Predicting Pt-195 NMR chemical shift using new relativistic all-electron basis set.
Paschoal, D; Guerra, C Fonseca; de Oliveira, M A L; Ramalho, T C; Dos Santos, H F
2016-10-01
Predicting NMR properties is a valuable tool to assist the experimentalists in the characterization of molecular structure. For heavy metals, such as Pt-195, only a few computational protocols are available. In the present contribution, all-electron Gaussian basis sets, suitable to calculate the Pt-195 NMR chemical shift, are presented for Pt and all elements commonly found as Pt-ligands. The new basis sets identified as NMR-DKH were partially contracted as a triple-zeta doubly polarized scheme with all coefficients obtained from a Douglas-Kroll-Hess (DKH) second-order scalar relativistic calculation. The Pt-195 chemical shift was predicted through empirical models fitted to reproduce experimental data for a set of 183 Pt(II) complexes which NMR sign ranges from -1000 to -6000 ppm. Furthermore, the models were validated using a new set of 75 Pt(II) complexes, not included in the descriptive set. The models were constructed using non-relativistic Hamiltonian at density functional theory (DFT-PBEPBE) level with NMR-DKH basis set for all atoms. For the best model, the mean absolute deviation (MAD) and the mean relative deviation (MRD) were 150 ppm and 6%, respectively, for the validation set (75 Pt-complexes) and 168 ppm (MAD) and 5% (MRD) for all 258 Pt(II) complexes. These results were comparable with relativistic DFT calculation, 200 ppm (MAD) and 6% (MRD). © 2016 Wiley Periodicals, Inc. PMID:27510431
NASA Astrophysics Data System (ADS)
Jorge, F. E.; Martins, L. S. C.; Franco, M. L.
2016-01-01
Segmented all-electron basis sets of valence double zeta quality plus polarization functions (DZP) for the elements from Ce to Lu are generated to be used with the non-relativistic and Douglas-Kroll-Hess (DKH) Hamiltonians. At the B3LYP level, the DZP-DKH atomic ionization energies and equilibrium bond lengths and atomization energies of the lanthanide trifluorides are evaluated and compared with benchmark theoretical and experimental data reported in the literature. In general, this compact size set shows to have a regular, efficient, and reliable performance. It can be particularly useful in molecular property calculations that require explicit treatment of the core electrons.
Evarestov, R A; Losev, M V
2009-12-01
For the first time the convergence of the phonon frequencies and dispersion curves in terms of the supercell size is studied in ab initio frozen phonon calculations on LiF crystal. Helmann-Feynman forces over atomic displacements are found in all-electron calculations with the localized atomic functions (LCAO) basis using CRYSTAL06 program. The Parlinski-Li-Kawazoe method and FROPHO program are used to calculate the dynamical matrix and phonon frequencies of the supercells. For fcc lattice, it is demonstrated that use of the full supercell space group (including the supercell inner translations) enables to reduce essentially the number of the displacements under consideration. For Hartree-Fock (HF), PBE and hybrid PBE0, B3LYP, and B3PW exchange-correlation functionals the atomic basis set optimization is performed. The supercells up to 216 atoms (3 x 3 x 3 conventional unit cells) are considered. The phonon frequencies using the supercells of different size and shape are compared. For the commensurate with supercell k-points the best agreement of the theoretical results with the experimental data is found for B3PW exchange-correlation functional calculations with the optimized basis set. The phonon frequencies at the most non-commensurate k-points converged for the supercell consisting of 4 x 4 x 4 primitive cells and ensures the accuracy 1-2% in the thermodynamic properties calculated (the Helmholtz free energy, entropy, and heat capacity at the room temperature). PMID:19382176
Correlation consistent basis sets for the atoms In–Xe
Mahler, Andrew; Wilson, Angela K.
2015-02-28
In this work, the correlation consistent family of Gaussian basis sets has been expanded to include all-electron basis sets for In–Xe. The methodology for developing these basis sets is described, and several examples of the performance and utility of the new sets have been provided. Dissociation energies and bond lengths for both homonuclear and heteronuclear diatomics demonstrate the systematic convergence behavior with respect to increasing basis set quality expected by the family of correlation consistent basis sets in describing molecular properties. Comparison with recently developed correlation consistent sets designed for use with the Douglas-Kroll Hamiltonian is provided.
All-electron mixed basis G W calculations of TiO2 and ZnO crystals
NASA Astrophysics Data System (ADS)
Zhang, Ming; Ono, Shota; Nagatsuka, Naoki; Ohno, Kaoru
2016-04-01
In transition metal oxide systems, there exists a serious discrepancy between the theoretical quasiparticle energies and the experimental photoemission energies. To improve the accuracy of electronic structure calculations for these systems, we use the all-electron mixed basis GW method, in which single-particle wave functions are accurately described by the linear combinations of plane waves and atomic orbitals. We adopt the full ω integration to evaluate the correlation part of the self-energy and compare the results with those obtained by plasmon pole models. We present the quasiparticle energies and band gap of titanium dioxide (TiO2) and zinc oxide (ZnO) within the one-shot GW approximation. The results are in reasonable agreement with experimental data in the case of TiO2 but underestimated by about 0.6-1.4 eV from experimental data in the case of ZnO, although our results are comparable to previous one-shot GW calculations. We also explain a new approach to perform ω integration very efficiently and accurately.
Kuwahara, Riichi; Tadokoro, Yoichi; Ohno, Kaoru
2014-08-28
In this paper, we calculate kinetic and potential energy contributions to the electronic ground-state total energy of several isolated atoms (He, Be, Ne, Mg, Ar, and Ca) by using the local density approximation (LDA) in density functional theory, the Hartree-Fock approximation (HFA), and the self-consistent GW approximation (GWA). To this end, we have implemented self-consistent HFA and GWA routines in our all-electron mixed basis code, TOMBO. We confirm that virial theorem is fairly well satisfied in all of these approximations, although the resulting eigenvalue of the highest occupied molecular orbital level, i.e., the negative of the ionization potential, is in excellent agreement only in the case of the GWA. We find that the wave function of the lowest unoccupied molecular orbital level of noble gas atoms is a resonating virtual bound state, and that of the GWA spreads wider than that of the LDA and thinner than that of the HFA. PMID:25173006
Feller, D; Schuchardt, Karen L.; Didier, Brett T.; Elsethagen, Todd; Sun, Lisong; Gurumoorthi, Vidhya; Chase, Jared; Li, Jun
The Basis Set Exchange (BSE) provides a web-based user interface for downloading and uploading Gaussian-type (GTO) basis sets, including effective core potentials (ECPs), from the EMSL Basis Set Library. It provides an improved user interface and capabilities over its predecessor, the EMSL Basis Set Order Form, for exploring the contents of the EMSL Basis Set Library. The popular Basis Set Order Form and underlying Basis Set Library were originally developed by Dr. David Feller and have been available from the EMSL webpages since 1994. BSE not only allows downloading of the more than 500 Basis sets in various formats; it allows users to annotate existing sets and to upload new sets. (Specialized Interface)
NASA Astrophysics Data System (ADS)
Levchenko, Sergey V.; Ren, Xinguo; Wieferink, Jürgen; Johanni, Rainer; Rinke, Patrick; Blum, Volker; Scheffler, Matthias
2015-07-01
We describe a framework to evaluate the Hartree-Fock exchange operator for periodic electronic-structure calculations based on general, localized atom-centered basis functions. The functionality is demonstrated by hybrid-functional calculations of properties for several semiconductors. In our implementation of the Fock operator, the Coulomb potential is treated either in reciprocal space or in real space, where the sparsity of the density matrix can be exploited for computational efficiency. Computational aspects, such as the rigorous avoidance of on-the-fly disk storage, and a load-balanced parallel implementation, are also discussed. We demonstrate linear scaling of our implementation with system size by calculating the electronic structure of a bulk semiconductor (GaAs) with up to 1,024 atoms per unit cell without compromising the accuracy.
Spackman, Peter R.; Karton, Amir
2015-05-15
Coupled cluster calculations with all single and double excitations (CCSD) converge exceedingly slowly with the size of the one-particle basis set. We assess the performance of a number of approaches for obtaining CCSD correlation energies close to the complete basis-set limit in conjunction with relatively small DZ and TZ basis sets. These include global and system-dependent extrapolations based on the A + B/L{sup α} two-point extrapolation formula, and the well-known additivity approach that uses an MP2-based basis-set-correction term. We show that the basis set convergence rate can change dramatically between different systems(e.g.it is slower for molecules with polar bonds and/or second-row elements). The system-dependent basis-set extrapolation scheme, in which unique basis-set extrapolation exponents for each system are obtained from lower-cost MP2 calculations, significantly accelerates the basis-set convergence relative to the global extrapolations. Nevertheless, we find that the simple MP2-based basis-set additivity scheme outperforms the extrapolation approaches. For example, the following root-mean-squared deviations are obtained for the 140 basis-set limit CCSD atomization energies in the W4-11 database: 9.1 (global extrapolation), 3.7 (system-dependent extrapolation), and 2.4 (additivity scheme) kJ mol{sup –1}. The CCSD energy in these approximations is obtained from basis sets of up to TZ quality and the latter two approaches require additional MP2 calculations with basis sets of up to QZ quality. We also assess the performance of the basis-set extrapolations and additivity schemes for a set of 20 basis-set limit CCSD atomization energies of larger molecules including amino acids, DNA/RNA bases, aromatic compounds, and platonic hydrocarbon cages. We obtain the following RMSDs for the above methods: 10.2 (global extrapolation), 5.7 (system-dependent extrapolation), and 2.9 (additivity scheme) kJ mol{sup –1}.
Rossi, Tuomas P. Sakko, Arto; Puska, Martti J.; Lehtola, Susi; Nieminen, Risto M.
2015-03-07
We present an approach for generating local numerical basis sets of improving accuracy for first-principles nanoplasmonics simulations within time-dependent density functional theory. The method is demonstrated for copper, silver, and gold nanoparticles that are of experimental interest but computationally demanding due to the semi-core d-electrons that affect their plasmonic response. The basis sets are constructed by augmenting numerical atomic orbital basis sets by truncated Gaussian-type orbitals generated by the completeness-optimization scheme, which is applied to the photoabsorption spectra of homoatomic metal atom dimers. We obtain basis sets of improving accuracy up to the complete basis set limit and demonstrate that the performance of the basis sets transfers to simulations of larger nanoparticles and nanoalloys as well as to calculations with various exchange-correlation functionals. This work promotes the use of the local basis set approach of controllable accuracy in first-principles nanoplasmonics simulations and beyond.
Rossi, Tuomas P; Lehtola, Susi; Sakko, Arto; Puska, Martti J; Nieminen, Risto M
2015-03-01
We present an approach for generating local numerical basis sets of improving accuracy for first-principles nanoplasmonics simulations within time-dependent density functional theory. The method is demonstrated for copper, silver, and gold nanoparticles that are of experimental interest but computationally demanding due to the semi-core d-electrons that affect their plasmonic response. The basis sets are constructed by augmenting numerical atomic orbital basis sets by truncated Gaussian-type orbitals generated by the completeness-optimization scheme, which is applied to the photoabsorption spectra of homoatomic metal atom dimers. We obtain basis sets of improving accuracy up to the complete basis set limit and demonstrate that the performance of the basis sets transfers to simulations of larger nanoparticles and nanoalloys as well as to calculations with various exchange-correlation functionals. This work promotes the use of the local basis set approach of controllable accuracy in first-principles nanoplasmonics simulations and beyond. PMID:25747068
Accurate basis set truncation for wavefunction embedding
NASA Astrophysics Data System (ADS)
Barnes, Taylor A.; Goodpaster, Jason D.; Manby, Frederick R.; Miller, Thomas F.
2013-07-01
Density functional theory (DFT) provides a formally exact framework for performing embedded subsystem electronic structure calculations, including DFT-in-DFT and wavefunction theory-in-DFT descriptions. In the interest of efficiency, it is desirable to truncate the atomic orbital basis set in which the subsystem calculation is performed, thus avoiding high-order scaling with respect to the size of the MO virtual space. In this study, we extend a recently introduced projection-based embedding method [F. R. Manby, M. Stella, J. D. Goodpaster, and T. F. Miller III, J. Chem. Theory Comput. 8, 2564 (2012)], 10.1021/ct300544e to allow for the systematic and accurate truncation of the embedded subsystem basis set. The approach is applied to both covalently and non-covalently bound test cases, including water clusters and polypeptide chains, and it is demonstrated that errors associated with basis set truncation are controllable to well within chemical accuracy. Furthermore, we show that this approach allows for switching between accurate projection-based embedding and DFT embedding with approximate kinetic energy (KE) functionals; in this sense, the approach provides a means of systematically improving upon the use of approximate KE functionals in DFT embedding.
Sharkey, Keeper L.; Pavanello, Michele; Bubin, Sergiy; Adamowicz, Ludwik
2009-12-15
A new algorithm for calculating the Hamiltonian matrix elements with all-electron explicitly correlated Gaussian functions for quantum-mechanical calculations of atoms with two p electrons or a single d electron have been derived and implemented. The Hamiltonian used in the approach was obtained by rigorously separating the center-of-mass motion and it explicitly depends on the finite mass of the nucleus. The approach was employed to perform test calculations on the isotopes of the carbon atom in their ground electronic states and to determine the finite-nuclear-mass corrections for these states.
Sharkey, Keeper L; Kirnosov, Nikita; Adamowicz, Ludwik
2013-03-14
A new algorithm for quantum-mechanical nonrelativistic calculation of the Hamiltonian matrix elements with all-electron explicitly correlated Gaussian functions for atoms with an arbitrary number of s electrons and with three p electrons, or one p electron and one d electron, or one f electron is developed and implemented. In particular the implementation concerns atomic states with L = 3 and M = 0. The Hamiltonian used in the approach is obtained by rigorously separating the center-of-mass motion from the laboratory-frame all particle Hamiltonian, and thus it explicitly depends on the finite mass of the nucleus. The approach is employed to perform test calculations on the lowest (2)F state of the two main isotopes of the lithium atom, (7)Li and (6)Li. PMID:23514465
Many-Body Basis Set Superposition Effect.
Ouyang, John F; Bettens, Ryan P A
2015-11-10
The basis set superposition effect (BSSE) arises in electronic structure calculations of molecular clusters when questions relating to interactions between monomers within the larger cluster are asked. The binding energy, or total energy, of the cluster may be broken down into many smaller subcluster calculations and the energies of these subsystems linearly combined to, hopefully, produce the desired quantity of interest. Unfortunately, BSSE can plague these smaller fragment calculations. In this work, we carefully examine the major sources of error associated with reproducing the binding energy and total energy of a molecular cluster. In order to do so, we decompose these energies in terms of a many-body expansion (MBE), where a "body" here refers to the monomers that make up the cluster. In our analysis, we found it necessary to introduce something we designate here as a many-ghost many-body expansion (MGMBE). The work presented here produces some surprising results, but perhaps the most significant of all is that BSSE effects up to the order of truncation in a MBE of the total energy cancel exactly. In the case of the binding energy, the only BSSE correction terms remaining arise from the removal of the one-body monomer total energies. Nevertheless, our earlier work indicated that BSSE effects continued to remain in the total energy of the cluster up to very high truncation order in the MBE. We show in this work that the vast majority of these high-order many-body effects arise from BSSE associated with the one-body monomer total energies. Also, we found that, remarkably, the complete basis set limit values for the three-body and four-body interactions differed very little from that at the MP2/aug-cc-pVDZ level for the respective subclusters embedded within a larger cluster. PMID:26574311
Gravitational Lens Modeling with Basis Sets
NASA Astrophysics Data System (ADS)
Birrer, Simon; Amara, Adam; Refregier, Alexandre
2015-11-01
We present a strong lensing modeling technique based on versatile basis sets for the lens and source planes. Our method uses high performance Monte Carlo algorithms, allows for an adaptive build up of complexity, and bridges the gap between parametric and pixel based reconstruction methods. We apply our method to a Hubble Space Telescope image of the strong lens system RX J1131-1231 and show that our method finds a reliable solution and is able to detect substructure in the lens and source planes simultaneously. Using mock data, we show that our method is sensitive to sub-clumps with masses four orders of magnitude smaller than the main lens, which corresponds to about {10}8{M}⊙ , without prior knowledge of the position and mass of the sub-clump. The modeling approach is flexible and maximizes automation to facilitate the analysis of the large number of strong lensing systems expected in upcoming wide field surveys. The resulting search for dark sub-clumps in these systems, without mass-to-light priors, offers promise for probing physics beyond the standard model in the dark matter sector.
Miliordos, Evangelos; Xantheas, Sotiris S.
2015-03-07
We report the variation of the binding energy of the Formic Acid Dimer with the size of the basis set at the Coupled Cluster with iterative Singles, Doubles and perturbatively connected Triple replacements [CCSD(T)] level of theory, estimate the Complete Basis Set (CBS) limit, and examine the validity of the Basis Set Superposition Error (BSSE)-correction for this quantity that was previously challenged by Kalescky, Kraka, and Cremer (KKC) [J. Chem. Phys. 140, 084315 (2014)]. Our results indicate that the BSSE correction, including terms that account for the substantial geometry change of the monomers due to the formation of two strong hydrogen bonds in the dimer, is indeed valid for obtaining accurate estimates for the binding energy of this system as it exhibits the expected decrease with increasing basis set size. We attribute the discrepancy between our current results and those of KKC to their use of a valence basis set in conjunction with the correlation of all electrons (i.e., including the 1s of C and O). We further show that the use of a core-valence set in conjunction with all electron correlation converges faster to the CBS limit as the BSSE correction is less than half than the valence electron/valence basis set case. The uncorrected and BSSE-corrected binding energies were found to produce the same (within 0.1 kcal/mol) CBS limits. We obtain CCSD(T)/CBS best estimates for D{sub e} = − 16.1 ± 0.1 kcal/mol and for D{sub 0} = − 14.3 ± 0.1 kcal/mol, the later in excellent agreement with the experimental value of −14.22 ± 0.12 kcal/mol.
Entanglement patterns in mutually unbiased basis sets
Lawrence, Jay
2011-08-15
A few simply stated rules govern the entanglement patterns that can occur in mutually unbiased basis sets (MUBs) and constrain the combinations of such patterns that can coexist in full complements of MUBs. We consider Hilbert spaces of prime power dimensions (D=p{sup N}), as realized by systems of N prime-state particles, where full complements of D+1 MUBs are known to exist, and we assume only that MUBs are eigenbases of generalized Pauli operators, without using any particular construction. The general rules include the following: (1) In any MUB, a given particle appears either in a pure state or totally entangled and (2) in any full MUB complement, each particle is pure in (p+1) bases (not necessarily the same ones) and totally entangled in the remaining (p{sup N}-p). It follows that the maximum number of product bases is p+1 and, when this number is realized, all remaining (p{sup N}-p) bases in the complement are characterized by the total entanglement of every particle. This ''standard distribution'' is inescapable for two-particle systems (of any p), where only product and generalized Bell bases are admissible MUB types. This and the following results generalize previous results for qubits [Phys. Rev. A 65. 032320 (2002); Phys. Rev. A 72, 062310 (2005)] and qutrits [Phys. Rev. A 70, 012302 (2004)], drawing particularly upon [Phys. Rev. A 72, 062310 (2005)]. With three particles there are three MUB types, and these may be combined in (p+2) different ways to form full complements. With N=4, there are 6 MUB types for p=2, but new MUB types become possible with larger p, and these are essential to realizing full complements. With this example, we argue that new MUB types that show new entanglement patterns should enter with every step in N and, also, when N is a prime plus 1, at a critical p value, p=N-1. Such MUBs should play critical roles in filling complements.
QUALITY: A program to assess basis set quality
NASA Astrophysics Data System (ADS)
Sordo, J. A.
1998-09-01
A program to analyze in detail the quality of basis sets is presented. The information provided by the application of a wide variety of (atomic and/or molecular) quality criteria is processed by using a methodology that allows one to determine the most appropriate quality test to select a basis set to compute a given (atomic or molecular) property. Fuzzy set theory is used to choose the most adequate basis set to compute simultaneously a set of properties.
Property-optimized Gaussian basis sets for molecular response calculations
NASA Astrophysics Data System (ADS)
Rappoport, Dmitrij; Furche, Filipp
2010-10-01
With recent advances in electronic structure methods, first-principles calculations of electronic response properties, such as linear and nonlinear polarizabilities, have become possible for molecules with more than 100 atoms. Basis set incompleteness is typically the main source of error in such calculations since traditional diffuse augmented basis sets are too costly to use or suffer from near linear dependence. To address this problem, we construct the first comprehensive set of property-optimized augmented basis sets for elements H-Rn except lanthanides. The new basis sets build on the Karlsruhe segmented contracted basis sets of split-valence to quadruple-zeta valence quality and add a small number of moderately diffuse basis functions. The exponents are determined variationally by maximization of atomic Hartree-Fock polarizabilities using analytical derivative methods. The performance of the resulting basis sets is assessed using a set of 313 molecular static Hartree-Fock polarizabilities. The mean absolute basis set errors are 3.6%, 1.1%, and 0.3% for property-optimized basis sets of split-valence, triple-zeta, and quadruple-zeta valence quality, respectively. Density functional and second-order Møller-Plesset polarizabilities show similar basis set convergence. We demonstrate the efficiency of our basis sets by computing static polarizabilities of icosahedral fullerenes up to C720 using hybrid density functional theory.
Tests for Wavelets as a Basis Set
NASA Astrophysics Data System (ADS)
Baker, Thomas; Evenbly, Glen; White, Steven
A wavelet transformation is a special type of filter usually reserved for image processing and other applications. We develop metrics to evaluate wavelets for general problems on test one-dimensional systems. The goal is to eventually use a wavelet basis in electronic structure calculations. We compare a variety of orthogonal wavelets such as coiflets, symlets, and daubechies wavelets. We also evaluate a new type of orthogonal wavelet with dilation factor three which is both symmetric and compact in real space. This work was supported by the U.S. Department of Energy, Office of Science, Basic Energy Sciences under Award #DE-SC008696.
Optimization of selected molecular orbitals in group basis sets.
Ferenczy, György G; Adams, William H
2009-04-01
We derive a local basis equation which may be used to determine the orbitals of a group of electrons in a system when the orbitals of that group are represented by a group basis set, i.e., not the basis set one would normally use but a subset suited to a specific electronic group. The group orbitals determined by the local basis equation minimize the energy of a system when a group basis set is used and the orbitals of other groups are frozen. In contrast, under the constraint of a group basis set, the group orbitals satisfying the Huzinaga equation do not minimize the energy. In a test of the local basis equation on HCl, the group basis set included only 12 of the 21 functions in a basis set one might ordinarily use, but the calculated active orbital energies were within 0.001 hartree of the values obtained by solving the Hartree-Fock-Roothaan (HFR) equation using all 21 basis functions. The total energy found was just 0.003 hartree higher than the HFR value. The errors with the group basis set approximation to the Huzinaga equation were larger by over two orders of magnitude. Similar results were obtained for PCl(3) with the group basis approximation. Retaining more basis functions allows an even higher accuracy as shown by the perfect reproduction of the HFR energy of HCl with 16 out of 21 basis functions in the valence basis set. When the core basis set was also truncated then no additional error was introduced in the calculations performed for HCl with various basis sets. The same calculations with fixed core orbitals taken from isolated heavy atoms added a small error of about 10(-4) hartree. This offers a practical way to calculate wave functions with predetermined fixed core and reduced base valence orbitals at reduced computational costs. The local basis equation can also be used to combine the above approximations with the assignment of local basis sets to groups of localized valence molecular orbitals and to derive a priori localized orbitals. An
Basis Set Exchange: A Community Database for Computational Sciences
Schuchardt, Karen L.; Didier, Brett T.; Elsethagen, Todd O.; Sun, Lisong; Gurumoorthi, Vidhya; Chase, Jared M.; Li, Jun; Windus, Theresa L.
2007-05-01
Basis sets are one of the most important input data for computational models in the chemistry, materials, biology and other science domains that utilize computational quantum mechanics methods. Providing a shared, web accessible environment where researchers can not only download basis sets in their required format, but browse the data, contribute new basis sets, and ultimately curate and manage the data as a community will facilitate growth of this resource and encourage sharing both data and knowledge. We describe the Basis Set Exchange (BSE), a web portal that provides advanced browsing and download capabilities, facilities for contributing basis set data, and an environment that incorporates tools to foster development and interaction of communities. The BSE leverages and enables continued development of the basis set library originally assembled at the Environmental Molecular Sciences Laboratory.
A novel Gaussian-Sinc mixed basis set for electronic structure calculations.
Jerke, Jonathan L; Lee, Young; Tymczak, C J
2015-08-14
A Gaussian-Sinc basis set methodology is presented for the calculation of the electronic structure of atoms and molecules at the Hartree-Fock level of theory. This methodology has several advantages over previous methods. The all-electron electronic structure in a Gaussian-Sinc mixed basis spans both the "localized" and "delocalized" regions. A basis set for each region is combined to make a new basis methodology-a lattice of orthonormal sinc functions is used to represent the "delocalized" regions and the atom-centered Gaussian functions are used to represent the "localized" regions to any desired accuracy. For this mixed basis, all the Coulomb integrals are definable and can be computed in a dimensional separated methodology. Additionally, the Sinc basis is translationally invariant, which allows for the Coulomb singularity to be placed anywhere including on lattice sites. Finally, boundary conditions are always satisfied with this basis. To demonstrate the utility of this method, we calculated the ground state Hartree-Fock energies for atoms up to neon, the diatomic systems H2, O2, and N2, and the multi-atom system benzene. Together, it is shown that the Gaussian-Sinc mixed basis set is a flexible and accurate method for solving the electronic structure of atomic and molecular species. PMID:26277128
A novel Gaussian-Sinc mixed basis set for electronic structure calculations
Jerke, Jonathan L.; Lee, Young; Tymczak, C. J.
2015-08-14
A Gaussian-Sinc basis set methodology is presented for the calculation of the electronic structure of atoms and molecules at the Hartree–Fock level of theory. This methodology has several advantages over previous methods. The all-electron electronic structure in a Gaussian-Sinc mixed basis spans both the “localized” and “delocalized” regions. A basis set for each region is combined to make a new basis methodology—a lattice of orthonormal sinc functions is used to represent the “delocalized” regions and the atom-centered Gaussian functions are used to represent the “localized” regions to any desired accuracy. For this mixed basis, all the Coulomb integrals are definable and can be computed in a dimensional separated methodology. Additionally, the Sinc basis is translationally invariant, which allows for the Coulomb singularity to be placed anywhere including on lattice sites. Finally, boundary conditions are always satisfied with this basis. To demonstrate the utility of this method, we calculated the ground state Hartree–Fock energies for atoms up to neon, the diatomic systems H{sub 2}, O{sub 2}, and N{sub 2}, and the multi-atom system benzene. Together, it is shown that the Gaussian-Sinc mixed basis set is a flexible and accurate method for solving the electronic structure of atomic and molecular species.
High quality Gaussian basis sets for fourth-row atoms
NASA Technical Reports Server (NTRS)
Partridge, Harry; Faegri, Knut, Jr.
1992-01-01
Energy optimized Gaussian basis sets of triple-zeta quality for the atoms Rb-Xe have been derived. Two series of basis sets are developed: (24s 16p 10d) and (26s 16p 10d) sets which were expanded to 13d and 19p functions as the 4d and 5p shells become occupied. For the atoms lighter than Cd, the (24s 16p 10d) sets with triple-zeta valence distributions are higher in energy than the corresponding double-zeta distribution. To ensure a triple-zeta distribution and a global energy minimum, the (26s 16p 10d) sets were derived. Total atomic energies from the largest basis sets are between 198 and 284 (mu)E(sub H) above the numerical Hartree-Fock energies.
