small active-space calculations. With the exception of the selection of M values, many computational settings in these practical DMRG calculations have been tuned and black-boxed in our interface, and so the resulting DMRG-CASSCF and DMRG-CASPT2 calculations are now available to novice users as a common tool to compute strongly correlated electronic wavefunctions.
NASA Astrophysics Data System (ADS)
Jacobs, Verne; Kutana, Alex
The frequency-dependent transition rates for single-photon and multi-photon processes in quantized many-electron systems are evaluated using a reduced-density-matrix approach. We provide a fundamental quantum-mechanical foundation for systematic spectral simulations. A perturbation expansion of the frequency-domain Liouville-space self-energy operator is introduced for detailed evaluations of the spectral-line shapes. In the diagonal-resolvent (isolated-line) and short-memory-time (Markov) approximations, the lowest-order contributions to the spectral-line widths and shifts associated with environmental electron-photon and electron-phonon interactions are systematically evaluated. Our description is directly applicable to electromagnetic processes in a wide variety of many-electron systems, without premature approximations. In particular, our approach can be applied to investigate quantum optical phenomena involving electrons in both bulk and nanoscale semiconductor materials entirely from first principles, using a single-electron basis set obtained from density functional theory as a starting point for a many-electron description. Work supported by the Office of Naval Research through the Basic Research Program at The Naval Research Laboratory. A portion of this work was performed under the ASEE post doc program at NRL.
Random matrix theory for closed quantum dots with weak spin-orbit coupling.
Held, K; Eisenberg, E; Altshuler, B L
2003-03-14
To lowest order in the coupling strength, the spin-orbit coupling in quantum dots results in a spin-dependent Aharonov-Bohm flux. This flux decouples the spin-up and spin-down random matrix theory ensembles of the quantum dot. We employ this ensemble and find significant changes in the distribution of the Coulomb blockade peak height, in particular, a decrease of the width of the distribution. The puzzling disagreement between standard random matrix theory and the experimental distributions by Patel et al. [Phys. Rev. Lett. 81, 5900 (1998)
Cohen, D; Kottos, T
2001-03-01
We study a classically chaotic system that is described by a Hamiltonian H(Q,P;x), where (Q,P) are the canonical coordinates of a particle in a two-dimensional well, and x is a parameter. By changing x we can deform the "shape" of the well. The quantum eigenstates of the system are /n(x)>. We analyze numerically how the parametric kernel P(n/m)=/
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.
Dynamical Density Functional Theory and Hydrodynamic Interactions in Confined Systems
NASA Astrophysics Data System (ADS)
Goddard, Benjamin; Nold, Andreas; Kalliadasis, Serafim
2016-11-01
Colloidal systems consist of nano- to micrometer-sized particles suspended in a bath of many more, much smaller and much lighter particles. Motion of the colloidal particles through the bath, e.g. when driven by external forces such as gravity, induces flows in the bath. These flows in turn impart forces on the colloid particles. These bath-mediated forces, known as Hydrodynamic Interactions (HIs) strongly influence the dynamics of the colloid particles. This is particularly true in confined systems, in which the presence of walls substantially modifies the HIs compared to unbounded geometries. For many-particle systems, the many of degrees of freedom prohibit a direct solution of the underlying stochastic equations and a reduced model is necessary. We employ elements from the statistical mechanics of classical fluids, namely Dynamical Density Functional Theory (DDFT), the computational complexity of which is independent of the number of particles to include both inter-particle and particle-wall HI and demonstrate the physical importance of using the correct description of HIs in confined systems. In addition, DDFT allows us to isolate and investigate different components of HIs. Supported by EPSRC Grant EP/L025159.
Self-interaction corrections in density functional theory
Tsuneda, Takao; Hirao, Kimihiko
2014-05-14
Self-interaction corrections for Kohn-Sham density functional theory are reviewed for their physical meanings, formulations, and applications. The self-interaction corrections get rid of the self-interaction error, which is the sum of the Coulomb and exchange self-interactions that remains because of the use of an approximate exchange functional. The most frequently used self-interaction correction is the Perdew-Zunger correction. However, this correction leads to instabilities in the electronic state calculations of molecules. To avoid these instabilities, several self-interaction corrections have been developed on the basis of the characteristic behaviors of self-interacting electrons, which have no two-electron interactions. These include the von Weizsäcker kinetic energy and long-range (far-from-nucleus) asymptotic correction. Applications of self-interaction corrections have shown that the self-interaction error has a serious effect on the states of core electrons, but it has a smaller than expected effect on valence electrons. This finding is supported by the fact that the distribution of self-interacting electrons indicates that they are near atomic nuclei rather than in chemical bonds.
Density functional theory investigation of sodium azide at high pressure
NASA Astrophysics Data System (ADS)
Steele, B. A.; Landerville, A. C.; Oleynik, I. I.
2014-05-01
High pressure experiments utilizing Raman spectroscopy indicate that the a phase of sodium azide undergoes a polymeric phase transition at high pressure. In this work, the structural and vibrational properties, including the first order Raman and infrared spectra, of the a phase of sodium azide are calculated using first-principles density functional theory up to 92 GPa. The equation of state of α NaN3 is obtained within the quasi-harmonic approximation at various temperatures. Each Raman-active mode blue shifts under compression whereas the doubly degenerate IR-active azide bending mode red-shifts under compression. However, at 70 GPa, the intensity of the Bu IR-active bending mode decreases substantially, and a new distorted azide bending lattice mode appears in the IR spectrum. In contrast to the bending mode, this new mode blue-shifts under compression. No new modes appear in the Raman spectra at high pressure, indicating that the changes in the Raman spectrum seen in experiment at high pressure are signs of new high nitrogen content structures, but not due to sodium azide.
Hardness of FeB4: density functional theory investigation.
Zhang, Miao; Lu, Mingchun; Du, Yonghui; Gao, Lili; Lu, Cheng; Liu, Hanyu
2014-05-07
A recent experimental study reported the successful synthesis of an orthorhombic FeB4 with a high hardness of 62(5) GPa [H. Gou et al., Phys. Rev. Lett. 111, 157002 (2013)], which has reignited extensive interests on whether transition-metal borides compounds will become superhard materials. However, it is contradicted with some theoretical studies suggesting transition-metal boron compounds are unlikely to become superhard materials. Here, we examined structural and electronic properties of FeB4 using density functional theory. The electronic calculations show the good metallicity and covalent Fe-B bonding. Meanwhile, we extensively investigated stress-strain relations of FeB4 under various tensile and shear loading directions. The calculated weakest tensile and shear stresses are 40 GPa and 25 GPa, respectively. Further simulations (e.g., electron localization function and bond length along the weakest loading direction) on FeB4 show the weak Fe-B bonding is responsible for this low hardness. Moreover, these results are consistent with the value of Vickers hardness (11.7-32.3 GPa) by employing different empirical hardness models and below the superhardness threshold of 40 GPa. Our current results suggest FeB4 is a hard material and unlikely to become superhard (>40 GPa).
Density functional theory study of phase IV of solid hydrogen
NASA Astrophysics Data System (ADS)
Pickard, Chris J.; Martinez-Canales, Miguel; Needs, Richard J.
2012-06-01
We have studied solid hydrogen up to pressures of 300 GPa and temperatures of 350 K using density functional theory methods and have found “mixed structures” that are more stable than those predicted earlier. Mixed structures consist of alternate layers of strongly bonded molecules and weakly bonded graphene-like sheets. Quasiharmonic vibrational calculations show that mixed structures are the most stable at room temperature over the pressure range 250-295 GPa. These structures are stabilized with respect to strongly bonded molecular phases at room temperature by the presence of lower frequency vibrational modes arising from the graphene-like sheets. Our results for the mixed structures are consistent with the experimental Raman data [M. I. Eremets and I. A. Troyan, Nat. Mater.1476-112210.1038/nmat3175 10, 927 (2011) and R. T. Howie , Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.108.125501 108, 125501 (2012)]. We find that mixed phases are reasonable structural models for phase IV of hydrogen.
Insights into phase transitions and entanglement from density functional theory
NASA Astrophysics Data System (ADS)
Wei, Bo-Bo
2016-11-01
Density functional theory (DFT) has met great success in solid state physics, quantum chemistry and in computational material sciences. In this work we show that DFT could shed light on phase transitions and entanglement at finite temperatures. Specifically, we show that the equilibrium state of an interacting quantum many-body system which is in thermal equilibrium with a heat bath at a fixed temperature is a universal functional of the first derivatives of the free energy with respect to temperature and other control parameters respectively. This insight from DFT enables us to express the average value of any physical observable and any entanglement measure as a universal functional of the first derivatives of the free energy with respect to temperature and other control parameters. Since phase transitions are marked by the nonanalytic behavior of free energy with respect to control parameters, the physical quantities and entanglement measures may present nonanalytic behavior at critical point inherited from their dependence on the first derivative of free energy. We use two solvable models to demonstrate these ideas. These results give new insights for phase transitions and provide new profound connections between entanglement and phase transitions in interacting quantum many-body physics.
Excess electrons in ice: a density functional theory study.
Bhattacharya, Somesh Kr; Inam, Fakharul; Scandolo, Sandro
2014-02-21
We present a density functional theory study of the localization of excess electrons in the bulk and on the surface of crystalline and amorphous water ice. We analyze the initial stages of electron solvation in crystalline and amorphous ice. In the case of crystalline ice we find that excess electrons favor surface states over bulk states, even when the latter are localized at defect sites. In contrast, in amorphous ice excess electrons find it equally favorable to localize in bulk and in surface states which we attribute to the preexisting precursor states in the disordered structure. In all cases excess electrons are found to occupy the vacuum regions of the molecular network. The electron localization in the bulk of amorphous ice is assisted by its distorted hydrogen bonding network as opposed to the crystalline phase. Although qualitative, our results provide a simple interpretation of the large differences observed in the dynamics and localization of excess electrons in crystalline and amorphous ice films on metals.
Density Functional Theory for Phase-Ordering Transitions
Wu, Jianzhong
2016-03-30
Colloids display astonishing structural and dynamic properties that can be dramatically altered by modest changes in the solution condition or an external field. This complex behavior stems from a subtle balance of colloidal forces and intriguing mesoscopic and macroscopic phase transitions that are sensitive to the processing conditions and the dispersing environment. Whereas the knowledge on the microscopic structure and phase behavior of colloidal systems at equilibrium is now well-advanced, quantitative predictions of the dynamic properties and the kinetics of phase-ordering transitions in colloids are not always realized. Many important mesoscopic and off-equilibrium colloidal states remain poorly understood. The proposed research aims to develop a new, unifying approach to describe colloidal dynamics and the kinetics of phase-ordering transitions based on accomplishments from previous work for the equilibrium properties of both uniform and inhomogeneous systems and on novel concepts from the state-of-the-art dynamic density functional theory. In addition to theoretical developments, computational research is designed to address a number of fundamental questions on phase-ordering transitions in colloids, in particular those pertinent to a competition of the dynamic pathways leading to various mesoscopic structures, off-equilibrium states, and crystalline phases. By providing a generic theoretical framework to describe equilibrium, metastable as well as non-ergodic phase transitions concurrent with the colloidal self-assembly processes, accomplishments from this work will have major impacts on both fundamental research and technological applications.
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.
Density functional theory for comprehensive orbital energy calculations.
Nakata, Ayako; Tsuneda, Takao
2013-08-14
This study reveals the reason core 1s orbital energies and the highest occupied molecular orbital (HOMO) energies of hydrogen and rare gas atoms are underestimated by long-range corrected (LC) density functional theory (DFT), which quantitatively reproduces the HOMO energies of other systems and the lowest unoccupied molecular orbital (LUMO) energies. Applying the pseudospectral regional (PR) self-interaction correction (SIC) drastically improved the underestimated orbital energies in LC-DFT calculations, while maintaining or improving the accuracies in the calculated valence HOMO and LUMO energies. This indicates that the self-interaction error in exchange functionals causes the underestimations of core 1s orbital energies and the HOMO energies of hydrogen and rare gas atoms in LC-DFT calculations. To clarify the reason for the improvement, the fractional occupation dependences of total electronic energies and orbital energies were examined. The calculated results clearly showed that the LC-PR functional gives almost linear dependences of total electronic energies for a slight decrease in the occupation number of core 1s orbitals, although this linear dependence disappears for significant decrease due to the shrinking of exchange self-interaction regions. It was also clarified that the PRSIC hardly affects the occupation number dependences of the total electronic energies and orbital energies for the fractional occupations of HOMOs and LUMOs. As a result, it was concluded that core orbital energies are obtained accurately by combining LC-DFT with PRSIC.
Density functional theory study of oxygen migration in molten carbonate
NASA Astrophysics Data System (ADS)
Lei, Xueling; Haines, Kahla; Huang, Kevin; Qin, Changyong
2016-02-01
The process of oxygen migration in alkali molten carbonate salts has been examined using density functional theory method. All geometries were optimized at the B3LYP/6-31G(d) level, while single point energy corrections were performed using MP4 and CCSD(T). At TS, a O-O-O linkage is formed and O-O bond forming and breaking is concerted. A cooperative "cogwheel" mechanism as described in the equation of CO42- + CO32- → CO32- ⋯O ⋯ CO32- → CO32- + CO42- is involved. The energy barrier is calculated to be 103.0, 136.3 and 127.9 kJ/mol through an intra-carbonate pathway in lithium, sodium and potassium carbonate, respectively. The reliability and accuracy of B3LYP/6-31G(d) were confirmed by CCSD(T). The calculated low values of activation energy indicate that the oxygen transfer in molten carbonate salts is fairly easy. In addition, it is found that lithium carbonate is not only a favorable molten carbonate salt for better cathode kinetics, but also it is widely used for reducing the melting point of Li/Na and Li/K eutectic MC mixtures. The current results imply that the process of oxygen reduction in MC modified cathodes is facilitated by the presence of MC, resulting in an enhancement of cell performance at low operating temperatures.
Computational characterization of sodium selenite using density functional theory.
Barraza-Jiménez, Diana; Flores-Hidalgo, Manuel Alberto; Galvan, Donald H; Sánchez, Esteban; Glossman-Mitnik, Daniel
2011-04-01
In this theoretical study we used density functional theory to calculate the molecular and crystalline structures of sodium selenite. Our structural results were compared with experimental data. From the molecular structure we determined the ionization potential, electronic affinity, and global reactivity parameters like electronegativity, hardness, softness and global electrophilic index. A significant difference in the IP and EA values was observed, and this difference was dependent on the calculation method used (employing either vertical or adiabatic energies). Thus, values obtained for the electrophilic index (2.186 eV from vertical energies and 2.188 eV from adiabatic energies) were not significantly different. Selectivity was calculated using the Fukui functions. Since the Mulliken charge study predicted a negative value, it is recommended that AIM should be used in selectivity characterization. It was evident from the selectivity index that sodium atoms are the most sensitive sites to nucleophilic attack. The results obtained in this work provide data that will aid the characterization of compounds used in crop biofortification.
Embedding germanium in graphene: A density functional theory study
NASA Astrophysics Data System (ADS)
Xu, Zhuo; Li, Yangping; Tan, Tingting; Liu, Zhengtang
2017-03-01
Based on the density functional theory, we investigate the structural, electronic, and magnetic properties of graphene sheet with substitutional Ge atoms in both single and double vacancies, and graphene sheet with Ge-chain impurity. We find the substitutional Ge is chemically bonded to graphene, and is more stable in the double vacancy site. The electronic properties indicate that metallic and semiconductor states with a range of band gaps from 0 to 0.87 eV could be obtained depending on different substitution sites, concentrations, and vacancy types. Magnetic moment is observed in graphene with single vacancy. Tunable electronic behaviors are also observed in graphene sheet with Ge-chain impurity, and a magnetic moment of 2.9 μB is observed in single Ge-chain incorporated 4 × 4 graphene supercell. From these investigations, we conclude that by doping of Ge in vacancy-contained graphene, it could provide great advantages for its application in future nanoscale devices.
Predicting Stability Constants for Uranyl Complexes Using Density Functional Theory
Vukovic, Sinisa; Hay, Benjamin P.; Bryantsev, Vyacheslav S.
2015-04-02
The ability to predict the equilibrium constants for the formation of 1:1 uranyl:ligand complexes (log K_{1 }values) provides the essential foundation for the rational design of ligands with enhanced uranyl affinity and selectivity. We also use density functional theory (B3LYP) and the IEFPCM continuum solvation model to compute aqueous stability constants for UO_{2}^{2+} complexes with 18 donor ligands. Theoretical calculations permit reasonably good estimates of relative binding strengths, while the absolute log K_{1} values are significantly overestimated. Accurate predictions of the absolute log K_{1} values (root mean square deviation from experiment < 1.0 for log K_{1} values ranging from 0 to 16.8) can be obtained by fitting the experimental data for two groups of mono and divalent negative oxygen donor ligands. The utility of correlations is demonstrated for amidoxime and imide dioxime ligands, providing a useful means of screening for new ligands with strong chelate capability to uranyl.
Predicting Stability Constants for Uranyl Complexes Using Density Functional Theory
Vukovic, Sinisa; Hay, Benjamin P.; Bryantsev, Vyacheslav S.
2015-04-02
The ability to predict the equilibrium constants for the formation of 1:1 uranyl:ligand complexes (log K1 values) provides the essential foundation for the rational design of ligands with enhanced uranyl affinity and selectivity. We also use density functional theory (B3LYP) and the IEFPCM continuum solvation model to compute aqueous stability constants for UO22+ complexes with 18 donor ligands. Theoretical calculations permit reasonably good estimates of relative binding strengths, while the absolute log K1 values are significantly overestimated. Accurate predictions of the absolute log K1 values (root mean square deviation from experiment < 1.0 for log K1 values ranging from 0more » to 16.8) can be obtained by fitting the experimental data for two groups of mono and divalent negative oxygen donor ligands. The utility of correlations is demonstrated for amidoxime and imide dioxime ligands, providing a useful means of screening for new ligands with strong chelate capability to uranyl.« less
Kajzer-Bonk, Joanna; Skórka, Piotr; Nowicki, Piotr; Bonk, Maciej; Król, Wiesław; Szpiłyk, Damian; Woyciechowski, Michal
2016-01-01
The type of matrix, the landscape surrounding habitat patches, may determine the distribution and function of local populations. However, the matrix is often heterogeneous, and its various components may differentially contribute to metapopulation processes at different spatial scales, a phenomenon that has rarely been investigated. The aim of this study was to estimate the relative importance of matrix composition and spatial scale, habitat quality, and management intensity on the occurrence and density of local populations of two endangered large blue butterflies: Phengaris teleius and P. nausithous. Presence and abundance data were assessed over two years, 2011-12, in 100 local patches within two heterogeneous regions (near Kraków and Tarnów, southern Poland). The matrix composition was analyzed at eight spatial scales. We observed high occupancy rates in both species, regions and years. With the exception of area and isolation, almost all of the matrix components contributed to Phengaris sp. densities. The different matrix components acted at different spatial scales (grassland cover within 4 and 3 km, field cover within 0.4 and 0.3 km and water cover within 4 km radii for P. teleius and P. nausithous, respectively) and provided the highest independent contribution to the butterfly densities. Additionally, the effects of a 0.4 km radius of forest cover and a food plant cover on P. teleius, and a 1 km radius of settlement cover and management intensity on P. nausithous densities were observed. Contrary to former studies we conclude that the matrix heterogeneity and spatial scale rather than general matrix type are of relevance for densities of butterflies. Conservation strategies for these umbrella species should concentrate on maintaining habitat quality and managing matrix composition at the most appropriate spatial scales.
Skórka, Piotr; Nowicki, Piotr; Bonk, Maciej; Król, Wiesław; Szpiłyk, Damian; Woyciechowski, Michal
2016-01-01
The type of matrix, the landscape surrounding habitat patches, may determine the distribution and function of local populations. However, the matrix is often heterogeneous, and its various components may differentially contribute to metapopulation processes at different spatial scales, a phenomenon that has rarely been investigated. The aim of this study was to estimate the relative importance of matrix composition and spatial scale, habitat quality, and management intensity on the occurrence and density of local populations of two endangered large blue butterflies: Phengaris teleius and P. nausithous. Presence and abundance data were assessed over two years, 2011–12, in 100 local patches within two heterogeneous regions (near Kraków and Tarnów, southern Poland). The matrix composition was analyzed at eight spatial scales. We observed high occupancy rates in both species, regions and years. With the exception of area and isolation, almost all of the matrix components contributed to Phengaris sp. densities. The different matrix components acted at different spatial scales (grassland cover within 4 and 3 km, field cover within 0.4 and 0.3 km and water cover within 4 km radii for P. teleius and P. nausithous, respectively) and provided the highest independent contribution to the butterfly densities. Additionally, the effects of a 0.4 km radius of forest cover and a food plant cover on P. teleius, and a 1 km radius of settlement cover and management intensity on P. nausithous densities were observed. Contrary to former studies we conclude that the matrix heterogeneity and spatial scale rather than general matrix type are of relevance for densities of butterflies. Conservation strategies for these umbrella species should concentrate on maintaining habitat quality and managing matrix composition at the most appropriate spatial scales. PMID:28005942
Johnson, Christopher D; Worrall, Fred
2007-06-01
This paper reports the preparation and properties of a new low density granular absorbent material based on a zeolite/vermiculite composite. The composite prepared addresses a number of important issues relating to the use of zeolites in environmental and waste management applications. The material prepared has large particle size due to binderless adhesion of zeolite crystals within the protective lamellar matrix provided by the vermiculite granule. Additionally, the porous nature of new material ensures that it outperforms natural zeolite grains in ion-exchange tests. The material was shown to have a low bulk density (0.75 g cm(-3)) adding the benefit that the majority of grains float on water for over 15 h. The conclusion of the study is that the use of composite matrices enable the preparation of materials which show the physical properties of the host, (e.g., granular and low density), whilst maintaining the powder-like properties (e.g., high ion-exchange and small crystal size) of the active component. The resulting material can be easily handled and separated from aqueous waste streams using either flotation or exploiting its granular nature.
Theory of melting at high pressures: Amending density functional theory with quantum Monte Carlo
NASA Astrophysics Data System (ADS)
Shulenburger, L.; Desjarlais, M. P.; Mattsson, T. R.
2014-10-01
We present an improved first-principles description of melting under pressure based on thermodynamic integration comparing density functional theory (DFT) and quantum Monte Carlo (QMC) treatments. The method is applied to address the longstanding discrepancy between DFT calculations and diamond anvil cell (DAC) experiments on the melting curve of xenon, a noble gas solid where van der Waals binding is challenging for traditional DFT methods. The calculations show agreement with data below 20 GPa and that the high-pressure melt curve is well described by a Lindemann behavior up to at least 80 GPa, in contrast to DAC data.
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.
NASA Astrophysics Data System (ADS)
Huo, Pengfei; Coker, David F.
2011-11-01
An approach for treating dissipative, non-adiabatic quantum dynamics in general model systems at finite temperature based on linearizing the density matrix evolution in the forward-backward path difference for the environment degrees of freedom is presented. We demonstrate that the approach can capture both short time coherent quantum dynamics and long time thermal equilibration in an application to excitation energy transfer in a model photosynthetic light harvesting complex. Results are also presented for some nonadiabatic scattering models which indicate that, even though the method is based on a "mean trajectory" like scheme, it can accurately capture electronic population branching through multiple avoided crossing regions and that the approach offers a robust and reliable way to treat quantum dynamical phenomena in a wide range of condensed phase applications.
N-leg spin-S Heisenberg ladders: A density-matrix renormalization group study
NASA Astrophysics Data System (ADS)
Ramos, F. B.; Xavier, J. C.
2014-03-01
We investigate the N-leg spin-S Heisenberg ladders by using the density matrix renormalization group method. We present estimates of the spin gap Δs and of the ground-state energy per site e∞N in the thermodynamic limit for ladders with widths up to six legs and spin S≤5/2. We also estimate the ground-state energy per site e∞2D for the infinite two-dimensional spin-S Heisenberg model. Our results support that for ladders with semi-integer spins the spin excitation is gapless for N odd and gapped for N even, whereas for integer spin ladders the spin gap is nonzero, independent of the number of legs. Those results agree with the well-known conjectures of Haldane and Sénéchal-Sierra for chains and ladders, respectively. We also observe edge states for ladders with N odd, similar to what happens in spin chains.
NASA Astrophysics Data System (ADS)
Ghosh, Debashree; Hachmann, Johannes; Yanai, Takeshi; Chan, Garnet Kin-Lic
2008-04-01
In previous work we have shown that the density matrix renormalization group (DMRG) enables near-exact calculations in active spaces much larger than are possible with traditional complete active space algorithms. Here, we implement orbital optimization with the DMRG to further allow the self-consistent improvement of the active orbitals, as is done in the complete active space self-consistent field (CASSCF) method. We use our resulting DMRG-CASSCF method to study the low-lying excited states of the all-trans polyenes up to C24H26 as well as β-carotene, correlating with near-exact accuracy the optimized complete π-valence space with up to 24 active electrons and orbitals, and analyze our results in the light of the recent discovery from resonance Raman experiments of new optically dark states in the spectrum.
NASA Astrophysics Data System (ADS)
Hachmann, Johannes; Cardoen, Wim; Chan, Garnet Kin-Lic
2006-10-01
We have devised a local ab initio density matrix renormalization group algorithm to describe multireference correlations in large systems. For long molecules that are extended in one of their spatial dimensions, we can obtain an exact characterization of correlation, in the given basis, with a cost that scales only quadratically with the size of the system. The reduced scaling is achieved solely through integral screening and without the construction of correlation domains. We demonstrate the scaling, convergence, and robustness of the algorithm in polyenes and hydrogen chains. We converge to exact correlation energies (in the sense of full configuration interaction, with 1-10μEh precision) in all cases and correlate up to 100 electrons in 100 active orbitals. We further use our algorithm to obtain exact energies for the metal-insulator transition in hydrogen chains and compare and contrast our results with those from conventional quantum chemical methods.
Hu, Weifeng; Chan, Garnet Kin-Lic
2015-07-14
We describe and extend the formalism of state-specific analytic density matrix renormalization group (DMRG) energy gradients, first used by Liu et al. [J. Chem. Theor. Comput. 2013, 9, 4462]. We introduce a DMRG wave function maximum overlap following technique to facilitate state-specific DMRG excited-state optimization. Using DMRG configuration interaction (DMRG-CI) gradients, we relax the low-lying singlet states of a series of trans-polyenes up to C20H22. Using the relaxed excited-state geometries, as well as correlation functions, we elucidate the exciton, soliton, and bimagnon ("single-fission") character of the excited states, and find evidence for a planar conical intersection.
NASA Astrophysics Data System (ADS)
Mukhopadhyay, S.; Ramasesha, S.
2009-08-01
We have used the density matrix renormalization group (DMRG) method to study the linear and nonlinear optical responses of first generation nitrogen based dendrimers with donor acceptor groups. We have employed Pariser-Parr-Pople Hamiltonian to model the interacting π electrons in these systems. Within the DMRG method we have used an innovative scheme to target excited states with large transition dipole to the ground state. This method reproduces exact optical gaps and polarization in systems where exact diagonalization of the Hamiltonian is possible. We have used a correction vector method which tacitly takes into account the contribution of all excited states, to obtain the ground state polarizibility, first hyperpolarizibility, and two photon absorption cross sections. We find that the lowest optical excitations as well as the lowest excited triplet states are localized. It is interesting to note that the first hyperpolarizibility saturates more rapidly with system size compared to linear polarizibility unlike that of linear polyenes.
Density matrix model for polarons in a terahertz quantum dot cascade laser
NASA Astrophysics Data System (ADS)
Burnett, Benjamin A.; Williams, Benjamin S.
2014-10-01
A density matrix based method is introduced for computation of steady-state dynamics in quantum cascade systems of arbitrary size, which incorporates an optical field coherently. The method is applied to a model terahertz quantum dot cascade laser system, where a means of treating coherent electron-optical-phonon coupling is also introduced. Results predict a strong increase in the upper state lifetime and operating temperature as compared to traditional well-based terahertz quantum cascade lasers. However, new complications also arise, including multiple peaks in the gain spectrum due to strong electron-phonon coupling, and strong parasitic subthreshold current channels that arise due to reduced dephasing. It is anticipated that novel design schemes will be necessary for such lasers to become a reality.
Symmetry-conserving purification of quantum states within the density matrix renormalization group
Nocera, Alberto; Alvarez, Gonzalo
2016-01-28
The density matrix renormalization group (DMRG) algorithm was originally designed to efficiently compute the zero-temperature or ground-state properties of one-dimensional strongly correlated quantum systems. The development of the algorithm at finite temperature has been a topic of much interest, because of the usefulness of thermodynamics quantities in understanding the physics of condensed matter systems, and because of the increased complexity associated with efficiently computing temperature-dependent properties. The ancilla method is a DMRG technique that enables the computation of these thermodynamic quantities. In this paper, we review the ancilla method, and improve its performance by working on reduced Hilbert spaces andmore » using canonical approaches. Furthermore we explore its applicability beyond spins systems to t-J and Hubbard models.« less
Symmetry-conserving purification of quantum states within the density matrix renormalization group
Nocera, Alberto; Alvarez, Gonzalo
2016-01-28
The density matrix renormalization group (DMRG) algorithm was originally designed to efficiently compute the zero-temperature or ground-state properties of one-dimensional strongly correlated quantum systems. The development of the algorithm at finite temperature has been a topic of much interest, because of the usefulness of thermodynamics quantities in understanding the physics of condensed matter systems, and because of the increased complexity associated with efficiently computing temperature-dependent properties. The ancilla method is a DMRG technique that enables the computation of these thermodynamic quantities. In this paper, we review the ancilla method, and improve its performance by working on reduced Hilbert spaces and using canonical approaches. Furthermore we explore its applicability beyond spins systems to t-J and Hubbard models.
Density matrix renormalization group approach to two-fluid open many-fermion systems
NASA Astrophysics Data System (ADS)
Rotureau, J.; Michel, N.; Nazarewicz, W.; Płoszajczak, M.; Dukelsky, J.
2009-01-01
We have extended the density matrix renormalization group (DMRG) approach to two-fluid open many-fermion systems governed by complex-symmetric Hamiltonians. The applications are carried out for three- and four-nucleon (proton-neutron) systems within the Gamow shell model (GSM) in the complex-energy plane. We study necessary and sufficient conditions for the GSM+DMRG method to yield the correct ground-state eigenvalue and discuss different truncation schemes within the DMRG. The proposed approach will enable configuration interaction studies of weakly bound and unbound strongly interacting complex systems, which, because of a prohibitively large size of Fock space, cannot be treated by means of the direct diagonalization.
Mukhopadhyay, S; Ramasesha, S
2009-08-21
We have used the density matrix renormalization group (DMRG) method to study the linear and nonlinear optical responses of first generation nitrogen based dendrimers with donor acceptor groups. We have employed Pariser-Parr-Pople Hamiltonian to model the interacting pi electrons in these systems. Within the DMRG method we have used an innovative scheme to target excited states with large transition dipole to the ground state. This method reproduces exact optical gaps and polarization in systems where exact diagonalization of the Hamiltonian is possible. We have used a correction vector method which tacitly takes into account the contribution of all excited states, to obtain the ground state polarizibility, first hyperpolarizibility, and two photon absorption cross sections. We find that the lowest optical excitations as well as the lowest excited triplet states are localized. It is interesting to note that the first hyperpolarizibility saturates more rapidly with system size compared to linear polarizibility unlike that of linear polyenes.
Low-density, high-strength intermetallic matrix composites by XD (trademark) synthesis
NASA Technical Reports Server (NTRS)
Kumar, K. S.; Dipietro, M. S.; Brown, S. A.; Whittenberger, J. D.
1991-01-01
A feasibility study was conducted to evaluate the potential of particulate composites based on low-density, L1(sub 2) trialuminide matrices for high-temperature applications. The compounds evaluated included Al22Fe3Ti8 (as a multiphase matrix), Al67Ti25Cr8, and Al66Ti25Mn9. The reinforcement consisted of TiB2 particulates. The TiB2 composites were processed by ingot and powder metallurgy techniques. Microstructural characterization and mechanical testing were performed in the hot-pressed and hot-isostatic-pressed condition. The casting were sectioned and isothermally forged into pancakes. All the materials were tested in compression as a function of temperature, and at high temperatures as a function of strain rate. The test results are discussed.
TIEG1-NULL OSTEOCYTES DISPLAY DEFECTS IN THEIR MORPHOLOGY, DENSITY AND SURROUNDING BONE MATRIX
Haddad, Oualid; Hawse, John R.; Subramaniam, Malayannan; Spelsberg, Thomas C.; Bensamoun, Sabine F.