Peterson, Kirk A.; Figgen, Detlev; Goll, Erich; Stoll, Hermann; Dolg, Michael F.
2003-12-01
Series of correlation consistent basis sets have been developed for the post-d group 16-18 elements in conjunction with small-core relativistic pseudopotentials (PPs) of the energy-consistent variety. The latter were adjusted to multiconfiguration Dirac-Hartree-Fock data based on the Dirac-Coulomb-Breit Hamiltonian. The outer-core (n-1)spd shells are explicitly treated together with the nsp valence shell with these PPs. The accompanying cc-pVnZ-PP and aug-cc-pVnZ-PP basis sets range in size from DZ to 5Z quality and yield systematic convergence of both Hartree-Fock and correlated total energies. In addition to the calculation of atomic electron affinities and dipole polarizabilities of the rare gas atoms, numerous molecular benchmark calculations (HBr, HI, HAt, Br2, I2, At2, SiSe, SiTe, SiPo, KrH+, XeH+, and RnH+) are also reported at the coupled cluster level of theory. For the purposes of comparison, all-electron calculations using the Douglas-Kroll-Hess Hamiltonian have also been carried out for the halogen-containing molecules using basis sets of 5Z quality.
Choi, Sunghwan; Hong, Kwangwoo; Kim, Jaewook; Kim, Woo Youn
2015-03-07
We developed a self-consistent field program based on Kohn-Sham density functional theory using Lagrange-sinc functions as a basis set and examined its numerical accuracy for atoms and molecules through comparison with the results of Gaussian basis sets. The result of the Kohn-Sham inversion formula from the Lagrange-sinc basis set manifests that the pseudopotential method is essential for cost-effective calculations. The Lagrange-sinc basis set shows faster convergence of the kinetic and correlation energies of benzene as its size increases than the finite difference method does, though both share the same uniform grid. Using a scaling factor smaller than or equal to 0.226 bohr and pseudopotentials with nonlinear core correction, its accuracy for the atomization energies of the G2-1 set is comparable to all-electron complete basis set limits (mean absolute deviation ≤1 kcal/mol). The same basis set also shows small mean absolute deviations in the ionization energies, electron affinities, and static polarizabilities of atoms in the G2-1 set. In particular, the Lagrange-sinc basis set shows high accuracy with rapid convergence in describing density or orbital changes by an external electric field. Moreover, the Lagrange-sinc basis set can readily improve its accuracy toward a complete basis set limit by simply decreasing the scaling factor regardless of systems.
An extended basis set {ital ab} {ital initio} study of alkali metal cation--water clusters
Feller, D.; Glendening, E.D.; Woon, D.E.; Feyereisen, M.W.
1995-09-01
Ionic clusters comprised of a single alkali metal cation and up to eight water molecules were studied at the Hartree--Fock and correlated levels of theory using the correlation consistent sequence of basis sets. Estimates of the degree of convergence in the computed properties with respect to the complete basis set limit were facilitated by the underlying systematic manner in which the correlation consistent sets approach completeness. In favorable cases, improved property values could be obtained by fitting finite basis set results with a simple analytical expression in order to extrapolate to the complete basis set limit. The sensitivity of structures and binding energies were analyzed with regard to the inclusion of valence and core-valence correlation recovery at the MP2, MP4, and CCSD(T) levels of theory. The replacement of metal core electrons and the introduction of relativistic contributions via effective core potentials was compared to corresponding all-electron results. {copyright} {ital 1995} {ital American} {ital Institute} {ital of} {ital Physics}.
Point Set Denoising Using Bootstrap-Based Radial Basis Function
Ramli, Ahmad; Abd. Majid, Ahmad
2016-01-01
This paper examines the application of a bootstrap test error estimation of radial basis functions, specifically thin-plate spline fitting, in surface smoothing. The presence of noisy data is a common issue of the point set model that is generated from 3D scanning devices, and hence, point set denoising is one of the main concerns in point set modelling. Bootstrap test error estimation, which is applied when searching for the smoothing parameters of radial basis functions, is revisited. The main contribution of this paper is a smoothing algorithm that relies on a bootstrap-based radial basis function. The proposed method incorporates a k-nearest neighbour search and then projects the point set to the approximated thin-plate spline surface. Therefore, the denoising process is achieved, and the features are well preserved. A comparison of the proposed method with other smoothing methods is also carried out in this study. PMID:27315105
Relativistic correlating basis sets for actinide atoms from 90Th to 103Lr.
Noro, Takeshi; Sekiya, Masahiro; Osanai, You; Koga, Toshikatsu; Matsuyama, Hisashi
2007-12-01
For 14 actinide atoms from (90)Th to (103)Lr, contracted Gaussian-type function sets are developed for the description of correlations of the 5f, 6d, and 7s electrons. Basis sets for the 6d orbitals are also prepared, since the orbitals are important in molecular environments despite their vacancy in the ground state of some actinides. A segmented contraction scheme is employed for the compactness and efficiency. Contraction coefficients and exponents are so determined as to minimize the deviation from accurate natural orbitals of the lowest term arising from the 5f(n-1)6d(1)7s(2) configuration. The spin-free relativistic effects are considered through the third-order Douglas-Kroll approximation. To test the present correlating sets, all-electron calculations are performed on the ground state of (90)ThO molecule. The calculated spectroscopic constants are in excellent agreement with experimental values. PMID:17508413
Atomic orbital basis sets for use with effective core potentials
Blaudeau, J.P.; Brozell, S.R.; Matsika, S.; Zhang, Z.; Pitzer, R.M.
2000-03-15
Basis sets developed for use with effective core potentials describe pseudo-orbitals rather than orbitals. The primitive Gaussian functions and the contraction coefficients in the basis set must therefore both describe the valence region effectively and allow the pseudo-orbital to be small in the core region. The latter is particularly difficult using 1s primitive functions, which have their maxima at the nucleus. Several methods of choosing contraction coefficients are tried, and it is found that natural orbitals give the best results. The number and optimization of primitive functions are done following Dunning's correlation-consistent procedure. Optimization of orbital exponents for larger atoms frequently results in coalescence of adjacent exponents; use of orbitals with higher principal quantum number is one alternative. Actinide atoms or ions provide the most difficult cases in that basis sets must be optimized for valence shells of different radial size simultaneously considering correlation energy and spin-orbit energy.
Localized orbitals from basis sets augmented with diffuse functions
NASA Astrophysics Data System (ADS)
Høyvik, Ida-Marie; Jørgensen, Poul
2013-05-01
Orbital localization of occupied and virtual Hartree-Fock orbitals generated from basis sets augmented with diffuse functions is performed using the Pipek-Mezey, Boys, powers of the second central moment, and powers of the fourth central moment localizations. The locality of the obtained orbital sets are presented in terms of second and fourth moment orbital spreads. The results show that both local occupied and virtual orbitals may be obtained when using powers of the second central moment and powers of the fourth central moment localizations, while the Pipek-Mezey and Boys localizations fail to produce sets of local virtual orbitals. The locality of the fourth central moment virtual orbitals exhibits a locality similar to the locality of a Boys localization for non-augmented basis sets.
NASA Astrophysics Data System (ADS)
Goldey, Matthew; Head-Gordon, Martin
2015-03-01
Second order Møller-Plesset perturbation theory (MP2) in finite basis sets describes several classes of noncovalent interactions poorly due to basis set superposition error (BSSE) and underlying inaccurate physics for dispersion interactions. Attenuation of the Coulomb operator provides a direct path toward improving MP2 for noncovalent interactions. In limited basis sets, we demonstrate improvements in accuracy for intermolecular interactions with a three to five-fold reduction in RMS errors. For a range of inter- and intermolecular test cases, attenuated MP2 even outperforms complete basis set estimates of MP2. Finite basis attenuated MP2 is useful for inter- and intramolecular interactions where higher cost approaches are intractable. Extending this approach, recent research pairs attenuated MP2 with long-range correction to describe potential energy landscapes, and further results for large systems with noncovalent interactions are shown. This work was supported by the U.S. Department of Energy under Contract No. DE-AC02-05CH11231. We acknowledge computational resources obtained under NSF Award CHE-1048789.
NASA Astrophysics Data System (ADS)
Balabin, Roman M.
2011-03-01
The quantum chemistry of conformation equilibrium is a field where great accuracy (better than 100 cal mol-1) is needed because the energy difference between molecular conformers rarely exceeds 1000-3000 cal mol-1. The conformation equilibrium of straight-chain (normal) alkanes is of particular interest and importance for modern chemistry. In this paper, an extra error source for high-quality ab initio (first principles) and DFT calculations of the conformation equilibrium of normal alkanes, namely the intramolecular basis set superposition error (BSSE), is discussed. In contrast to out-of-plane vibrations in benzene molecules, diffuse functions on carbon and hydrogen atoms were found to greatly reduce the relative BSSE of n-alkanes. The corrections due to the intramolecular BSSE were found to be almost identical for the MP2, MP4, and CCSD(T) levels of theory. Their cancelation is expected when CCSD(T)/CBS (CBS, complete basis set) energies are evaluated by addition schemes. For larger normal alkanes (N > 12), the magnitude of the BSSE correction was found to be up to three times larger than the relative stability of the conformer; in this case, the basis set superposition error led to a two orders of magnitude difference in conformer abundance. No error cancelation due to the basis set superposition was found. A comparison with amino acid, peptide, and protein data was provided.
Universal perturbative explicitly correlated basis set incompleteness correction
NASA Astrophysics Data System (ADS)
Torheyden, Martin; Valeev, Edward F.
2009-11-01
Basis set incompleteness error for an arbitrary approximate electronic wave function is robustly reduced using a second-order perturbative correction into a basis of explicitly correlated, internally contracted geminal functions. The Hylleraas functional for the second-order energy correction is evaluated algebraically involving at most a four-electron reduced density matrix and four-electron integrals. By using the R12 technology in combination with screening approximations such a correction only requires a two-electron reduced density matrix and two-electron integrals. Preliminary investigations of potential energy surfaces of hydrogen fluoride and nitrogen molecules at the multireference configuration interaction singles and doubles indicate that with the perturbative correction only an aug-cc-pVDZ basis is necessary to compute correlation energies of an aug-cc-pVQZ quality, or better. The proposed correction, dubbed [2]R12, can in principle be combined with any single reference and multireference method in use today.
Correlation consistent basis sets for actinides. I. The Th and U atoms
Peterson, Kirk A.
2015-02-21
New correlation consistent basis sets based on both pseudopotential (PP) and all-electron Douglas-Kroll-Hess (DKH) Hamiltonians have been developed from double- to quadruple-zeta quality for the actinide atoms thorium and uranium. Sets for valence electron correlation (5f6s6p6d), cc − pV nZ − PP and cc − pV nZ − DK3, as well as outer-core correlation (valence + 5s5p5d), cc − pwCV nZ − PP and cc − pwCV nZ − DK3, are reported (n = D, T, Q). The -PP sets are constructed in conjunction with small-core, 60-electron PPs, while the -DK3 sets utilized the 3rd-order Douglas-Kroll-Hess scalar relativistic Hamiltonian. Both series of basis sets show systematic convergence towards the complete basis set limit, both at the Hartree-Fock and correlated levels of theory, making them amenable to standard basis set extrapolation techniques. To assess the utility of the new basis sets, extensive coupled cluster composite thermochemistry calculations of ThF{sub n} (n = 2 − 4), ThO{sub 2}, and UF{sub n} (n = 4 − 6) have been carried out. After accurately accounting for valence and outer-core correlation, spin-orbit coupling, and even Lamb shift effects, the final 298 K atomization enthalpies of ThF{sub 4}, ThF{sub 3}, ThF{sub 2}, and ThO{sub 2} are all within their experimental uncertainties. Bond dissociation energies of ThF{sub 4} and ThF{sub 3}, as well as UF{sub 6} and UF{sub 5}, were similarly accurate. The derived enthalpies of formation for these species also showed a very satisfactory agreement with experiment, demonstrating that the new basis sets allow for the use of accurate composite schemes just as in molecular systems composed only of lighter atoms. The differences between the PP and DK3 approaches were found to increase with the change in formal oxidation state on the actinide atom, approaching 5-6 kcal/mol for the atomization enthalpies of ThF{sub 4} and ThO{sub 2}. The DKH3 atomization energy of ThO{sub 2} was calculated to be smaller than the DKH2
Correlation consistent basis sets for actinides. I. The Th and U atoms.
Peterson, Kirk A
2015-02-21
New correlation consistent basis sets based on both pseudopotential (PP) and all-electron Douglas-Kroll-Hess (DKH) Hamiltonians have been developed from double- to quadruple-zeta quality for the actinide atoms thorium and uranium. Sets for valence electron correlation (5f6s6p6d), cc - pV nZ - PP and cc - pV nZ - DK3, as well as outer-core correlation (valence + 5s5p5d), cc - pwCV nZ - PP and cc - pwCV nZ - DK3, are reported (n = D, T, Q). The -PP sets are constructed in conjunction with small-core, 60-electron PPs, while the -DK3 sets utilized the 3rd-order Douglas-Kroll-Hess scalar relativistic Hamiltonian. Both series of basis sets show systematic convergence towards the complete basis set limit, both at the Hartree-Fock and correlated levels of theory, making them amenable to standard basis set extrapolation techniques. To assess the utility of the new basis sets, extensive coupled cluster composite thermochemistry calculations of ThFn (n = 2 - 4), ThO2, and UFn (n = 4 - 6) have been carried out. After accurately accounting for valence and outer-core correlation, spin-orbit coupling, and even Lamb shift effects, the final 298 K atomization enthalpies of ThF4, ThF3, ThF2, and ThO2 are all within their experimental uncertainties. Bond dissociation energies of ThF4 and ThF3, as well as UF6 and UF5, were similarly accurate. The derived enthalpies of formation for these species also showed a very satisfactory agreement with experiment, demonstrating that the new basis sets allow for the use of accurate composite schemes just as in molecular systems composed only of lighter atoms. The differences between the PP and DK3 approaches were found to increase with the change in formal oxidation state on the actinide atom, approaching 5-6 kcal/mol for the atomization enthalpies of ThF4 and ThO2. The DKH3 atomization energy of ThO2 was calculated to be smaller than the DKH2 value by ∼1 kcal/mol. PMID:25702000
Correlation consistent basis sets for actinides. I. The Th and U atoms
NASA Astrophysics Data System (ADS)
Peterson, Kirk A.
2015-02-01
New correlation consistent basis sets based on both pseudopotential (PP) and all-electron Douglas-Kroll-Hess (DKH) Hamiltonians have been developed from double- to quadruple-zeta quality for the actinide atoms thorium and uranium. Sets for valence electron correlation (5f6s6p6d), cc - pV nZ - PP and cc - pV nZ - DK3, as well as outer-core correlation (valence + 5s5p5d), cc - pwCV nZ - PP and cc - pwCV nZ - DK3, are reported (n = D, T, Q). The -PP sets are constructed in conjunction with small-core, 60-electron PPs, while the -DK3 sets utilized the 3rd-order Douglas-Kroll-Hess scalar relativistic Hamiltonian. Both series of basis sets show systematic convergence towards the complete basis set limit, both at the Hartree-Fock and correlated levels of theory, making them amenable to standard basis set extrapolation techniques. To assess the utility of the new basis sets, extensive coupled cluster composite thermochemistry calculations of ThFn (n = 2 - 4), ThO2, and UFn (n = 4 - 6) have been carried out. After accurately accounting for valence and outer-core correlation, spin-orbit coupling, and even Lamb shift effects, the final 298 K atomization enthalpies of ThF4, ThF3, ThF2, and ThO2 are all within their experimental uncertainties. Bond dissociation energies of ThF4 and ThF3, as well as UF6 and UF5, were similarly accurate. The derived enthalpies of formation for these species also showed a very satisfactory agreement with experiment, demonstrating that the new basis sets allow for the use of accurate composite schemes just as in molecular systems composed only of lighter atoms. The differences between the PP and DK3 approaches were found to increase with the change in formal oxidation state on the actinide atom, approaching 5-6 kcal/mol for the atomization enthalpies of ThF4 and ThO2. The DKH3 atomization energy of ThO2 was calculated to be smaller than the DKH2 value by ˜1 kcal/mol.
Coupled-cluster based basis sets for valence correlation calculations
NASA Astrophysics Data System (ADS)
Claudino, Daniel; Gargano, Ricardo; Bartlett, Rodney J.
2016-03-01
Novel basis sets are generated that target the description of valence correlation in atoms H through Ar. The new contraction coefficients are obtained according to the Atomic Natural Orbital (ANO) procedure from CCSD(T) (coupled-cluster singles and doubles with perturbative triples correction) density matrices starting from the primitive functions of Dunning et al. [J. Chem. Phys. 90, 1007 (1989); ibid. 98, 1358 (1993); ibid. 100, 2975 (1993)] (correlation consistent polarized valence X-tuple zeta, cc-pVXZ). The exponents of the primitive Gaussian functions are subject to uniform scaling in order to ensure satisfaction of the virial theorem for the corresponding atoms. These new sets, named ANO-VT-XZ (Atomic Natural Orbital Virial Theorem X-tuple Zeta), have the same number of contracted functions as their cc-pVXZ counterparts in each subshell. The performance of these basis sets is assessed by the evaluation of the contraction errors in four distinct computations: correlation energies in atoms, probing the density in different regions of space via
Coupled-cluster based basis sets for valence correlation calculations.
Claudino, Daniel; Gargano, Ricardo; Bartlett, Rodney J
2016-03-14
Novel basis sets are generated that target the description of valence correlation in atoms H through Ar. The new contraction coefficients are obtained according to the Atomic Natural Orbital (ANO) procedure from CCSD(T) (coupled-cluster singles and doubles with perturbative triples correction) density matrices starting from the primitive functions of Dunning et al. [J. Chem. Phys. 90, 1007 (1989); ibid. 98, 1358 (1993); ibid. 100, 2975 (1993)] (correlation consistent polarized valence X-tuple zeta, cc-pVXZ). The exponents of the primitive Gaussian functions are subject to uniform scaling in order to ensure satisfaction of the virial theorem for the corresponding atoms. These new sets, named ANO-VT-XZ (Atomic Natural Orbital Virial Theorem X-tuple Zeta), have the same number of contracted functions as their cc-pVXZ counterparts in each subshell. The performance of these basis sets is assessed by the evaluation of the contraction errors in four distinct computations: correlation energies in atoms, probing the density in different regions of space via ⟨r(n)⟩ (-3 ≤ n ≤ 3) in atoms, correlation energies in diatomic molecules, and the quality of fitting potential energy curves as measured by spectroscopic constants. All energy calculations with ANO-VT-QZ have contraction errors within "chemical accuracy" of 1 kcal/mol, which is not true for cc-pVQZ, suggesting some improvement compared to the correlation consistent series of Dunning and co-workers. PMID:26979680
Scar Functions, Barriers for Chemical Reactivity, and Vibrational Basis Sets.
Revuelta, F; Vergini, E; Benito, R M; Borondo, F
2016-07-14
The performance of a recently proposed method to efficiently calculate scar functions is analyzed in problems of chemical interest. An application to the computation of wave functions associated with barriers relevant for the LiNC ⇄ LiCN isomerization reaction is presented as an illustration. These scar functions also constitute excellent elements for basis sets suitable for quantum calculation of vibrational energy levels. To illustrate their efficiency, a calculation of the LiNC/LiCN eigenfunctions is also presented. PMID:26905100
Sharkey, Keeper L; Adamowicz, Ludwik
2014-05-01
An algorithm for quantum-mechanical nonrelativistic variational calculations of L = 0 and M = 0 states of atoms with an arbitrary number of s electrons and with three p electrons have been implemented and tested in the calculations of the ground (4)S state of the nitrogen atom. The spatial part of the wave function is expanded in terms of all-electrons explicitly correlated Gaussian functions with the appropriate pre-exponential Cartesian angular factors for states with the L = 0 and M = 0 symmetry. The algorithm includes formulas for calculating the Hamiltonian and overlap matrix elements, as well as formulas for calculating the analytic energy gradient determined with respect to the Gaussian exponential parameters. The gradient is used in the variational optimization of these parameters. The Hamiltonian used in the approach is obtained by rigorously separating the center-of-mass motion from the laboratory-frame all-particle Hamiltonian, and thus it explicitly depends on the finite mass of the nucleus. With that, the mass effect on the total ground-state energy is determined. PMID:24811630
Correlation consistent basis sets for lanthanides: The atoms La-Lu.
Lu, Qing; Peterson, Kirk A
2016-08-01
Using the 3rd-order Douglas-Kroll-Hess (DKH3) Hamiltonian, all-electron correlation consistent basis sets of double-, triple-, and quadruple-zeta quality have been developed for the lanthanide elements La through Lu. Basis sets designed for the recovery of valence correlation (defined here as 4f5s5p5d6s), cc-pVnZ-DK3, and outer-core correlation (valence + 4s4p4d), cc-pwCVnZ-DK3, are reported (n = D, T, and Q). Systematic convergence of both Hartree-Fock and correlation energies towards their respective complete basis set (CBS) limits are observed. Benchmark calculations of the first three ionization potentials (IPs) of La through Lu are reported at the DKH3 coupled cluster singles and doubles with perturbative triples, CCSD(T), level of theory, including effects of correlation down through the 4s electrons. Spin-orbit coupling is treated at the 2-component HF level. After extrapolation to the CBS limit, the average errors with respect to experiment were just 0.52, 1.14, and 4.24 kcal/mol for the 1st, 2nd, and 3rd IPs, respectively, compared to the average experimental uncertainties of 0.03, 1.78, and 2.65 kcal/mol, respectively. The new basis sets are also used in CCSD(T) benchmark calculations of the equilibrium geometries, atomization energies, and heats of formation for Gd2, GdF, and GdF3. Except for the equilibrium geometry and harmonic frequency of GdF, which are accurately known from experiment, all other calculated quantities represent significant improvements compared to the existing experimental quantities. With estimated uncertainties of about ±3 kcal/mol, the 0 K atomization energies (298 K heats of formation) are calculated to be (all in kcal/mol): 33.2 (160.1) for Gd2, 151.7 (-36.6) for GdF, and 447.1 (-295.2) for GdF3. PMID:27497543
Correlation consistent basis sets for lanthanides: The atoms La-Lu
NASA Astrophysics Data System (ADS)
Lu, Qing; Peterson, Kirk A.
2016-08-01
Using the 3rd-order Douglas-Kroll-Hess (DKH3) Hamiltonian, all-electron correlation consistent basis sets of double-, triple-, and quadruple-zeta quality have been developed for the lanthanide elements La through Lu. Basis sets designed for the recovery of valence correlation (defined here as 4f5s5p5d6s), cc-pVnZ-DK3, and outer-core correlation (valence + 4s4p4d), cc-pwCVnZ-DK3, are reported (n = D, T, and Q). Systematic convergence of both Hartree-Fock and correlation energies towards their respective complete basis set (CBS) limits are observed. Benchmark calculations of the first three ionization potentials (IPs) of La through Lu are reported at the DKH3 coupled cluster singles and doubles with perturbative triples, CCSD(T), level of theory, including effects of correlation down through the 4s electrons. Spin-orbit coupling is treated at the 2-component HF level. After extrapolation to the CBS limit, the average errors with respect to experiment were just 0.52, 1.14, and 4.24 kcal/mol for the 1st, 2nd, and 3rd IPs, respectively, compared to the average experimental uncertainties of 0.03, 1.78, and 2.65 kcal/mol, respectively. The new basis sets are also used in CCSD(T) benchmark calculations of the equilibrium geometries, atomization energies, and heats of formation for Gd2, GdF, and GdF3. Except for the equilibrium geometry and harmonic frequency of GdF, which are accurately known from experiment, all other calculated quantities represent significant improvements compared to the existing experimental quantities. With estimated uncertainties of about ±3 kcal/mol, the 0 K atomization energies (298 K heats of formation) are calculated to be (all in kcal/mol): 33.2 (160.1) for Gd2, 151.7 (-36.6) for GdF, and 447.1 (-295.2) for GdF3.
Basis set expansion for inverse problems in plasma diagnostic analysis.
Jones, B; Ruiz, C L
2013-07-01
A basis set expansion method [V. Dribinski, A. Ossadtchi, V. A. Mandelshtam, and H. Reisler, Rev. Sci. Instrum. 73, 2634 (2002)] is applied to recover physical information about plasma radiation sources from instrument data, which has been forward transformed due to the nature of the measurement technique. This method provides a general approach for inverse problems, and we discuss two specific examples relevant to diagnosing fast z pinches on the 20-25 MA Z machine [M. E. Savage, L. F. Bennett, D. E. Bliss, W. T. Clark, R. S. Coats, J. M. Elizondo, K. R. LeChien, H. C. Harjes, J. M. Lehr, J. E. Maenchen, D. H. McDaniel, M. F. Pasik, T. D. Pointon, A. C. Owen, D. B. Seidel, D. L. Smith, B. S. Stoltzfus, K. W. Struve, W. A. Stygar, L. K. Warne, J. R. Woodworth, C. W. Mendel, K. R. Prestwich, R. W. Shoup, D. L. Johnson, J. P. Corley, K. C. Hodge, T. C. Wagoner, and P. E. Wakeland, in Proceedings of the Pulsed Power Plasma Sciences Conference (IEEE, 2007), p. 979]. First, Abel inversion of time-gated, self-emission x-ray images from a wire array implosion is studied. Second, we present an approach for unfolding neutron time-of-flight measurements from a deuterium gas puff z pinch to recover information about emission time history and energy distribution. Through these examples, we discuss how noise in the measured data limits the practical resolution of the inversion, and how the method handles discontinuities in the source function and artifacts in the projected image. We add to the method a propagation of errors calculation for estimating uncertainties in the inverted solution. PMID:23902066
Basis set expansion for inverse problems in plasma diagnostic analysis
NASA Astrophysics Data System (ADS)
Jones, B.; Ruiz, C. L.
2013-07-01
A basis set expansion method [V. Dribinski, A. Ossadtchi, V. A. Mandelshtam, and H. Reisler, Rev. Sci. Instrum. 73, 2634 (2002)], 10.1063/1.1482156 is applied to recover physical information about plasma radiation sources from instrument data, which has been forward transformed due to the nature of the measurement technique. This method provides a general approach for inverse problems, and we discuss two specific examples relevant to diagnosing fast z pinches on the 20-25 MA Z machine [M. E. Savage, L. F. Bennett, D. E. Bliss, W. T. Clark, R. S. Coats, J. M. Elizondo, K. R. LeChien, H. C. Harjes, J. M. Lehr, J. E. Maenchen, D. H. McDaniel, M. F. Pasik, T. D. Pointon, A. C. Owen, D. B. Seidel, D. L. Smith, B. S. Stoltzfus, K. W. Struve, W. A. Stygar, L. K. Warne, J. R. Woodworth, C. W. Mendel, K. R. Prestwich, R. W. Shoup, D. L. Johnson, J. P. Corley, K. C. Hodge, T. C. Wagoner, and P. E. Wakeland, in Proceedings of the Pulsed Power Plasma Sciences Conference (IEEE, 2007), p. 979]. First, Abel inversion of time-gated, self-emission x-ray images from a wire array implosion is studied. Second, we present an approach for unfolding neutron time-of-flight measurements from a deuterium gas puff z pinch to recover information about emission time history and energy distribution. Through these examples, we discuss how noise in the measured data limits the practical resolution of the inversion, and how the method handles discontinuities in the source function and artifacts in the projected image. We add to the method a propagation of errors calculation for estimating uncertainties in the inverted solution.
Basis set expansion for inverse problems in plasma diagnostic analysis
Jones, B.; Ruiz, C. L.