2011-01-01
Through the development of TGFβ-inducible early gene-1 (TIEG1) knockout (KO) mice, we have demonstrated that TIEG1 plays an important role in osteoblast-mediated bone mineralization, and in bone resistance to mechanical strain. To further investigate the influence of TIEG1 in skeletal maintenance, osteocytes were analyzed by transmission electron microscopy using TIEG1 KO and wild-type mouse femurs at one, three and eight months of age. The results revealed an age-dependent change in osteocyte surface and density, suggesting a role for TIEG1 in osteocyte development. Moreover, there was a decrease in the amount of hypomineralized bone matrix surrounding the osteocytes in TIEG1 KO mice relative to wild-type controls. While little is known about the function or importance of this hypomineralized bone matrix immediately adjacent to osteocytes, this study reveals significant differences in this bone microenvironment and suggests that osteocyte function may be compromised in the absence of TIEG1 expression. PMID:22121306
One plus two-body random matrix ensembles with parity: Density of states and parity ratios
Vyas, Manan; Srivastava, P. C.; Kota, V. K. B.
2011-06-15
One plus two-body embedded Gaussian orthogonal ensemble of random matrices with parity [EGOE(1+2)-{pi}] generated by a random two-body interaction (modeled by GOE in two-particle spaces) in the presence of a mean field for spinless identical fermion systems is defined, generalizing the two-body ensemble with parity analyzed by Papenbrock and Weidenmueller [Phys. Rev. C 78, 054305 (2008)], in terms of two mixing parameters and a gap between the positive ({pi}=+) and negative ({pi}=-) parity single-particle (sp) states. Numerical calculations are used to demonstrate, using realistic values of the mixing parameters appropriate for some nuclei, that the EGOE(1+2)-{pi} ensemble generates Gaussian form (with corrections) for fixed parity eigenvalue densities (i.e., state densities). The random matrix model also generates many features in parity ratios of state densities that are similar to those predicted by a method based on the Fermi-gas model for nuclei. We have also obtained, by applying the formulation due to Chang et al. [Ann. Phys. (NY) 66, 137 (1971)], a simple formula for the spectral variances defined over fixed-(m{sub 1},m{sub 2}) spaces, where m{sub 1} is the number of fermions in the positive parity sp states and m{sub 2} is the number of fermions in the negative parity sp states. Similarly, using the binary correlation approximation, in the dilute limit, we have derived expressions for the lowest two-shape parameters. The smoothed densities generated by the sum of fixed-(m{sub 1},m{sub 2}) Gaussians with lowest two-shape corrections describe the numerical results in many situations. The model also generates preponderance of positive parity ground states for small values of the mixing parameters, and this is a feature seen in nuclear shell-model results.
Large-scale All-electron Density Functional Theory Calculations using Enriched Finite Element Method
NASA Astrophysics Data System (ADS)
Kanungo, Bikash; Gavini, Vikram
We present a computationally efficient method to perform large-scale all-electron density functional theory calculations by enriching the Lagrange polynomial basis in classical finite element (FE) discretization with atom-centered numerical basis functions, which are obtained from the solutions of the Kohn-Sham (KS) problem for single atoms. We term these atom-centered numerical basis functions as enrichment functions. The integrals involved in the construction of the discrete KS Hamiltonian and overlap matrix are computed using an adaptive quadrature grid based on gradients in the enrichment functions. Further, we propose an efficient scheme to invert the overlap matrix by exploiting its LDL factorization and employing spectral finite elements along with Gauss-Lobatto quadrature rules. Finally, we use a Chebyshev polynomial based acceleration technique to compute the occupied eigenspace in each self-consistent iteration. We demonstrate the accuracy, efficiency and scalability of the proposed method on various metallic and insulating benchmark systems, with systems ranging in the order of 10,000 electrons. We observe a 50-100 fold reduction in the overall computational time when compared to classical FE calculations while being commensurate with the desired chemical accuracy. We acknowledge the support of NSF (Grant No. 1053145) and ARO (Grant No. W911NF-15-1-0158) in conducting this work.
Ruiz-Serrano, Álvaro; Skylaris, Chris-Kriton
2013-08-07
A new method for finite-temperature density functional theory calculations which significantly increases the number of atoms that can be simulated in metallic systems is presented. A self-consistent, direct minimization technique is used to obtain the Helmholtz free energy of the electronic system, described in terms of a set of non-orthogonal, localized functions which are optimized in situ using a periodic-sinc basis set, equivalent to plane waves. Most parts of the calculation, including the demanding operation of building the Hamiltonian matrix, have a computational cost that scales linearly with the number of atoms in the system. Also, this approach ensures that the Hamiltonian matrix has a minimal size, which reduces the computational overhead due to diagonalization, a cubic-scaling operation that is still required. Large basis set accuracy is retained via the optimization of the localized functions. This method allows accurate simulations of entire metallic nanostructures, demonstrated with calculations on a supercell of bulk copper with 500 atoms and on gold nanoparticles with up to 2057 atoms.
Semiclassical S-matrix theory of vibrationally inelastic collisions between two diatomic molecules
NASA Technical Reports Server (NTRS)
Cohen, S. C.; Alexander, M. H.
1974-01-01
We derive a semiclassical S matrix for vibrationally inelastic collisions between two diatomic molecules, assuming a collinear geometry. Our theory incorporates a quantum mechanical superposition principle with classical dynamics and, as such, is an extension of the atom-diatomic molecule theory of Miller. The several approximations to the S matrix differ in the complexity with which the interference between various classical trajectories is treated. We report numerical calculations for H2-D2 and D2-D2 collisions based on two different interaction potentials. The cruder approximations yield transition probabilities which agree with exact quantum mechanical results to within a factor of 2. More sophisticated approximations to the S matrix yield excellent quantitative agreement with the quantum calculations.
ERIC Educational Resources Information Center
Scott, Karen Wilson
2004-01-01
This paper describes the process for employing two principal instruments for relating the categories identifying the central phenomenon in grounded theory analysis. The Conditional Relationship Guide contextualizes the central phenomenon and relates structure with process. The second tool, the Reflective Coding Matrix, captures the higher level of…
Random-matrix-theory approach to mesoscopic fluctuations of heat current.
Schmidt, Martin; Kottos, Tsampikos; Shapiro, Boris
2013-08-01
We consider an ensemble of fully connected networks of N oscillators coupled harmonically with random springs and show, using random-matrix-theory considerations, that both the average phonon heat current and its variance are scale invariant and take universal values in the large N limit. These anomalous mesoscopic fluctuations is the hallmark of strong correlations between normal modes.
Open problems in applying random-matrix theory to nuclear reactions
NASA Astrophysics Data System (ADS)
Weidenmüller, H. A.
2014-09-01
Problems in applying random-matrix theory (RMT) to nuclear reactions arise in two domains. To justify the approach, statistical properties of isolated resonances observed experimentally must agree with RMT predictions. That agreement is less striking than would be desirable. In the implementation of the approach, the range of theoretically predicted observables is too narrow.
Light-like big bang singularities in string and matrix theories
NASA Astrophysics Data System (ADS)
Craps, Ben; Evnin, Oleg
2011-10-01
Important open questions in cosmology require a better understanding of the big bang singularity. In string and matrix theories, light-like analogues of cosmological singularities (singular plane wave backgrounds) turn out to be particularly tractable. We give a status report on the current understanding of such light-like big bang models, presenting both solved and open problems.
Antioxidant Properties of Kynurenines: Density Functional Theory Calculations
2016-01-01
Kynurenines, the main products of tryptophan catabolism, possess both prooxidant and anioxidant effects. Having multiple neuroactive properties, kynurenines are implicated in the development of neurological and cognitive disorders, such as Alzheimer's, Parkinson's, and Huntington's diseases. Autoxidation of 3-hydroxykynurenine (3HOK) and its derivatives, 3-hydroxyanthranilic acid (3HAA) and xanthommatin (XAN), leads to the hyperproduction of reactive oxygen species (ROS) which damage cell structures. At the same time, 3HOK and 3HAA have been shown to be powerful ROS scavengers. Their ability to quench free radicals is believed to result from the presence of the aromatic hydroxyl group which is able to easily abstract an electron and H-atom. In this study, the redox properties for kynurenines and several natural and synthetic antioxidants have been calculated at different levels of density functional theory in the gas phase and water solution. Hydroxyl bond dissociation enthalpy (BDE) and ionization potential (IP) for 3HOK and 3HAA appear to be lower than for xanthurenic acid (XAA), several phenolic antioxidants, and ascorbic acid. BDE and IP for the compounds with aromatic hydroxyl group are lower than for their precursors without hydroxyl group. The reaction rate for H donation to *O-atom of phenoxyl radical (Ph-O*) and methyl peroxy radical (Met-OO*) decreases in the following rankings: 3HOK ~ 3HAA > XAAOXO > XAAENOL. The enthalpy absolute value for Met-OO* addition to the aromatic ring of the antioxidant radical increases in the following rankings: 3HAA* < 3HOK* < XAAOXO* < XAAENOL*. Thus, the high free radical scavenging activity of 3HAA and 3HOK can be explained by the easiness of H-atom abstraction and transfer to O-atom of the free radical, rather than by Met-OO* addition to the kynurenine radical. PMID:27861556
Density functional theory based generalized effective fragment potential method
Nguyen, Kiet A. E-mail: ruth.pachter@wpafb.af.mil; Pachter, Ruth E-mail: ruth.pachter@wpafb.af.mil; Day, Paul N.
2014-06-28
We present a generalized Kohn-Sham (KS) density functional theory (DFT) based effective fragment potential (EFP2-DFT) method for the treatment of solvent effects. Similar to the original Hartree-Fock (HF) based potential with fitted parameters for water (EFP1) and the generalized HF based potential (EFP2-HF), EFP2-DFT includes electrostatic, exchange-repulsion, polarization, and dispersion potentials, which are generated for a chosen DFT functional for a given isolated molecule. The method does not have fitted parameters, except for implicit parameters within a chosen functional and the dispersion correction to the potential. The electrostatic potential is modeled with a multipolar expansion at each atomic center and bond midpoint using Stone's distributed multipolar analysis. The exchange-repulsion potential between two fragments is composed of the overlap and kinetic energy integrals and the nondiagonal KS matrices in the localized molecular orbital basis. The polarization potential is derived from the static molecular polarizability. The dispersion potential includes the intermolecular D3 dispersion correction of Grimme et al. [J. Chem. Phys. 132, 154104 (2010)]. The potential generated from the CAMB3LYP functional has mean unsigned errors (MUEs) with respect to results from coupled cluster singles, doubles, and perturbative triples with a complete basis set limit (CCSD(T)/CBS) extrapolation, of 1.7, 2.2, 2.0, and 0.5 kcal/mol, for the S22, water-benzene clusters, water clusters, and n-alkane dimers benchmark sets, respectively. The corresponding EFP2-HF errors for the respective benchmarks are 2.41, 3.1, 1.8, and 2.5 kcal/mol. Thus, the new EFP2-DFT-D3 method with the CAMB3LYP functional provides comparable or improved results at lower computational cost and, therefore, extends the range of applicability of EFP2 to larger system sizes.
Global and local curvature in density functional theory
NASA Astrophysics Data System (ADS)
Zhao, Qing; Ioannidis, Efthymios I.; Kulik, Heather J.
2016-08-01
Piecewise linearity of the energy with respect to fractional electron removal or addition is a requirement of an electronic structure method that necessitates the presence of a derivative discontinuity at integer electron occupation. Semi-local exchange-correlation (xc) approximations within density functional theory (DFT) fail to reproduce this behavior, giving rise to deviations from linearity with a convex global curvature that is evidence of many-electron, self-interaction error and electron delocalization. Popular functional tuning strategies focus on reproducing piecewise linearity, especially to improve predictions of optical properties. In a divergent approach, Hubbard U-augmented DFT (i.e., DFT+U) treats self-interaction errors by reducing the local curvature of the energy with respect to electron removal or addition from one localized subshell to the surrounding system. Although it has been suggested that DFT+U should simultaneously alleviate global and local curvature in the atomic limit, no detailed study on real systems has been carried out to probe the validity of this statement. In this work, we show when DFT+U should minimize deviations from linearity and demonstrate that a "+U" correction will never worsen the deviation from linearity of the underlying xc approximation. However, we explain varying degrees of efficiency of the approach over 27 octahedral transition metal complexes with respect to transition metal (Sc-Cu) and ligand strength (CO, NH3, and H2O) and investigate select pathological cases where the delocalization error is invisible to DFT+U within an atomic projection framework. Finally, we demonstrate that the global and local curvatures represent different quantities that show opposing behavior with increasing ligand field strength, and we identify where these two may still coincide.
Spectra of empirical autocorrelation matrices: A random-matrix-theory-inspired perspective
NASA Astrophysics Data System (ADS)
Jamali, Tayeb; Jafari, G. R.
2015-07-01
We construct an autocorrelation matrix of a time series and analyze it based on the random-matrix theory (RMT) approach. The autocorrelation matrix is capable of extracting information which is not easily accessible by the direct analysis of the autocorrelation function. In order to provide a precise conclusion based on the information extracted from the autocorrelation matrix, the results must be first evaluated. In other words they need to be compared with some sort of criterion to provide a basis for the most suitable and applicable conclusions. In the context of the present study, the criterion is selected to be the well-known fractional Gaussian noise (fGn). We illustrate the applicability of our method in the context of stock markets. For the former, despite the non-Gaussianity in returns of the stock markets, a remarkable agreement with the fGn is achieved.
Density matrix renormalization group study of the Anyon-Hubbard model
NASA Astrophysics Data System (ADS)
Arcila-Forero, J.; Franco, R.; Silva-Valencia, J.
2016-02-01
Recently optical lattices allow us to observe phase transition without the uncertainty posed by complex materials, and the simulations of these systems are an excellent bridge between materials-based condensed matter physics and cold atoms. In this way, the computational physics related to many-body problems have increased in importance. Using the density matrix renormalization group method, we studied a Hubbard model for anyons, which is an equivalent to a variant of the Bose-Hubbard model in which the bosonic hopping depends on the local density. This is an exact mapping between anyons and bosons in one dimension. The anyons interlope between bosons and fermions. For two anyons under particle exchange, the wave function acquires a fractional phase eiθ . We conclude that this system exhibits two phases: Mott-insulator and superfluid. We present the phase diagram for some angles. The Mott lobe increases with an increase of the statistical. We observed a reentrance phase transition for all lobes. We showed that the model studied is in the same universality class as the Bose-Hubbard model with two-body interactions.
Density-matrix based determination of low-energy model Hamiltonians from ab initio wavefunctions
Changlani, Hitesh J.; Zheng, Huihuo; Wagner, Lucas K.
2015-09-14
We propose a way of obtaining effective low energy Hubbard-like model Hamiltonians from ab initio quantum Monte Carlo calculations for molecular and extended systems. The Hamiltonian parameters are fit to best match the ab initio two-body density matrices and energies of the ground and excited states, and thus we refer to the method as ab initio density matrix based downfolding. For benzene (a finite system), we find good agreement with experimentally available energy gaps without using any experimental inputs. For graphene, a two dimensional solid (extended system) with periodic boundary conditions, we find the effective on-site Hubbard U{sup ∗}/t to be 1.3 ± 0.2, comparable to a recent estimate based on the constrained random phase approximation. For molecules, such parameterizations enable calculation of excited states that are usually not accessible within ground state approaches. For solids, the effective Hamiltonian enables large-scale calculations using techniques designed for lattice models.
The single-particle density matrix of a quantum bright soliton from the coordinate Bethe ansatz
NASA Astrophysics Data System (ADS)
Ayet, Alex; Brand, Joachim
2017-02-01
We present a novel approach for computing reduced density matrices for superpositions of eigenstates of a Bethe-ansatz solvable model by direct integration of the wave function in coordinate representation. A diagrammatic approach is developed to keep track of relevant terms and identify symmetries, which helps to reduce the number of terms that have to be evaluated numerically. As a first application we compute with modest numerical resources the single-particle density matrix and its eigenvalues including the condensate fraction for a quantum bright soliton with up to N = 10 bosons. The latter are constructed as superpositions of string-type Bethe-ansatz eigenstates of nonrelativistic bosons in one spatial dimension with attractive contact interaction. Upon delocalising the superposition in momentum space we find that the condensate fraction reaches maximum values larger than 97% with weak particle-number dependence in the range of particles studied. The presented approach is suitable for studying time-dependent problems and generalises to higher-order correlation functions.
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.