2013-07-15
A basis set expansion method [V. Dribinski, A. Ossadtchi, V. A. Mandelshtam, and H. Reisler, Rev. Sci. Instrum. 73, 2634 (2002)] is applied to recover physical information about plasma radiation sources from instrument data, which has been forward transformed due to the nature of the measurement technique. This method provides a general approach for inverse problems, and we discuss two specific examples relevant to diagnosing fast z pinches on the 20–25 MA Z machine [M. E. Savage, L. F. Bennett, D. E. Bliss, W. T. Clark, R. S. Coats, J. M. Elizondo, K. R. LeChien, H. C. Harjes, J. M. Lehr, J. E. Maenchen, D. H. McDaniel, M. F. Pasik, T. D. Pointon, A. C. Owen, D. B. Seidel, D. L. Smith, B. S. Stoltzfus, K. W. Struve, W. A. Stygar, L. K. Warne, J. R. Woodworth, C. W. Mendel, K. R. Prestwich, R. W. Shoup, D. L. Johnson, J. P. Corley, K. C. Hodge, T. C. Wagoner, and P. E. Wakeland, in Proceedings of the Pulsed Power Plasma Sciences Conference (IEEE, 2007), p. 979]. First, Abel inversion of time-gated, self-emission x-ray images from a wire array implosion is studied. Second, we present an approach for unfolding neutron time-of-flight measurements from a deuterium gas puff z pinch to recover information about emission time history and energy distribution. Through these examples, we discuss how noise in the measured data limits the practical resolution of the inversion, and how the method handles discontinuities in the source function and artifacts in the projected image. We add to the method a propagation of errors calculation for estimating uncertainties in the inverted solution.
Evaluation of Density Functionals and Basis Sets for Carbohydrates
Technology Transfer Automated Retrieval System (TEKTRAN)
Correlated ab initio wave function calculations using MP2/aug-cc-pVTZ model chemistry have been performed for three test sets of gas phase saccharide conformations to provide reference values for their relative energies. The test sets consist of 15 conformers of alpha and beta-D-allopyranose, 15 of ...
NASA Astrophysics Data System (ADS)
Nikolaev, A. V.; Lamoen, D.; Partoens, B.
2016-07-01
In order to increase the accuracy of the linearized augmented plane wave (LAPW) method, we present a new approach where the plane wave basis function is augmented by two different atomic radial components constructed at two different linearization energies corresponding to two different electron bands (or energy windows). We demonstrate that this case can be reduced to the standard treatment within the LAPW paradigm where the usual basis set is enriched by the basis functions of the tight binding type, which go to zero with zero derivative at the sphere boundary. We show that the task is closely related with the problem of extended core states which is currently solved by applying the LAPW method with local orbitals (LAPW+LO). In comparison with LAPW+LO, the number of supplemented basis functions in our approach is doubled, which opens up a new channel for the extension of the LAPW and LAPW+LO basis sets. The appearance of new supplemented basis functions absent in the LAPW+LO treatment is closely related with the existence of the u ˙ l -component in the canonical LAPW method. We discuss properties of additional tight binding basis functions and apply the extended basis set for computation of electron energy bands of lanthanum (face and body centered structures) and hexagonal close packed lattice of cadmium. We demonstrate that the new treatment gives lower total energies in comparison with both canonical LAPW and LAPW+LO, with the energy difference more pronounced for intermediate and poor LAPW basis sets.
On the performance of atomic natural orbital basis sets: A full configuration interaction study
Illas, F. Departament de Quimica Fisica, Grup de Quimica Quantica, Facultat de Quimica, Universitat de Barcelona, C Ricart, J.M. ); Rubio, J. ); Bagus, P.S. )
1990-10-01
The performance of atomic natural orbital (ANO) basis sets has been studied by comparing self-consistant field (SCF) and full configuration interaction (CI) results obtained for the first row atoms and hydrides. The ANO results have been compared with those obtained using a segmented basis set containing the same number of contracted basis functions. The total energies obtained with the ANO basis sets are always lower than the one obtained by using the segmented one. However, for the hydrides, differential electronic correlation energy obtained with the ANO basis set may be smaller than the one recovered with the segmented set. We relate this poorer differential correlation energy for the ANO basis set to the fact that only one contracted {ital d} function is used for the ANO and segmented basis sets.
Hill, J. Grant E-mail: kipeters@wsu.edu; Peterson, Kirk A. E-mail: kipeters@wsu.edu
2014-09-07
New correlation consistent basis sets, cc-pVnZ-PP-F12 (n = D, T, Q), for all the post-d main group elements Ga–Rn have been optimized for use in explicitly correlated F12 calculations. The new sets, which include not only orbital basis sets but also the matching auxiliary sets required for density fitting both conventional and F12 integrals, are designed for correlation of valence sp, as well as the outer-core d electrons. The basis sets are constructed for use with the previously published small-core relativistic pseudopotentials of the Stuttgart-Cologne variety. Benchmark explicitly correlated coupled-cluster singles and doubles with perturbative triples [CCSD(T)-F12b] calculations of the spectroscopic properties of numerous diatomic molecules involving 4p, 5p, and 6p elements have been carried out and compared to the analogous conventional CCSD(T) results. In general the F12 results obtained with a n-zeta F12 basis set were comparable to conventional aug-cc-pVxZ-PP or aug-cc-pwCVxZ-PP basis set calculations obtained with x = n + 1 or even x = n + 2. The new sets used in CCSD(T)-F12b calculations are particularly efficient at accurately recovering the large correlation effects of the outer-core d electrons.
Nikolaev, A V; Lamoen, D; Partoens, B
2016-07-01
In order to increase the accuracy of the linearized augmented plane wave (LAPW) method, we present a new approach where the plane wave basis function is augmented by two different atomic radial components constructed at two different linearization energies corresponding to two different electron bands (or energy windows). We demonstrate that this case can be reduced to the standard treatment within the LAPW paradigm where the usual basis set is enriched by the basis functions of the tight binding type, which go to zero with zero derivative at the sphere boundary. We show that the task is closely related with the problem of extended core states which is currently solved by applying the LAPW method with local orbitals (LAPW+LO). In comparison with LAPW+LO, the number of supplemented basis functions in our approach is doubled, which opens up a new channel for the extension of the LAPW and LAPW+LO basis sets. The appearance of new supplemented basis functions absent in the LAPW+LO treatment is closely related with the existence of the u̇l-component in the canonical LAPW method. We discuss properties of additional tight binding basis functions and apply the extended basis set for computation of electron energy bands of lanthanum (face and body centered structures) and hexagonal close packed lattice of cadmium. We demonstrate that the new treatment gives lower total energies in comparison with both canonical LAPW and LAPW+LO, with the energy difference more pronounced for intermediate and poor LAPW basis sets. PMID:27394093
Gidofalvi, Gergely; Mazziotti, David A
2014-01-16
Molecule-optimized basis sets, based on approximate natural orbitals, are developed for accelerating the convergence of quantum calculations with strongly correlated (multireferenced) electrons. We use a low-cost approximate solution of the anti-Hermitian contracted Schrödinger equation (ACSE) for the one- and two-electron reduced density matrices (RDMs) to generate an approximate set of natural orbitals for strongly correlated quantum systems. The natural-orbital basis set is truncated to generate a molecule-optimized basis set whose rank matches that of a standard correlation-consistent basis set optimized for the atoms. We show that basis-set truncation by approximate natural orbitals can be viewed as a one-electron unitary transformation of the Hamiltonian operator and suggest an extension of approximate natural-orbital truncations through two-electron unitary transformations of the Hamiltonian operator, such as those employed in the solution of the ACSE. The molecule-optimized basis set from the ACSE improves the accuracy of the equivalent standard atom-optimized basis set at little additional computational cost. We illustrate the method with the potential energy curves of hydrogen fluoride and diatomic nitrogen. Relative to the hydrogen fluoride potential energy curve from the ACSE in a polarized triple-ζ basis set, the ACSE curve in a molecule-optimized basis set, equivalent in size to a polarized double-ζ basis, has a nonparallelity error of 0.0154 au, which is significantly better than the nonparallelity error of 0.0252 au from the polarized double-ζ basis set. PMID:24387056
Derivation of a formula for the resonance integral for a nonorthogonal basis set
Yim, Yung-Chang; Eyring, Henry
1981-01-01
In a self-consistent field calculation, a formula for the off-diagonal matrix elements of the core Hamiltonian is derived for a nonorthogonal basis set by a polyatomic approach. A set of parameters is then introduced for the repulsion integral formula of Mataga-Nishimoto to fit the experimental data. The matrix elements computed for the nonorthogonal basis set in the π-electron approximation are transformed to those for an orthogonal basis set by the Löwdin symmetrical orthogonalization. PMID:16593009
Basis Set Dependence of Vibrational Raman and Raman Optical Activity Intensities.
Cheeseman, James R; Frisch, Michael J
2011-10-11
We present a systematic study of the basis set dependence of the backscattering vibrational Raman intensities and Raman Optical Activity (ROA) intensity differences. The accuracies of computed Raman intensities and ROA intensity differences for a series of commonly used basis sets are reported, relative to large reference basis sets, using the B3LYP density functional. This study attempts to separately quantify the relative accuracies obtained from particular basis set combinations: one for the geometry optimization and force field computation and the other for the computation of Raman and ROA tensors. We demonstrate here that the basis set requirements for the geometry and force fields are not similar to those of the Raman and ROA tensors. The Raman and ROA tensors require basis sets with diffuse functions, while geometry optimizations and force field computations typically do not. Eleven molecules were examined: (S)-methyloxirane, (S)-methylthirane, (R)-epichlorhydrin, (S)-CHFClBr, (1S,5S)-α-pinene, (1S,5S)-β-pinene, (1S,4S)-norborneneone, (M)-σ-[4]-helicene, an enone precursor to a cytotoxic sesquiterpene, the gauche-gauche conformer of the monosaccharide methyl-β-d-glucopyranose, and the dipeptide Ac-(alanine)2-NH2. For the molecules examined here, intensities and intensity differences obtained from Raman and ROA tensors computed using the aug-cc-pVDZ basis set are nearly equivalent to those computed with the larger aug-cc-pVTZ basis set. We find that modifying the aug-cc-pVDZ basis set by removing the set of diffuse d functions on all atoms (while keeping the diffuse s and p sets), denoted as aug(sp)-cc-pVDZ, results in a basis set which is significantly faster without much reduction in the overall accuracy. In addition, the popular rDPS basis set introduced by Zuber and Hug offers a good compromise between accuracy and efficiency. The combination of either the aug(sp)-pVDZ or rDPS basis for the computation of the Raman and ROA tensors with the 6-31G
A Hartree-Fock study of the confined helium atom: Local and global basis set approaches
NASA Astrophysics Data System (ADS)
Young, Toby D.; Vargas, Rubicelia; Garza, Jorge
2016-02-01
Two different basis set methods are used to calculate atomic energy within Hartree-Fock theory. The first is a local basis set approach using high-order real-space finite elements and the second is a global basis set approach using modified Slater-type orbitals. These two approaches are applied to the confined helium atom and are compared by calculating one- and two-electron contributions to the total energy. As a measure of the quality of the electron density, the cusp condition is analyzed.
Dynamical basis sets for algebraic variational calculations in quantum-mechanical scattering theory
NASA Technical Reports Server (NTRS)
Sun, Yan; Kouri, Donald J.; Truhlar, Donald G.; Schwenke, David W.
1990-01-01
New basis sets are proposed for linear algebraic variational calculations of transition amplitudes in quantum-mechanical scattering problems. These basis sets are hybrids of those that yield the Kohn variational principle (KVP) and those that yield the generalized Newton variational principle (GNVP) when substituted in Schlessinger's stationary expression for the T operator. Trial calculations show that efficiencies almost as great as that of the GNVP and much greater than the KVP can be obtained, even for basis sets with the majority of the members independent of energy.
Pseudospectral sampling of Gaussian basis sets as a new avenue to high-dimensional quantum dynamics
NASA Astrophysics Data System (ADS)
Heaps, Charles
This thesis presents a novel approach to modeling quantum molecular dynamics (QMD). Theoretical approaches to QMD are essential to understanding and predicting chemical reactivity and spectroscopy. We implement a method based on a trajectory-guided basis set. In this case, the nuclei are propagated in time using classical mechanics. Each nuclear configuration corresponds to a basis function in the quantum mechanical expansion. Using the time-dependent configurations as a basis set, we are able to evolve in time using relatively little information at each time step. We use a basis set of moving frozen (time-independent width) Gaussian functions that are well-known to provide a simple and efficient basis set for nuclear dynamics. We introduce a new perspective to trajectory-guided Gaussian basis sets based on existing numerical methods. The distinction is based on the Galerkin and collocation methods. In the former, the basis set is tested using basis functions, projecting the solution onto the functional space of the problem and requiring integration over all space. In the collocation method, the Dirac delta function tests the basis set, projecting the solution onto discrete points in space. This effectively reduces the integral evaluation to function evaluation, a fundamental characteristic of pseudospectral methods. We adopt this idea for independent trajectory-guided Gaussian basis functions. We investigate a series of anharmonic vibrational models describing dynamics in up to six dimensions. The pseudospectral sampling is found to be as accurate as full integral evaluation, while the former method is fully general and integration is only possible on very particular model potential energy surfaces. Nonadiabatic dynamics are also investigated in models of photodissociation and collinear triatomic vibronic coupling. Using Ehrenfest trajectories to guide the basis set on multiple surfaces, we observe convergence to exact results using hundreds of basis functions
Adapting DFT+U for the Chemically Motivated Correction of Minimal Basis Set Incompleteness.
Kulik, Heather J; Seelam, Natasha; Mar, Brendan D; Martínez, Todd J
2016-07-28
Recent algorithmic and hardware advances have enabled the application of electronic structure methods to the study of large-scale systems such as proteins with O(10(3)) atoms. Most such methods benefit greatly from the use of reduced basis sets to further enhance their speed, but truly minimal basis sets are well-known to suffer from incompleteness error that gives rise to incorrect descriptions of chemical bonding, preventing minimal basis set use in production calculations. We present a strategy for improving these well-known shortcomings in minimal basis sets by selectively tuning the energetics and bonding of nitrogen and oxygen atoms within proteins and small molecules to reproduce polarized double-ζ basis set geometries at minimal basis set cost. We borrow the well-known +U correction from the density functional theory community normally employed for self-interaction errors and demonstrate its power in the context of correcting basis set incompleteness within a formally self-interaction-free Hartree-Fock framework. We tune the Hubbard U parameters for nitrogen and oxygen atoms on small-molecule tautomers (e.g., cytosine), demonstrate the applicability of the approach on a number of amide-containing molecules (e.g., formamide, alanine tripeptide), and test our strategy on a 10 protein test set where anomalous proton transfer events are reduced by 90% from RHF/STO-3G to RHF/STO-3G+U, bringing the latter into quantitative agreement with RHF/6-31G* results. Although developed with the study of biological molecules in mind, this empirically tuned U approach shows promise as an alternative strategy for correction of basis set incompleteness errors. PMID:27383567
What is the most efficient way to reach the canonical MP2 basis set limit?
NASA Astrophysics Data System (ADS)
Liakos, Dimitrios G.; Izsák, Róbert; Valeev, Edward F.; Neese, Frank
2013-09-01
Various ways of reaching the complete basis set limit at the second-order Møller-Plesset perturbation theory (MP2) level are compared with respect to their cost-to-accuracy ratio. These include: (1) traditional MP2 calculations with correlation consistent basis sets of increasing size, with and without the resolution of identity for Coulomb and exchange (RIJK) or the combined RIJ and 'chain of spheres' (RIJCOSX) approximations; (2) basis set extrapolation obtained with the same MP2 variants; and (3) explicitly correlated F12-MP2 methods. The time required to solve the Hartree-Fock equations is part of the evaluation because the overall efficiency is of central interest in this work. Results were obtained for the ISO34, DC9 and S66 test sets and were analysed in terms of efficiency and accuracy for total energies, reaction energies and their effect on the basis set superposition error. Among the methods studied, the RIJK-MP2-F12 and RIJK-MP2-EP1 (where EP1 stands for 'Extrapolation Protocol 1' as explained in the text) methods perform outstandingly well. Although extrapolation is, in general, slightly faster than explicit correlation, it is found that for reaction energies, RIJK-MP2-F12 performs systematically better. This holds especially in combination with a triple zeta basis set, in which case it even outperforms the much more costly extrapolation involving quadruple- and quintuple-zeta correlation consistent basis sets.
On basis set superposition error corrected stabilization energies for large n-body clusters.
Walczak, Katarzyna; Friedrich, Joachim; Dolg, Michael
2011-10-01
In this contribution, we propose an approximate basis set superposition error (BSSE) correction scheme for the site-site function counterpoise and for the Valiron-Mayer function counterpoise correction of second order to account for the basis set superposition error in clusters with a large number of subunits. The accuracy of the proposed scheme has been investigated for a water cluster series at the CCSD(T), CCSD, MP2, and self-consistent field levels of theory using Dunning's correlation consistent basis sets. The BSSE corrected stabilization energies for a series of water clusters are presented. A study regarding the possible savings with respect to computational resources has been carried out as well as a monitoring of the basis set dependence of the approximate BSSE corrections. PMID:21992293
Basis-set extensions for two-component spin-orbit treatments of heavy elements.
Armbruster, Markus K; Klopper, Wim; Weigend, Florian
2006-11-14
The accuracy of standard basis sets of quadruple-zeta and lower quality for the use in two-component self-consistent field procedures including spin-orbit coupling is investigated for the elements In-I and Au-At. Spin-orbit coupling leads to energetic and spatial splittings of inner shells, which are not described accurately with standard basis sets optimized for scalar relativistic calculations. This results in large errors in total atomic energies and significant errors in atomization energies of compounds containing these atoms. We show how these errors can be corrected by adding just a few steep sets of basis functions and demonstrate the quality of the resulting extended basis sets. PMID:17066175
Near Hartree-Fock quality GTO basis sets for the second-row atoms
NASA Technical Reports Server (NTRS)
Partridge, Harry
1987-01-01
Energy optimized, near Hartree-Fock quality Gaussian basis sets ranging in size from (17s12p) to (20s15p) are presented for the ground states of the second-row atoms for Na(2P), Na(+), Na(-), Mg(3P), P(-), S(-), and Cl(-). In addition, optimized supplementary functions are given for the ground state basis sets to describe the negative ions, and the excited Na(2P) and Mg(3P) atomic states. The ratios of successive orbital exponents describing the inner part of the 1s and 2p orbitals are found to be nearly independent of both nuclear charge and basis set size. This provides a method of obtaining good starting estimates for other basis set optimizations.
Informatics-Based Energy Fitting Scheme for Correlation Energy at Complete Basis Set Limit.
Seino, Junji; Nakai, Hiromi
2016-09-30
Energy fitting schemes based on informatics techniques using hierarchical basis sets with small cardinal numbers were numerically investigated to estimate correlation energies at the complete basis set limits. Numerical validations confirmed that the conventional two-point extrapolation models can be unified into a simple formula with optimal parameters obtained by the same test sets. The extrapolation model was extended to two-point fitting models by a relaxation of the relationship between the extrapolation coefficients or a change of the fitting formula. Furthermore, n-scheme fitting models were developed by the combinations of results calculated at several theory levels and basis sets to compensate for the deficiencies in the fitting model at one level of theory. Systematic assessments on the Gaussian-3X and Gaussian-2 sets revealed that the fitting models drastically reduced errors with equal or smaller computational effort. © 2016 Wiley Periodicals, Inc. PMID:27454327
NASA Astrophysics Data System (ADS)
Kupka, Teobald
2008-08-01
Based on B3LYP spin-spin coupling constants (SSCC) of several molecules calculated with cc-pV xZ, cc-pCV xZ, cc-pCV xZ-sd and cc-pCV xZ-sd+ t basis sets, a reasonably fit, using the two-parameter formula, to the Kohn-Sham complete basis set limit (CBS) is shown. Improvement in the CBS values going from cc-pV xZ to the most elaborated cc-pCV xZ-sd+ t basis set family is observed: standard deviation for all data drops from 33.7 to 23.1, and from 6.0 to 4.8 Hz after excluding problematic 1J(F,H) and 1J(F,C). Calculation of water's 1J(OH) using B3LYP/cc-pCV xZ and B3LYP/pcJ- n significantly improved the FC term convergence.
NASA Astrophysics Data System (ADS)
Betzinger, Markus; Friedrich, Christoph; Görling, Andreas; Blügel, Stefan
2015-12-01
We present a methodology to calculate frequency and momentum dependent all-electron response functions determined within Kohn-Sham density functional theory. It overcomes the main obstacle in calculating response functions in practice, which is the slow convergence with respect to the number of unoccupied states and the basis-set size. In this approach, the usual sum-over-states expression of perturbation theory is complemented by the response of the orbital basis functions, explicitly constructed by radial integrations of frequency-dependent Sternheimer equations. To an essential extent an infinite number of unoccupied states are included in this way. Furthermore, the response of the core electrons is treated virtually exactly, which is out of reach otherwise. The method is an extension of the recently introduced incomplete-basis-set correction (IBC) [Betzinger et al., Phys. Rev. B 85, 245124 (2012), 10.1103/PhysRevB.85.245124; Phys. Rev. B 88, 075130 (2013), 10.1103/PhysRevB.88.075130] to the frequency and momentum domain. We have implemented the generalized IBC within the all-electron full-potential linearized augmented-plane-wave method and demonstrate for rocksalt BaO the improved convergence of the dynamical Kohn-Sham polarizability. We apply this technique to compute (a) quasiparticle energies employing the COHSEX approximation for the self-energy of many-body perturbation theory and (b) all-electron RPA correlation energies. It is shown that the favorable convergence of the polarizability is passed over to the COHSEX and RPA calculation.
NASA Astrophysics Data System (ADS)
Booth, George H.; Cleland, Deidre; Alavi, Ali; Tew, David P.
2012-10-01
By performing a stochastic dynamic in a space of Slater determinants, the full configuration interaction quantum Monte Carlo (FCIQMC) method has been able to obtain energies which are essentially free from systematic error to the basis set correlation energy, within small and systematically improvable error bars. However, the weakly exponential scaling with basis size makes converging the energy with respect to basis set costly and in larger systems, impossible. To ameliorate these basis set issues, here we use perturbation theory to couple the FCIQMC wavefunction to an explicitly correlated strongly orthogonal basis of geminals, following the { [2]_{{R12}} } approach of Valeev et al. The required one- and two-particle density matrices are computed on-the-fly during the FCIQMC dynamic, using a sampling procedure which incurs relatively little additional computation expense. The F12 energy corrections are shown to converge rapidly as a function of sampling, both in imaginary time and number of walkers. Our pilot calculations on the binding curve for the carbon dimer, which exhibits strong correlation effects as well as substantial basis set dependence, demonstrate that the accuracy of the FCIQMC-F12 method surpasses that of all previous FCIQMC calculations, and that the F12 correction improves results equivalent to increasing the quality of the one-electron basis by two cardinal numbers.
Magnetic properties with multiwavelets and DFT: the complete basis set limit achieved.
Jensen, Stig Rune; Flå, Tor; Jonsson, Dan; Monstad, Rune Sørland; Ruud, Kenneth; Frediani, Luca
2016-08-01
Multiwavelets are emerging as an attractive alternative to traditional basis sets such as Gaussian-type orbitals and plane waves. One of their distinctive properties is the ability to reach the basis set limit (often a chimera for traditional approaches) reliably and consistently by fixing the desired precision ε. We present our multiwavelet implementation of the linear response formalism, applied to static magnetic properties, at the self-consistent field level of theory (both for Hartree-Fock and density functional theories). We demonstrate that the multiwavelets consistently improve the accuracy of the results when increasing the desired precision, yielding results that have four to five digits precision, thus providing a very useful benchmark which could otherwise only be estimated by extrapolation methods. Our results show that magnetizabilities obtained with the augmented quadruple-ζ basis (aug-cc-pCVQZ) are practically at the basis set limit, whereas absolute nuclear magnetic resonance shielding tensors are more challenging: even by making use of a standard extrapolation method, the accuracy is not substantially improved. In contrast, our results provide a benchmark that: (1) confirms the validity of the extrapolation ansatz; (2) can be used as a reference to achieve a property-specific extrapolation scheme, thus providing a means to obtain much better extrapolated results; (3) allows us to separate functional-specific errors from basis-set ones and thus to assess the level of cancellation between basis set and functional errors often exploited in density functional theory. PMID:27087397
Systematic Study of Locally Dense Basis Sets for NMR Shielding Constants.
Reid, David M; Kobayashi, Rika; Collins, Michael A
2014-01-14
This paper presents a systematic study of partitioning schemes for locally dense basis sets in the context of NMR shielding calculations. The partitionings explored were based exclusively on connectivity and utilized the basis sets from the pcS-n series. Deviations from pcS-4 shieldings were calculated for a set of 28 organic molecules at the HF, B3LYP, and KT3 levels of theory, with the primary goal being the determination of an efficient scheme that achieves maximal deviations of 0.1 ppm for (1)H and 1 ppm for (13)C. Both atom based and group based divisions of basis sets were examined, with the latter providing the most promising results. It is demonstrated that for the systems studied, at least pcS-1 is required for all parts of the molecule. This, coupled with pcS-3 on the group of interest and pcS-2 on the adjacent groups, is sufficient to achieve the desired level of accuracy at a minimal computational expense. In addition, the suitability of the pcS-n basis sets for post-SCF methods was confirmed through a comparison with other standard basis sets at the MP2 level. PMID:26579898
Atomization Energies of SO and SO2; Basis Set Extrapolation Revisted
NASA Technical Reports Server (NTRS)
Bauschlicher, Charles W., Jr.; Ricca, Alessandra; Arnold, James (Technical Monitor)
1998-01-01
The addition of tight functions to sulphur and extrapolation to the complete basis set limit are required to obtain accurate atomization energies. Six different extrapolation procedures are tried. The best atomization energies come from the series of basis sets that yield the most consistent results for all extrapolation techniques. In the variable alpha approach, alpha values larger than 4.5 or smaller than 3, appear to suggest that the extrapolation may not be reliable. It does not appear possible to determine a reliable basis set series using only the triple and quadruple zeta based sets. The scalar relativistic effects reduce the atomization of SO and SO2 by 0.34 and 0.81 kcal/mol, respectively, and clearly must be accounted for if a highly accurate atomization energy is to be computed. The magnitude of the core-valence (CV) contribution to the atomization is affected by missing diffuse valence functions. The CV contribution is much more stable if basis set superposition errors are accounted for. A similar study of SF, SF(+), and SF6 shows that the best family of basis sets varies with the nature of the S bonding.
Segmented contracted basis sets for one- and two-component Dirac-Fock effective core potentials.