NASA Astrophysics Data System (ADS)
Gavryusev, V.; Signoles, A.; Ferreira-Cao, M.; Zürn, G.; Hofmann, C. S.; Günter, G.; Schempp, H.; Robert-de-Saint-Vincent, M.; Whitlock, S.; Weidemüller, M.
2016-08-01
We present combined measurements of the spatially resolved optical spectrum and the total excited-atom number in an ultracold gas of three-level atoms under electromagnetically induced transparency conditions involving high-lying Rydberg states. The observed optical transmission of a weak probe laser at the center of the coupling region exhibits a double peaked spectrum as a function of detuning, while the Rydberg atom number shows a comparatively narrow single resonance. By imaging the transmitted light onto a charge-coupled-device camera, we record hundreds of spectra in parallel, which are used to map out the spatial profile of Rabi frequencies of the coupling laser. Using all the information available we can reconstruct the full one-body density matrix of the three-level system, which provides the optical susceptibility and the Rydberg density as a function of spatial position. These results help elucidate the connection between three-level interference phenomena, including the interplay of matter and light degrees of freedom and will facilitate new studies of many-body effects in optically driven Rydberg gases.
Bultinck, Patrick; Van Neck, Dimitri; Acke, Guillaume; Ayers, Paul W
2012-02-21
The Fukui function is considered as the diagonal element of the Fukui matrix in position space, where the Fukui matrix is the derivative of the one particle density matrix (1DM) with respect to the number of electrons. Diagonalization of the Fukui matrix, expressed in an orthogonal orbital basis, explains why regions in space with negative Fukui functions exist. Using a test set of molecules, electron correlation is found to have a remarkable effect on the eigenvalues of the Fukui matrix. The Fukui matrices at the independent electron model level are mathematically proven to always have an eigenvalue equal to exactly unity while the rest of the eigenvalues possibly differ from zero but sum to zero. The loss of idempotency of the 1DM at correlated levels of theory causes the loss of these properties. The influence of electron correlation is examined in detail and the frontier molecular orbital concept is extended to correlated levels of theory by defining it as the eigenvector of the Fukui matrix with the largest eigenvalue. The effect of degeneracy on the Fukui matrix is examined in detail, revealing that this is another way by which the unity eigenvalue and perfect pairing of eigenvalues can disappear.
Analytic evaluation of the dipole Hessian matrix in coupled-cluster theory
NASA Astrophysics Data System (ADS)
Jagau, Thomas-C.; Gauss, Jürgen; Ruud, Kenneth
2013-10-01
The general theory required for the calculation of analytic third energy derivatives at the coupled-cluster level of theory is presented and connected to preceding special formulations for hyperpolarizabilities and polarizability gradients. Based on our theory, we have implemented a scheme for calculating the dipole Hessian matrix in a fully analytical manner within the coupled-cluster singles and doubles approximation. The dipole Hessian matrix is the second geometrical derivative of the dipole moment and thus a third derivative of the energy. It plays a crucial role in IR spectroscopy when taking into account anharmonic effects and is also essential for computing vibrational corrections to dipole moments. The superior accuracy of the analytic evaluation of third energy derivatives as compared to numerical differentiation schemes is demonstrated in some pilot calculations.
Fractional supersymmetric Liouville theory and the multi-cut matrix models
NASA Astrophysics Data System (ADS)
Irie, Hirotaka
2009-10-01
We point out that the non-critical version of the k-fractional superstring theory can be described by k-cut critical points of the matrix models. In particular, in comparison with the spectrum structure of fractional super-Liouville theory, we show that (p,q) minimal fractional superstring theories appear in the Z-symmetry breaking critical points of the k-cut two-matrix models and the operator contents and string susceptibility coincide on both sides. By using this correspondence, we also propose a set of primary operators of the fractional superconformal ghost system which consistently produces the correct gravitational scaling critical exponents of the on-shell vertex operators.
Advanced Density Functional Theory Methods for Materials Science
NASA Astrophysics Data System (ADS)
Demers, Steven
In this work we chiefly deal with two broad classes of problems in computational materials science, determining the doping mechanism in a semiconductor and developing an extreme condition equation of state. While solving certain aspects of these questions is well-trodden ground, both require extending the reach of existing methods to fully answer them. Here we choose to build upon the framework of density functional theory (DFT) which provides an efficient means to investigate a system from a quantum mechanics description. Zinc Phosphide (Zn3P2) could be the basis for cheap and highly efficient solar cells. Its use in this regard is limited by the difficulty in n-type doping the material. In an effort to understand the mechanism behind this, the energetics and electronic structure of intrinsic point defects in zinc phosphide are studied using generalized Kohn-Sham theory and utilizing the Heyd, Scuseria, and Ernzerhof (HSE) hybrid functional for exchange and correlation. Novel 'perturbation extrapolation' is utilized to extend the use of the computationally expensive HSE functional to this large-scale defect system. According to calculations, the formation energy of charged phosphorus interstitial defects are very low in n-type Zn3P2 and act as 'electron sinks', nullifying the desired doping and lowering the fermi-level back towards the p-type regime. Going forward, this insight provides clues to fabricating useful zinc phosphide based devices. In addition, the methodology developed for this work can be applied to further doping studies in other systems. Accurate determination of high pressure and temperature equations of state is fundamental in a variety of fields. However, it is often very difficult to cover a wide range of temperatures and pressures in an laboratory setting. Here we develop methods to determine a multi-phase equation of state for Ta through computation. The typical means of investigating thermodynamic properties is via 'classical' molecular
Franco de Carvalho, F.; Tavernelli, I.
2015-12-14
In this work, we derive a method to perform trajectory-based nonadiabatic dynamics that is able to describe both nonadiabatic transitions and intersystem crossing events (transitions between states of different spin-multiplicity) at the same level of theory, namely, time-dependent density functional theory (TDDFT). To this end, we combined our previously developed TDDFT-based trajectory surface hopping scheme with an accurate and efficient algorithm for the calculation of the spin-orbit coupling (SOC) matrix elements. More specifically, we designed two algorithms for the calculation of intersystem crossing transitions, one based on an extended Tully’s surface hopping scheme including SOC and the second based on a Landau-Zener approximation applied to the spin sector of the electronic Hilbert space. This development allows for the design of an efficient on-the-fly nonadiabatic approach that can handle, on an equal footing, nonadiabatic and intersystem crossing transitions. The method is applied to the study of the photophysics of sulfur dioxide (SO{sub 2}) in gas and liquid phases.
Franco de Carvalho, F; Tavernelli, I
2015-12-14
In this work, we derive a method to perform trajectory-based nonadiabatic dynamics that is able to describe both nonadiabatic transitions and intersystem crossing events (transitions between states of different spin-multiplicity) at the same level of theory, namely, time-dependent density functional theory (TDDFT). To this end, we combined our previously developed TDDFT-based trajectory surface hopping scheme with an accurate and efficient algorithm for the calculation of the spin-orbit coupling (SOC) matrix elements. More specifically, we designed two algorithms for the calculation of intersystem crossing transitions, one based on an extended Tully's surface hopping scheme including SOC and the second based on a Landau-Zener approximation applied to the spin sector of the electronic Hilbert space. This development allows for the design of an efficient on-the-fly nonadiabatic approach that can handle, on an equal footing, nonadiabatic and intersystem crossing transitions. The method is applied to the study of the photophysics of sulfur dioxide (SO2) in gas and liquid phases.
Fragment approach to constrained density functional theory calculations using Daubechies wavelets
Ratcliff, Laura E.; Genovese, Luigi; Mohr, Stephan; Deutsch, Thierry
2015-06-21
In a recent paper, we presented a linear scaling Kohn-Sham density functional theory (DFT) code based on Daubechies wavelets, where a minimal set of localized support functions are optimized in situ and therefore adapted to the chemical properties of the molecular system. Thanks to the systematically controllable accuracy of the underlying basis set, this approach is able to provide an optimal contracted basis for a given system: accuracies for ground state energies and atomic forces are of the same quality as an uncontracted, cubic scaling approach. This basis set offers, by construction, a natural subset where the density matrix of the system can be projected. In this paper, we demonstrate the flexibility of this minimal basis formalism in providing a basis set that can be reused as-is, i.e., without reoptimization, for charge-constrained DFT calculations within a fragment approach. Support functions, represented in the underlying wavelet grid, of the template fragments are roto-translated with high numerical precision to the required positions and used as projectors for the charge weight function. We demonstrate the interest of this approach to express highly precise and efficient calculations for preparing diabatic states and for the computational setup of systems in complex environments.
Fragment approach to constrained density functional theory calculations using Daubechies wavelets.
Ratcliff, Laura E; Genovese, Luigi; Mohr, Stephan; Deutsch, Thierry
2015-06-21
In a recent paper, we presented a linear scaling Kohn-Sham density functional theory (DFT) code based on Daubechies wavelets, where a minimal set of localized support functions are optimized in situ and therefore adapted to the chemical properties of the molecular system. Thanks to the systematically controllable accuracy of the underlying basis set, this approach is able to provide an optimal contracted basis for a given system: accuracies for ground state energies and atomic forces are of the same quality as an uncontracted, cubic scaling approach. This basis set offers, by construction, a natural subset where the density matrix of the system can be projected. In this paper, we demonstrate the flexibility of this minimal basis formalism in providing a basis set that can be reused as-is, i.e., without reoptimization, for charge-constrained DFT calculations within a fragment approach. Support functions, represented in the underlying wavelet grid, of the template fragments are roto-translated with high numerical precision to the required positions and used as projectors for the charge weight function. We demonstrate the interest of this approach to express highly precise and efficient calculations for preparing diabatic states and for the computational setup of systems in complex environments.
Density functional theory study of the oligomerization of carboxylic acids.
Di Tommaso, Devis; Watson, Ken L
2014-11-20
We present a density functional theory [M06-2X/6-31+G(d,p)] study of the structures and free energies of formation of oligomers of four carboxylic acids (formic acid, acetic acid, tetrolic acid, and benzoic acid) in water, chloroform, and carbon tetrachloride. Solvation effects were treated using the SMD continuum solvation model. The low-lying energy structures of molecular complexes were located by adopting an efficient search procedure to probe the potential energy surfaces of the oligomers of carboxylic acids (CA)n (n = 2-6). The free energies of the isomers of (CA)n in solution were determined as the sum of the electronic energy, vibrational-rotational-translational gas-phase contribution, and solvation free energy. The assessment of the computational protocol adopted in this study with respect to the dimerization of acetic acid, (AA)2, and formic acid, (FA)2, located new isomers of (AA)2 and (FA)2 and gave dimerization constants in good agreement with the experimental values. The calculation of the self-association of acetic acid, tetrolic acid, and benzoic acid shows the following: (i) Classic carboxylic dimers are the most stable isomer of (CA)2 in both the gas phase and solution. (ii) Trimers of carboxylic acid are stable in apolar aprotic solvents. (iii) Molecular clusters consisting of two interacting classic carboxylic dimers (CA)4,(D+D) are the most stable type of tetramers, but their formation from the self-association of classic carboxylic dimers is highly unfavorable. (iv) For acetic acid and tetrolic acid the reactions (CA)2 + 2CA → (CA)4,(D+D) and (CA)3 + CA → (CA)4,(D+D) are exoergonic, but these aggregation pathways go through unstable clusters that could hinder the formation of tetrameric species. (v) For tetrolic acid the prenucleation species that are more likely to form in solution are dimeric and trimeric structures that have encoded structural motifs resembling the α and β solid forms of tetrolic acid. (vi) Stable tetramers of
Density Functional Theory Calculations of Mass Transport in UO2
Andersson, Anders D.; Dorado, Boris; Uberuaga, Blas P.; Stanek, Christopher R.
2012-06-26
In this talk we present results of density functional theory (DFT) calculations of U, O and fission gas diffusion in UO{sub 2}. These processes all impact nuclear fuel performance. For example, the formation and retention of fission gas bubbles induce fuel swelling, which leads to mechanical interaction with the clad thereby increasing the probability for clad breach. Alternatively, fission gas can be released from the fuel to the plenum, which increases the pressure on the clad walls and decreases the gap thermal conductivity. The evolution of fuel microstructure features is strongly coupled to diffusion of U vacancies. Since both U and fission gas transport rates vary strongly with the O stoichiometry, it is also important to understand O diffusion. In order to better understand bulk Xe behavior in UO{sub 2{+-}x} we first calculate the relevant activation energies using DFT techniques. By analyzing a combination of Xe solution thermodynamics, migration barriers and the interaction of dissolved Xe atoms with U, we demonstrate that Xe diffusion predominantly occurs via a vacancy-mediated mechanism. Since Xe transport is closely related to diffusion of U vacancies, we have also studied the activation energy for this process. In order to explain the low value of 2.4 eV found for U migration from independent damage experiments (not thermal equilibrium) the presence of vacancy clusters must be included in the analysis. Next we investigate species transport on the (111) UO{sub 2} surface, which is motivated by the formation of small voids partially filled with fission gas atoms (bubbles) in UO{sub 2} under irradiation. Surface diffusion could be the rate-limiting step for diffusion of such bubbles, which is an alternative mechanism for mass transport in these materials. As expected, the activation energy for surface diffusion is significantly lower than for bulk transport. These results are further discussed in terms of engineering-scale fission gas release models
Understanding trichloroethylene chemisorption to iron surfaces using density functional theory.
Zhang, Nianliu; Luo, Jing; Blowers, Paul; Farrell, James
2008-03-15
This research investigated the thermodynamic favorability and resulting structures for chemical adsorption of trichloroethylene (TCE) to metallic iron using periodic density functional theory (DFT). Three initial TCE positions having the plane defined by HCC atoms parallel to the iron surface resulted in formation of three different chemisorption complexes between carbon atoms in TCE and the iron surface. The Cl-bridge initial configuration with the HCC plane of TCE perpendicular to the iron surface did not result in C-Fe bond formation. The most energetically favorable complex formed at the C-bridge site where the initial configuration had the C=C bond in TCE at a bridge site between adjacent iron atoms. In the C-bridge complex, one C atom formed two a bonds to different Fe atoms, while the second C atom formed a sigma bond with a second Fe atom. Surface complexation atthe C-bridge site resulted in scission of all three C-Cl bonds and also resulted in a shortening of the C==C bond to a distance intermediate between a double and a triple bond. Initial configurations with the C==C bond adsorbed at top or hollow sites on the iron surface resulted in formation of C-Fe a bonds between a single C and two adjacent Fe atoms, and the scission of only two C==Cl bonds. Bond angles and bond lengths indicated that there were no changes in bond order of the C==C bond for top and hollow adsorption. Chemisorption at the C-bridge site had an activation energy of 49 kJ/mol and an early transition state where all three C-CI bonds were activated. The early transition state and the loss of all three Cl atoms upon chemisorption are consistent with most experimental observations that TCE undergoes complete dechlorination in one interaction with the iron surface. The absence of chemisorption and scission of only two C--Cl bonds at the Cl-bridge site is consistent with experimental observations that trace amounts of chloroacetylene may also be produced from reactions of TCE with iron.
Zinc surface complexes on birnessite: A density functional theory study
Kwon, Kideok D.; Refson, Keith; Sposito, Garrison
2009-01-05
Biogeochemical cycling of zinc is strongly influenced by sorption on birnessite minerals (layer-type MnO2), which are found in diverse terrestrial and aquatic environments. Zinc has been observed to form both tetrahedral (Zn{sup IV}) and octahedral (Zn{sup VI}) triple-corner-sharing surface complexes (TCS) at Mn(IV) vacancy sites in hexagonal birnessite. The octahedral complex is expected to be similar to that of Zn in the Mn oxide mineral, chalcophanite (ZnMn{sub 3}O{sub 7} {center_dot} 3H{sub 2}O), but the reason for the occurrence of the four-coordinate Zn surface species remains unclear. We address this issue computationally using spin-polarized Density Functional Theory (DFT) to examine the Zn{sub IV}-TCS and Zn{sup VI}-TCS species. Structural parameters obtained by DFT geometry optimization were in excellent agreement with available experimental data on Zn-birnessites. Total energy, magnetic moments, and electron-overlap populations obtained by DFT for isolated Zn{sup IV}-TCS revealed that this species is stable in birnessite without a need for Mn(III) substitution in the octahedral sheet and that it is more effective in reducing undersaturation of surface O at a Mn vacancy than is Zn{sub VI}-TCS. Comparison between geometry-optimized ZnMn{sub 3}O{sub 7} {center_dot} 3H{sub 2}O (chalcophanite) and the hypothetical monohydrate mineral, ZnMn{sub 3}O{sub 7} {center_dot} H{sub 2}O, which contains only tetrahedral Zn, showed that the hydration state of Zn significantly affects birnessite structural stability. Finally, our study also revealed that, relative to their positions in an ideal vacancy-free MnO{sub 2}, Mn nearest to Zn in a TCS surface complex move toward the vacancy by 0.08-0.11 {angstrom}, while surface O bordering the vacancy move away from it by 0.16-0.21 {angstrom}, in agreement with recent X-ray absorption spectroscopic analyses.