Weigend, Florian; Baldes, Alexander
2010-11-01
Segmented contracted basis sets for 4d, 5d, 5s, and 6s elements of split (double zeta) valence to quadruple zeta valence quality optimized for Dirac-Fock effective core potentials (ECPs) are presented. They were obtained from previous bases optimized for Wood-Boring ECPs by comparably small modifications and reoptimizations. Additionally extensions for two-component self-consistent-field treatments accounting for spin-orbit (SO) coupling were designed and optimized. Reliability for chemical applications was assessed by comparing results to those obtained with a very large (19s16p17d7f6g) reference basis for a set of more than 80 representatively chosen 5s-5d compounds. Moreover, the effect of different types of ECPs and that of the SO-coupling at the basis set limit of density functional theory is documented for the above set of molecules extended by 40 5p-6p compounds. PMID:21054001
Al-Saidi, W A; Krakauer, Henry; Zhang, Shiwei
2007-05-21
The authors present phaseless auxiliary-field (AF) quantum Monte Carlo (QMC) calculations of the ground states of some hydrogen-bonded systems. These systems were selected to test and benchmark different aspects of the new phaseless AF QMC method. They include the transition state of H+H(2) near the equilibrium geometry and in the van der Walls limit, as well as the H(2)O, OH, and H(2)O(2) molecules. Most of these systems present significant challenges for traditional independent-particle electronic structure approaches, and many also have exact results available. The phaseless AF QMC method is used either with a plane wave basis with pseudopotentials or with all-electron Gaussian basis sets. For some systems, calculations are done with both to compare and characterize the performance of AF QMC under different basis sets and different Hubbard-Stratonovich decompositions. Excellent results are obtained using as input single Slater determinant wave functions taken from independent-particle calculations. Comparisons of the Gaussian based AF QMC results with exact full configuration interaction show that the errors from controlling the phase problem with the phaseless approximation are small. At the large basis-size limit, the AF QMC results using both types of basis sets are in good agreement with each other and with experimental values. PMID:17523796
Representability of Bloch states on Projector-augmented-wave (PAW) basis sets
NASA Astrophysics Data System (ADS)
Agapito, Luis; Ferretti, Andrea; Curtarolo, Stefano; Buongiorno Nardelli, Marco
2015-03-01
Design of small, yet `complete', localized basis sets is necessary for an efficient dual representation of Bloch states on both plane-wave and localized basis. Such simultaneous dual representation permits the development of faster more accurate (beyond DFT) electronic-structure methods for atomistic materials (e.g. the ACBN0 method.) by benefiting from algorithms (real and reciprocal space) and hardware acceleration (e.g. GPUs) used in the quantum-chemistry and solid-state communities. Finding a `complete' atomic-orbital basis (partial waves) is also a requirement in the generation of robust and transferable PAW pseudopotentials. We have employed the atomic-orbital basis from available PAW data sets, which extends through most of the periodic table, and tested the representability of Bloch states on such basis. Our results show that PAW data sets allow systematic and accurate representability of the PAW Bloch states, better than with traditional quantum-chemistry double-zeta- and double-zeta-polarized-quality basis sets.
Efficient calculation of integrals in mixed ramp-Gaussian basis sets
McKemmish, Laura K.
2015-04-07
Algorithms for the efficient calculation of two-electron integrals in the newly developed mixed ramp-Gaussian basis sets are presented, alongside a Fortran90 implementation of these algorithms, RAMPITUP. These new basis sets have significant potential to (1) give some speed-up (estimated at up to 20% for large molecules in fully optimised code) to general-purpose Hartree-Fock (HF) and density functional theory quantum chemistry calculations, replacing all-Gaussian basis sets, and (2) give very large speed-ups for calculations of core-dependent properties, such as electron density at the nucleus, NMR parameters, relativistic corrections, and total energies, replacing the current use of Slater basis functions or very large specialised all-Gaussian basis sets for these purposes. This initial implementation already demonstrates roughly 10% speed-ups in HF/R-31G calculations compared to HF/6-31G calculations for large linear molecules, demonstrating the promise of this methodology, particularly for the second application. As well as the reduction in the total primitive number in R-31G compared to 6-31G, this timing advantage can be attributed to the significant reduction in the number of mathematically complex intermediate integrals after modelling each ramp-Gaussian basis-function-pair as a sum of ramps on a single atomic centre.
On the performance of large Gaussian basis sets for the computation of total atomization energies
NASA Technical Reports Server (NTRS)
Martin, J. M. L.
1992-01-01
The total atomization energies of a number of molecules have been computed using an augmented coupled-cluster method and (5s4p3d2f1g) and 4s3p2d1f) atomic natural orbital (ANO) basis sets, as well as the correlation consistent valence triple zeta plus polarization (cc-pVTZ) correlation consistent valence quadrupole zeta plus polarization (cc-pVQZ) basis sets. The performance of ANO and correlation consistent basis sets is comparable throughout, although the latter can result in significant CPU time savings. Whereas the inclusion of g functions has significant effects on the computed Sigma D(e) values, chemical accuracy is still not reached for molecules involving multiple bonds. A Gaussian-1 (G) type correction lowers the error, but not much beyond the accuracy of the G1 model itself. Using separate corrections for sigma bonds, pi bonds, and valence pairs brings down the mean absolute error to less than 1 kcal/mol for the spdf basis sets, and about 0.5 kcal/mol for the spdfg basis sets. Some conclusions on the success of the Gaussian-1 and Gaussian-2 models are drawn.
Accurate Complete Basis Set Extrapolation of Direct Random Phase Correlation Energies.
Mezei, Pál D; Csonka, Gábor I; Ruzsinszky, Adrienn
2015-08-11
The direct random phase approximation (dRPA) is a promising way to obtain improvements upon the standard semilocal density functional results in many aspects of computational chemistry. In this paper, we address the slow convergence of the calculated dRPA correlation energy with the increase of the quality and size of the popular Gaussian-type Dunning's correlation consistent aug-cc-pVXZ split valence atomic basis set family. The cardinal number X controls the size of the basis set, and we use X = 3-6 in this study. It is known that even the very expensive X = 6 basis sets lead to large errors for the dRPA correlation energy, and thus complete basis set extrapolation is necessary. We study the basis set convergence of the dRPA correlation energies on a set of 65 hydrocarbon isomers from CH4 to C6H6. We calculate the iterative density fitted dRPA correlation energies using an efficient algorithm based on the CC-like form of the equations using the self-consistent HF orbitals. We test the popular inverse cubic, the optimized exponential, and inverse power formulas for complete basis set extrapolation. We have found that the optimized inverse power based extrapolation delivers the best energies. Further analysis showed that the optimal exponent depends on the molecular structure, and the most efficient two-point energy extrapolations that use X = 3 and 4 can be improved considerably by considering the atomic composition and hybridization states of the atoms in the molecules. Our results also show that the optimized exponents that yield accurate X = 3 and 4 extrapolated dRPA energies for atoms or small molecules might be inaccurate for larger molecules. PMID:26574475
Woon, D.E.; Dunning, T.H. Jr. )
1994-02-15
An accurate description of the electrical properties of atoms and molecules is critical for quantitative predictions of the nonlinear properties of molecules and of long-range atomic and molecular interactions between both neutral and charged species. We report a systematic study of the basis sets required to obtain accurate correlated values for the static dipole ([alpha][sub 1]), quadrupole ([alpha][sub 2]), and octopole ([alpha][sub 3]) polarizabilities and the hyperpolarizability ([gamma]) of the rare gas atoms He, Ne, and Ar. Several methods of correlation treatment were examined, including various orders of Moller--Plesset perturbation theory (MP2, MP3, MP4), coupled-cluster theory with and without perturbative treatment of triple excitations [CCSD, CCSD(T)], and singles and doubles configuration interaction (CISD). All of the basis sets considered here were constructed by adding even-tempered sets of diffuse functions to the correlation consistent basis sets of Dunning and co-workers. With multiply-augmented sets we find that the electrical properties of the rare gas atoms converge smoothly to values that are in excellent agreement with the available experimental data and/or previously computed results. As a further test of the basis sets presented here, the dipole polarizabilities of the F[sup [minus
Influence of basis sets and electron correlation on theoretically predicted infrared intensities
Miller, M.D. ); Jensen, F. ); Chapman, O.L.; Houk, K.N. )
1989-06-01
A systematic study of the effects of basis sets and electron correlation on calculated infrared intensities has been performed with ab initio molecular orbital calculations and Moeller-Plesset perturbation theory. Absolute IR intensities of hydrogen fluoride, hydroxy radical, carbon monoxide, hydrogen cyanide, and formaldehyde have been calculated with basis sets ranging from 3-21G to 6-311++G(2dd{prime},2pp{prime}) and with electron correlation corrections up through MP4(SDTQ). A basis set with polarization and diffuse functions is necessary to obtain reasonably accurate intensities. Electron correlation significantly improves the agreement between experimental and calculated values. Except for carbon monoxide, the intensities calculated at the MP4 level compare favorably with experimental intensities, the errors being less than the measured difference between those obtained from inert-gas matrices at low temperature and those reported for the gas phase.
On the basis set convergence of electron-electron entanglement measures: helium-like systems.
Hofer, Thomas S
2013-01-01
A systematic investigation of three different electron-electron entanglement measures, namely the von Neumann, the linear and the occupation number entropy at full configuration interaction level has been performed for the four helium-like systems hydride, helium, Li(+) and Be(2+) using a large number of different basis sets. The convergence behavior of the resulting energies and entropies revealed that the latter do in general not show the expected strictly monotonic increase upon increase of the one-electron basis. Overall, the three different entanglement measures show good agreement among each other, the largest deviations being observed for small basis sets. The data clearly demonstrates that it is important to consider the nature of the chemical system when investigating entanglement phenomena in the framework of Gaussian type basis sets: while in case of hydride the use of augmentation functions is crucial, the application of core functions greatly improves the accuracy in case of cationic systems such as Li(+) and Be(2+). In addition, numerical derivatives of the entanglement measures with respect to the nucleic charge have been determined, which proved to be a very sensitive probe of the convergence leading to qualitatively wrong results (i.e., the wrong sign) if too small basis sets are used. PMID:24790952
On the basis set convergence of electron–electron entanglement measures: helium-like systems
Hofer, Thomas S.
2013-01-01
A systematic investigation of three different electron–electron entanglement measures, namely the von Neumann, the linear and the occupation number entropy at full configuration interaction level has been performed for the four helium-like systems hydride, helium, Li+ and Be2+ using a large number of different basis sets. The convergence behavior of the resulting energies and entropies revealed that the latter do in general not show the expected strictly monotonic increase upon increase of the one–electron basis. Overall, the three different entanglement measures show good agreement among each other, the largest deviations being observed for small basis sets. The data clearly demonstrates that it is important to consider the nature of the chemical system when investigating entanglement phenomena in the framework of Gaussian type basis sets: while in case of hydride the use of augmentation functions is crucial, the application of core functions greatly improves the accuracy in case of cationic systems such as Li+ and Be2+. In addition, numerical derivatives of the entanglement measures with respect to the nucleic charge have been determined, which proved to be a very sensitive probe of the convergence leading to qualitatively wrong results (i.e., the wrong sign) if too small basis sets are used. PMID:24790952
NASA Astrophysics Data System (ADS)
Huang, Jingsong; Kertesz, Miklos
2004-05-01
Intermolecular transfer integrals, and associated band-structures of organic molecular materials can be calculated through a dimer approach. Extensive numerical studies are performed on an ethylene π-dimer to investigate the basis sets dependence of transfer integrals. Convergence of calculated transfer integrals is achieved with respect to both Gaussian and plane-wave basis sets, provided the same level of theory is used. Effects of diffuse and polarization Gaussian functions on transfer integrals are identified. Comparison of experimental and theoretical values of transfer integrals of the TTF-TCNQ charge transfer salt is also presented.
Strategies for reducing basis set superposition error (BSSE) in O/AU and O/Ni
NASA Astrophysics Data System (ADS)
Shuttleworth, I. G.
2015-11-01
The effect of basis set superposition error (BSSE) and effective strategies for the minimisation have been investigated using the SIESTA-LCAO DFT package. Variation of the energy shift parameter ΔEPAO has been shown to reduce BSSE for bulk Au and Ni and across their oxygenated surfaces. Alternative strategies based on either the expansion or contraction of the basis set have been shown to be ineffective in reducing BSSE. Comparison of the binding energies for the surface systems obtained using LCAO were compared with BSSE-free plane wave energies.
NASA Astrophysics Data System (ADS)
Boffi, Nicholas M.; Jain, Manish; Natan, Amir
2016-02-01
A real-space high order finite difference method is used to analyze the effect of spherical domain size on the Hartree-Fock (and density functional theory) virtual eigenstates. We show the domain size dependence of both positive and negative virtual eigenvalues of the Hartree-Fock equations for small molecules. We demonstrate that positive states behave like a particle in spherical well and show how they approach zero. For the negative eigenstates, we show that large domains are needed to get the correct eigenvalues. We compare our results to those of Gaussian basis sets and draw some conclusions for real-space, basis-sets, and plane-waves calculations.
Miliordos, Evangelos; Xantheas, Sotiris S.
2015-03-07
We report the variation of the binding energy of the formic acid dimer at the CCSD(T)/ Complete Basis Set limit and examine the validity of the BSSE-correction, previously challenged by Kalescky, Kraka and Cremer [J. Chem. Phys. 140 (2014) 084315]. Our best estimate of D0=14.3±0.1 kcal/mol is in excellent agreement with the experimental value of 14.22±0.12 kcal/mol. The BSSE correction is indeed valid for this system since it exhibits the expected behavior of decreasing with increasing basis set size and its inclusion produces the same limit (within 0.1 kcal/mol) as the one obtained from extrapolation of the uncorrected binding energy. This work was supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, Division of Chemical Sciences, Geosciences and Biosciences. Pacific Northwest National Laboratory (PNNL) is a multiprogram national laboratory operated for DOE by Battelle. A portion of this research was performed using the Molecular Science Computing Facility (MSCF) in EMSL, a national scientific user facility sponsored by the Department of Energy’s Office of Biological and Environmental Research and located at PNNL.
Molecular Dipole Moments within the Incremental Scheme Using the Domain-Specific Basis-Set Approach.
Fiedler, Benjamin; Coriani, Sonia; Friedrich, Joachim
2016-07-12
We present the first implementation of the fully automated incremental scheme for CCSD unrelaxed dipole moments using the domain-specific basis-set approach. Truncation parameters are varied, and the accuracy of the method is statistically analyzed for a test set of 20 molecules. The local approximations introduce small errors at second order and negligible ones at third order. For a third-order incremental CCSD expansion with a CC2 error correction, a cc-pVDZ/SV domain-specific basis set (tmain = 3.5 Bohr), and the truncation parameter f = 30 Bohr, we obtain a mean error of 0.00 mau (-0.20 mau) and a standard deviation of 1.95 mau (2.17 mau) for the total dipole moments (Cartesian components of the dipole vectors). By analyzing incremental CCSD energies, we demonstrate that the MP2 and CC2 error correction schemes are an exclusive correction for the domain-specific basis-set error. Our implementation of the incremental scheme provides fully automated computations of highly accurate dipole moments at reduced computational cost and is fully parallelized in terms of the calculation of the increments. Therefore, one can utilize the incremental scheme, on the same hardware, to extend the basis set in comparison to standard CCSD and thus obtain a better total accuracy. PMID:27300371
NASA Astrophysics Data System (ADS)
Gidopoulos, Nikitas I.; Lathiotakis, Nektarios N.
2013-10-01
The Comment by Friedrich does not dispute the central result of our paper [Phys. Rev. APLRAAN1050-294710.1103/PhysRevA.85.052508 85, 052508 (2012)] that nonanalytic behavior is present in long-established mathematical pathologies arising in the solution of finite basis optimized effective potential (OEP) equations. In the Comment, the terms “balancing of basis sets” and “basis-set convergence” imply a particular order towards the limit of a large orbital basis sets where the large-orbital-base limit is always taken first, before the large-auxiliary-base limit, until overall convergence is achieved, at a high computational cost. The authors claim that, on physical grounds, this order of limits is not only sufficient, but also necessary in order to avoid the mathematical pathologies. In response to the Comment, we remark that it is already written in our paper that the nonanalyticity trivially disappears with large orbital basis sets. We point out that the authors of the Comment give an incorrect proof of this statement. We also show that the order of limits towards convergence of the potential is immaterial. A recent paper by the authors of the Comment proposes a partial correction for the incomplete orbital basis error in the full-potential linearized augmented-plane-wave method. Similar to the correction developed in our paper, this correction also benefits from an effectively complete orbital basis, even though only a finite orbital basis is employed in the calculation. This shows that it is unnecessary to take, in practice, the limit of an infinite orbital basis in order to avoid mathematical pathologies in the OEP. Our paper is a significant contribution in that direction with general applicability to any choice of basis sets. Finally, contrary to an allusion in the abstract and assertions in the main text of the Comment that unphysical oscillations of the OEP are supposedly attributed to the common energy denominator approximation, in fact, such
Zhao, Chunyu; Burge, James H
2013-12-16
Zernike polynomials are an orthonormal set of scalar functions over a circular domain, and are commonly used to represent wavefront phase or surface irregularity. In optical testing, slope or curvature of a surface or wavefront is sometimes measured instead, from which the surface or wavefront map is obtained. Previously we derived an orthonormal set of vector polynomials that fit to slope measurement data and yield the surface or wavefront map represented by Zernike polynomials. Here we define a 3-element curvature vector used to represent the second derivatives of a continuous surface, and derive a set of orthonormal curvature basis functions that are written in terms of Zernike polynomials. We call the new curvature functions the C polynomials. Closed form relations for the complete basis set are provided, and we show how to determine Zernike surface coefficients from the curvature data as represented by the C polynomials. PMID:24514717
How to spoil a good basis set for Rayleigh-Ritz calculations
Pupyshev, Vladimir I.; Montgomery, H. E. Jr.
2013-08-15
For model quantum mechanical systems such as the harmonic oscillator and a particle in an impenetrable box, we consider the set of exact discrete spectrum functions and define the modified basis set by subtraction of the ground state wavefunction from all the other wavefunctions with some real weights. It is demonstrated that the modified set of functions is complete in the space of square integrable functions if and only if the series of the squared weights diverges. A similar, but nonequivalent criterion is derived for convergence of Rayleigh-Ritz ground state energy calculations to the exact ground state energy value with the basis set extension. Some numerical illustrations are provided which demonstrate a wide variety of possible situations for model systems.
A Novel Gaussian-Sinc mixed Basis Set for Electronic Structure calculations
NASA Astrophysics Data System (ADS)
Jerke, Jonathan; Lee, Young; Tymczak, C. J.
2015-03-01
A Gaussian-Sinc mixed basis set for the computation of the electronic structure of atoms and molecules is presented. Excellent bases functions are known for ``core'' and ``valence'' separately, such as Gaussians for the ``core'' wave functions and Plane-waves for ``valance'' wave functions, but as yet no method is known that can accurately deal with both regimes in a single basis. A Gaussian-Sinc mixed basis can do both. This method resolves several issues such as: i) the Sincs basis spans the same space as the plane-waves basis, yet are semi-local enough to define all interaction elements including Exchange; ii) the Gaussians span the spherically symmetric core states and can be mixed with the Sinc functions in a computationally efficient methodology; iii) together, this mixed basis set is a flexible, computationally efficient and a highly accurate method for solving atomic and molecular problems. This methodology has been implemented within the Hartree-Fock level of theory within ultra-strong magnetic fields. To demonstrate the utility of this new method, we calculated the ground state Hartree-Fock energies to five digits accuracy in ultra strong magnetic fields for Helium to Neon, Molecular Hydrogen, Water, Carbon dioxide and Benzene. Welch Foundation (Grant J-1675), the ARO (Grant W911Nf-13-1-0162), the Texas Southern University High Performance Computing Center (http:/hpcc.tsu.edu/; Grant PHY-1126251) and NSF-CREST CRCN project (Grant HRD-1137732).
NASA Astrophysics Data System (ADS)
Borges, A.; Solomon, G. C.
2016-05-01
Single molecule conductance measurements are often interpreted through computational modeling, but the complexity of these calculations makes it difficult to directly link them to simpler concepts and models. Previous work has attempted to make this connection using maximally localized Wannier functions and symmetry adapted basis sets, but their use can be ambiguous and non-trivial. Starting from a Hamiltonian and overlap matrix written in a hydrogen-like basis set, we demonstrate a simple approach to obtain a new basis set that is chemically more intuitive and allows interpretation in terms of simple concepts and models. By diagonalizing the Hamiltonians corresponding to each atom in the molecule, we obtain a basis set that can be partitioned into pseudo-σ and -π and allows partitioning of the Landuaer-Büttiker transmission as well as create simple Hückel models that reproduce the key features of the full calculation. This method provides a link between complex calculations and simple concepts and models to provide intuition or extract parameters for more complex model systems.
Borges, A; Solomon, G C
2016-05-21
Single molecule conductance measurements are often interpreted through computational modeling, but the complexity of these calculations makes it difficult to directly link them to simpler concepts and models. Previous work has attempted to make this connection using maximally localized Wannier functions and symmetry adapted basis sets, but their use can be ambiguous and non-trivial. Starting from a Hamiltonian and overlap matrix written in a hydrogen-like basis set, we demonstrate a simple approach to obtain a new basis set that is chemically more intuitive and allows interpretation in terms of simple concepts and models. By diagonalizing the Hamiltonians corresponding to each atom in the molecule, we obtain a basis set that can be partitioned into pseudo-σ and -π and allows partitioning of the Landuaer-Büttiker transmission as well as create simple Hückel models that reproduce the key features of the full calculation. This method provides a link between complex calculations and simple concepts and models to provide intuition or extract parameters for more complex model systems. PMID:27208940
Sensitivity of the properties of ruthenium ``blue dimer'' to method, basis set, and continuum model
NASA Astrophysics Data System (ADS)
Ozkanlar, Abdullah; Clark, Aurora E.
2012-05-01
The ruthenium "blue dimer" [(bpy)2RuIIIOH2]2O4+ is best known as the first well-defined molecular catalyst for water oxidation. It has been subject to numerous computational studies primarily employing density functional theory. However, those studies have been limited in the functionals, basis sets, and continuum models employed. The controversy in the calculated electronic structure and the reaction energetics of this catalyst highlights the necessity of benchmark calculations that explore the role of density functionals, basis sets, and continuum models upon the essential features of blue-dimer reactivity. In this paper, we report Kohn-Sham complete basis set (KS-CBS) limit extrapolations of the electronic structure of "blue dimer" using GGA (BPW91 and BP86), hybrid-GGA (B3LYP), and meta-GGA (M06-L) density functionals. The dependence of solvation free energy corrections on the different cavity types (UFF, UA0, UAHF, UAKS, Bondi, and Pauling) within polarizable and conductor-like polarizable continuum model has also been investigated. The most common basis sets of double-zeta quality are shown to yield results close to the KS-CBS limit; however, large variations are observed in the reaction energetics as a function of density functional and continuum cavity model employed.
Pulay forces from localized orbitals optimized in situ using a psinc basis set.
Ruiz-Serrano, Álvaro; Hine, Nicholas D M; Skylaris, Chris-Kriton
2012-06-21
In situ optimization of a set of localized orbitals with respect to a systematically improvable basis set independent of the position of the atoms, such as psinc functions, would theoretically eliminate the correction due to Pulay forces from the total ionic forces. We demonstrate that for strict localization constraints, especially with small localization regions, there can be non-negligible Pulay forces that must be calculated as a correction to the Hellmann-Feynman forces in the ground state. Geometry optimization calculations, which rely heavily upon accurate evaluation of the total ionic forces, show much better convergence when Pulay forces are included. The more conventional case, where the local orbitals remain fixed to pseudo-atomic orbital multiple-ζ basis sets, also benefits from this implementation. We have validated the method on several test cases, including a DNA fragment with 1045 atoms. PMID:22779575
Heats of formation for third-period hydrides: test of an extended basis set
Gordon, M.S.; Heitzinger, J.
1987-04-23
The extended basis set developed by McLean and Chandler for third-period atoms is combined with the -311G hydrogen basis and augmented by polarization functions to predict the heats of formation of third-period hydrides at the full MP4 computational level. The calculated heats of formation are at least as accurate as those predicted for second-row hydrides by using MP4/6-311G(d,p) wave functions, with a root mean square error of approximately 4 kcal/mol.
Truncated spherical-wave basis set for first-principles pseudopotential calculations
NASA Astrophysics Data System (ADS)
Monserrat, B.; Haynes, P. D.
2010-11-01
Analytic results for two- and three-centre integrals are derived for the truncated spherical-wave basis set designed for first-principles pseudopotential calculations within density-functional theory. These allow the overlap, kinetic energy and non-local pseudopotential matrix elements to be calculated efficiently and accurately. In particular, the scaling of the computational effort with maximum angular momentum component is dramatically improved and the projection method takes full account of the discontinuities in the basis functions arising from their localization within spherical regions.
Benchmarks of electronically excited states: Basis set effects on CASPT2 results
NASA Astrophysics Data System (ADS)
Silva-Junior, Mario R.; Schreiber, Marko; Sauer, Stephan P. A.; Thiel, Walter
2010-11-01
Vertical excitation energies and one-electron properties are computed for the valence excited states of 28 medium-sized organic benchmark molecules using multistate multiconfigurational second-order perturbation theory (MS-CASPT2) and the augmented correlation-consistent aug-cc-pVTZ basis set. They are compared with previously reported MS-CASPT2 results obtained with the smaller TZVP basis. The basis set extension from TZVP to aug-cc-pVTZ causes rather minor and systematic shifts in the vertical excitation energies that are normally slightly reduced (on average by 0.11 eV for the singlets and by 0.09 eV for the triplets), whereas the changes in the calculated oscillator strengths and dipole moments are somewhat more pronounced on a relative scale. These basis set effects at the MS-CASPT2 level are qualitatively and quantitatively similar to those found at the coupled cluster level for the same set of benchmark molecules. The previously proposed theoretical best estimates (TBE-1) for the vertical excitation energies for 104 singlet and 63 triplet excited states of the benchmark molecules are upgraded by replacing TZVP with aug-cc-pVTZ data that yields a new reference set (TBE-2). Statistical evaluations of the performance of density functional theory (DFT) and semiempirical methods lead to the same ranking and very similar quantitative results for TBE-1 and TBE-2, with slightly better performance measures with respect to TBE-2. DFT/MRCI is most accurate among the investigated DFT-based approaches, while the OMx methods with orthogonalization corrections perform best at the semiempirical level.
Method and Basis Set Analysis of Oxorhenium(V) Complexes for Theoretical Calculations
Demoin, Dustin Wayne; Li, Yawen; Jurisson, Silvia S.; Deakyne, Carol A.
2012-01-01
A variety of method and basis set combinations has been evaluated for monooxorhenium(V) complexes with N, O, P, S, Cl, and Se donor atoms. The geometries and energies obtained are compared to both high-level computations and literature structures. These calculations show that the PBE0 method outperforms the B3LYP method with respect to both structure and energetics. The combination of 6-31G** basis set on the nonmetal atoms and LANL2TZ effective core potential on the rhenium center gives reliable equilibrium structures with minimal computational resources for both model and literature compounds. Single-point energy calculations at the PBE0/LANL2TZ,6-311+G* level of theory are recommended for energetics. PMID:23087847
Polyatomic molecular Dirac-Hartree-Fock calculations with Gaussian basis sets
NASA Technical Reports Server (NTRS)
Dyall, Kenneth G.; Faegri, Knut, Jr.; Taylor, Peter R.
1990-01-01
Numerical methods have been used successfully in atomic Dirac-Hartree-Fock (DHF) calculations for many years. Some DHF calculations using numerical methods have been done on diatomic molecules, but while these serve a useful purpose for calibration, the computational effort in extending this approach to polyatomic molecules is prohibitive. An alternative more in line with traditional quantum chemistry is to use an analytical basis set expansion of the wave function. This approach fell into disrepute in the early 1980's due to problems with variational collapse and intruder states, but has recently been put on firm theoretical foundations. In particular, the problems of variational collapse are well understood, and prescriptions for avoiding the most serious failures have been developed. Consequently, it is now possible to develop reliable molecular programs using basis set methods. This paper describes such a program and reports results of test calculations to demonstrate the convergence and stability of the method.
Basis set limit geometries for ammonia at the SCF and MP2 levels of theory
NASA Technical Reports Server (NTRS)
Defrees, D. J.; Mclean, A. D.
1984-01-01
The controversy over the Hartree-Fock bond angle of NH3 is resolved and the convergence of the geometry for the molecule as the basis set is systematically improved with both SCF and correlated MP2 wave functions. The results of the geometrical optimizations, carried out in four stages with a series of uncontracted bases sets, are shown. The obtained structure for NH3 supports the results of Radom and Rodwell (1980) that the Hartree-Fock limit angle is significantly greater than was previously believed.