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
Hammond, Jeff R.; Mazziotti, David A.
2006-01-15
An alternative approach to open-shell molecular calculations using the variational two-electron reduced-density-matrix (2-RDM) theory [Mazziotti, Phys. Rev. Lett. 93, 213001 (2004)] is presented. The energy and 2-RDM of the open-shell molecule (or radical) are computed from the limit of dissociating one or more hydrogen atoms from a molecule in a singlet state. Because the ground-state energy of an 'infinitely' separated hydrogen atom in a given finite basis is known, we can determine the energy of the radical by subtracting the energy of one or more hydrogen atoms from the energy of the total dissociated system. The 2-RDM is constrained to have singlet symmetry in all calculations. Two sets of N-representability conditions are employed: (i) two-positivity conditions, and (ii) two-positivity conditions plus the T{sub 2} condition, which is a subset of the three-positivity conditions. Optimization of the energy with respect to the 2-RDM is performed with a first-order algorithm for solving the semidefinite program within the variational 2-RDM method. We present calculations of several radicals near equilibrium as well as the dissociation curves of the diatomic radicals CH and OH.
Drábek, Jiří
2016-01-01
In this paper I tested whether Contradictory Matrix with 40 Inventive Principles, the simplest instrument from the Theory of Inventive Problem Solving (TRIZ), is a useful approach to a real-life PCR scenario. The PCR challenge consisted of standardization of fluorescence melting curve measurements in Competitive Amplification of Differentially Melting Amplicons (CADMA) PCR for multiple targets. Here I describe my way of using the TRIZ Matrix to generate seven alternative solutions from which I can choose the successful solution, consisting of repeated cycles of amplification and melting in a single PCR run.
Li, Qu; Yao, Min; Yang, Jianhua; Xu, Ning
2014-01-01
Online friend recommendation is a fast developing topic in web mining. In this paper, we used SVD matrix factorization to model user and item feature vector and used stochastic gradient descent to amend parameter and improve accuracy. To tackle cold start problem and data sparsity, we used KNN model to influence user feature vector. At the same time, we used graph theory to partition communities with fairly low time and space complexity. What is more, matrix factorization can combine online and offline recommendation. Experiments showed that the hybrid recommendation algorithm is able to recommend online friends with good accuracy.
Kussmann, Jörg; Luenser, Arne; Beer, Matthias; Ochsenfeld, Christian
2015-03-07
An analytical method to calculate the molecular vibrational Hessian matrix at the self-consistent field level is presented. By analysis of the multipole expansions of the relevant derivatives of Coulomb-type two-electron integral contractions, we show that the effect of the perturbation on the electronic structure due to the displacement of nuclei decays at least as r{sup −2} instead of r{sup −1}. The perturbation is asymptotically local, and the computation of the Hessian matrix can, in principle, be performed with O(N) complexity. Our implementation exhibits linear scaling in all time-determining steps, with some rapid but quadratic-complexity steps remaining. Sample calculations illustrate linear or near-linear scaling in the construction of the complete nuclear Hessian matrix for sparse systems. For more demanding systems, scaling is still considerably sub-quadratic to quadratic, depending on the density of the underlying electronic structure.
Accuracy of Pseudo-Inverse Covariance Learning--A Random Matrix Theory Analysis.
Hoyle, David C
2011-07-01
For many learning problems, estimates of the inverse population covariance are required and often obtained by inverting the sample covariance matrix. Increasingly for modern scientific data sets, the number of sample points is less than the number of features and so the sample covariance is not invertible. In such circumstances, the Moore-Penrose pseudo-inverse sample covariance matrix, constructed from the eigenvectors corresponding to nonzero sample covariance eigenvalues, is often used as an approximation to the inverse population covariance matrix. The reconstruction error of the pseudo-inverse sample covariance matrix in estimating the true inverse covariance can be quantified via the Frobenius norm of the difference between the two. The reconstruction error is dominated by the smallest nonzero sample covariance eigenvalues and diverges as the sample size becomes comparable to the number of features. For high-dimensional data, we use random matrix theory techniques and results to study the reconstruction error for a wide class of population covariance matrices. We also show how bagging and random subspace methods can result in a reduction in the reconstruction error and can be combined to improve the accuracy of classifiers that utilize the pseudo-inverse sample covariance matrix. We test our analysis on both simulated and benchmark data sets.
NASA Astrophysics Data System (ADS)
Orantin, N.
2007-09-01
The 2-matrix model has been introduced to study Ising model on random surfaces. Since then, the link between matrix models and combinatorics of discrete surfaces has strongly tightened. This manuscript aims to investigate these deep links and extend them beyond the matrix models, following my work's evolution. First, I take care to define properly the hermitian 2 matrix model which gives rise to generating functions of discrete surfaces equipped with a spin structure. Then, I show how to compute all the terms in the topological expansion of any observable by using algebraic geometry tools. They are obtained as differential forms on an algebraic curve associated to the model: the spectral curve. In a second part, I show how to define such differentials on any algebraic curve even if it does not come from a matrix model. I then study their numerous symmetry properties under deformations of the algebraic curve. In particular, I show that these objects coincide with the topological expansion of the observable of a matrix model if the algebraic curve is the spectral curve of this model. Finally, I show that fine tuning the parameters ensure that these objects can be promoted to modular invariants and satisfy the holomorphic anomaly equation of the Kodaira-Spencer theory. This gives a new hint that the Dijkgraaf-Vafa conjecture is correct.
The ABCDEF's of matrix models for supersymmetric Chern-Simons theories
NASA Astrophysics Data System (ADS)
Gulotta, Daniel R.; Herzog, Christopher P.; Nishioka, Tatsuma
2012-04-01
We consider {N} = {3} supersymmetric Chern-Simons gauge theories with product unitary and orthosymplectic groups and bifundamental and fundamental fields. We study the partition functions on an S 3 by using the Kapustin-Willett-Yaakov matrix model. The saddlepoint equations in a large N limit lead to a constraint that the long range forces between the eigenvalues must cancel; the resulting quiver theories are of affine Dynkin type. We introduce a folding/unfolding trick which lets us, at the level of the large N matrix model, (i) map quivers with orthosymplectic groups to those with unitary groups, and (ii) obtain non-simply laced quivers from the corresponding simply laced quivers using a {{{Z}}_{{2}}} outer automorphism. The brane configurations of the quivers are described in string theory and the folding/unfolding is interpreted as the addition/subtraction of orientifold and orbifold planes. We also relate the U( N) quiver theories to the affine ADE quiver matrix models with a Stieltjes-Wigert type potential, and derive the generalized Seiberg duality in 2 + 1 dimensions from Seiberg duality in 3 + 1 dimensions.
Tekwa, Edward W; Gonzalez, Andrew; Loreau, Michel
2015-09-07
Cooperation plays a crucial role in many aspects of biology. We use the spatial ecological metrics of local densities to measure and model cooperative interactions. While local densities can be found as technical details in current theories, we aim to establish them as central to an approach that describes spatial effects in the evolution of cooperation. A resulting local interaction model neatly partitions various spatial and non-spatial selection mechanisms. Furthermore, local densities are shown to be fundamental for important metrics of game theory, multilevel selection theory and inclusive fitness theory. The corresponding metrics include structure coefficients, spatial variance, contextual covariance, relatedness, and inbreeding coefficient or F-statistics. Local densities serve as the basis of an emergent spatial theory that draws from and brings unity to multiple theories of cooperation.
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.
Properties and Theory of Lower-Hybrid Density Cavities
NASA Astrophysics Data System (ADS)
Knudsen, D. J.; Bock, B.; Burchill, J. K.; Curtis, J.; Pfaff, R. F.; Bounds, S. R.; Clemmons, J. H.; Wallis, D. D.
2002-12-01
Lower-hybrid cavities are wave-filled, cylindrical density cavities aligned with the geomagnetic field. They have relative density depletions of several to tens of percent, diameters of order 20-50 m, and are associated with ion heating transverse to the geomagnetic field. Several aspects of these structures remain unexplained, including the cause of the density depletion and the reason for their relatively narrow distribution of diameters. We present statistical properties of several hundred cavities observed on the OEDIPUS-C and GEODESIC sounding rockets, flown into the nightside auroral ionosphere through plasma densities varying over two orders of magnitude. The average cavity chord lengths are observed not to depend on density, demonstrating that cavity sizes are not determined by electron inertial length, for example. A subset of cavities also exhibit slight density increases or ``shoulders'' at the their perimeters. Density cavities with these features can be explained by tracing ion trajectories in the presence of ion heating localized on the scale of an ion gyroradius. The dependence of cavity depth and shape on heating intensity and scale size is predicted using Monte Carlo and semi-analytical descriptions of heated ion motion near cavities.
NASA Astrophysics Data System (ADS)
Duran-Olivencia, Miguel A.; Yatsyshin, Peter; Lutsko, James F.; Kalliadasis, Serafim
2016-11-01
Classical density functional theory (DFT) for fluids and its dynamic extension (DDFT) provide an appealing mean-field framework for describing equilibrium and dynamics of complex soft matter systems. For a long time, homogeneous nucleation was considered to be outside the limits of applicability of DDFT. However, our recently developed mesoscopic nucleation theory (MeNT) based on fluctuating hydrodynamics, reconciles the inherent randomness of the nucleation process with the deterministic nature of DDFT. It turns out that in the weak-noise limit, the most likely path (MLP) for nucleation to occur is determined by the DDFT equations. We present computations of MLPs for homogeneous and heterogeneous nucleation in colloidal suspensions. For homogeneous nucleation, the MLP obtained is in excellent agreement with the reduced order-parameter description of MeNT, which predicts a multistage nucleation pathway. For heterogeneous nucleation, the presence of impurities in the fluid affects the MLP, but remarkably, the overall qualitative picture of homogeneous nucleation persists. Finally, we highlight the use of DDFT as a simulation tool, which is especially appealing as there are no known applications of MeNT to heterogeneous nucleation. We acknowledge financial support from the European Research Council via Advanced Grant No. 247031 and from EPSRC via Grants No. EP/L020564 and EP/L025159.
NASA Astrophysics Data System (ADS)
Lim, S. P.; Sheng, D. N.
2016-07-01
A many-body localized (MBL) state is a new state of matter emerging in a disordered interacting system at high-energy densities through a disorder-driven dynamic phase transition. The nature of the phase transition and the evolution of the MBL phase near the transition are the focus of intense theoretical studies with open issues in the field. We develop an entanglement density matrix renormalization group (En-DMRG) algorithm to accurately target highly excited states for MBL systems. By studying the one-dimensional Heisenberg spin chain in a random field, we demonstrate the accuracy of the method in obtaining energy eigenstates and the corresponding statistical results of quantum states in the MBL phase. Based on large system simulations by En-DMRG for excited states, we demonstrate some interesting features in the entanglement entropy distribution function, which is characterized by two peaks: one at zero and another one at the quantized entropy S =ln2 with an exponential decay tail on the S >ln2 side. Combining En-DMRG with exact diagonalization simulations, we demonstrate that the transition from the MBL phase to the delocalized ergodic phase is driven by rare events where the locally entangled spin pairs develop power-law correlations. The corresponding phase diagram contains an intermediate or crossover regime, which has power-law spin-z correlations resulting from contributions of the rare events. We discuss the physical picture for the numerical observations in this regime, where various distribution functions are distinctly different from results deep in the ergodic and MBL phases for finite-size systems. Our results may provide new insights for understanding the phase transition in such systems.
Theory of tokamak equilibria with central current density reversal.
Wang, Shaojie
2004-10-08
It is found that, with a model current profile, the Grad-Shafranov equation can be reduced to the Helmholtz equation, which can describe a variety of equilibrium configurations. With the eigenvalue problem solved in the toroidal coordinate system, an analytical solution to the Grad-Shafranov equation is found. It is demonstrated that current reversal equilibrium configurations exist with finite radial gradient of plasma pressure and continuous current density, and that current density reversal is accompanied by pressure gradient reversal.
Permutationally Invariant Part of a Density Matrix and Nonseparability of N-Qubit States
NASA Astrophysics Data System (ADS)
Gao, Ting; Yan, Fengli; van Enk, S. J.
2014-05-01
We consider the concept of "the permutationally invariant (PI) part of a density matrix," which has proven very useful for both efficient quantum state estimation and entanglement characterization of N-qubit systems. We show here that the concept is, in fact, basis dependent but that this basis dependence makes it an even more powerful concept than has been appreciated so far. By considering the PI part ρPI of a general (mixed) N-qubit state ρ, we obtain (i) strong bounds on quantitative nonseparability measures, (ii) a whole hierarchy of multipartite separability criteria (one of which entails a sufficient criterion for genuine N-partite entanglement) that can be experimentally determined by just 2N +1 measurement settings, (iii) a definition of an efficiently measurable degree of separability, which can be used for quantifying a novel aspect of decoherence of N qubits, and (iv) an explicit example that shows there are, for increasing N, genuinely N-partite entangled states lying closer and closer to the maximally mixed state. Moreover, we show that if the PI part of a state is k nonseparable, then so is the actual state. We further argue to add as requirement on any multipartite entanglement measure E that it satisfy E(ρ)≥E(ρPI), even though the operation that maps ρ→ρPI is not local.
Pisani, Cesare; Erba, Alessandro; Ferrabone, Matteo; Dovesi, Roberto
2012-07-28
In the frame of the Born-Oppenheimer approximation, nuclear motions in crystals can be simulated rather accurately using a harmonic model. In turn, the electronic first-order density matrix (DM) can be expressed as the statistically weighted average over all its determinations each resulting from an instantaneous nuclear configuration. This model has been implemented in a computational scheme which adopts an ab initio one-electron (Hartree-Fock or Kohn-Sham) Hamiltonian in the CRYSTAL program. After selecting a supercell of reasonable size and solving the corresponding vibrational problem in the harmonic approximation, a Metropolis algorithm is adopted for generating a sample of nuclear configurations which reflects their probability distribution at a given temperature. For each configuration in the sample the "instantaneous" DM is calculated, and its contribution to the observables of interest is extracted. Translational and point symmetry of the crystal as reflected in its average DM are fully exploited. The influence of zero-point and thermal motion of nuclei on such important first-order observables as x-ray structure factors and Compton profiles can thus be estimated.
Reduced-density-matrix spectrum and block entropy of permutationally invariant many-body systems.
Salerno, Mario; Popkov, Vladislav
2010-07-01
Spectral properties of the reduced density matrix (RDM) of permutational invariant quantum many-body systems are investigated. The RDM block diagonalization which accounts for all symmetries of the Hamiltonian is achieved. The analytical expression of the RDM spectrum is provided for arbitrary parameters and rigorously proved in the thermodynamical limit. The existence of several sum rules and recurrence relations among RDM eigenvalues is also demonstrated and the distribution function of RDM eigenvalues (including degeneracies) characterized. In particular, we prove that the distribution function approaches a two-dimensional Gaussian in the limit of large subsystem sizes n>1. As a physical application we discuss the von Neumann entropy (VNE) of a block of size n for a system of hard-core bosons on a complete graph, as a function of n and of the temperature T. The occurrence of a crossover of VNE from purely logarithmic behavior at T=0 to a purely linear behavior in n for T≥Tc, is demonstrated.
Matrix models for supersymmetric Chern-Simons theories with an ADE classification
NASA Astrophysics Data System (ADS)
Gulotta, Daniel R.; Ang, J. P.; Herzog, Christopher P.
2012-01-01
We consider mathcal{N} = 3 supersymmetric Chern-Simons (CS) theories that contain product U(N ) gauge groups and bifundamental matter fields. Using the matrix model of Kapustin, Willett and Yaakov, we examine the Euclidean partition function of these theories on an S 3 in the large N limit. We show that the only such CS theories for which the long range forces between the eigenvalues cancel have quivers which are in one-to-one correspondence with the simply laced affine Dynkin diagrams. As the A n series was studied in detail before, in this paper we compute the partition function for the D 4 quiver. The D 4 example gives further evidence for a conjecture that the saddle point eigenvalue distribution is determined by the distribution of gauge invariant chiral operators. We also see that the partition function is invariant under a generalized Seiberg duality for CS theories.