Elimination of the linearization error and improved basis-set convergence within the FLAPW method
NASA Astrophysics Data System (ADS)
Michalicek, Gregor; Betzinger, Markus; Friedrich, Christoph; Blügel, Stefan
2013-12-01
We analyze in detail the error that arises from the linearization in linearized augmented-plane-wave (LAPW) basis functions around predetermined energies El and show that it can lead to undesirable dependences of the calculated results on method-inherent parameters such as energy parameters El and muffin-tin sphere radii. To overcome these dependences, we evaluate approaches that eliminate the linearization error systematically by adding local orbitals (LOs) to the basis set. We consider two kinds of LOs: (i) constructed from solutions ul(r,E) to the scalar-relativistic approximation of the radial Dirac equation with E>El and (ii) constructed from second energy derivatives ∂2ul(r,E)/∂E2 at E=El. We find that the latter eliminates the error most efficiently and yields the density functional answer to many electronic and materials properties with very high precision. Finally, we demonstrate that the so constructed LAPW +LO basis shows a more favorable convergence behavior than the conventional LAPW basis due to a better decoupling of muffin-tin and interstitial regions, similarly to the related APW +lo approach, which, however, requires an extra set of LOs to reach the same total energy.
Geminal embedding scheme for optimal atomic basis set construction in correlated calculations
Sorella, S.; Devaux, N.; Dagrada, M.; Mazzola, G.; Casula, M.
2015-12-28
We introduce an efficient method to construct optimal and system adaptive basis sets for use in electronic structure and quantum Monte Carlo calculations. The method is based on an embedding scheme in which a reference atom is singled out from its environment, while the entire system (atom and environment) is described by a Slater determinant or its antisymmetrized geminal power (AGP) extension. The embedding procedure described here allows for the systematic and consistent contraction of the primitive basis set into geminal embedded orbitals (GEOs), with a dramatic reduction of the number of variational parameters necessary to represent the many-body wave function, for a chosen target accuracy. Within the variational Monte Carlo method, the Slater or AGP part is determined by a variational minimization of the energy of the whole system in presence of a flexible and accurate Jastrow factor, representing most of the dynamical electronic correlation. The resulting GEO basis set opens the way for a fully controlled optimization of many-body wave functions in electronic structure calculation of bulk materials, namely, containing a large number of electrons and atoms. We present applications on the water molecule, the volume collapse transition in cerium, and the high-pressure liquid hydrogen.
Geminal embedding scheme for optimal atomic basis set construction in correlated calculations
NASA Astrophysics Data System (ADS)
Sorella, S.; Devaux, N.; Dagrada, M.; Mazzola, G.; Casula, M.
2015-12-01
We introduce an efficient method to construct optimal and system adaptive basis sets for use in electronic structure and quantum Monte Carlo calculations. The method is based on an embedding scheme in which a reference atom is singled out from its environment, while the entire system (atom and environment) is described by a Slater determinant or its antisymmetrized geminal power (AGP) extension. The embedding procedure described here allows for the systematic and consistent contraction of the primitive basis set into geminal embedded orbitals (GEOs), with a dramatic reduction of the number of variational parameters necessary to represent the many-body wave function, for a chosen target accuracy. Within the variational Monte Carlo method, the Slater or AGP part is determined by a variational minimization of the energy of the whole system in presence of a flexible and accurate Jastrow factor, representing most of the dynamical electronic correlation. The resulting GEO basis set opens the way for a fully controlled optimization of many-body wave functions in electronic structure calculation of bulk materials, namely, containing a large number of electrons and atoms. We present applications on the water molecule, the volume collapse transition in cerium, and the high-pressure liquid hydrogen.
Representing the behavior of partially coherent optical systems by using overcomplete basis sets
NASA Astrophysics Data System (ADS)
Withington, Stafford; Hobson, Michael P.; Berry, Rachel H.
2004-02-01
A technique is described for representing the behavior of partially coherent optical systems by using overcomplete basis sets. The scheme is closely related to Gabor function theory. Through singular-value decomposition it is shown that if E is a matrix containing the sampled basis functions, then all of the information needed for optical calculations is contained in S=EE† and R=E†E. For overcomplete sets, S can be inverted to give a dual basis set, E~=S-1E, which can be used to find the correlation matrix elements A of a sampled bimodal expansion of the spatial coherence function. Overcomplete correlation matrices can be scattered easily at optical components. They can be used to determine (i) the natural modes of a field; (ii) the total power in a field, Pt=Tr[RA] (iii) the power coupled between two fields, A and B, that are in different states of coherence, Pc=Tr[RARB] and (iv) the entropy of a field, Q=Tr[ZΣr(I-Z)r/r], where Z=RA/Tr[RA].
Representing the behavior of partially coherent optical systems by using overcomplete basis sets.
Withington, Stafford; Hobson, Michael P; Berry, Rachel H
2004-02-01
A technique is described for representing the behavior of partially coherent optical systems by using overcomplete basis sets. The scheme is closely related to Gabor function theory. Through singular-value decomposition it is shown that if E is a matrix containing the sampled basis functions, then all of the information needed for optical calculations is contained in S = EE(dagger) and R = E(dagger)E. For overcomplete sets, S can be inverted to give a dual basis set, E = S(-1)E, which can be used to find the correlation matrix elements A of a sampled bimodal expansion of the spatial coherence function. Overcomplete correlation matrices can be scattered easily at optical components. They can be used to determine (i) the natural modes of a field; (ii) the total power in a field, Pt = Tr[RA]; (iii) the power coupled between two fields, A and B, that are in different states of coherence, Pc = Tr[RARB]; and (iv) the entropy of a field, Q = Tr[Zsigmar(I-Z)r/r], where Z = RA/Tr[RA]. PMID:14763763
Kjaer, Hanna; Nielsen, Monia R; Pagola, Gabriel I; Ferraro, Marta B; Lazzeretti, Paolo; Sauer, Stephan P A
2012-09-01
In this article, we present the so far most extended investigation of the calculation of the coupling constant polarizability of a molecule. The components of the coupling constant polarizability are derivatives of the nuclear magnetic resonance (NMR) indirect nuclear spin-spin coupling constant with respect to an external electric field and play an important role for both chiral discrimination and solvation effects on NMR coupling constants. In this study, we illustrate the effects of one-electron basis sets and electron correlation both at the level of density functional theory as well as second-order polarization propagator approximation for the small molecule hydrogen peroxide, which allowed us to perform calculations with the largest available basis sets optimized for the calculation of NMR coupling constants. We find a systematic but rather slow convergence with the one-electron basis set and that augmentation functions are required. We observe also large and nonsystematic correlation effects with significant differences between the density functional and wave function theory methods. PMID:22618604
Geminal embedding scheme for optimal atomic basis set construction in correlated calculations.
Sorella, S; Devaux, N; Dagrada, M; Mazzola, G; Casula, M
2015-12-28
We introduce an efficient method to construct optimal and system adaptive basis sets for use in electronic structure and quantum Monte Carlo calculations. The method is based on an embedding scheme in which a reference atom is singled out from its environment, while the entire system (atom and environment) is described by a Slater determinant or its antisymmetrized geminal power (AGP) extension. The embedding procedure described here allows for the systematic and consistent contraction of the primitive basis set into geminal embedded orbitals (GEOs), with a dramatic reduction of the number of variational parameters necessary to represent the many-body wave function, for a chosen target accuracy. Within the variational Monte Carlo method, the Slater or AGP part is determined by a variational minimization of the energy of the whole system in presence of a flexible and accurate Jastrow factor, representing most of the dynamical electronic correlation. The resulting GEO basis set opens the way for a fully controlled optimization of many-body wave functions in electronic structure calculation of bulk materials, namely, containing a large number of electrons and atoms. We present applications on the water molecule, the volume collapse transition in cerium, and the high-pressure liquid hydrogen. PMID:26723656
Mao, Yuezhi; Horn, Paul R; Mardirossian, Narbe; Head-Gordon, Teresa; Skylaris, Chris-Kriton; Head-Gordon, Martin
2016-07-28
Recently developed density functionals have good accuracy for both thermochemistry (TC) and non-covalent interactions (NC) if very large atomic orbital basis sets are used. To approach the basis set limit with potentially lower computational cost, a new self-consistent field (SCF) scheme is presented that employs minimal adaptive basis (MAB) functions. The MAB functions are optimized on each atomic site by minimizing a surrogate function. High accuracy is obtained by applying a perturbative correction (PC) to the MAB calculation, similar to dual basis approaches. Compared to exact SCF results, using this MAB-SCF (PC) approach with the same large target basis set produces <0.15 kcal/mol root-mean-square deviations for most of the tested TC datasets, and <0.1 kcal/mol for most of the NC datasets. The performance of density functionals near the basis set limit can be even better reproduced. With further improvement to its implementation, MAB-SCF (PC) is a promising lower-cost substitute for conventional large-basis calculations as a method to approach the basis set limit of modern density functionals. PMID:27475350
NASA Astrophysics Data System (ADS)
Mao, Yuezhi; Horn, Paul R.; Mardirossian, Narbe; Head-Gordon, Teresa; Skylaris, Chris-Kriton; Head-Gordon, Martin
2016-07-01
Recently developed density functionals have good accuracy for both thermochemistry (TC) and non-covalent interactions (NC) if very large atomic orbital basis sets are used. To approach the basis set limit with potentially lower computational cost, a new self-consistent field (SCF) scheme is presented that employs minimal adaptive basis (MAB) functions. The MAB functions are optimized on each atomic site by minimizing a surrogate function. High accuracy is obtained by applying a perturbative correction (PC) to the MAB calculation, similar to dual basis approaches. Compared to exact SCF results, using this MAB-SCF (PC) approach with the same large target basis set produces <0.15 kcal/mol root-mean-square deviations for most of the tested TC datasets, and <0.1 kcal/mol for most of the NC datasets. The performance of density functionals near the basis set limit can be even better reproduced. With further improvement to its implementation, MAB-SCF (PC) is a promising lower-cost substitute for conventional large-basis calculations as a method to approach the basis set limit of modern density functionals.
On fast computation of finite-time coherent sets using radial basis functions
NASA Astrophysics Data System (ADS)
Froyland, Gary; Junge, Oliver
2015-08-01
Finite-time coherent sets inhibit mixing over finite times. The most expensive part of the transfer operator approach to detecting coherent sets is the construction of the operator itself. We present a numerical method based on radial basis function collocation and apply it to a recent transfer operator construction [G. Froyland, "Dynamic isoperimetry and the geometry of Lagrangian coherent structures," Nonlinearity (unpublished); preprint arXiv:1411.7186] that has been designed specifically for purely advective dynamics. The construction [G. Froyland, "Dynamic isoperimetry and the geometry of Lagrangian coherent structures," Nonlinearity (unpublished); preprint arXiv:1411.7186] is based on a "dynamic" Laplace operator and minimises the boundary size of the coherent sets relative to their volume. The main advantage of our new approach is a substantial reduction in the number of Lagrangian trajectories that need to be computed, leading to large speedups in the transfer operator analysis when this computation is costly.
On fast computation of finite-time coherent sets using radial basis functions.
Froyland, Gary; Junge, Oliver
2015-08-01
Finite-time coherent sets inhibit mixing over finite times. The most expensive part of the transfer operator approach to detecting coherent sets is the construction of the operator itself. We present a numerical method based on radial basis function collocation and apply it to a recent transfer operator construction [G. Froyland, "Dynamic isoperimetry and the geometry of Lagrangian coherent structures," Nonlinearity (unpublished); preprint arXiv:1411.7186] that has been designed specifically for purely advective dynamics. The construction [G. Froyland, "Dynamic isoperimetry and the geometry of Lagrangian coherent structures," Nonlinearity (unpublished); preprint arXiv:1411.7186] is based on a "dynamic" Laplace operator and minimises the boundary size of the coherent sets relative to their volume. The main advantage of our new approach is a substantial reduction in the number of Lagrangian trajectories that need to be computed, leading to large speedups in the transfer operator analysis when this computation is costly. PMID:26328580
Ghost transmission: How large basis sets can make electron transport calculations worse
Herrmann, Carmen; Solomon, Gemma C.; Subotnik, Joseph E.; Mujica, Vladimiro; Ratner, Mark A.
2010-01-01
The Landauer approach has proven to be an invaluable tool for calculating the electron transport properties of single molecules, especially when combined with a nonequilibrium Green’s function approach and Kohn–Sham density functional theory. However, when using large nonorthogonal atom-centered basis sets, such as those common in quantum chemistry, one can find erroneous results if the Landauer approach is applied blindly. In fact, basis sets of triple-zeta quality or higher sometimes result in an artificially high transmission and possibly even qualitatively wrong conclusions regarding chemical trends. In these cases, transport persists when molecular atoms are replaced by basis functions alone (“ghost atoms”). The occurrence of such ghost transmission is correlated with low-energy virtual molecular orbitals of the central subsystem and may be interpreted as a biased and thus inaccurate description of vacuum transmission. An approximate practical correction scheme is to calculate the ghost transmission and subtract it from the full transmission. As a further consequence of this study, it is recommended that sensitive molecules be used for parameter studies, in particular those whose transmission functions show antiresonance features such as benzene-based systems connected to the electrodes in meta positions and other low-conducting systems such as alkanes and silanes.
Time Domain Propagation of Quantum and Classical Systems using a Wavelet Basis Set Method
NASA Astrophysics Data System (ADS)
Lombardini, Richard; Nowara, Ewa; Johnson, Bruce
2015-03-01
The use of an orthogonal wavelet basis set (Optimized Maximum-N Generalized Coiflets) to effectively model physical systems in the time domain, in particular the electromagnetic (EM) pulse and quantum mechanical (QM) wavefunction, is examined in this work. Although past research has demonstrated the benefits of wavelet basis sets to handle computationally expensive problems due to their multiresolution properties, the overlapping supports of neighboring wavelet basis functions poses problems when dealing with boundary conditions, especially with material interfaces in the EM case. Specifically, this talk addresses this issue using the idea of derivative matching creating fictitious grid points (T.A. Driscoll and B. Fornberg), but replaces the latter element with fictitious wavelet projections in conjunction with wavelet reconstruction filters. Two-dimensional (2D) systems are analyzed, EM pulse incident on silver cylinders and the QM electron wave packet circling the proton in a hydrogen atom system (reduced to 2D), and the new wavelet method is compared to the popular finite-difference time-domain technique.
Norm-conserving pseudopotentials with chemical accuracy compared to all-electron calculations
NASA Astrophysics Data System (ADS)
Willand, Alex; Kvashnin, Yaroslav O.; Genovese, Luigi; Vázquez-Mayagoitia, Álvaro; Deb, Arpan Krishna; Sadeghi, Ali; Deutsch, Thierry; Goedecker, Stefan
2013-03-01
By adding a nonlinear core correction to the well established dual space Gaussian type pseudopotentials for the chemical elements up to the third period, we construct improved pseudopotentials for the Perdew-Burke-Ernzerhof [J. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996), 10.1103/PhysRevLett.77.3865] functional and demonstrate that they exhibit excellent accuracy. Our benchmarks for the G2-1 test set show average atomization energy errors of only half a kcal/mol. The pseudopotentials also remain highly reliable for high pressure phases of crystalline solids. When supplemented by empirical dispersion corrections [S. Grimme, J. Comput. Chem. 27, 1787 (2006), 10.1002/jcc.20495; S. Grimme, J. Antony, S. Ehrlich, and H. Krieg, J. Chem. Phys. 132, 154104 (2010), 10.1063/1.3382344] the average error in the interaction energy between molecules is also about half a kcal/mol. The accuracy that can be obtained by these pseudopotentials in combination with a systematic basis set is well superior to the accuracy that can be obtained by commonly used medium size Gaussian basis sets in all-electron calculations.
Grimme, Stefan Brandenburg, Jan Gerit; Bannwarth, Christoph; Hansen, Andreas
2015-08-07
A density functional theory (DFT) based composite electronic structure approach is proposed to efficiently compute structures and interaction energies in large chemical systems. It is based on the well-known and numerically robust Perdew-Burke-Ernzerhoff (PBE) generalized-gradient-approximation in a modified global hybrid functional with a relatively large amount of non-local Fock-exchange. The orbitals are expanded in Ahlrichs-type valence-double zeta atomic orbital (AO) Gaussian basis sets, which are available for many elements. In order to correct for the basis set superposition error (BSSE) and to account for the important long-range London dispersion effects, our well-established atom-pairwise potentials are used. In the design of the new method, particular attention has been paid to an accurate description of structural parameters in various covalent and non-covalent bonding situations as well as in periodic systems. Together with the recently proposed three-fold corrected (3c) Hartree-Fock method, the new composite scheme (termed PBEh-3c) represents the next member in a hierarchy of “low-cost” electronic structure approaches. They are mainly free of BSSE and account for most interactions in a physically sound and asymptotically correct manner. PBEh-3c yields good results for thermochemical properties in the huge GMTKN30 energy database. Furthermore, the method shows excellent performance for non-covalent interaction energies in small and large complexes. For evaluating its performance on equilibrium structures, a new compilation of standard test sets is suggested. These consist of small (light) molecules, partially flexible, medium-sized organic molecules, molecules comprising heavy main group elements, larger systems with long bonds, 3d-transition metal systems, non-covalently bound complexes (S22 and S66×8 sets), and peptide conformations. For these sets, overall deviations from accurate reference data are smaller than for various other tested DFT
NASA Astrophysics Data System (ADS)
Grimme, Stefan; Brandenburg, Jan Gerit; Bannwarth, Christoph; Hansen, Andreas
2015-08-01
A density functional theory (DFT) based composite electronic structure approach is proposed to efficiently compute structures and interaction energies in large chemical systems. It is based on the well-known and numerically robust Perdew-Burke-Ernzerhoff (PBE) generalized-gradient-approximation in a modified global hybrid functional with a relatively large amount of non-local Fock-exchange. The orbitals are expanded in Ahlrichs-type valence-double zeta atomic orbital (AO) Gaussian basis sets, which are available for many elements. In order to correct for the basis set superposition error (BSSE) and to account for the important long-range London dispersion effects, our well-established atom-pairwise potentials are used. In the design of the new method, particular attention has been paid to an accurate description of structural parameters in various covalent and non-covalent bonding situations as well as in periodic systems. Together with the recently proposed three-fold corrected (3c) Hartree-Fock method, the new composite scheme (termed PBEh-3c) represents the next member in a hierarchy of "low-cost" electronic structure approaches. They are mainly free of BSSE and account for most interactions in a physically sound and asymptotically correct manner. PBEh-3c yields good results for thermochemical properties in the huge GMTKN30 energy database. Furthermore, the method shows excellent performance for non-covalent interaction energies in small and large complexes. For evaluating its performance on equilibrium structures, a new compilation of standard test sets is suggested. These consist of small (light) molecules, partially flexible, medium-sized organic molecules, molecules comprising heavy main group elements, larger systems with long bonds, 3d-transition metal systems, non-covalently bound complexes (S22 and S66×8 sets), and peptide conformations. For these sets, overall deviations from accurate reference data are smaller than for various other tested DFT methods
Berry, Rachel H; Hobson, Michael P; Withington, Stafford
2004-05-01
We discuss a general theoretical framework for representing and propagating fully coherent, fully incoherent, and the intermediate regime of partially coherent submillimeter-wave fields by means of general sampled basis functions, which may have any degree of completeness. Partially coherent fields arise when finite-throughput systems induce coherence on incoherent fields. This powerful extension to traditional modal analysis methods by using undercomplete Gaussian-Hermite modes can be employed to analyze and optimize such Gaussian quasi-optical techniques. We focus on one particular basis set, the Gabor basis, which consists of overlapping translated and modulated Gaussian beams. We present high-accuracy numerical results from field reconstructions and propagations. In particular, we perform one-dimensional analyses illustrating the Van Cittert-Zernike theorem and then extend our simulations to two dimensions, including simple models of horn and bolometer arrays. Our methods and results are of practical importance as a method for analyzing terahertz fields, which are often partially coherent and diffraction limited so that ray tracing is inaccurate and physical optics computationally prohibitive. PMID:15139431
Many-body calculations of molecular electric polarizabilities in asymptotically complete basis sets
NASA Astrophysics Data System (ADS)
Monten, Ruben; Hajgató, Balázs; Deleuze, Michael S.
2011-10-01
The static dipole polarizabilities of Ne, CO, N2, F2, HF, H2O, HCN, and C2H2 (acetylene) have been determined close to the Full-CI limit along with an asymptotically complete basis set (CBS), according to the principles of a Focal Point Analysis. For this purpose the results of Finite Field calculations up to the level of Coupled Cluster theory including Single, Double, Triple, Quadruple and perturbative Pentuple excitations [CCSDTQ(P)] were used, in conjunction with suited extrapolations of energies obtained using augmented and doubly-augmented Dunning's correlation consistent polarized valence basis sets of improving quality. The polarizability characteristics of C2H4 (ethylene) and C2H6 (ethane) have been determined on the same grounds at the CCSDTQ level in the CBS limit. Comparison is made with results obtained using lower levels in electronic correlation, or taking into account the relaxation of the molecular structure due to an adiabatic polarization process. Vibrational corrections to electronic polarizabilities have been empirically estimated according to Born-Oppenheimer Molecular Dynamical simulations employing Density Functional Theory. Confrontation with experiment ultimately indicates relative accuracies of the order of 1 to 2%.
Spectral fitting using basis set modified by measured B0 field distribution.
Li, Ningzhi; An, Li; Shen, Jun
2015-12-01
This study sought to demonstrate and evaluate a novel spectral fitting method to improve quantification accuracy in the presence of large magnetic field distortion, especially with high fields. MRS experiments were performed using a point-resolved spectroscopy (PRESS)-type sequence at 7 T. A double-echo gradient echo (GRE) sequence was used to acquire B0 maps following MRS experiments. The basis set was modified based on the measured B0 distribution within the MRS voxel. Quantification results were obtained after fitting the measured MRS data using the modified basis set. The proposed method was validated using numerical Monte Carlo simulations, phantom measurements, and comparison of occipital lobe MRS measurements under homogeneous and inhomogeneous magnetic field conditions. In vivo results acquired from voxels placed in thalamus and prefrontal cortex regions close to the frontal sinus agreed well with published values. Instead of noise-amplifying complex division, the proposed method treats field variations as part of the signal model, thereby avoiding inherent statistical bias associated with regularization. Simulations and experiments showed that the proposed approach reliably quantified results in the presence of relatively large magnetic field distortion. Published 2015. This article is a U.S. Government work and is in the public domain in the USA. PMID:26503305
Analytic basis set for high-Z atomic QED calculations: Heavy He-like ions
Hylton, D.J.; Snyderman, N.J.
1997-04-01
A relativistic Sturmian analytic basis set representation for the Coulomb-Dirac Green function, previously studied by Zapryagaev, Manakov, and Pal{close_quote}chikov [Opt. Spectrosc. {bold 52}, 248 (1982)], is investigated for application to high-Z atomic QED calculations. This pseudoeigenfunction representation follows from exact identities starting from the Whittaker function representation. It eliminates the radial ordering problem of that representation, and so is particularly useful for numerical calculation of the perturbation theory Feynman diagrams with more than one electron Green function. While the Green function represents discrete bound states, and both positive and negative energy continuum states, the Sturmian (bound-state-like) form for the pseudoeigenfunctions makes it possible to more analytically calculate matrix elements for full photon exchange, reducing numerical problems for high photon frequency. For He-like Fm (Z=100) we calculate the perturbation theory equivalent of the Dirac-Fock-Breit ground-state energy, agreeing well with the Grant code and with the numerical B-spline basis set approach results of Blundell, Mohr, Johnson, and Sapirstein [Phys. Rev. A {bold 48}, 2615 (1993)]. Preliminary results on the relativistic and QED correlation are also reported. {copyright} {ital 1997} {ital The American Physical Society}
Atomic self-consistent-field program by the basis set expansion method: Columbus version
NASA Astrophysics Data System (ADS)
Pitzer, Russell M.
2005-08-01
A revised and extended (Columbus) version of the Chicago atomic self-consistent-field (Hartree-Fock) program of 1963 is described. Its principal present use is in developing Gaussian basis sets for molecular calculations. Complete memory allocation (using Fortran 90) has been added as well as improved integral formulas and efficient and simple programming features. Energy-expression coefficients have been added sufficient to treat the ground states of all atoms to the extent that Russell-Saunders (LS) coupling applies. Excited states with large angular-momentum orbitals can be treated. Relativistic effects can be included to the extent possible with relativistic effective core potentials. A review of earlier work is included. Program summaryProgram title: atmscf Catalogue identifier: ADVR Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADVR Program available from: CPC Program Library, Queen's University of Belfast, N. Ireland Programming language: Fortran 90 Computer: Sun, SGI, PC Operating system: Solaris, Irix, Linux RAM: 10 Mbytes No. of lines in distributed program, including test data, etc.: 2113 No. of bytes in distributed program, including test data, etc.: 15 379 Distribution format: tar.gz Nature of problem: Energies and wave functions, at the Hartree-Fock level Solution method: Expansions in Gaussian or Slater functions. Iterative minimization of the total energy. Optimization of exponential parameters. Used frequently for developing Gaussian basis sets for molecular use Running time: Typical 30 s per calculation
Green's function multiple-scattering theory with a truncated basis set: An augmented-KKR formalism
Alam, Aftab; Khan, Suffian N.; Smirnov, A. V.; Nicholson, D. M.; Johnson, Duane D.
2014-11-04
Korringa-Kohn-Rostoker (KKR) Green's function, multiple-scattering theory is an ecient sitecentered, electronic-structure technique for addressing an assembly of N scatterers. Wave-functions are expanded in a spherical-wave basis on each scattering center and indexed up to a maximum orbital and azimuthal number L_{max} = (l,m)_{max}, while scattering matrices, which determine spectral properties, are truncated at L_{tr} = (l,m)_{tr} where phase shifts δl>l_{tr} are negligible. Historically, L_{max} is set equal to L_{tr}, which is correct for large enough L_{max} but not computationally expedient; a better procedure retains higher-order (free-electron and single-site) contributions for L_{max} > L_{tr} with δl>l_{tr} set to zero [Zhang and Butler, Phys. Rev. B 46, 7433]. We present a numerically ecient and accurate augmented-KKR Green's function formalism that solves the KKR equations by exact matrix inversion [R^{3} process with rank N(l_{tr} + 1)^{2}] and includes higher-L contributions via linear algebra [R^{2} process with rank N(l_{max} +1)^{2}]. Augmented-KKR approach yields properly normalized wave-functions, numerically cheaper basis-set convergence, and a total charge density and electron count that agrees with Lloyd's formula. We apply our formalism to fcc Cu, bcc Fe and L1_{0} CoPt, and present the numerical results for accuracy and for the convergence of the total energies, Fermi energies, and magnetic moments versus L_{max} for a given L_{tr}.
Green's function multiple-scattering theory with a truncated basis set: An augmented-KKR formalism
Alam, Aftab; Khan, Suffian N.; Smirnov, A. V.; Nicholson, D. M.; Johnson, Duane D.
2014-11-04
Korringa-Kohn-Rostoker (KKR) Green's function, multiple-scattering theory is an ecient sitecentered, electronic-structure technique for addressing an assembly of N scatterers. Wave-functions are expanded in a spherical-wave basis on each scattering center and indexed up to a maximum orbital and azimuthal number Lmax = (l,m)max, while scattering matrices, which determine spectral properties, are truncated at Ltr = (l,m)tr where phase shifts δl>ltr are negligible. Historically, Lmax is set equal to Ltr, which is correct for large enough Lmax but not computationally expedient; a better procedure retains higher-order (free-electron and single-site) contributions for Lmax > Ltr with δl>ltr set to zero [Zhang andmore » Butler, Phys. Rev. B 46, 7433]. We present a numerically ecient and accurate augmented-KKR Green's function formalism that solves the KKR equations by exact matrix inversion [R3 process with rank N(ltr + 1)2] and includes higher-L contributions via linear algebra [R2 process with rank N(lmax +1)2]. Augmented-KKR approach yields properly normalized wave-functions, numerically cheaper basis-set convergence, and a total charge density and electron count that agrees with Lloyd's formula. We apply our formalism to fcc Cu, bcc Fe and L10 CoPt, and present the numerical results for accuracy and for the convergence of the total energies, Fermi energies, and magnetic moments versus Lmax for a given Ltr.« less
Green's function multiple-scattering theory with a truncated basis set: An augmented-KKR formalism
NASA Astrophysics Data System (ADS)
Alam, Aftab; Khan, Suffian N.; Smirnov, A. V.; Nicholson, D. M.; Johnson, Duane D.
2014-11-01
The Korringa-Kohn-Rostoker (KKR) Green's function, multiple-scattering theory is an efficient site-centered, electronic-structure technique for addressing an assembly of N scatterers. Wave functions are expanded in a spherical-wave basis on each scattering center and indexed up to a maximum orbital and azimuthal number Lmax=(l,mmax), while scattering matrices, which determine spectral properties, are truncated at Lt r=(l,mt r) where phase shifts δl >ltr are negligible. Historically, Lmax is set equal to Lt r, which is correct for large enough Lmax but not computationally expedient; a better procedure retains higher-order (free-electron and single-site) contributions for Lmax>Lt r with δl >ltr set to zero [X.-G. Zhang and W. H. Butler, Phys. Rev. B 46, 7433 (1992), 10.1103/PhysRevB.46.7433]. We present a numerically efficient and accurate augmented-KKR Green's function formalism that solves the KKR equations by exact matrix inversion [R3 process with rank N (ltr+1 ) 2 ] and includes higher-L contributions via linear algebra [R2 process with rank N (lmax+1) 2 ]. The augmented-KKR approach yields properly normalized wave functions, numerically cheaper basis-set convergence, and a total charge density and electron count that agrees with Lloyd's formula. We apply our formalism to fcc Cu, bcc Fe, and L 1 0 CoPt and present the numerical results for accuracy and for the convergence of the total energies, Fermi energies, and magnetic moments versus Lmax for a given Lt r.
All-electron Kohn–Sham density functional theory on hierarchic finite element spaces
Schauer, Volker; Linder, Christian
2013-10-01
In this work, a real space formulation of the Kohn–Sham equations is developed, making use of the hierarchy of finite element spaces from different polynomial order. The focus is laid on all-electron calculations, having the highest requirement onto the basis set, which must be able to represent the orthogonal eigenfunctions as well as the electrostatic potential. A careful numerical analysis is performed, which points out the numerical intricacies originating from the singularity of the nuclei and the necessity for approximations in the numerical setting, with the ambition to enable solutions within a predefined accuracy. In this context the influence of counter-charges in the Poisson equation, the requirement of a finite domain size, numerical quadratures and the mesh refinement are examined as well as the representation of the electrostatic potential in a high order finite element space. The performance and accuracy of the method is demonstrated in computations on noble gases. In addition the finite element basis proves its flexibility in the calculation of the bond-length as well as the dipole moment of the carbon monoxide molecule.
Crystal orbital Hamilton population (COHP) analysis as projected from plane-wave basis sets.
Deringer, Volker L; Tchougréeff, Andrei L; Dronskowski, Richard
2011-06-01
Simple, yet predictive bonding models are essential achievements of chemistry. In the solid state, in particular, they often appear in the form of visual bonding indicators. Because the latter require the crystal orbitals to be constructed from local basis sets, the application of the most popular density-functional theory codes (namely, those based on plane waves and pseudopotentials) appears as being ill-fitted to retrieve the chemical bonding information. In this paper, we describe a way to re-extract Hamilton-weighted populations from plane-wave electronic-structure calculations to develop a tool analogous to the familiar crystal orbital Hamilton population (COHP) method. We derive the new technique, dubbed "projected COHP" (pCOHP), and demonstrate its viability using examples of covalent, ionic, and metallic crystals (diamond, GaAs, CsCl, and Na). For the first time, this chemical bonding information is directly extracted from the results of plane-wave calculations. PMID:21548594
AgH, Ag/sub 2/, and AgO revisited: Basis set extensions
Martin, R.L.
1987-05-01
An extended basis set has been developed for Ag which significantly improves the agreement between theoretical and experimental spectroscopic parameters for AgH, AgO, and Ag/sub 2/. The major improvement comes about as a result of the improved treatment of electron correlation in the Ag d shell upon the introduction of f functions. Their inclusion produces very slight differences at the SCF level, but significant reductions in r/sub e/ and increases in ..omega../sub e/ and D/sub e/ in the Mo-dash-barller--Plesset perturbation theory expansion. At the MP4(SDTQ) level, typical results are 0.02 A too long for r/sub e/, 4% too low for ..omega../sub e/, and 10 kcal too small for D/sub e/. From a pragmatic standpoint, MP2 give results very similar to this at a much reduced level of effort.
Li, Z.; Pan, Y.K.; Tao, F.M.
1996-01-15
Bond function basis sets combined with the counterpoise procedure are used to calculate the molecular dissociation energies D{sub e} of 24 diatomic molecules and ions. The calculated values of D{sub e} are compared to those without bond functions and/or counterpoise corrections. The equilibrium bond lengths r{sub e}, and harmonic frequencies w{sub e} are also calculated for a few selected molecules. The calculations at the fourth-order-Moller-Plesset approximation (MP4) have consistently recovered about 95-99% of the experimental values for D{sub e}, compared to as low as 75% without use of bond functions. The calculated values of r{sub 3} are typically 0.01 {Angstrom} larger than the experimental values, and the calculated values of w{sub e} are over 95% of the experimental values. 37 refs., 2 tabs.
A two-dimensional volatility basis set - Part 3: Prognostic modeling and NOx dependence
NASA Astrophysics Data System (ADS)
Chuang, W. K.; Donahue, N. M.
2015-06-01
When NOx is introduced to organic emissions, aerosol production is sometimes, but not always, reduced. Under certain conditions, these interactions will instead increase aerosol concentrations. We expanded the two-dimensional volatility basis set (2-D-VBS) to include the effects of NOx on aerosol formation. This includes the formation of organonitrates, where the addition of a nitrate group contributes to a decrease of 2.5 orders of magnitude in volatility. With this refinement, we model outputs from experimental results, such as the atomic N : C ratio, organonitrate mass, and nitrate fragments in AMS measurements. We also discuss the mathematical methods underlying the implementation of the 2-D-VBS and provide the complete code in the Supplemental material. A developer version is available on Bitbucket, an online community repository.
A two-dimensional volatility basis set - Part 3: Prognostic modeling and NOx dependence
NASA Astrophysics Data System (ADS)
Chuang, W. K.; Donahue, N. M.
2016-01-01
When NOx is introduced to organic emissions, aerosol production is sometimes, but not always, reduced. Under certain conditions, these interactions will instead increase aerosol concentrations. We expanded the two-dimensional volatility basis set (2D-VBS) to include the effects of NOx on aerosol formation. This includes the formation of organonitrates, where the addition of a nitrate group contributes to a decrease of 2.5 orders of magnitude in volatility. With this refinement, we model outputs from experimental results, such as the atomic N : C ratio, organonitrate mass, and nitrate fragments in Aerosol Mass Spectrometer (AMS) measurements. We also discuss the mathematical methods underlying the implementation of the 2D-VBS and provide the complete code in the Supplement. A developer version is available on Bitbucket, an online community repository.
Near Hartree-Fock quality Gaussian type orbital basis sets for the first- and third-row atoms
NASA Technical Reports Server (NTRS)
Partridge, Harry
1989-01-01
Energy-optimized, near Hartree-Fock (NHF) quality Gaussian type orbital (GTO) basis sets are reported for the second-row (Li to Ne) and fourth-row (K to Kr) atoms. The most accurate basis sets reported for the second row are (18s 13p) sets which are with 4 micro E(H) of the numerical Hartree-Fock (NHF) results. For B to Ne basis sets with more than 15s functions are quadruple zeta in the valence space. For the second-row transition metal atoms the (20s 12p 9d) basis sets are triple zeta in the valence space and are approximately equivalent to Clementi and Roetti's accurate Slater type orbital sets. Supplementing the (20s 12p 9d) basis sets optimized for the lowest state with the 4s(2)3d(n) occupation with a diffuse d function gives self-consistent-field energy separations to the 4s(1)3d(n+1) and 3d(n+2) states which are within 100 micro E(H) of the NHF results. The most accurate basis sets for the transition metal atoms are with 30 micro E(H) of the NHF results. In addition, energy optimized sets are reported for He(3P), Li(2P) and Be(3P).
Tsuzuki, Seiji; Tanabe, Kazutoshi )
1991-03-21
Intermolecular interaction energies of methane dimer were calculated by using several basis sets up to 6-311G(3d,4p) with electron correlation energy correction by the Moeller-Plesset perturbation method and basis set superposition error (BSSE) correction by the counterpoise method to evaluate the basis set effect. The calculated interaction energies depended on the basis set considerably. Whereas the interaction energies of repulsive component calculated at HF level were not affected by the change of basis set, the dispersion energy component dependent greatly on the basis set used. The dispersion energies calculated with the Moeller-Plesset second- and third-order perturbation by using 6-311G(2d,2p) basis set were 0-10% and 4-6% smaller than those obtained with the fourth-order (MP4(SDTQ)) perturbation, respectively. The BSSE's calculated by the counterpoise method were still about 30% of the calculated intermolecular interaction energies for the conformers of energy minima event at the MP4(SDTQ)/6-311G(2d,2p) level. The calculated interaction potentials of dimers at the MP4(SDTQ)/6-311G(2d,2p) level were considerably shallower than those obtained by MM2 force fields but were close to the potentials given by the Williams potential and by the recently reported MM3 force field.
NASA Astrophysics Data System (ADS)
Hsu, Po Jen; Lai, S. K.; Rapallo, Arnaldo
2014-03-01
Improved basis sets for the study of polymer dynamics by means of the diffusion theory, and tests on a melt of cis-1,4-polyisoprene decamers, and a toluene solution of a 71-mer syndiotactic trans-1,2-polypentadiene were presented recently [R. Gaspari and A. Rapallo, J. Chem. Phys. 128, 244109 (2008)]. The proposed hybrid basis approach (HBA) combined two techniques, the long time sorting procedure and the maximum correlation approximation. The HBA takes advantage of the strength of these two techniques, and its basis sets proved to be very effective and computationally convenient in describing both local and global dynamics in cases of flexible synthetic polymers where the repeating unit is a unique type of monomer. The question then arises if the same efficacy continues when the HBA is applied to polymers of different monomers, variable local stiffness along the chain and with longer persistence length, which have different local and global dynamical properties against the above-mentioned systems. Important examples of this kind of molecular chains are the proteins, so that a fragment of the protein transthyretin is chosen as the system of the present study. This peptide corresponds to a sequence that is structured in β-sheets of the protein and is located on the surface of the channel with thyroxin. The protein transthyretin forms amyloid fibrils in vivo, whereas the peptide fragment has been shown [C. P. Jaroniec, C. E. MacPhee, N. S. Astrof, C. M. Dobson, and R. G. Griffin, Proc. Natl. Acad. Sci. U.S.A. 99, 16748 (2002)] to form amyloid fibrils in vitro in extended β-sheet conformations. For these reasons the latter is given considerable attention in the literature and studied also as an isolated fragment in water solution where both experimental and theoretical efforts have indicated the propensity of the system to form β turns or α helices, but is otherwise predominantly unstructured. Differing from previous computational studies that employed implicit
Hsu, Po Jen; Lai, S K; Rapallo, Arnaldo
2014-03-14
Improved basis sets for the study of polymer dynamics by means of the diffusion theory, and tests on a melt of cis-1,4-polyisoprene decamers, and a toluene solution of a 71-mer syndiotactic trans-1,2-polypentadiene were presented recently [R. Gaspari and A. Rapallo, J. Chem. Phys. 128, 244109 (2008)]. The proposed hybrid basis approach (HBA) combined two techniques, the long time sorting procedure and the maximum correlation approximation. The HBA takes advantage of the strength of these two techniques, and its basis sets proved to be very effective and computationally convenient in describing both local and global dynamics in cases of flexible synthetic polymers where the repeating unit is a unique type of monomer. The question then arises if the same efficacy continues when the HBA is applied to polymers of different monomers, variable local stiffness along the chain and with longer persistence length, which have different local and global dynamical properties against the above-mentioned systems. Important examples of this kind of molecular chains are the proteins, so that a fragment of the protein transthyretin is chosen as the system of the present study. This peptide corresponds to a sequence that is structured in β-sheets of the protein and is located on the surface of the channel with thyroxin. The protein transthyretin forms amyloid fibrils in vivo, whereas the peptide fragment has been shown [C. P. Jaroniec, C. E. MacPhee, N. S. Astrof, C. M. Dobson, and R. G. Griffin, Proc. Natl. Acad. Sci. U.S.A. 99, 16748 (2002)] to form amyloid fibrils in vitro in extended β-sheet conformations. For these reasons the latter is given considerable attention in the literature and studied also as an isolated fragment in water solution where both experimental and theoretical efforts have indicated the propensity of the system to form β turns or α helices, but is otherwise predominantly unstructured. Differing from previous computational studies that employed implicit
Hsu, Po Jen; Lai, S. K.; Rapallo, Arnaldo
2014-03-14
Improved basis sets for the study of polymer dynamics by means of the diffusion theory, and tests on a melt of cis-1,4-polyisoprene decamers, and a toluene solution of a 71-mer syndiotactic trans-1,2-polypentadiene were presented recently [R. Gaspari and A. Rapallo, J. Chem. Phys. 128, 244109 (2008)]. The proposed hybrid basis approach (HBA) combined two techniques, the long time sorting procedure and the maximum correlation approximation. The HBA takes advantage of the strength of these two techniques, and its basis sets proved to be very effective and computationally convenient in describing both local and global dynamics in cases of flexible synthetic polymers where the repeating unit is a unique type of monomer. The question then arises if the same efficacy continues when the HBA is applied to polymers of different monomers, variable local stiffness along the chain and with longer persistence length, which have different local and global dynamical properties against the above-mentioned systems. Important examples of this kind of molecular chains are the proteins, so that a fragment of the protein transthyretin is chosen as the system of the present study. This peptide corresponds to a sequence that is structured in β-sheets of the protein and is located on the surface of the channel with thyroxin. The protein transthyretin forms amyloid fibrils in vivo, whereas the peptide fragment has been shown [C. P. Jaroniec, C. E. MacPhee, N. S. Astrof, C. M. Dobson, and R. G. Griffin, Proc. Natl. Acad. Sci. U.S.A. 99, 16748 (2002)] to form amyloid fibrils in vitro in extended β-sheet conformations. For these reasons the latter is given considerable attention in the literature and studied also as an isolated fragment in water solution where both experimental and theoretical efforts have indicated the propensity of the system to form β turns or α helices, but is otherwise predominantly unstructured. Differing from previous computational studies that employed implicit
Model for the fast estimation of basis set superposition error in biomolecular systems
Faver, John C.; Zheng, Zheng; Merz, Kenneth M.
2011-01-01
Basis set superposition error (BSSE) is a significant contributor to errors in quantum-based energy functions, especially for large chemical systems with many molecular contacts such as folded proteins and protein-ligand complexes. While the counterpoise method has become a standard procedure for correcting intermolecular BSSE, most current approaches to correcting intramolecular BSSE are simply fragment-based analogues of the counterpoise method which require many (two times the number of fragments) additional quantum calculations in their application. We propose that magnitudes of both forms of BSSE can be quickly estimated by dividing a system into interacting fragments, estimating each fragment's contribution to the overall BSSE with a simple statistical model, and then propagating these errors throughout the entire system. Such a method requires no additional quantum calculations, but rather only an analysis of the system's interacting fragments. The method is described herein and is applied to a protein-ligand system, a small helical protein, and a set of native and decoy protein folds. PMID:22010701
European air quality modelled by CAMx including the volatility basis set scheme
NASA Astrophysics Data System (ADS)
Ciarelli, G.; Aksoyoglu, S.; Crippa, M.; Jimenez, J. L.; Nemitz, E.; Sellegri, K.; Äijälä, M.; Carbone, S.; Mohr, C.; O'Dowd, C.; Poulain, L.; Baltensperger, U.; Prévôt, A. S. H.
2015-12-01
Four periods of EMEP (European Monitoring and Evaluation Programme) intensive measurement campaigns (June 2006, January 2007, September-October 2008 and February-March 2009) were modelled using the regional air quality model CAMx with VBS (Volatility Basis Set) approach for the first time in Europe within the framework of the EURODELTA-III model intercomparison exercise. More detailed analysis and sensitivity tests were performed for the period of February-March 2009 and June 2006 to investigate the uncertainties in emissions as well as to improve the modelling of organic aerosols (OA). Model performance for selected gas phase species and PM2.5 was evaluated using the European air quality database Airbase. Sulfur dioxide (SO2) and ozone (O3) were found to be overestimated for all the four periods with O3 having the largest mean bias during June 2006 and January-February 2007 periods (8.93 and 12.30 ppb mean biases, respectively). In contrast, nitrogen dioxide (NO2) and carbon monoxide (CO) were found to be underestimated for all the four periods. CAMx reproduced both total concentrations and monthly variations of PM2.5 very well for all the four periods with average biases ranging from -2.13 to 1.04 μg m-3. Comparisons with AMS (Aerosol Mass Spectrometer) measurements at different sites in Europe during February-March 2009, showed that in general the model over-predicts the inorganic aerosol fraction and under-predicts the organic one, such that the good agreement for PM2.5 is partly due to compensation of errors. The effect of the choice of volatility basis set scheme (VBS) on OA was investigated as well. Two sensitivity tests with volatility distributions based on previous chamber and ambient measurements data were performed. For February-March 2009 the chamber-case reduced the total OA concentrations by about 43 % on average. On the other hand, a test based on ambient measurement data increased OA concentrations by about 47 % for the same period bringing model
Toward accurate thermochemical models for transition metals : G3large basis sets for atoms Sc-Zn.
Mayhall, N. J.; Raghavachari, K.; Redfern, P. C.; Curtiss, L. A.; Rassolov, V.; Indiana Univ.; Univ. of South Carolina
2008-04-01
An augmented valence triple-zeta basis set, referred to as G3Large, is reported for the first-row transition metal elements Sc through Zn. The basis set is constructed in a manner similar to the G3Large basis set developed previously for other elements (H-Ar, K, Ca, Ga-Kr) and used as a key component in Gaussian-3 theory. It is based on a contraction of a set of 15s13p5d Gaussian primitives to 8s7p3d, and also includes sets of f and g polarization functions, diffuse spd functions, and core df polarization functions. The basis set is evaluated with triples-augmented coupled cluster [CCSD(T)] and Brueckner orbital [BD(T)] methods for a small test set involving energies of atoms, atomic ions, and diatomic hydrides. It performs well for the low-lying s{yields}d excitation energies of atoms, atomic ionization energies, and the dissociation energies of the diatomic hydrides. The Brueckner orbital-based BD(T) method performs substantially better than Hartree-Fock-based CCSD(T) for molecules such as NiH, where the starting unrestricted Hartree-Fock wavefunction suffers from a high degree of spin contamination. Comparison with available data for geometries of transition metal hydrides also shows good agreement. A smaller basis set without core polarization functions, G3MP2Large, is also defined.
Dharmarajan, Venkatasubramanian; Lee, Jeong-Heon; Patel, Anamika; Skalnik, David G.; Cosgrove, Michael S.
2012-01-01
Translocations and amplifications of the mixed lineage leukemia-1 (MLL1) gene are associated with aggressive myeloid and lymphocytic leukemias in humans. MLL1 is a member of the SET1 family of histone H3 lysine 4 (H3K4) methyltransferases, which are required for transcription of genes involved in hematopoiesis and development. MLL1 associates with a subcomplex containing WDR5, RbBP5, Ash2L, and DPY-30 (WRAD), which together form the MLL1 core complex that is required for sequential mono- and dimethylation of H3K4. We previously demonstrated that WDR5 binds the conserved WDR5 interaction (Win) motif of MLL1 in vitro, an interaction that is required for the H3K4 dimethylation activity of the MLL1 core complex. In this investigation, we demonstrate that arginine 3765 of the MLL1 Win motif is required to co-immunoprecipitate WRAD from mammalian cells, suggesting that the WDR5-Win motif interaction is important for the assembly of the MLL1 core complex in vivo. We also demonstrate that peptides that mimic SET1 family Win motif sequences inhibit H3K4 dimethylation by the MLL1 core complex with varying degrees of efficiency. To understand the structural basis for these differences, we determined structures of WDR5 bound to six different naturally occurring Win motif sequences at resolutions ranging from 1.9 to 1.2 Å. Our results reveal that binding energy differences result from interactions between non-conserved residues C-terminal to the Win motif and to a lesser extent from subtle variation of residues within the Win motif. These results highlight a new class of methylation inhibitors that may be useful for the treatment of MLL1-related malignancies. PMID:22665483
NASA Astrophysics Data System (ADS)
Holden, Zachary C.; Richard, Ryan M.; Herbert, John M.
2013-12-01
An implementation of Ewald summation for use in mixed quantum mechanics/molecular mechanics (QM/MM) calculations is presented, which builds upon previous work by others that was limited to semi-empirical electronic structure for the QM region. Unlike previous work, our implementation describes the wave function's periodic images using "ChElPG" atomic charges, which are determined by fitting to the QM electrostatic potential evaluated on a real-space grid. This implementation is stable even for large Gaussian basis sets with diffuse exponents, and is thus appropriate when the QM region is described by a correlated wave function. Derivatives of the ChElPG charges with respect to the QM density matrix are a potentially serious bottleneck in this approach, so we introduce a ChElPG algorithm based on atom-centered Lebedev grids. The ChElPG charges thus obtained exhibit good rotational invariance even for sparse grids, enabling significant cost savings. Detailed analysis of the optimal choice of user-selected Ewald parameters, as well as timing breakdowns, is presented.
Electron affinities of the first-row atoms revisited. Systematic basis sets and wave functions
Kendall, R.A.; Dunning, T.H. Jr. ); Harrison, R.J. )
1992-05-01
The calculation of accurate electron affinities (EAs) of atomic or molecular species is one of the most challenging tasks in quantum chemistry. We describe a reliable procedure for calculating the electron affinity of an atom and present results for hydrogen, boron, carbon, oxygen, and fluorine (hydrogen is included for completeness). This procedure involves the use of the recently proposed correlation-consistent basis sets augmented with functions to describe the more diffuse character of the atomic anion coupled with a straightforward, uniform expansion of the reference space for multireference singles and doubles configuration-interaction (MRSD-CI) calculations. Comparison with previous results and with corresponding full CI calculations are given. The most accurate EAs obtained from the MRSD-CI calculations are (with experimental values in parentheses) hydrogen 0.740 eV (0.754), boron 0.258 (0.277), carbon 1.245 (1.263), oxygen 1.384 (1.461), and fluorine 3.337 (3.401). The EAs obtained from the MR-SDCI calculations differ by less than 0.03 eV from those predicted by the full CI calculations.
Holden, Zachary C.; Richard, Ryan M.; Herbert, John M.
2013-12-28
An implementation of Ewald summation for use in mixed quantum mechanics/molecular mechanics (QM/MM) calculations is presented, which builds upon previous work by others that was limited to semi-empirical electronic structure for the QM region. Unlike previous work, our implementation describes the wave function's periodic images using “ChElPG” atomic charges, which are determined by fitting to the QM electrostatic potential evaluated on a real-space grid. This implementation is stable even for large Gaussian basis sets with diffuse exponents, and is thus appropriate when the QM region is described by a correlated wave function. Derivatives of the ChElPG charges with respect to the QM density matrix are a potentially serious bottleneck in this approach, so we introduce a ChElPG algorithm based on atom-centered Lebedev grids. The ChElPG charges thus obtained exhibit good rotational invariance even for sparse grids, enabling significant cost savings. Detailed analysis of the optimal choice of user-selected Ewald parameters, as well as timing breakdowns, is presented.
NASA Astrophysics Data System (ADS)
Park, R.; Jo, D.; Kim, M.; Spracklen, D. V.; Hodzic, A.
2014-12-01
Organic aerosol (OA) constitutes significant mass fractions (20-90%) of total dry fine aerosols in the atmosphere. However, global models of OA have shown large discrepancies when compared to the observations because of the limited capability to simulate secondary OA (SOA). For reducing the discrepancies between observations and models, recent studies have shown that chemical aging reactions in the atmosphere are important because they can lead to decreases in organic volatility, resulting in increase of SOA mass yields. To efficiently simulate chemical aging of SOA in the atmosphere, we implemented the volatility basis set approach in a global 3-D chemical transport model (GEOS-Chem). We present full-year simulations and their comparisons with multiple observations - global aerosol mass spectrometer dataset, the Interagency Monitoring of Protected Visual Environments from the United States, the European Monitoring and Evaluation Programme dataset and water-soluble organic carbon observation data collected over East Asia. Using different input parameters in the model, we also explore the uncertainty of the SOA simulation for which we use an observational constraint to find the optimized values with which the model reduces the discrepancy from the observations. Finally, we estimate the effect of OA on climate using our best simulation results.
The Scientific Basis of Uncertainty Factors Used in Setting Occupational Exposure Limits
Dankovic, D. A.; Naumann, B. D.; Maier, A.; Dourson, M. L.; Levy, L. S.
2015-01-01
The uncertainty factor concept is integrated into health risk assessments for all aspects of public health practice, including by most organizations that derive occupational exposure limits. The use of uncertainty factors is predicated on the assumption that a sufficient reduction in exposure from those at the boundary for the onset of adverse effects will yield a safe exposure level for at least the great majority of the exposed population, including vulnerable subgroups. There are differences in the application of the uncertainty factor approach among groups that conduct occupational assessments; however, there are common areas of uncertainty which are considered by all or nearly all occupational exposure limit-setting organizations. Five key uncertainties that are often examined include interspecies variability in response when extrapolating from animal studies to humans, response variability in humans, uncertainty in estimating a no-effect level from a dose where effects were observed, extrapolation from shorter duration studies to a full life-time exposure, and other insufficiencies in the overall health effects database indicating that the most sensitive adverse effect may not have been evaluated. In addition, a modifying factor is used by some organizations to account for other remaining uncertainties—typically related to exposure scenarios or accounting for the interplay among the five areas noted above. Consideration of uncertainties in occupational exposure limit derivation is a systematic process whereby the factors applied are not arbitrary, although they are mathematically imprecise. As the scientific basis for uncertainty factor application has improved, default uncertainty factors are now used only in the absence of chemical-specific data, and the trend is to replace them with chemical-specific adjustment factors whenever possible. The increased application of scientific data in the development of uncertainty factors for individual chemicals also
The Scientific Basis of Uncertainty Factors Used in Setting Occupational Exposure Limits.