A T-matrix theory of galactic heavy-ion fragmentation
NASA Technical Reports Server (NTRS)
Norbury, J. W.; Townsend, L. W.; Deutchman, P. A.
1985-01-01
The theory of galactic heavy ion fragmentation is furthered by incorporating a T matrix approach into the description of the three step process of abrasion, ablation, and final state interations. The connection between this T matrix and the interaction potential is derived. For resonant states, the substitution of complex energies for real energies in the transition rate is formerly justified for up to third order processes. The previously developed abrasion-ablation fragmentation theory is rederived from first principles and is shown to result from time ordering, classical probability, and zero width resonance approximations. Improvements in the accuracy of the total fragmentation cross sections require an alternative to the latter two approximations. A Lorentz invariant differential abrasion-ablation cross section is derived which explicitly includes the previously derived abrasion total cross sections. It is demonstrated that spectral and angular distributions can be obtained from the general Lorentz invariant form.
NASA Technical Reports Server (NTRS)
Goldberg, Robert K.
2000-01-01
A research program is in progress to develop strain rate dependent deformation and failure models for the analysis of polymer matrix composites subject to impact loads. Previously, strain rate dependent inelastic constitutive equations developed to model the polymer matrix were implemented into a mechanics of materials based micromechanics method. In the current work, the computation of the effective inelastic strain in the micromechanics model was modified to fully incorporate the Poisson effect. The micromechanics equations were also combined with classical laminate theory to enable the analysis of symmetric multilayered laminates subject to in-plane loading. A quasi-incremental trapezoidal integration method was implemented to integrate the constitutive equations within the laminate theory. Verification studies were conducted using an AS4/PEEK composite using a variety of laminate configurations and strain rates. The predicted results compared well with experimentally obtained values.
Integrating random matrix theory predictions with short-time dynamical effects in chaotic systems.
Smith, A Matthew; Kaplan, Lev
2010-07-01
We discuss a modification to random matrix theory eigenstate statistics that systematically takes into account the nonuniversal short-time behavior of chaotic systems. The method avoids diagonalization of the Hamiltonian; instead it requires only knowledge of short-time dynamics for a chaotic system or ensemble of similar systems. Standard random matrix theory and semiclassical predictions are recovered in the limits of zero Ehrenfest time and infinite Heisenberg time, respectively. As examples, we discuss wave-function autocorrelations and cross correlations, and show that significant improvement in accuracy is obtained for simple chaotic systems where comparison can be made with brute-force diagonalization. The accuracy of the method persists even when the short-time dynamics of the system or ensemble is known only in a classical approximation. Further improvement in the rate of convergence is obtained when the method is combined with the correlation function bootstrapping approach introduced previously.
Application of random matrix theory to microarray data for discovering functional gene modules.
Luo, Feng; Zhong, Jianxin; Yang, Yunfeng; Zhou, Jizhong
2006-03-01
We show that spectral fluctuation of coexpression correlation matrices of yeast gene microarray profiles follows the description of the Gaussian orthogonal ensemble (GOE) of the random matrix theory (RMT) and removal of small values of the correlation coefficients results in a transition from the GOE statistics to the Poisson statistics of the RMT. This transition is directly related to the structural change of the gene expression network from a global network to a network of isolated modules.
Cao, Haihui; Ackerman, Jerome L; Hrovat, Mirko I; Graham, Lila; Glimcher, Melvin J; Wu, Yaotang
2008-12-01
The density of the organic matrix of bone substance is a critical parameter necessary to clinically evaluate and distinguish structural and metabolic pathological conditions such as osteomalacia in adults and rickets in growing children. Water- and fat-suppressed proton projection MRI (WASPI) was developed as a noninvasive means to obtain this information. In this study, a density calibration phantom was developed to convert WASPI intensity to true bone matrix density. The phantom contained a specifically designed poly(ethylene oxide)/poly(methyl methacrylate) (PEO/PMMA) blend, whose MRI properties (T(1), T(2), and resonance linewidth) were similar to those of solid bone matrix (collagen, tightly bound water, and other immobile molecules), minimizing the need to correct for differences in T(1) and/or T(2) relaxation between the phantom and the subject. Cortical and trabecular porcine bone specimens were imaged using WASPI with the calibration phantom in the field of view (FOV) as a stable intensity reference. Gravimetric and amino acid analyses were carried out on the same specimens after WASPI, and the chemical results were found to be highly correlated (r(2) = 0.98 and 0.95, respectively) to the WASPI intensity. By this procedure the WASPI intensity can be used to obtain the true bone matrix mass density in g cm(-3).
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).
Matrix elements of Δ B =0 operators in heavy hadron chiral perturbation theory
NASA Astrophysics Data System (ADS)
Lee, Jong-Wan
2015-05-01
We study the light-quark mass and spatial volume dependence of the matrix elements of Δ B =0 four-quark operators relevant for the determination of Vu b and the lifetime ratios of single-b hadrons. To this end, one-loop diagrams are computed in the framework of heavy hadron chiral perturbation theory with partially quenched formalism for three light-quark flavors in the isospin limit; flavor-connected and -disconnected diagrams are carefully analyzed. These calculations include the leading light-quark flavor and heavy-quark spin symmetry breaking effects in the heavy hadron spectrum. Our results can be used in the chiral extrapolation of lattice calculations of the matrix elements to the physical light-quark masses and to infinite volume. To provide insight on such chiral extrapolation, we evaluate the one-loop contributions to the matrix elements containing external Bd, Bs mesons and Λb baryon in the QCD limit, where sea and valence quark masses become equal. In particular, we find that the matrix elements of the λ3 flavor-octet operators with an external Bd meson receive the contributions solely from connected diagrams in which current lattice techniques are capable of precise determination of the matrix elements. Finite volume effects are at most a few percent for typical lattice sizes and pion masses.
A density functional theory for colloids with two multiple bonding associating sites.
Haghmoradi, Amin; Wang, Le; Chapman, Walter G
2016-06-22
Wertheim's multi-density formalism is extended for patchy colloidal fluids with two multiple bonding patches. The theory is developed as a density functional theory to predict the properties of an associating inhomogeneous fluid. The equation of state developed for this fluid depends on the size of the patch, and includes formation of cyclic, branched and linear clusters of associated species. The theory predicts the density profile and the fractions of colloids in different bonding states versus the distance from one wall as a function of bulk density and temperature. The predictions from our theory are compared with previous results for a confined fluid with four single bonding association sites. Also, comparison between the present theory and Monte Carlo simulation indicates a good agreement.
Element orbitals for Kohn-Sham density functional theory
Lin, Lin; Ying, Lexing
2012-05-08
We present a method to discretize the Kohn-Sham Hamiltonian matrix in the pseudopotential framework by a small set of basis functions automatically contracted from a uniform basis set such as planewaves. Each basis function is localized around an element, which is a small part of the global domain containing multiple atoms. We demonstrate that the resulting basis set achieves meV accuracy for 3D densely packed systems with a small number of basis functions per atom. The procedure is applicable to insulating and metallic systems.
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.
Xie, Hang; Jiang, Feng; Tian, Heng; Zheng, Xiao; Kwok, Yanho; Chen, Shuguang; Yam, ChiYung; Yan, YiJing; Chen, Guanhua
2012-07-28
Basing on our hierarchical equations of motion for time-dependent quantum transport [X. Zheng, G. H. Chen, Y. Mo, S. K. Koo, H. Tian, C. Y. Yam, and Y. J. Yan, J. Chem. Phys. 133, 114101 (2010)], we develop an efficient and accurate numerical algorithm to solve the Liouville-von-Neumann equation. We solve the real-time evolution of the reduced single-electron density matrix at the tight-binding level. Calculations are carried out to simulate the transient current through a linear chain of atoms, with each represented by a single orbital. The self-energy matrix is expanded in terms of multiple Lorentzian functions, and the Fermi distribution function is evaluated via the Padè spectrum decomposition. This Lorentzian-Padè decomposition scheme is employed to simulate the transient current. With sufficient Lorentzian functions used to fit the self-energy matrices, we show that the lead spectral function and the dynamics response can be treated accurately. Compared to the conventional master equation approaches, our method is much more efficient as the computational time scales cubically with the system size and linearly with the simulation time. As a result, the simulations of the transient currents through systems containing up to one hundred of atoms have been carried out. As density functional theory is also an effective one-particle theory, the Lorentzian-Padè decomposition scheme developed here can be generalized for first-principles simulation of realistic systems.
Luo, Feng; Yang, Yunfeng; Zhong, Jianxin; Gao, Haichun; Khan, Latifur; Thompson, Dorothea K; Zhou, Jizhong
2007-01-01
Background Large-scale sequencing of entire genomes has ushered in a new age in biology. One of the next grand challenges is to dissect the cellular networks consisting of many individual functional modules. Defining co-expression networks without ambiguity based on genome-wide microarray data is difficult and current methods are not robust and consistent with different data sets. This is particularly problematic for little understood organisms since not much existing biological knowledge can be exploited for determining the threshold to differentiate true correlation from random noise. Random matrix theory (RMT), which has been widely and successfully used in physics, is a powerful approach to distinguish system-specific, non-random properties embedded in complex systems from random noise. Here, we have hypothesized that the universal predictions of RMT are also applicable to biological systems and the correlation threshold can be determined by characterizing the correlation matrix of microarray profiles using random matrix theory. Results Application of random matrix theory to microarray data of S. oneidensis, E. coli, yeast, A. thaliana, Drosophila, mouse and human indicates that there is a sharp transition of nearest neighbour spacing distribution (NNSD) of correlation matrix after gradually removing certain elements insider the matrix. Testing on an in silico modular model has demonstrated that this transition can be used to determine the correlation threshold for revealing modular co-expression networks. The co-expression network derived from yeast cell cycling microarray data is supported by gene annotation. The topological properties of the resulting co-expression network agree well with the general properties of biological networks. Computational evaluations have showed that RMT approach is sensitive and robust. Furthermore, evaluation on sampled expression data of an in silico modular gene system has showed that under-sampled expressions do not affect the
Density Functional Theory in Surface Chemistry and Catalysis
Norskov, Jens
2011-05-19
Recent advances in the understanding of reactivity trends for chemistry at transition metal surfaces have enabled in silico design of heterogeneous catalysts in a few cases. Current status of the field is discussed with an emphasis on the role of coupling between theory and experiment and future challenges.
Density functional theory in surface chemistry and catalysis
Nørskov, Jens K.; Abild-Pedersen, Frank; Studt, Felix; Bligaard, Thomas
2011-01-01
Recent advances in the understanding of reactivity trends for chemistry at transition-metal surfaces have enabled in silico design of heterogeneous catalysts in a few cases. The current status of the field is discussed with an emphasis on the role of coupling theory and experiment and future challenges. PMID:21220337
Magnetic and antimagnetic rotation in covariant density functional theory
Zhao, P. W.; Liang, H. Z.; Peng, J.; Ring, P.; Zhang, S. Q.; Meng, J.
2012-10-20
Progress on microscopic and self-consistent description of the magnetic rotation and antimagnetic rotation phenomena in tilted axis cranking relativistic mean-field theory based on a point-coupling interaction are briefly reviewed. In particular, the microscopic pictures of the shears mechanism in {sup 60}Ni and the two shears-like mechanism in {sup 105}Cd are discussed.
Density functional theory in surface chemistry and catalysis.
Nørskov, Jens K; Abild-Pedersen, Frank; Studt, Felix; Bligaard, Thomas
2011-01-18
Recent advances in the understanding of reactivity trends for chemistry at transition-metal surfaces have enabled in silico design of heterogeneous catalysts in a few cases. The current status of the field is discussed with an emphasis on the role of coupling theory and experiment and future challenges.
Moments of the transmission eigenvalues, proper delay times and random matrix theory II
NASA Astrophysics Data System (ADS)
Mezzadri, F.; Simm, N. J.
2012-05-01
We systematically study the first three terms in the asymptotic expansions of the moments of the transmission eigenvalues and proper delay times as the number of quantum channels n in the leads goes to infinity. The computations are based on the assumption that the Landauer-Büttiker scattering matrix for chaotic ballistic cavities can be modelled by the circular ensembles of random matrix theory. The starting points are the finite-n formulae that we recently discovered [F. Mezzadri and N. J. Simm, "Moments of the transmission eigenvalues, proper delay times and random matrix theory," J. Math. Phys. 52, 103511 (2011)], 10.1063/1.3644378. Our analysis includes all the symmetry classes β ∈ {1, 2, 4}; in addition, it applies to the transmission eigenvalues of Andreev billiards, whose symmetry classes were classified by Zirnbauer ["Riemannian symmetric superspaces and their origin in random-matrix theory," J. Math. Phys. 37(10), 4986 (1996)], 10.1063/1.531675 and Altland and Zirnbauer ["Random matrix theory of a chaotic Andreev quantum dot," Phys. Rev. Lett. 76(18), 3420 (1996), 10.1103/PhysRevLett.76.3420; Altland and Zirnbauer "Nonstandard symmetry classes in mesoscopic normal-superconducting hybrid structures," Phys. Rev. B 55(2), 1142 (1997)], 10.1103/PhysRevB.55.1142. Where applicable, our results are in complete agreement with the semiclassical theory of mesoscopic systems developed by Berkolaiko et al. ["Full counting statistics of chaotic cavities from classical action correlations," J. Phys. A: Math. Theor. 41(36), 365102 (2008)], 10.1088/1751-8113/41/36/365102 and Berkolaiko and Kuipers ["Moments of the Wigner delay times," J. Phys. A: Math. Theor. 43(3), 035101 (2010), 10.1088/1751-8113/43/3/035101; Berkolaiko and Kuipers "Transport moments beyond the leading order," New J. Phys. 13(6), 063020 (2011)], 10.1088/1367-2630/13/6/063020. Our approach also applies to the Selberg-like integrals. We calculate the first two terms in their asymptotic expansion
Dissipative quantum molecular dynamics in gases and condensed media: A density matrix treatment
NASA Astrophysics Data System (ADS)
Leathers, Andrew S.
We present a study of dissipative quantum molecular dynamics, covering several different methods of treating the dissipation. We use a reduced density matrix framework, which leads to coupled integro-differential equations in time. We then develop a numerical algorithm for solving these equations. This algorithm is tested by comparing the results to a solved model. The method is then applied to the vibrational relaxation of adsorbates on metal surfaces. We also use this model to test approximations which transform the integro-differential equations into simpler integral equations. Our results compare well to experiment, and demonstrate the need for a full treatment without approximations. This model is then expanded to allow for electronic relaxation, as well as excitation by a light pulse. The electronic relaxation occurs on a different time scale, and is treated differently than the vibrational relaxation. Our method is shown to be general enough to handle both cases. Our next model is light-induced electron transfer in a metal cluster on a semiconductor surface. We consider both direct electronic excitation causing electron transfer, as well as indirect transfer, where there is excitation to an intermediate state which is coupled to the electron transferred state. Our results indicate vibrational relaxation plays a small role in the direct transfer dynamics, but is still important in the indirect case. Finally, we present a mixed quantum-classical study of the effect of initial conditions, with the goal of moving towards a method capable of treating dissipation in both quantum and mixed quatum-classical systems. (Full text of this dissertation may be available via the University of Florida Libraries web site. Please check http://www.uflib.ufl.edu/etd.html)
Harris, Travis V.; Morokuma, Keiji; Kurashige, Yuki; Yanai, Takeshi
2014-02-07
The applicability of ab initio multireference wavefunction-based methods to the study of magnetic complexes has been restricted by the quickly rising active-space requirements of oligonuclear systems and dinuclear complexes with S > 1 spin centers. Ab initio density matrix renormalization group (DMRG) methods built upon an efficient parameterization of the correlation network enable the use of much larger active spaces, and therefore may offer a way forward. Here, we apply DMRG-CASSCF to the dinuclear complexes [Fe{sub 2}OCl{sub 6}]{sup 2−} and [Cr{sub 2}O(NH{sub 3}){sub 10}]{sup 4+}. After developing the methodology through systematic basis set and DMRG M testing, we explore the effects of extended active spaces that are beyond the limit of conventional methods. We find that DMRG-CASSCF with active spaces including the metal d orbitals, occupied bridging-ligand orbitals, and their virtual double shells already capture a major portion of the dynamic correlation effects, accurately reproducing the experimental magnetic coupling constant (J) of [Fe{sub 2}OCl{sub 6}]{sup 2−} with (16e,26o), and considerably improving the smaller active space results for [Cr{sub 2}O(NH{sub 3}){sub 10}]{sup 4+} with (12e,32o). For comparison, we perform conventional MRCI+Q calculations and find the J values to be consistent with those from DMRG-CASSCF. In contrast to previous studies, the higher spin states of the two systems show similar deviations from the Heisenberg spectrum, regardless of the computational method.