Dankovic, D A; Naumann, B D; Maier, A; Dourson, M L; Levy, L S
2015-01-01
The uncertainty factor concept is integrated into health risk assessments for all aspects of public health practice, including by most organizations that derive occupational exposure limits. The use of uncertainty factors is predicated on the assumption that a sufficient reduction in exposure from those at the boundary for the onset of adverse effects will yield a safe exposure level for at least the great majority of the exposed population, including vulnerable subgroups. There are differences in the application of the uncertainty factor approach among groups that conduct occupational assessments; however, there are common areas of uncertainty which are considered by all or nearly all occupational exposure limit-setting organizations. Five key uncertainties that are often examined include interspecies variability in response when extrapolating from animal studies to humans, response variability in humans, uncertainty in estimating a no-effect level from a dose where effects were observed, extrapolation from shorter duration studies to a full life-time exposure, and other insufficiencies in the overall health effects database indicating that the most sensitive adverse effect may not have been evaluated. In addition, a modifying factor is used by some organizations to account for other remaining uncertainties-typically related to exposure scenarios or accounting for the interplay among the five areas noted above. Consideration of uncertainties in occupational exposure limit derivation is a systematic process whereby the factors applied are not arbitrary, although they are mathematically imprecise. As the scientific basis for uncertainty factor application has improved, default uncertainty factors are now used only in the absence of chemical-specific data, and the trend is to replace them with chemical-specific adjustment factors whenever possible. The increased application of scientific data in the development of uncertainty factors for individual chemicals also has
The study of basis sets for the calculation of the structure and dynamics of the benzene-Kr complex.
Shirkov, Leonid; Makarewicz, Jan
2015-05-28
An ab initio intermolecular potential energy surface (PES) has been constructed for the benzene-krypton (BKr) van der Waals (vdW) complex. The interaction energy has been calculated at the coupled cluster level of theory with single, double, and perturbatively included triple excitations using different basis sets. As a result, a few analytical PESs of the complex have been determined. They allowed a prediction of the complex structure and its vibrational vdW states. The vibrational energy level pattern exhibits a distinct polyad structure. Comparison of the equilibrium structure, the dipole moment, and vibrational levels of BKr with their experimental counterparts has allowed us to design an optimal basis set composed of a small Dunning's basis set for the benzene monomer, a larger effective core potential adapted basis set for Kr and additional midbond functions. Such a basis set yields vibrational energy levels that agree very well with the experimental ones as well as with those calculated from the available empirical PES derived from the microwave spectra of the BKr complex. The basis proposed can be applied to larger complexes including Kr because of a reasonable computational cost and accurate results. PMID:26026434
The study of basis sets for the calculation of the structure and dynamics of the benzene-Kr complex
Shirkov, Leonid; Makarewicz, Jan
2015-05-28
An ab initio intermolecular potential energy surface (PES) has been constructed for the benzene-krypton (BKr) van der Waals (vdW) complex. The interaction energy has been calculated at the coupled cluster level of theory with single, double, and perturbatively included triple excitations using different basis sets. As a result, a few analytical PESs of the complex have been determined. They allowed a prediction of the complex structure and its vibrational vdW states. The vibrational energy level pattern exhibits a distinct polyad structure. Comparison of the equilibrium structure, the dipole moment, and vibrational levels of BKr with their experimental counterparts has allowed us to design an optimal basis set composed of a small Dunning’s basis set for the benzene monomer, a larger effective core potential adapted basis set for Kr and additional midbond functions. Such a basis set yields vibrational energy levels that agree very well with the experimental ones as well as with those calculated from the available empirical PES derived from the microwave spectra of the BKr complex. The basis proposed can be applied to larger complexes including Kr because of a reasonable computational cost and accurate results.
The study of basis sets for the calculation of the structure and dynamics of the benzene-Kr complex
NASA Astrophysics Data System (ADS)
Shirkov, Leonid; Makarewicz, Jan
2015-05-01
An ab initio intermolecular potential energy surface (PES) has been constructed for the benzene-krypton (BKr) van der Waals (vdW) complex. The interaction energy has been calculated at the coupled cluster level of theory with single, double, and perturbatively included triple excitations using different basis sets. As a result, a few analytical PESs of the complex have been determined. They allowed a prediction of the complex structure and its vibrational vdW states. The vibrational energy level pattern exhibits a distinct polyad structure. Comparison of the equilibrium structure, the dipole moment, and vibrational levels of BKr with their experimental counterparts has allowed us to design an optimal basis set composed of a small Dunning's basis set for the benzene monomer, a larger effective core potential adapted basis set for Kr and additional midbond functions. Such a basis set yields vibrational energy levels that agree very well with the experimental ones as well as with those calculated from the available empirical PES derived from the microwave spectra of the BKr complex. The basis proposed can be applied to larger complexes including Kr because of a reasonable computational cost and accurate results.
Fast Electron Correlation Methods for Molecular Clusters without Basis Set Superposition Errors
Kamiya, Muneaki; Hirata, So; Valiev, Marat
2008-02-19
Two critical extensions to our fast, accurate, and easy-to-implement binary or ternary interaction method for weakly-interacting molecular clusters [Hirata et al. Mol. Phys. 103, 2255 (2005)] have been proposed, implemented, and applied to water hexamers, hydrogen fluoride chains and rings, and neutral and zwitterionic glycine–water clusters with an excellent result for an initial performance assessment. Our original method included up to two- or three-body Coulomb, exchange, and correlation energies exactly and higher-order Coulomb energies in the dipole–dipole approximation. In this work, the dipole moments are replaced by atom-centered point charges determined so that they reproduce the electrostatic potentials of the cluster subunits as closely as possible and also self-consistently with one another in the cluster environment. They have been shown to lead to dramatic improvement in the description of short-range electrostatic potentials not only of large, charge-separated subunits like zwitterionic glycine but also of small subunits. Furthermore, basis set superposition errors (BSSE) known to plague direct evaluation of weak interactions have been eliminated by com-bining the Valiron–Mayer function counterpoise (VMFC) correction with our binary or ternary interaction method in an economical fashion (quadratic scaling n2 with respect to the number of subunits n when n is small and linear scaling when n is large). A new variant of VMFC has also been proposed in which three-body and all higher-order Coulomb effects on BSSE are estimated approximately. The BSSE-corrected ternary interaction method with atom-centered point charges reproduces the VMFC-corrected results of conventional electron correlation calculations within 0.1 kcal/mol. The proposed method is significantly more accurate and also efficient than conventional correlation methods uncorrected of BSSE.
Temperature dependence of source specific volatility basis sets for motor vehicle exhaust
NASA Astrophysics Data System (ADS)
Roy, Anirban; Choi, Yunsoo
2015-10-01
Recent work on emissions testing has focused on developing source specific volatility distributions which could be used to improve emissions inventories. One problem about these volatility profiles is that they are evaluated only at one temperature which is usually 298 K. This study uses a simple statistical model to evaluate the temperature dependence of the source-resolved volatility basis set, considering gasoline and diesel vehicle exhaust. The steps involved (a) fitting a distribution to the emissions data (b) evaluating the goodness of fit using a statistical test (c) updating the volatility bins using the Clausius-Clayperon equation; calculating the heats of vaporization of each volatility class using a regression model (d) assessing how the volatility of different VOC classes-Extremely Low Volatile, Low Volatile, Semi-Volatile, Intermediate Volatile and Volatile Organic Compounds - are affected by temperature. The results indicated that there could be significant changes in gas-particle partitioning of these emissions. For diesel exhaust at 298 K, the fractions are 5.4 × 10-4 (ELVOC), 0.074 (LVOC), 0.76 (SVOC), 0.17 (IVOC) and 10-5 (VOC) respectively. Looking at a window of ∓20 K, the partitioning for 278 K is 3 × 10-3 (ELVOC), 0.26 (LVOC), 0.67 (SVOC), 0.07 (IVOC) with no VOC fraction; while at 318 K it is 1.5 × 10-7 (ELVOC), 9 × 10-3 (LVOC), 0.64 (SVOC), 0.35 (IVOC) and 2 × 10-5 (VOC); demonstrating a significant change with temperature. The parameterizations developed in this work could be used to improve motor vehicle emissions inventory models such as MOVES.
Basis set dependence using DFT/B3LYP calculations to model the Raman spectrum of thymine.
Bielecki, Jakub; Lipiec, Ewelina
2016-02-01
Raman spectroscopy (including surface enhanced Raman spectroscopy (SERS) and tip enhanced Raman spectroscopy (TERS)) is a highly promising experimental method for investigations of biomolecule damage induced by ionizing radiation. However, proper interpretation of changes in experimental spectra for complex systems is often difficult or impossible, thus Raman spectra calculations based on density functional theory (DFT) provide an invaluable tool as an additional layer of understanding of underlying processes. There are many works that address the problem of basis set dependence for energy and bond length consideration, nevertheless there is still lack of consistent research on basis set influence on Raman spectra intensities for biomolecules. This study fills this gap by investigating of the influence of basis set choice for the interpretation of Raman spectra of the thymine molecule calculated using the DFT/B3LYP framework and comparing these results with experimental spectra. Among 19 selected Pople's basis sets, the best agreement was achieved using 6-31[Formula: see text](d,p), 6-31[Formula: see text](d,p) and 6-11[Formula: see text]G(d,p) sets. Adding diffuse functions or polarized functions for small basis set or use of a medium or large basis set without diffuse or polarized functions is not sufficient to reproduce Raman intensities correctly. The introduction of the diffuse functions ([Formula: see text]) on hydrogen atoms is not necessary for gas phase calculations. This work serves as a benchmark for further research on the interaction of ionizing radiation with DNA molecules by means of ab initio calculations and Raman spectroscopy. Moreover, this work provides a set of new scaling factors for Raman spectra calculation in the framework of DFT/B3LYP method. PMID:26508426
NASA Astrophysics Data System (ADS)
Kobus, J.; Moncrieff, D.; Wilson, S.
2004-02-01
In a previous paper, we have made a comparison of the accuracy with which the electric dipole polarizability agrzz and hyperpolarizability bgrzzz can be calculated by using either the finite basis set approach (the algebraic approximation) or the finite difference method in calculations for the ground states of the H2, LiH, BH and FH molecules, at their respective experimental equilibrium geometries, within the Hartree-Fock model. A re-examination of the hyperpolarizability of the BH molecule shows it to be very sensitive both to the choice of grid employed in the finite difference Hartree-Fock calculation and the construction of the basis set used in the matrix Hartree-Fock study. A new comparison of finite difference and finite basis set hyperpolarizabilities for the BH molecule is made, together with new calculations for the LiH and FH ground states.
An 'optimal' spawning algorithm for adaptive basis set expansion in nonadiabatic dynamics
Yang, Sandy; Coe, Joshua D.; Kaduk, Benjamin; Martinez, Todd J.
2009-04-07
The full multiple spawning (FMS) method has been developed to simulate quantum dynamics in the multistate electronic problem. In FMS, the nuclear wave function is represented in a basis of coupled, frozen Gaussians, and a 'spawning' procedure prescribes a means of adaptively increasing the size of this basis in order to capture population transfer between electronic states. Herein we detail a new algorithm for specifying the initial conditions of newly spawned basis functions that minimizes the number of spawned basis functions needed for convergence. 'Optimally' spawned basis functions are placed to maximize the coupling between parent and child trajectories at the point of spawning. The method is tested with a two-state, one-mode avoided crossing model and a two-state, two-mode conical intersection model.
Optical properties of alkali halide crystals from all-electron hybrid TD-DFT calculations
Webster, R. Harrison, N. M.; Bernasconi, L.
2015-06-07
We present a study of the electronic and optical properties of a series of alkali halide crystals AX, with A = Li, Na, K, Rb and X = F, Cl, Br based on a recent implementation of hybrid-exchange time-dependent density functional theory (TD-DFT) (TD-B3LYP) in the all-electron Gaussian basis set code CRYSTAL. We examine, in particular, the impact of basis set size and quality on the prediction of the optical gap and exciton binding energy. The formation of bound excitons by photoexcitation is observed in all the studied systems and this is shown to be correlated to specific features of the Hartree-Fock exchange component of the TD-DFT response kernel. All computed optical gaps and exciton binding energies are however markedly below estimated experimental and, where available, 2-particle Green’s function (GW-Bethe-Salpeter equation, GW-BSE) values. We attribute this reduced exciton binding to the incorrect asymptotics of the B3LYP exchange correlation ground state functional and of the TD-B3LYP response kernel, which lead to a large underestimation of the Coulomb interaction between the excited electron and hole wavefunctions. Considering LiF as an example, we correlate the asymptotic behaviour of the TD-B3LYP kernel to the fraction of Fock exchange admixed in the ground state functional c{sub HF} and show that there exists one value of c{sub HF} (∼0.32) that reproduces at least semi-quantitatively the optical gap of this material.
NASA Astrophysics Data System (ADS)
Betzinger, Markus; Friedrich, Christoph; Blügel, Stefan
2013-08-01
In a previous publication [Betzinger, Friedrich, Görling, and Blügel, Phys. Rev. BPRBMDO1098-012110.1103/PhysRevB.85.245124 85, 245124 (2012)] we presented a technique to compute accurate all-electron response functions, e.g., the density response function, within the full-potential linearized augmented-plane-wave (FLAPW) method. Response contributions that are not captured (completely) within the finite Hilbert space spanned by the LAPW basis are taken into account by an incomplete-basis-set correction (IBC). The latter is based on a formal response of the basis functions themselves, which is derived by exploiting their dependence on the effective potential. Its construction requires the solution of radial differential equations, having the form of Sternheimer equations, by numerical integration. The approach includes a formally exact treatment of the response contribution from the core states. While we restricted the formalism to spherical perturbations in the previous work, we here generalize the formalism to nonspherical perturbations. The improvements are demonstrated with exact-exchange optimized-effective-potential (EXX-OEP) calculations of antiferromagnetic NiO. It is shown that with the generalized IBC a basis-set convergence is realized that is as fast as in density-functional theory calculations using standard local or semilocal functionals. The EXX-OEP band gap, magnetic moment, and spectral function of NiO are in substantially better agreement with experiment than results obtained from calculations with local and semilocal functionals.
Simulating the oxygen content of ambient organic aerosol with the 2D volatility basis set
NASA Astrophysics Data System (ADS)
Murphy, B. N.; Donahue, N. M.; Fountoukis, C.; Pandis, S. N.
2011-08-01
A module predicting the oxidation state of organic aerosol (OA) has been developed using the two-dimensional volatility basis set (2D-VBS) framework. This model is an extension of the 1D-VBS framework and tracks saturation concentration and oxygen content of organic species during their atmospheric lifetime. The host model, a one-dimensional Lagrangian transport model, is used to simulate air parcels arriving at Finokalia, Greece during the Finokalia Aerosol Measurement Experiment in May 2008 (FAME-08). Extensive observations were collected during this campaign using an aerosol mass spectrometer (AMS) and a thermodenuder to determine the chemical composition and volatility, respectively, of the ambient OA. Although there are several uncertain model parameters, the consistently high oxygen content of OA measured during FAME-08 (O:C = 0.8) can help constrain these parameters and elucidate OA formation and aging processes that are necessary for achieving the high degree of oxygenation observed. The base-case model reproduces observed OA mass concentrations (measured mean = 3.1 μg m-3, predicted mean = 3.3 μg m-3) and O:C (predicted O:C = 0.78) accurately. A suite of sensitivity studies explore uncertainties due to (1) the anthropogenic secondary OA (SOA) aging rate constant, (2) assumed enthalpies of vaporization, (3) the volatility change and number of oxygen atoms added for each generation of aging, (4) heterogeneous chemistry, (5) the oxidation state of the first generation of compounds formed from SOA precursor oxidation, and (6) biogenic SOA aging. Perturbations in most of these parameters do impact the ability of the model to predict O:C well throughout the simulation period. By comparing measurements of the O:C from FAME-08, several sensitivity cases including a high oxygenation case, a low oxygenation case, and biogenic SOA aging case are found to unreasonably depict OA aging, keeping in mind that this study does not consider possibly important processes
Simulating the oxygen content of ambient organic aerosol with the 2D volatility basis set
NASA Astrophysics Data System (ADS)
Murphy, B. N.; Donahue, N. M.; Fountoukis, C.; Pandis, S. N.
2011-03-01
A module predicting the oxidation state of organic aerosol (OA) has been developed using the two-dimensional volatility basis set (2D-VBS) framework. This model is an extension of the 1D-VBS framework and tracks saturation concentration and oxygen content of organic species during their atmospheric lifetime. The host model, a one-dimensional Lagrangian transport model, is used to simulate air parcels arriving at Finokalia, Greece during the Finokalia Aerosol Measurement Experiment in May 2008 (FAME-08). Extensive observations were collected during this campaign using an aerosol mass spectrometer (AMS) and a thermodenuder to determine the chemical composition and volatility, respectively, of the ambient OA. Although there are several uncertain model parameters, the consistently high oxygen content of OA measured during FAME-08 (O:C = 0.8) can help constrain these parameters and elucidate OA formation and aging processes that are necessary for achieving the high degree of oxygenation observed. The base-case model reproduces observed OA mass concentrations (measured mean = 3.1 μg m-3, predicted mean = 3.3 μg m-3) and O:C ratio (predicted O:C = 0.78) accurately. A suite of sensitivity studies explore uncertainties due to (1) the anthropogenic secondary OA (SOA) aging rate constant, (2) assumed enthalpies of vaporization, (3) the volatility change and number of oxygen atoms added for each generation of aging, (4) heterogeneous chemistry, (5) the oxidation state of the first generation of compounds formed from SOA precursor oxidation, and (6) biogenic SOA aging. Perturbations in most of these parameters do impact the ability of the model to predict O:C ratios well throughout the simulation period. By comparing measurements of the O:C ratio from FAME-08, several sensitivity cases including a high oxygenation case, low oxygenation case, and biogenic SOA aging case are found to unreasonably depict OA aging. However, many of the cases chosen for this study predict average
A Complete Basis Set Estimate of Cation-p Bond Strengths: Na+(ethylene) and Na+(benzene)
Feller, David F.
2000-06-02
Large scale second order perturbation theory and couple cluster theory calculations were performed on the Na+(ethylene) and Na+(benzene) complexes in an effort to estimate binding enthalpies in the complete basis set limit. The resulting best estimates are DH0[Na+(ethylene)] = -13.7 ? 0.2 kcal/mol and DH0[Na+(benzene)] = -23.9 ? 0.3 kcal/mol, which include small corrections for core/valence correlation effects. The former value can be compared to a measurement of -10.3 ? 1.0 kcal/mol obtained from collision induced dissociation, while the latter value is approximately midway between the two existing experimental values which differed by 6.5 kcal/mol. For the basis sets considered in this study, the counterpoise-corrected binding energies were found to be in much worse agreement with the complete basis set limit than the raw values.
NASA Astrophysics Data System (ADS)
Turovtsev, V. V.; Orlov, Yu. D.; Tsirulev, A. N.
2015-08-01
The advantages of the orthonormal basis set of 2π-periodic Mathieu functions compared to the trigonometric basis set in calculations of torsional states of molecules are substantiated. Explicit expressions are derived for calculating the Hamiltonian matrix elements of a one-dimensional torsional Schrödinger equation with a periodic potential of the general form in the basis set of Mathieu functions. It is shown that variation of a parameter of Mathieu functions allows the rotation potential and the structural function to be approximated with a good accuracy by a small number of series terms. The conditions for the best choice of this parameter are specified, and approximations are obtained for torsional potentials of n-butane upon rotation about the central C-C bond and of its univalent radical n-butyl C2H5C·H2 upon rotation of the C·H2 group. All algorithms are implemented in the Maple package.
NASA Astrophysics Data System (ADS)
de Jong, W. A.; Harrison, R. J.; Dixon, D. A.
2001-01-01
A parallel implementation of the spin-free one-electron Douglas-Kroll-Hess (DKH) Hamiltonian in NWChem is discussed. An efficient and accurate method to calculate DKH gradients is introduced. It is shown that the use of a standard (nonrelativistic) contracted basis set can produce erroneous results for elements beyond the first row elements. The generation of DKH contracted cc-pVXZ(X=D,T,Q,5) basis sets for H, He, B-Ne, Al-Ar, and Ga-Br is discussed. The effect of DKH at the Hartree-Fock level on the bond distances, vibrational frequencies, and total dissociation energies for CF4, SiH4, SiF4, and Br2CO is discussed. It is suggested that the predominant effect of the scalar relativistic correction on the total dissociation energy can be calculated at the Hartree-Fock level if an adequate basis set is used.
Friese, Daniel H; Ringholm, Magnus; Gao, Bin; Ruud, Kenneth
2015-10-13
We present theory, implementation, and applications of a recursive scheme for the calculation of single residues of response functions that can treat perturbations that affect the basis set. This scheme enables the calculation of nonlinear light absorption properties to arbitrary order for other perturbations than an electric field. We apply this scheme for the first treatment of two-photon circular dichroism (TPCD) using London orbitals at the Hartree-Fock level of theory. In general, TPCD calculations suffer from the problem of origin dependence, which has so far been solved by using the velocity gauge for the electric dipole operator. This work now enables comparison of results from London orbital and velocity gauge based TPCD calculations. We find that the results from the two approaches both exhibit strong basis set dependence but that they are very similar with respect to their basis set convergence. PMID:26574270
Brorsen, Kurt R.; Sirjoosingh, Andrew; Pak, Michael V.; Hammes-Schiffer, Sharon
2015-06-07
The nuclear electronic orbital (NEO) reduced explicitly correlated Hartree-Fock (RXCHF) approach couples select electronic orbitals to the nuclear orbital via Gaussian-type geminal functions. This approach is extended to enable the use of a restricted basis set for the explicitly correlated electronic orbitals and an open-shell treatment for the other electronic orbitals. The working equations are derived and the implementation is discussed for both extensions. The RXCHF method with a restricted basis set is applied to HCN and FHF{sup −} and is shown to agree quantitatively with results from RXCHF calculations with a full basis set. The number of many-particle integrals that must be calculated for these two molecules is reduced by over an order of magnitude with essentially no loss in accuracy, and the reduction factor will increase substantially for larger systems. Typically, the computational cost of RXCHF calculations with restricted basis sets will scale in terms of the number of basis functions centered on the quantum nucleus and the covalently bonded neighbor(s). In addition, the RXCHF method with an odd number of electrons that are not explicitly correlated to the nuclear orbital is implemented using a restricted open-shell formalism for these electrons. This method is applied to HCN{sup +}, and the nuclear densities are in qualitative agreement with grid-based calculations. Future work will focus on the significance of nonadiabatic effects in molecular systems and the further enhancement of the NEO-RXCHF approach to accurately describe such effects.
De Jong, Wibe A.; Harrison, Robert J.; Dixon, David A.
2001-01-01
A parallel implementation of the spin-free one-electron Douglas-Kroll(-Hess) Hamiltonian (DKH) in NWChem is discussed. An efficient and accurate method to calculate DKH gradients is introduced. It is shown that the use of standard (non-relativistic) contracted basis set can produce erroneous results for elements beyond the first row elements. The generation of DKH contracted cc-pVXZ (X = D, T, Q, 5) basis sets for H, He, B - Ne, Al - Ar, and Ga - Br will be discussed.
Kollmar, Christian Neese, Frank
2014-10-07
The role of the static Kohn-Sham (KS) response function describing the response of the electron density to a change of the local KS potential is discussed in both the theory of the optimized effective potential (OEP) and the so-called inverse Kohn-Sham problem involving the task to find the local KS potential for a given electron density. In a general discussion of the integral equation to be solved in both cases, it is argued that a unique solution of this equation can be found even in case of finite atomic orbital basis sets. It is shown how a matrix representation of the response function can be obtained if the exchange-correlation potential is expanded in terms of a Schmidt-orthogonalized basis comprising orbitals products of occupied and virtual orbitals. The viability of this approach in both OEP theory and the inverse KS problem is illustrated by numerical examples.
Code of Federal Regulations, 2010 CFR
2010-10-01
... 42 Public Health 3 2010-10-01 2010-10-01 false Conditions for payment on a fee schedule basis for physician services in a teaching setting. 415.170 Section 415.170 Public Health CENTERS FOR MEDICARE & MEDICAID SERVICES, DEPARTMENT OF HEALTH AND HUMAN SERVICES (CONTINUED) MEDICARE PROGRAM SERVICES FURNISHED BY PHYSICIANS IN PROVIDERS,...
Holocene sea level variations on the basis of integration of independent data sets
Sahagian, D.; Berkman, P. . Dept. of Geological Sciences and Byrd Polar Research Center)
1992-01-01
Variations in sea level through earth history have occurred at a wide variety of time scales. Sea level researchers have attacked the problem of measuring these sea level changes through a variety of approaches, each relevant only to the time scale in question, and usually only relevant to the specific locality from which a specific type of data are derived. There is a plethora of different data types that can and have been used (locally) for the measurement of Holocene sea level variations. The problem of merging different data sets for the purpose of constructing a global eustatic sea level curve for the Holocene has not previously been adequately addressed. The authors direct the efforts to that end. Numerous studies have been published regarding Holocene sea level changes. These have involved exposed fossil reef elevations, elevation of tidal deltas, elevation of depth of intertidal peat deposits, caves, tree rings, ice cores, moraines, eolian dune ridges, marine-cut terrace elevations, marine carbonate species, tide gauges, and lake level variations. Each of these data sets is based on particular set of assumptions, and is valid for a specific set of environments. In order to obtain the most accurate possible sea level curve for the Holocene, these data sets must be merged so that local and other influences can be filtered out of each data set. Since each data set involves very different measurements, each is scaled in order to define the sensitivity of the proxy measurement parameter to sea level, including error bounds. This effectively determines the temporal and spatial resolution of each data set. The level of independence of data sets is also quantified, in order to rule out the possibility of a common non-eustatic factor affecting more than one variety of data. The Holocene sea level curve is considered to be independent of other factors affecting the proxy data, and is taken to represent the relation between global ocean water and basin volumes.
NASA Astrophysics Data System (ADS)
Witte, Jonathon; Neaton, Jeffrey B.; Head-Gordon, Martin
2016-05-01
With the aim of systematically characterizing the convergence of common families of basis sets such that general recommendations for basis sets can be made, we have tested a wide variety of basis sets against complete-basis binding energies across the S22 set of intermolecular interactions—noncovalent interactions of small and medium-sized molecules consisting of first- and second-row atoms—with three distinct density functional approximations: SPW92, a form of local-density approximation; B3LYP, a global hybrid generalized gradient approximation; and B97M-V, a meta-generalized gradient approximation with nonlocal correlation. We have found that it is remarkably difficult to reach the basis set limit; for the methods and systems examined, the most complete basis is Jensen's pc-4. The Dunning correlation-consistent sequence of basis sets converges slowly relative to the Jensen sequence. The Karlsruhe basis sets are quite cost effective, particularly when a correction for basis set superposition error is applied: counterpoise-corrected def2-SVPD binding energies are better than corresponding energies computed in comparably sized Dunning and Jensen bases, and on par with uncorrected results in basis sets 3-4 times larger. These trends are exhibited regardless of the level of density functional approximation employed. A sense of the magnitude of the intrinsic incompleteness error of each basis set not only provides a foundation for guiding basis set choice in future studies but also facilitates quantitative comparison of existing studies on similar types of systems.