Photoelectron spectroscopy and density functional theory studies of N-rich energetic materials
NASA Astrophysics Data System (ADS)
Zeng, Zhen; Bernstein, Elliot R.
2016-10-01
The geometric and electronic structures of molecular anionic energetic materials (EMs) DAAF (3,3'-diamino-4,4'-azoxyfurazan), FOX-7 (1,1-diamino-2,2-dinitroethene), 5,5'-BT (5,5'-bistetrazole), and 1,5'-BT (1,5'-bistetrazole) are explored employing anionic photoelectron spectroscopy and density functional theory calculations. The electron binding energies of the observed anionic, energetic material related species are determined and their corresponding anionic structures are assigned. Decomposition reactions for negatively charged EMs can proceed with different energy barriers, and thus mechanisms, from those for their related neutral EMs. Reactivity based on the anionic initial fragments of these EM species further reinforces their respective highly reactive and explosive nature. Fragment ions of the form EM--H-X (X = N2, N2+NH, …) are additionally observed. Detection of such species suggests that EM--H could serve as promising new candidates for EMs, assuming that such species are synthetically available, perhaps as energetic salts. Vertical detachment energies for transitions to the ground and first triplet electronic excited states of neutral matrix dye anion DCM- are additionally determined.
Configuration interaction based on constrained density functional theory: A multireference method
NASA Astrophysics Data System (ADS)
Wu, Qin; Cheng, Chiao-Lun; Van Voorhis, Troy
2007-10-01
Existing density functional theory (DFT) methods are typically very effective in capturing dynamic correlation, but run into difficulty treating near-degenerate systems where static correlation becomes important. In this work, we propose a configuration interaction (CI) method that allows one to use a multireference approach to treat static correlation but incorporates DFT's efficacy for the dynamic part as well. The new technique uses localized charge or spin states built by a constrained DFT approach to construct an active space in which the effective Hamiltonian matrix is built. These local configurations have significantly less static correlation compared to their delocalized counterparts and possess an essentially constant amount of self-interaction error. Thus their energies can be reliably calculated by DFT with existing functionals. Using a small number of local configurations as different references in the active space, a simple CI step is then able to recover the static correlation missing from the localized states. Practical issues of choosing configurations and adjusting constraint values are discussed, employing as examples the ground state dissociation curves of H2+, H2, and LiF. Excellent results are obtained for these curves at all interatomic distances, which is a strong indication that this method can be used to accurately describe bond breaking and forming processes.
NASA Astrophysics Data System (ADS)
Marinescu, Maria; Tudorache, Diana Gabriela; Marton, George Iuliu; Zalaru, Christina-Marie; Popa, Marcela; Chifiriuc, Mariana-Carmen; Stavarache, Cristina-Elena; Constantinescu, Catalin
2017-02-01
Eco-friendly, one-pot, solvent-free synthesis of biologically active 2-substituted benzimidazoles is presented and discussed herein. Novel N-Mannich bases are synthesized from benzimidazoles, secondary amines and formaldehyde, and their structures are confirmed by 1H nuclear magnetic resonance (NMR), Fourier transform infrared (FTIR), and elemental analysis. All benzimidazole derivatives are evaluated by qualitative and quantitative methods against 9 bacterial strains. The largest microbicide and anti-biofilm effect is observed for the 2-(1-hydroxyethyl)-compounds. Density functional theory (DFT) modeling of the molecular structure and frontier molecular orbitals, i.e. highest occupied molecular orbital and lowest unoccupied molecular orbital (HOMO/LUMO), is accomplished by using the GAMESS 2012 software. Antimicrobial activity is correlated with the electronic parameters (chemical hardness, electronic chemical potential, global electrophilicity index), Mullikan atomic charges and geometric parameters of the benzimidazole compounds. The planarity of the compound, symmetry of the molecule, and the presence of a nucleophilic group, are advantages for a high antimicrobial activity. Finally, we briefly show that further accurate processing of such compounds into thin films and hybrid structures, e.g. by laser ablation matrix-assisted pulsed laser evaporation and/or laser-induced forward transfer, may indeed provide simple and environmental friendly, state-of-the-art solutions for antimicrobial coatings.
Streubel, A; Siepmann, J; Bodmeier, R
2003-01-01
The aim of this study was to develop and physicochemically characterize single unit, floating controlled drug delivery systems consisting of (i). polypropylene foam powder, (ii). matrix-forming polymer(s), (iii). drug, and (iv). filler (optional). The highly porous foam powder provided low density and, thus, excellent in vitro floating behavior of the tablets. All foam powder-containing tablets remained floating for at least 8 h in 0.1 N HCl at 37 degrees C. Different types of matrix-forming polymers were studied: hydroxypropyl methylcellulose (HPMC), polyacrylates, sodium alginate, corn starch, carrageenan, gum guar and gum arabic. The tablets eroded upon contact with the release medium, and the relative importance of drug diffusion, polymer swelling and tablet erosion for the resulting release patterns varied significantly with the type of matrix former. The release rate could effectively be modified by varying the "matrix-forming polymer/foam powder" ratio, the initial drug loading, the tablet geometry (radius and height), the type of matrix-forming polymer, the use of polymer blends and the addition of water-soluble or water-insoluble fillers (such as lactose or microcrystalline cellulose). The floating behavior of the low density drug delivery systems could successfully be combined with accurate control of the drug release patterns.
The spin polarized linear response from density functional theory: Theory and application to atoms
Fias, Stijn Boisdenghien, Zino; De Proft, Frank; Geerlings, Paul
2014-11-14
Within the context of spin polarized conceptual density functional theory, the spin polarized linear response functions are introduced both in the [N, N{sub s}] and [N{sub α}, N{sub β}] representations. The mathematical relations between the spin polarized linear response functions in both representations are examined and an analytical expression for the spin polarized linear response functions in the [N{sub α}, N{sub β}] representation is derived. The spin polarized linear response functions were calculated for all atoms up to and including argon. To simplify the plotting of our results, we integrated χ(r, r′) to a quantity χ(r, r{sup ′}), circumventing the θ and ϕ dependence. This allows us to plot and to investigate the periodicity throughout the first three rows in the periodic table within the two different representations. For the first time, χ{sub αβ}(r, r{sup ′}), χ{sub βα}(r, r{sup ′}), and χ{sub SS}(r, r{sup ′}) plots have been calculated and discussed. By integration of the spin polarized linear response functions, different components to the polarisability, α{sub αα}, α{sub αβ}, α{sub βα}, and α{sub ββ} have been calculated.
Efficient Diffuse Basis Sets for Density Functional Theory.
Papajak, Ewa; Truhlar, Donald G
2010-03-09
Eliminating all but the s and p diffuse functions on the non-hydrogenic atoms and all diffuse functions on the hydrogen atoms from the aug-cc-pV(x+d)Z basis sets of Dunning and co-workers, where x = D, T, Q, ..., yields the previously proposed "minimally augmented" basis sets, called maug-cc-pV(x+d)Z. Here, we present extensive and systematic tests of these basis sets for density functional calculations of chemical reaction barrier heights, hydrogen bond energies, electron affinities, ionization potentials, and atomization energies. The tests show that the maug-cc-pV(x+d)Z basis sets are as accurate as the aug-cc-pV(x+d)Z ones for density functional calculations, but the computational cost savings are a factor of about two to seven.
Lopata, Kenneth A.; Govind, Niranjan
2013-11-12
We present a real-time time-dependent density functional theory (RT-TDDFT) prescription for capturing near and post-ionization excitations based on non-Hermitian von Neumann density matrix propagation with atom-centered basis sets, tuned range-separated DFT, and a phenomenological imaginary molecular orbital-based absorbing potential to mimic coupling to the continuum. The computed extreme ultraviolet absorption spectra for acetylene (C2H2), water (H2O), and Freon 12 (CF2Cl2) agree well with electron energy loss spectroscopy (EELS) data over the range 0 to 50 eV. The absorbing potential removes spurious high energy finite basis artifacts, yielding correct bound to bound transitions, metastable (autoionizing) resonance states, and consistent overall absorption shapes.
NASA Astrophysics Data System (ADS)
Ito, Fumiyuki
2010-12-01
The supermolecule approach has been used to model molecules embedded in solid argon matrix, wherein interaction between the guest and the host atoms in the first solvation shell is evaluated with the use of density functional calculations. Structural stability and simulated spectra have been obtained for formic acid dimer (FAD)-Arn (n = 21-26) clusters. The calculations at the B971/6-31++G(3df,3pd) level have shown that the tetrasubstitutional site on Ar(111) plane is likely to incorporate FAD most stably, in view of consistency with the matrix shifts available experimentally.
Adaptive Finite Element Method for Solving the Exact Kohn-Sham Equation of Density Functional Theory
Bylaska, Eric J.; Holst, Michael; Weare, John H.
2009-04-14
Results of the application of an adaptive finite element (FE) based solution using the FETK library of M. Holst to Density Functional Theory (DFT) approximation to the electronic structure of atoms and molecules are reported. The severe problem associated with the rapid variation of the electronic wave functions in the near singular regions of the atomic centers is treated by implementing completely unstructured simplex meshes that resolve these features around atomic nuclei. This concentrates the computational work in the regions in which the shortest length scales are necessary and provides for low resolution in regions for which there is no electron density. The accuracy of the solutions significantly improved when adaptive mesh refinement was applied, and it was found that the essential difficulties of the Kohn-Sham eigenvalues equation were the result of the singular behavior of the atomic potentials. Even though the matrix representations of the discrete Hamiltonian operator in the adaptive finite element basis are always sparse with a linear complexity in the number of discretization points, the overall memory and computational requirements for the solver implemented were found to be quite high. The number of mesh vertices per atom as a function of the atomic number Z and the required accuracy e (in atomic units) was esitmated to be v (e;Z) = 122:37 * Z2:2346 /1:1173 , and the number of floating point operations per minimization step for a system of NA atoms was found to be 0(N3A*v(e,Z0) (e.g. Z=26, e=0.0015 au, and NA=100, the memory requirement and computational cost would be ~0.2 terabytes and ~25 petaflops). It was found that the high cost of the method could be reduced somewhat by using a geometric based refinement strategy to fix the error near the singularities.
Nakatani, Naoki; Chan, Garnet Kin-Lic
2013-04-07
We investigate tree tensor network states for quantum chemistry. Tree tensor network states represent one of the simplest generalizations of matrix product states and the density matrix renormalization group. While matrix product states encode a one-dimensional entanglement structure, tree tensor network states encode a tree entanglement structure, allowing for a more flexible description of general molecules. We describe an optimal tree tensor network state algorithm for quantum chemistry. We introduce the concept of half-renormalization which greatly improves the efficiency of the calculations. Using our efficient formulation we demonstrate the strengths and weaknesses of tree tensor network states versus matrix product states. We carry out benchmark calculations both on tree systems (hydrogen trees and π-conjugated dendrimers) as well as non-tree molecules (hydrogen chains, nitrogen dimer, and chromium dimer). In general, tree tensor network states require much fewer renormalized states to achieve the same accuracy as matrix product states. In non-tree molecules, whether this translates into a computational savings is system dependent, due to the higher prefactor and computational scaling associated with tree algorithms. In tree like molecules, tree network states are easily superior to matrix product states. As an illustration, our largest dendrimer calculation with tree tensor network states correlates 110 electrons in 110 active orbitals.
First-Principles Atomic Force Microscopy Image Simulations with Density Embedding Theory.
Sakai, Yuki; Lee, Alex J; Chelikowsky, James R
2016-05-11
We present an efficient first-principles method for simulating noncontact atomic force microscopy (nc-AFM) images using a "frozen density" embedding theory. Frozen density embedding theory enables one to efficiently compute the tip-sample interaction by considering a sample as a frozen external field. This method reduces the extensive computational load of first-principles AFM simulations by avoiding consideration of the entire tip-sample system and focusing on the tip alone. We demonstrate that our simulation with frozen density embedding theory accurately reproduces full density functional theory simulations of freestanding hydrocarbon molecules while the computational time is significantly reduced. Our method also captures the electronic effect of a Cu(111) substrate on the AFM image of pentacene and reproduces the experimental AFM image of Cu2N on a Cu(100) surface. This approach is applicable for theoretical imaging applications on large molecules, two-dimensional materials, and materials surfaces.
Poelmans, Ward; Van Raemdonck, Mario; Verstichel, Brecht; De Baerdemacker, Stijn; Torre, Alicia; Lain, Luis; Massaccesi, Gustavo E; Alcoba, Diego R; Bultinck, Patrick; Van Neck, Dimitri
2015-09-08
We perform a direct variational determination of the second-order (two-particle) density matrix corresponding to a many-electron system, under a restricted set of the two-index N-representability P-, Q-, and G-conditions. In addition, we impose a set of necessary constraints that the two-particle density matrix must be derivable from a doubly occupied many-electron wave function, i.e., a singlet wave function for which the Slater determinant decomposition only contains determinants in which spatial orbitals are doubly occupied. We rederive the two-index N-representability conditions first found by Weinhold and Wilson and apply them to various benchmark systems (linear hydrogen chains, He, N2, and CN(-)). This work is motivated by the fact that a doubly occupied many-electron wave function captures in many cases the bulk of the static correlation. Compared to the general case, the structure of doubly occupied two-particle density matrices causes the associate semidefinite program to have a very favorable scaling as L(3), where L is the number of spatial orbitals. Since the doubly occupied Hilbert space depends on the choice of the orbitals, variational calculation steps of the two-particle density matrix are interspersed with orbital-optimization steps (based on Jacobi rotations in the space of the spatial orbitals). We also point to the importance of symmetry breaking of the orbitals when performing calculations in a doubly occupied framework.
Testing the Predictions of Random Matrix Theory in Low Loss Wave Chaotic Scattering Systems
NASA Astrophysics Data System (ADS)
Yeh, Jen-Hao; Antonsen, Thomas; Ott, Edward; Anlage, Steven
2013-03-01
Wave chaos is a field where researchers apply random matrix theory (RMT) to predict the statistics of wave properties in complicated wave scattering systems. The RMT predictions have successfully demonstrated universality of the distributions of these wave properties, which only depend on the loss parameter of the system and the physical symmetry. Examination of these predictions in very low loss systems is interesting because extreme limits for the distribution functions and other predictions are encountered. Therefore, we use a wave-chaotic superconducting cavity to establish a low loss environment and test RMT predictions, including the statistics of the scattering (S) matrix and the impedance (Z) matrix, the universality (or lack thereof) of the Z- and S-variance ratios, and the statistics of the proper delay times of the Wigner-Smith time-delay matrix. We have applied an in-situ microwave calibration method (Thru-Reflection-Line method) to calibrate the cryostat system, and we also applied the random coupling model to remove the system-specific features. Our experimental results of different properties agree with the RMT predictions. This work is funded by the ONR/Maryland AppEl Center Task A2 (contract No. N000140911190), the AFOSR under grant FA95500710049, and Center for Nanophysics and Advanced 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.
Ability of nonperturbative density-functional theories to stabilize arbitrary solids
NASA Astrophysics Data System (ADS)
Kyrlidis, Agathagelos; Brown, Robert A.
1991-12-01
The effects of solid structure and interatomic potential are investigated for density-functional theories based on the definition of a weighted or effective density for approximating the solid phase in terms of the uniform liquid. The introduction of solidlike structure to the modified-weighted-density-approximation (MWDA) theory of Denton and Ashcroft [Phys. Rev. A 39, 4701 (1989)] leads to loss of existence of the weighted density for a system of hard spheres. This behavior is more pronounced for loose crystalline structures, such as the diamond lattice. By contrast, the generalized-effective-liquid-approximation theory (GELA) of Lutsko and Baus [Phys. Rev. A 41, 6647 (1990)] always predicts single-valued weighted densities in the cases studied here. The thermodynamic mapping, which is the core of both of the MWDA and GELA approximations, is ineffective for Lennard-Jones fluids, according to a criterion for the relative stability of the solid phase evaluated using liquid-state information.
Exact density functional theory for ideal polymer fluids with nearest neighbor bonding constraints
NASA Astrophysics Data System (ADS)
Woodward, Clifford E.; Forsman, Jan
2008-08-01
We present a new density functional theory of ideal polymer fluids, assuming nearest-neighbor bonding constraints. The free energy functional is expressed in terms of end site densities of chain segments and thus has a simpler mathematical structure than previously used expressions using multipoint distributions. This work is based on a formalism proposed by Tripathi and Chapman [Phys. Rev. Lett. 94, 087801 (2005)]. Those authors obtain an approximate free energy functional for ideal polymers in terms of monomer site densities. Calculations on both repulsive and attractive surfaces show that their theory is reasonably accurate in some cases, but does differ significantly from the exact result for longer polymers with attractive surfaces. We suggest that segment end site densities, rather than monomer site densities, are the preferred choice of ``site functions'' for expressing the free energy functional of polymer fluids. We illustrate the application of our theory to derive an expression for the free energy of an ideal fluid of infinitely long polymers.
Molecular Electron Density Theory: A Modern View of Reactivity in Organic Chemistry.
Domingo, Luis R
2016-09-30
A new theory for the study of the reactivity in Organic Chemistry, named Molecular Electron Density Theory (MEDT), is proposed herein. MEDT is based on the idea that while the electron density distribution at the ground state is responsible for physical and chemical molecular properties, as proposed by the Density Functional Theory (DFT), the capability for changes in electron density is responsible for molecular reactivity. Within MEDT, the reactivity in Organic Chemistry is studied through a rigorous quantum chemical analysis of the changes of the electron density as well as the energies associated with these changes along the reaction path in order to understand experimental outcomes. Studies performed using MEDT allow establishing a modern rationalisation and to gain insight into molecular mechanisms and reactivity in Organic Chemistry.
Covariant Density Functional Theory--highlights on recent progress and applications
Meng, J.; Li, J.; Zhao, P. W.; Liang, H. Z.; Yao, J. M.
2011-05-06
The density functional theory with a few number of parameters allows a very successful phenomenological description of ground state properties of nuclei all over the nuclear chart. The recent progress on the application of the covariant density functional theory (CDFT) for nuclear structure and astrophysics as well as its extensions by the group in Beijing is summarized. In particular, its application to magnetic moments is discussed in details.
NASA Astrophysics Data System (ADS)
Ye, Zhencheng; Cai, Jun; Liu, Honglai; Hu, Ying
2005-11-01
Density and chain conformation profiles of square-well chains between two parallel walls were studied by using density-functional theory. The free energy of square-well chains is separated into two contributions: the hard-sphere repulsion and the attraction. The Heaviside function is used as the weighting function for both of the two parts. The equation of state of Hu et al. is used to calculate the excess free energy of the repulsive part. The equation of state of statistical associating fluid theory for chain molecules with attractive potentials of variable range [A. Gil-Villegas et al. J. Chem. Phys. 106, 4168 (1997)] is used to calculate the excess free energy of the attractive part. Because the wall is inaccessible to a mass center of a longer chain, there exists a sharp fall in the distribution of end-to-end distance near the wall as the chain length increases. When the average density of the system is not too low, the prediction of this work is in good agreement with computer simulation results for the density profiles and the chain conformation over a wide range of chain length, temperature, and attraction strength of the walls. However, when the average density and the temperature are very low, the prediction deviates to a certain degree from the computer simulation results for molecules with long chain length. A more accurate functional approximation is needed.
Density Functional Theory (dft) Simulations of Shocked Liquid Xenon
NASA Astrophysics Data System (ADS)
Mattsson, Thomas R.; Magyar, Rudolph J.
2009-12-01
Xenon is not only a technologically important element used in laser technologies and jet propulsion, but it is also one of the most accessible materials in which to study the metal-insulator transition with increasing pressure. Because of its closed shell electronic configuration, xenon is often assumed to be chemically inert, interacting almost entirely through the van der Waals interaction, and at liquid density, is typically modeled well using Leonard-Jones potentials. However, such modeling has a limited range of validity as xenon is known to form compounds under normal conditions and likely exhibits considerably more chemistry at higher densities when hybridization of occupied orbitals becomes significant. We present DFT-MD simulations of shocked liquid xenon with the goal of developing an improved equation of state. The calculated Hugoniot to 2 MPa compares well with available experimental shock data. Sandia is a mul-tiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.
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.
Ruggenthaler, Michael; Penz, Markus; van Leeuwen, Robert
2015-05-27
In this work we review the mapping from densities to potentials in quantum mechanics, which is the basic building block of time-dependent density-functional theory and the Kohn-Sham construction. We first present detailed conditions such that a mapping from potentials to densities is defined by solving the time-dependent Schrödinger equation. We specifically discuss intricacies connected with the unboundedness of the Hamiltonian and derive the local-force equation. This equation is then used to set up an iterative sequence that determines a potential that generates a specified density via time propagation of an initial state. This fixed-point procedure needs the invertibility of a certain Sturm-Liouville problem, which we discuss for different situations. Based on these considerations we then present a discussion of the famous Runge-Gross theorem which provides a density-potential mapping for time-analytic potentials. Further we give conditions such that the general fixed-point approach is well-defined and converges under certain assumptions. Then the application of such a fixed-point procedure to lattice Hamiltonians is discussed and the numerical realization of the density-potential mapping is shown. We conclude by presenting an extension of the density-potential mapping to include vector-potentials and photons.
Band alignment of semiconductors from density-functional theory and many-body perturbation theory
NASA Astrophysics Data System (ADS)
Hinuma, Yoyo; Grüneis, Andreas; Kresse, Georg; Oba, Fumiyasu
2014-10-01
The band lineup, or alignment, of semiconductors is investigated via first-principles calculations based on density functional theory (DFT) and many-body perturbation theory (MBPT). Twenty-one semiconductors including C, Si, and Ge in the diamond structure, BN, AlP, AlAs, AlSb, GaP, GaAs, GaSb, InP, InAs, InSb, ZnS, ZnSe, ZnTe, CdS, CdSe, and CdTe in the zinc-blende structure, and GaN and ZnO in the wurtzite structure are considered in view of their fundamental and technological importance. Band alignments are determined using the valence and conduction band offsets from heterointerface calculations, the ionization potential (IP) and electron affinity (EA) from surface calculations, and the valence band maximum and conduction band minimum relative to the branch point energy, or charge neutrality level, from bulk calculations. The performance of various approximations to DFT and MBPT, namely the Perdew-Burke-Ernzerhof (PBE) semilocal functional, the Heyd-Scuseria-Ernzerhof (HSE) hybrid functional, and the GW approximation with and without vertex corrections in the screened Coulomb interaction, is assessed using the GWΓ1 approximation as a reference, where first-order vertex corrections are included in the self-energy. The experimental IPs, EAs, and band offsets are well reproduced by GWΓ1 for most of the semiconductor surfaces and heterointerfaces considered in this study. The PBE and HSE functionals show sizable errors in the IPs and EAs, in particular for group II-VI semiconductors with wide band gaps, but are much better in the prediction of relative band positions or band offsets due to error cancellation. The performance of the GW approximation is almost on par with GWΓ1 as far as relative band positions are concerned. The band alignments based on average interfacial band offsets for all pairs of 17 semiconductors and branch point energies agree with explicitly calculated interfacial band offsets with small mean absolute errors of both ˜0.1eV, indicating a
NASA Astrophysics Data System (ADS)
Lykissa, Iliana; Li, Shu-Yi; Ramzan, Muhammad; Chakraborty, Sudip; Ahuja, Rajeev; Granqvist, Claes G.; Niklasson, Gunnar A.
2014-05-01
Thin films of V2O5 were prepared by sputter deposition onto transparent and electrically conducting substrates and were found to be X-ray amorphous. Their electrochemical density of states was determined by chronopotentiometry and displayed a pronounced low-energy peak followed by an almost featureless contribution at higher energies. These results were compared with density functional theory calculations for amorphous V2O5. Significant similarities were found between measured data and computations; specifically, the experimental low-energy peak corresponds to a split-off part of the conduction band apparent in the computations. Furthermore, the calculations approximately reproduce the experimental band gap observed in optical measurements.
Simulations and Theory of Density-Dependent Dispersion in Weakly Heterogeneous Porous Media
NASA Astrophysics Data System (ADS)
Landman, A.; Schotting, R. J.
2004-12-01
The effect of density gradients on dispersive mixing of miscible fluids is studied. Density gradients not only affect dispersive transport for unstable flow, but also can significantly affect dispersion under stable conditions. For vertical displacements, laboratory experiments show a reduction of the longitudinal dispersivity under the influence of stabilizing density gradients. Linear Fick's law for the dispersive flux is inadequate to model these experiments. Therefore, alternative theories have been developed that incorporate the effect of density gradients. In this study, accurate numerical simulations of vertical displacements in weakly heterogeneous porous columns are performed. The numerical results confirm experimental observations. Furthermore, the computed concentration profiles are used to validate nonlinear dispersion theories applicable for high density gradients. A comparison is made with the stochastic theory of Welty and Gelhar, with homogenization theory, and with the nonlinear dispersion theory of Hassanizadeh and Leijnse. For small variances in log k, the stochastic and homogenization theory lead to reasonably good predictions of the computed concentration profiles and variances, without any fitting. In the theory of Hassanizadeh and Leijnse a fitting parameter is involved. This nonlinear dispersion parameter is not a true medium parameter, as it is found to be dependent on the flow rate and on the travel distance.
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.
Density Functional Plus Dynamical Mean Field Theory of Correlated Oxides
NASA Astrophysics Data System (ADS)
Millis, Andrew
2015-03-01
The density functional plus dynamical mean field method is outlined and a few recent successes including applications to spin crossover molecules, oxide superlattices and metal-insulator transitions in bulk transition metals are outlined. Insights from the method into the essential role played by lattice distortions (both rotations and bond length changes) in determining the phase diagrams of correlated materials are presented. The key theoretical issue of the double counting correction is outlined, different approaches are compared, and a connection to the energy level differences between strongly and weakly correlated orbitals is presented. Charge transfer across oxide interfaces shown to depend crucially on the double counting correction, suggesting that experiments on oxide superlattices may provide insights into this important problem. Future directions are discussed. This work is performed in collaboration with Jia Chen, Hung Dang, Hyowon Park and Chris Marianetti. This research supported by the DOE Office of Science, Grant ER 046169.
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.
Density functional theory study of hexagonal carbon phases.
Wang, Zhibin; Gao, Faming; Li, Na; Qu, Nianrui; Gou, Huiyang; Hao, Xianfeng
2009-06-10
It is reported frequently that the new carbon phases may be harder than diamond (Wang et al 2004 Proc. Natl Acad. Sci. 101 13699 and Mao et al 2003 Science 302 425). However, the mechanism is still unclear. In this paper we systematically investigate the structural, electronic, and mechanical properties of the diamond polytypes using first-principles density functional calculations. The results show that the bulk modulus and shear modulus for the hexagonal form of diamond approach those of diamond, suggesting they might be hard and low compressibility materials. According to the semiempirical method for hardness based on the Mulliken overlap population, the hardnesses for hexagonal forms have been evaluated and compared to diamond. The results indicate that these phases are superhard. More importantly, the bonds in some specific directions of the hexagonal phases are harder than those in diamond, which may lead to the noticeable indentation marks on the diamond anvils observed in experiments.
NASA Astrophysics Data System (ADS)
Dorfner, F.; Heidrich-Meisner, F.
2016-06-01
We study properties of the single-site reduced density matrix in the Bose-Bose resonance model as a function of system parameters. This model describes a single-component Bose gas with a resonant coupling to a diatomic molecular state, here defined on a lattice. A main goal is to demonstrate that the eigenstates of the single-site reduced density matrix have structures that are characteristic for the various quantum phases of this system. Since the Hamiltonian conserves only the global particle number but not the number of bosons and molecules individually, these eigenstates, referred to as optimal modes, can be nontrivial linear combinations of bare eigenstates of the molecular and boson particle number. We numerically analyze the optimal modes and their weights, the latter giving the importance of the corresponding state, in the ground state of the Bose-Bose resonance model. We find that the single-site von Neumann entropy is sensitive to the location of the phase boundaries. We explain the structure of the optimal modes and their weight spectra using perturbation theory and via a comparison to results for the single-component Bose-Hubbard model. We further study the dynamical evolution of the optimal modes and of the single-site entanglement entropy in two quantum quenches that cross phase boundaries of the model and show that these quantities are thermal in the steady state. For our numerical calculations, we use the density-matrix renormalization group method for ground-state calculations and time evolution in a Krylov subspace for the quench dynamics as well as exact diagonalization.
From dilute matter to the equilibrium point in the energy-density-functional theory
NASA Astrophysics Data System (ADS)
Yang, C. J.; Grasso, M.; Lacroix, D.
2016-09-01
Due to the large value of the scattering length in nuclear systems, standard density-functional theories based on effective interactions usually fail to reproduce the nuclear Fermi-liquid behavior both at very low densities and close to equilibrium. Guided on one side by the success of the Skyrme density functional and, on the other side, by resummation techniques used in effective field theories for systems with large scattering lengths, a new energy-density functional is proposed. This functional, adjusted on microscopic calculations, reproduces the nuclear equations of state of neutron and symmetric matter at various densities. Furthermore, it provides reasonable saturation properties as well as an appropriate density dependence for the symmetry energy.
Kaminski, S; Jakobi, A; Wilhelm, Chr
2014-12-01
This paper is intended to identify the uncertainties of activities in environmental samples measured with gamma-ray spectrometry that result from uncertainties in matrix composition, density and geometrical dimensions of the sample. For that purpose efficiencies were calculated for a wide range of environmental matrices such as fresh and ashed food samples, water samples and soil samples. Compositions were mainly taken from literature. Densities and geometry parameters were varied in a range occurring in practice. Considered energies cover a range from 46.5keV to 2000keV. Finally, a couple of recommendations in respect to gamma-ray spectrometric measurements of environmental samples are given.
Superstatistical random-matrix-theory approach to transition intensities in mixed systems.
Abul-Magd, A Y
2006-05-01
We study the fluctuation properties of transition intensities applying a recently proposed generalization of the random matrix theory, which is based on Beck and Cohen's superstatistics. We obtain an analytic expression for the distribution of the reduced transition probabilities that applies to systems undergoing a transition out of chaos. The obtained distribution fits the results of a previous nuclear shell model calculations for some electromagnetic transitions that deviate from the Porter-Thomas distribution. It agrees with the experimental reduced transition probabilities for the nucleus better than the commonly used chi(2) distribution.
Method to modify random matrix theory using short-time behavior in chaotic systems.
Smith, A Matthew; Kaplan, Lev
2009-09-01
We discuss a modification to random matrix theory (RMT) eigenstate statistics that systematically takes into account the nonuniversal short-time behavior of chaotic systems. The method avoids diagonalization of the Hamiltonian, instead requiring only knowledge of short-time dynamics for a chaotic system or ensemble of similar systems. Standard RMT and semiclassical predictions are recovered in the limits of zero Ehrenfest time and infinite Heisenberg time, respectively. As examples, we discuss wave-function autocorrelations and cross correlations and show how the approach leads to a significant improvement in the accuracy for simple chaotic systems where comparison can be made with brute-force diagonalization.
Levorson, Erica J.; Mountziaris, Paschalia M.; Hu, Olivia; Kasper, F. Kurtis
2014-01-01
This study investigated the coculture of chondrocytes and mesenchymal stem cells (MSCs) on electrospun fibrous polymer scaffolds to produce polymer/extracellular matrix (ECM) hybrid constructs with the objective of reducing the number of chondrocytes necessary to produce ample cartilage-like ECM within the scaffolds. To generate these hybrid constructs, electrospun poly(ɛ-caprolactone) fibrous scaffolds were seeded at both high and low initial densities with five different ratios of chondrocytes to MSCs: 1:0, 1:1, 1:3, 1:5, and 0:1, and cultured for 7, 14, and 21 days. Glycosaminoglycan production and distribution within the three coculture groups was similar to quantities generated by chondrocyte-only controls. Conversely, as the concentration of chondrocytes was increased, the collagen content of the constructs also increased at each time point, with a 1:1 chondrocyte to MSC ratio approximating the collagen production of chondrocytes alone. Histological staining suggested that cocultured constructs mimicked the well-distributed ECM patterns of chondrocyte generated constructs, while improving greatly over the restricted distribution of matrix within MSC-only constructs. These results support the capacity of cocultures of chondrocytes and MSCs to generate cartilaginous matrix within a polymeric scaffold. Further, the inclusion of MSCs in these cocultures enables the reduction of chondrocytes needed to produce cell-generated ECM. PMID:24007559