Brandenburg, Jan Gerit; Alessio, Maristella; Civalleri, Bartolomeo; Peintinger, Michael F; Bredow, Thomas; Grimme, Stefan
2013-09-26
We extend the previously developed geometrical correction for the inter- and intramolecular basis set superposition error (gCP) to periodic density functional theory (DFT) calculations. We report gCP results compared to those from the standard Boys-Bernardi counterpoise correction scheme and large basis set calculations. The applicability of the method to molecular crystals as the main target is tested for the benchmark set X23. It consists of 23 noncovalently bound crystals as introduced by Johnson et al. (J. Chem. Phys. 2012, 137, 054103) and refined by Tkatchenko et al. (J. Chem. Phys. 2013, 139, 024705). In order to accurately describe long-range electron correlation effects, we use the standard atom-pairwise dispersion correction scheme DFT-D3. We show that a combination of DFT energies with small atom-centered basis sets, the D3 dispersion correction, and the gCP correction can accurately describe van der Waals and hydrogen-bonded crystals. Mean absolute deviations of the X23 sublimation energies can be reduced by more than 70% and 80% for the standard functionals PBE and B3LYP, respectively, to small residual mean absolute deviations of about 2 kcal/mol (corresponding to 13% of the average sublimation energy). As a further test, we compute the interlayer interaction of graphite for varying distances and obtain a good equilibrium distance and interaction energy of 6.75 Å and -43.0 meV/atom at the PBE-D3-gCP/SVP level. We fit the gCP scheme for a recently developed pob-TZVP solid-state basis set and obtain reasonable results for the X23 benchmark set and the potential energy curve for water adsorption on a nickel (110) surface. PMID:23947824
NASA Astrophysics Data System (ADS)
Ma, Zhonghua; Zhang, Yanli; Tuckerman, Mark E.
2012-07-01
It is generally believed that studies of liquid water using the generalized gradient approximation to density functional theory require dispersion corrections in order to obtain reasonably accurate structural and dynamical properties. Here, we report on an ab initio molecular dynamics study of water in the isothermal-isobaric ensemble using a converged discrete variable representation basis set and an empirical dispersion correction due to Grimme [J. Comp. Chem. 27, 1787 (2006)], 10.1002/jcc.20495. At 300 K and an applied pressure of 1 bar, the density obtained without dispersion corrections is approximately 0.92 g/cm3 while that obtained with dispersion corrections is 1.07 g/cm3, indicating that the empirical dispersion correction overestimates the density by almost as much as it is underestimated without the correction for this converged basis. Radial distribution functions exhibit a loss of structure in the second solvation shell. Comparison of our results with other studies using the same empirical correction suggests the cause of the discrepancy: the Grimme dispersion correction is parameterized for use with a particular basis set; this parameterization is sensitive to this choice and, therefore, is not transferable to other basis sets.
NASA Astrophysics Data System (ADS)
Yang, Yue; Weaver, Michael N.; Merz, Kenneth M.
2009-08-01
Computational chemists have long demonstrated great interest in finding ways to reliably and accurately predict the molecular properties for transition-metal-containing complexes. This study is a continuation of our validation efforts of density functional theory (DFT) methods when applied to transition-metal-containing systems (Riley, K.E.; Merz, K. M., Jr. J. Phys. Chem. 2007, 111, 6044-6053). In our previous work we examined DFT using all-electron basis sets, but approaches incorporating effective core potentials (ECPs) are effective in reducing computational expense. With this in mind, our efforts were expanded to include evaluation of the performance of the basis set derived to approximate such an approach as well on the same set of density functionals. Indeed, employing an ECP basis such as LANL2DZ (Los Alamos National Laboratory 2 double ζ) for transition metals, while using all-electron basis sets for all other non-transition-metal atoms, has become more and more popular in computations on transition-metal-containing systems. In this study, we assess the performance of 12 different DFT functionals, from the GGA (generalized gradient approximation), hybrid-GGA, meta-GGA, and hybrid-meta-GGA classes, respectively, along with the 6-31+G** + LANL2DZ (on the transition metal) mixed basis set in predicting two important molecular properties, heats of formation and ionization potentials, for 94 and 58 systems containing first-row transition metals from Ti to Zn, which are all in the third row of the periodic table. An interesting note is that the inclusion of the exact exchange term in density functional methods generally increases the accuracy of ionization potential prediction for the hybrid-GGA methods but decreases the reliability of determining the heats of formation for transition-metal-containing complexes for all hybrid density functional methods. The hybrid-GGA functional B3LYP gives the best performance in predicting the ionization potentials, while the
Solving the Dirac equation, using the large component only, in a Dirac-type Slater orbital basis set
NASA Astrophysics Data System (ADS)
van Lenthe, E.; Baerends, E. J.; Snijders, J. G.
1995-04-01
We solve the Dirac equation by solving the two-component energy-dependent equation for the large component that results from the elimination of the small component. This requires for every occupied orbital the diagonalization of a Hamiltonian. Advantages are, however, that these Hamiltonians are all bounded from below, unlike the Dirac Hamiltonian, and that only a basis set for the large component is needed. We use Dirac-type Slater orbitals, adapted from solutions to the hydrogen-like atom. This offers the perspective of performing relativistic calculations to the same accuracy as non-relativistic ones, with a comparable number of basis functions.
Non-homogeneous solutions of a Coulomb Schrödinger equation as basis set for scattering problems
Del Punta, J. A.; Ambrosio, M. J.; Gasaneo, G.; Zaytsev, S. A.; Ancarani, L. U.
2014-05-15
We introduce and study two-body Quasi Sturmian functions which are proposed as basis functions for applications in three-body scattering problems. They are solutions of a two-body non-homogeneous Schrödinger equation. We present different analytic expressions, including asymptotic behaviors, for the pure Coulomb potential with a driven term involving either Slater-type or Laguerre-type orbitals. The efficiency of Quasi Sturmian functions as basis set is numerically illustrated through a two-body scattering problem.
NASA Astrophysics Data System (ADS)
Heaps, Charles W.; Mazziotti, David A.
2016-08-01
Quantum molecular dynamics requires an accurate representation of the molecular potential energy surface from a minimal number of electronic structure calculations, particularly for nonadiabatic dynamics where excited states are required. In this paper, we employ pseudospectral sampling of time-dependent Gaussian basis functions for the simulation of non-adiabatic dynamics. Unlike other methods, the pseudospectral Gaussian molecular dynamics tests the Schrödinger equation with N Dirac delta functions located at the centers of the Gaussian functions reducing the scaling of potential energy evaluations from O ( N 2 ) to O ( N ) . By projecting the Gaussian basis onto discrete points in space, the method is capable of efficiently and quantitatively describing the nonadiabatic population transfer and intra-surface quantum coherence. We investigate three model systems: the photodissociation of three coupled Morse oscillators, the bound state dynamics of two coupled Morse oscillators, and a two-dimensional model for collinear triatomic vibrational dynamics. In all cases, the pseudospectral Gaussian method is in quantitative agreement with numerically exact calculations. The results are promising for nonadiabatic molecular dynamics in molecular systems where strongly correlated ground or excited states require expensive electronic structure calculations.
NASA Astrophysics Data System (ADS)
Zhang, Jun; Dolg, Michael
2014-01-01
The third-order incremental dual-basis set zero-buffer approach was combined with CCSD(T)-F12x (x = a, b) theory to develop a new approach, i.e., the inc3-db-B0-CCSD(T)-F12 method, which can be applied as a black-box procedure to efficiently obtain the near complete basis set (CBS) limit of the CCSD(T) energies also for large systems. We tested this method for several cases of different chemical nature: four complexes taken from the standard benchmark sets S66 and X40, the energy difference between isomers of water hexamer and the rotation barrier of biphenyl. The results show that our method has an error relative to the best estimation of CBS energy of only 0.2 kcal/mol or less. By parallelization, our method can accomplish the CCSD(T)-F12 calculations of about 60 correlated electrons and 800 basis functions in only several days, which by standard implementation are impossible for ordinary hardware. We conclude that the inc3-db-B0-CCSD(T)-F12a/AVTZ method, which is of CCSD(T)/AV5Z quality, is close to the limit of accuracy that one can achieve for large systems currently.
Zhang, Jun Dolg, Michael
2014-01-28
The third-order incremental dual-basis set zero-buffer approach was combined with CCSD(T)-F12x (x = a, b) theory to develop a new approach, i.e., the inc3-db-B0-CCSD(T)-F12 method, which can be applied as a black-box procedure to efficiently obtain the near complete basis set (CBS) limit of the CCSD(T) energies also for large systems. We tested this method for several cases of different chemical nature: four complexes taken from the standard benchmark sets S66 and X40, the energy difference between isomers of water hexamer and the rotation barrier of biphenyl. The results show that our method has an error relative to the best estimation of CBS energy of only 0.2 kcal/mol or less. By parallelization, our method can accomplish the CCSD(T)-F12 calculations of about 60 correlated electrons and 800 basis functions in only several days, which by standard implementation are impossible for ordinary hardware. We conclude that the inc3-db-B0-CCSD(T)-F12a/AVTZ method, which is of CCSD(T)/AV5Z quality, is close to the limit of accuracy that one can achieve for large systems currently.
NASA Astrophysics Data System (ADS)
Purwanto, Wirawan; Krakauer, Henry; Zhang, Shiwei; Virgus, Yudistira
2011-03-01
Weak H2 physisorption energies present a significant challenge to first-principle theoretical modeling and prediction of materials for H storage. There has been controversy regarding the accuracy of DFT on systems involving Ca cations. We use the auxiliary-field quantum Monte Carlo (AFQMC) method to accurately predict the binding energy of Ca + , - 4{H}2 . AFQMC scales as Nbasis3and has demonstrated accuracy similar to or better than the gold-standard coupled cluster CCSD(T) method. We apply a modified Cholesky decomposition to achieve efficient Hubbard-Stratonovich transformation in AFQMC at large basis sizes. We employ the largest correlation consistent basis sets available, up to Ca/cc-pCV5Z, to extrapolate to the complete basis limit. The calculated potential energy curve exhibits binding with a double-well structure. Supported by DOE and NSF. Calculations were performed at OLCF Jaguar and CPD.
Liquid Water through Density-Functional Molecular Dynamics: Plane-Wave vs Atomic-Orbital Basis Sets.
Miceli, Giacomo; Hutter, Jürg; Pasquarello, Alfredo
2016-08-01
We determine and compare structural, dynamical, and electronic properties of liquid water at near ambient conditions through density-functional molecular dynamics simulations, when using either plane-wave or atomic-orbital basis sets. In both frameworks, the electronic structure and the atomic forces are self-consistently determined within the same theoretical scheme based on a nonlocal density functional accounting for van der Waals interactions. The overall properties of liquid water achieved within the two frameworks are in excellent agreement with each other. Thus, our study supports that implementations with plane-wave or atomic-orbital basis sets yield equivalent results and can be used indiscriminately in study of liquid water or aqueous solutions. PMID:27434607
Macedo, Luiz Guilherme M de Borin, Antonio Carlos; Silva, Alberico B.F. da
2007-11-15
Prolapse-free basis sets suitable for four-component relativistic quantum chemical calculations are presented for the superheavy elements up to {sub 118}Uuo ({sub 104}Rf, {sub 105}Db, {sub 106}Sg, {sub 107}Bh, {sub 108}Hs, {sub 109}Mt, {sub 110}Ds, {sub 111}Rg, {sub 112}Uub, {sub 113}Uut, {sub 114}Uuq, {sub 115}Uup, {sub 116}Uuh, {sub 117}Uus, {sub 118}Uuo) and {sub 103}Lr. These basis sets were optimized by minimizing the absolute values of the energy difference between the Dirac-Fock-Roothaan total energy and the corresponding numerical value at a milli-Hartree order of magnitude, resulting in a good balance between cost and accuracy. Parameters for generating exponents and new numerical data for some superheavy elements are also presented.
NASA Technical Reports Server (NTRS)
Almloef, Jan; Taylor, Peter R.
1989-01-01
A recently proposed scheme for using natural orbitals from atomic configuration interaction (CI) wave functions as a basis set for linear combination of atomic orbitals (LCAO) calculations is extended for the calculation of molecular properties. For one-electron properties like multipole moments, which are determined largely by the outermost regions of the molecular wave function, it is necessary to increase the flexibility of the basis in these regions. This is most easily done by uncontracting the outmost Gaussian primitives, and/or by adding diffuse primitives. A similar approach can be employed for the calculation of polarizabilities. Properties which are not dominated by the long-range part of the wave function, such as spectroscopic constants or electric field gradients at the nucleus, can generally be treated satisfactorily with the original atomic natural orbital (ANO) sets.
NASA Technical Reports Server (NTRS)
Almlof, Jan; Taylor, Peter R.
1990-01-01
A recently proposed scheme for using natural orbitals from atomic configuration interaction wave functions as a basis set for linear combination of atomic orbitals (LCAO) calculations is extended for the calculation of molecular properties. For one-electron properties like multipole moments, which are determined largely by the outermost regions of the molecular wave function, it is necessary to increase the flexibility of the basis in these regions. This is most easily done by uncontracting the outermost Gaussian primitives, and/or by adding diffuse primitives. A similar approach can be employed for the calculation of polarizabilities. Properties which are not dominated by the long-range part of the wave function, such as spectroscopic constants or electric field gradients at the nucleus, can generally be treated satisfactorily with the original atomic natural orbital sets.
NASA Astrophysics Data System (ADS)
de Silva, Piotr; Wesolowski, Tomasz A.
2012-03-01
Within the linear combination of atomic orbitals (LCAO) approximation, one can distinguish two different Kohn-Sham potentials. One is the potential available numerically in calculations, and the other is the exact potential corresponding to the LCAO density. The latter is usually not available, but can be obtained from the total density by a numerical inversion procedure or, as is done here, analytically using only one LCAO Kohn-Sham orbital. In the complete basis-set limit, the lowest-lying Kohn-Sham orbital suffices to perform the analytical inversion, and the two potentials differ by no more than a constant. The relation between these two potentials is investigated here for diatomic molecules and several atomic basis sets of increasing size and quality. The differences between the two potentials are usually qualitative (wrong behavior at nuclear cusps and far from the molecule even if Slater-type orbitals are used) and δ-like features at nodal planes of the lowest-lying LCAO Kohn-Sham orbital. Such nodes occur frequently in LCAO calculations and are not physical. Whereas the behavior of the potential can be systematically improved locally by the increase of the basis sets, the occurrence of nodes is not correlated with the size of the basis set. The presence of nodes in the lowest-lying LCAO orbital can be used to monitor whether the effective potential in LCAO Kohn-Sham equations can be interpreted as the potential needed for pure-state noninteracting v-representability of the LCAO density. Squares of such node-containing lowest-lying LCAO Kohn-Sham orbitals are nontrivial examples of two-electron densities which are not pure-state noninteracting v-representable.
NASA Astrophysics Data System (ADS)
Kolmann, Stephen J.; Jordan, Meredith J. T.
2010-02-01
One of the largest remaining errors in thermochemical calculations is the determination of the zero-point energy (ZPE). The fully coupled, anharmonic ZPE and ground state nuclear wave function of the SSSH radical are calculated using quantum diffusion Monte Carlo on interpolated potential energy surfaces (PESs) constructed using a variety of method and basis set combinations. The ZPE of SSSH, which is approximately 29 kJ mol-1 at the CCSD(T)/6-31G∗ level of theory, has a 4 kJ mol-1 dependence on the treatment of electron correlation. The anharmonic ZPEs are consistently 0.3 kJ mol-1 lower in energy than the harmonic ZPEs calculated at the Hartree-Fock and MP2 levels of theory, and 0.7 kJ mol-1 lower in energy at the CCSD(T)/6-31G∗ level of theory. Ideally, for sub-kJ mol-1 thermochemical accuracy, ZPEs should be calculated using correlated methods with as big a basis set as practicable. The ground state nuclear wave function of SSSH also has significant method and basis set dependence. The analysis of the nuclear wave function indicates that SSSH is localized to a single symmetry equivalent global minimum, despite having sufficient ZPE to be delocalized over both minima. As part of this work, modifications to the interpolated PES construction scheme of Collins and co-workers are presented.
Kolmann, Stephen J; Jordan, Meredith J T
2010-02-01
One of the largest remaining errors in thermochemical calculations is the determination of the zero-point energy (ZPE). The fully coupled, anharmonic ZPE and ground state nuclear wave function of the SSSH radical are calculated using quantum diffusion Monte Carlo on interpolated potential energy surfaces (PESs) constructed using a variety of method and basis set combinations. The ZPE of SSSH, which is approximately 29 kJ mol(-1) at the CCSD(T)/6-31G* level of theory, has a 4 kJ mol(-1) dependence on the treatment of electron correlation. The anharmonic ZPEs are consistently 0.3 kJ mol(-1) lower in energy than the harmonic ZPEs calculated at the Hartree-Fock and MP2 levels of theory, and 0.7 kJ mol(-1) lower in energy at the CCSD(T)/6-31G* level of theory. Ideally, for sub-kJ mol(-1) thermochemical accuracy, ZPEs should be calculated using correlated methods with as big a basis set as practicable. The ground state nuclear wave function of SSSH also has significant method and basis set dependence. The analysis of the nuclear wave function indicates that SSSH is localized to a single symmetry equivalent global minimum, despite having sufficient ZPE to be delocalized over both minima. As part of this work, modifications to the interpolated PES construction scheme of Collins and co-workers are presented. PMID:20136303
Řezáč, Jan; de la Lande, Aurélien
2015-02-10
Separation of the energetic contribution of charge transfer to interaction energy in noncovalent complexes would provide important insight into the mechanisms of the interaction. However, the calculation of charge-transfer energy is not an easy task. It is not a physically well-defined term, and the results might depend on how it is described in practice. Commonly, the charge transfer is defined in terms of molecular orbitals; in this framework, however, the charge transfer vanishes as the basis set size increases toward the complete basis set limit. This can be avoided by defining the charge transfer in terms of the spatial extent of the electron densities of the interacting molecules, but the schemes used so far do not reflect the actual electronic structure of each particular system and thus are not reliable. We propose a spatial partitioning of the system, which is based on a charge transfer-free reference state, namely superimposition of electron densities of the noninteracting fragments. We show that this method, employing constrained DFT for the calculation of the charge-transfer energy, yields reliable results and is robust with respect to the strength of the charge transfer, the basis set size, and the DFT functional used. Because it is based on DFT, the method is applicable to rather large systems. PMID:26580910
[The BASYS observation system for the analysis of aggressive behavior in classroom-settings].
Wettstein, Alexander
2012-01-01
Educational or therapeutic measures of aggressive student behavior are often based on the judgments of teachers. However, empirical studies show that the objectivity of these judgments is generally low. In order to assess aggressive behavior in classroom settings, we developed a context-sensitive observational system. The observation system exists in a version for teachers in action as well as a version for the uninvolved observer. The teacher version allows categorizing aggressive behavior while teaching. The aim is to differentiate the perception and the judgments of teachers, so that the judgments can serve as trustable diagnostic information. The version for an independent observer, in addition, contains categories to collect information about the context in which aggressions take place. The behavior observation system was tested in four field-studies in regular and special classes. The empirical results show that, after training, teachers were able to make objective observations, and that aggressive behavior depends to a large extent on situational factors. The system allows identification of problematic people-environment relationships and the derivation of intervention measures. PMID:22748725
Ermler, Walter V.; Tilson, Jeffrey L.
2012-12-15
A procedure for structuring generally contracted valence-core/valence basis sets of Gaussian-type functions for use with relativistic effective core potentials (gcv-c/v-RECP basis sets) is presented. Large valence basis sets are enhanced using a compact basis set derived for outer core electrons in the presence of small-core RECPs. When core electrons are represented by relativistic effective core potentials (RECPs), and appropriate levels of theory, these basis sets are shown to provide accurate representations of atomic and molecular valence and outer-core electrons. Core/valence polarization and correlation effects can be calculated using these basis sets through standard methods for treating electron correlation. Calculations of energies and spectra for Ru, Os, Ir, In and Cs are reported. Spectroscopic constants for RuO2+, OsO2+, Cs2 and InH are calculated and compared with experiment.
Rapid Bacterial Detection via an All-Electronic CMOS Biosensor.
Nikkhoo, Nasim; Cumby, Nichole; Gulak, P Glenn; Maxwell, Karen L
2016-01-01
The timely and accurate diagnosis of infectious diseases is one of the greatest challenges currently facing modern medicine. The development of innovative techniques for the rapid and accurate identification of bacterial pathogens in point-of-care facilities using low-cost, portable instruments is essential. We have developed a novel all-electronic biosensor that is able to identify bacteria in less than ten minutes. This technology exploits bacteriocins, protein toxins naturally produced by bacteria, as the selective biological detection element. The bacteriocins are integrated with an array of potassium-selective sensors in Complementary Metal Oxide Semiconductor technology to provide an inexpensive bacterial biosensor. An electronic platform connects the CMOS sensor to a computer for processing and real-time visualization. We have used this technology to successfully identify both Gram-positive and Gram-negative bacteria commonly found in human infections. PMID:27618185
Witte, Jonathon; Neaton, Jeffrey B; Head-Gordon, Martin
2016-05-21
With the aim of systematically characterizing the convergence of common families of basis sets such that general recommendations for basis sets can be made, we have tested a wide variety of basis sets against complete-basis binding energies across the S22 set of intermolecular interactions-noncovalent interactions of small and medium-sized molecules consisting of first- and second-row atoms-with three distinct density functional approximations: SPW92, a form of local-density approximation; B3LYP, a global hybrid generalized gradient approximation; and B97M-V, a meta-generalized gradient approximation with nonlocal correlation. We have found that it is remarkably difficult to reach the basis set limit; for the methods and systems examined, the most complete basis is Jensen's pc-4. The Dunning correlation-consistent sequence of basis sets converges slowly relative to the Jensen sequence. The Karlsruhe basis sets are quite cost effective, particularly when a correction for basis set superposition error is applied: counterpoise-corrected def2-SVPD binding energies are better than corresponding energies computed in comparably sized Dunning and Jensen bases, and on par with uncorrected results in basis sets 3-4 times larger. These trends are exhibited regardless of the level of density functional approximation employed. A sense of the magnitude of the intrinsic incompleteness error of each basis set not only provides a foundation for guiding basis set choice in future studies but also facilitates quantitative comparison of existing studies on similar types of systems. PMID:27208948
Structural basis for inhibition of the histone chaperone activity of SET/TAF-Iβ by cytochrome c
González-Arzola, Katiuska; Díaz-Moreno, Irene; Cano-González, Ana; Díaz-Quintana, Antonio; Velázquez-Campoy, Adrián; Moreno-Beltrán, Blas; López-Rivas, Abelardo; De la Rosa, Miguel A.
2015-01-01
Chromatin is pivotal for regulation of the DNA damage process insofar as it influences access to DNA and serves as a DNA repair docking site. Recent works identify histone chaperones as key regulators of damaged chromatin’s transcriptional activity. However, understanding how chaperones are modulated during DNA damage response is still challenging. This study reveals that the histone chaperone SET/TAF-Iβ interacts with cytochrome c following DNA damage. Specifically, cytochrome c is shown to be translocated into cell nuclei upon induction of DNA damage, but not upon stimulation of the death receptor or stress-induced pathways. Cytochrome c was found to competitively hinder binding of SET/TAF-Iβ to core histones, thereby locking its histone-binding domains and inhibiting its nucleosome assembly activity. In addition, we have used NMR spectroscopy, calorimetry, mutagenesis, and molecular docking to provide an insight into the structural features of the formation of the complex between cytochrome c and SET/TAF-Iβ. Overall, these findings establish a framework for understanding the molecular basis of cytochrome c-mediated blocking of SET/TAF-Iβ, which subsequently may facilitate the development of new drugs to silence the oncogenic effect of SET/TAF-Iβ’s histone chaperone activity. PMID:26216969
Structural basis for inhibition of the histone chaperone activity of SET/TAF-Iβ by cytochrome c.
González-Arzola, Katiuska; Díaz-Moreno, Irene; Cano-González, Ana; Díaz-Quintana, Antonio; Velázquez-Campoy, Adrián; Moreno-Beltrán, Blas; López-Rivas, Abelardo; De la Rosa, Miguel A
2015-08-11
Chromatin is pivotal for regulation of the DNA damage process insofar as it influences access to DNA and serves as a DNA repair docking site. Recent works identify histone chaperones as key regulators of damaged chromatin's transcriptional activity. However, understanding how chaperones are modulated during DNA damage response is still challenging. This study reveals that the histone chaperone SET/TAF-Iβ interacts with cytochrome c following DNA damage. Specifically, cytochrome c is shown to be translocated into cell nuclei upon induction of DNA damage, but not upon stimulation of the death receptor or stress-induced pathways. Cytochrome c was found to competitively hinder binding of SET/TAF-Iβ to core histones, thereby locking its histone-binding domains and inhibiting its nucleosome assembly activity. In addition, we have used NMR spectroscopy, calorimetry, mutagenesis, and molecular docking to provide an insight into the structural features of the formation of the complex between cytochrome c and SET/TAF-Iβ. Overall, these findings establish a framework for understanding the molecular basis of cytochrome c-mediated blocking of SET/TAF-Iβ, which subsequently may facilitate the development of new drugs to silence the oncogenic effect of SET/TAF-Iβ's histone chaperone activity. PMID:26216969
Sakhanenko, Nikita A.; Skupin, Alexander; Ignac, Tomasz
2014-01-01
Abstract Context dependence is central to the description of complexity. Keying on the pairwise definition of “set complexity,” we use an information theory approach to formulate general measures of systems complexity. We examine the properties of multivariable dependency starting with the concept of interaction information. We then present a new measure for unbiased detection of multivariable dependency, “differential interaction information.” This quantity for two variables reduces to the pairwise “set complexity” previously proposed as a context-dependent measure of information in biological systems. We generalize it here to an arbitrary number of variables. Critical limiting properties of the “differential interaction information” are key to the generalization. This measure extends previous ideas about biological information and provides a more sophisticated basis for the study of complexity. The properties of “differential interaction information” also suggest new approaches to data analysis. Given a data set of system measurements, differential interaction information can provide a measure of collective dependence, which can be represented in hypergraphs describing complex system interaction patterns. We investigate this kind of analysis using simulated data sets. The conjoining of a generalized set complexity measure, multivariable dependency analysis, and hypergraphs is our central result. While our focus is on complex biological systems, our results are applicable to any complex system. PMID:24377753
NASA Astrophysics Data System (ADS)
Feller, David; Peterson, Kirk A.
2013-08-01
The effectiveness of the recently developed, explicitly correlated coupled cluster method CCSD(T)-F12b is examined in terms of its ability to reproduce atomization energies derived from complete basis set extrapolations of standard CCSD(T). Most of the standard method findings were obtained with aug-cc-pV7Z or aug-cc-pV8Z basis sets. For a few homonuclear diatomic molecules it was possible to push the basis set to the aug-cc-pV9Z level. F12b calculations were performed with the cc-pVnZ-F12 (n = D, T, Q) basis set sequence and were also extrapolated to the basis set limit using a Schwenke-style, parameterized formula. A systematic bias was observed in the F12b method with the (VTZ-F12/VQZ-F12) basis set combination. This bias resulted in the underestimation of reference values associated with small molecules (valence correlation energies <0.5 Eh) and an even larger overestimation of atomization energies for bigger systems. Consequently, caution should be exercised in the use of F12b for high accuracy studies. Root mean square and mean absolute deviation error metrics for this basis set combination were comparable to complete basis set values obtained with standard CCSD(T) and the aug-cc-pVDZ through aug-cc-pVQZ basis set sequence. However, the mean signed deviation was an order of magnitude larger. Problems partially due to basis set superposition error were identified with second row compounds which resulted in a weak performance for the smaller VDZ-F12/VTZ-F12 combination of basis sets.
Storchi, Loriano; Rampino, Sergio; Belpassi, Leonardo; Tarantelli, Francesco; Quiney, Harry M
2013-12-10
We propose a new complete memory-distributed algorithm, which significantly improves the parallel implementation of the all-electron four-component Dirac-Kohn-Sham (DKS) module of BERTHA (J. Chem. Theory Comput. 2010, 6, 384). We devised an original procedure for mapping the DKS matrix between an efficient integral-driven distribution, guided by the structure of specific G-spinor basis sets and by density fitting algorithms, and the two-dimensional block-cyclic distribution scheme required by the ScaLAPACK library employed for the linear algebra operations. This implementation, because of the efficiency in the memory distribution, represents a leap forward in the applicability of the DKS procedure to arbitrarily large molecular systems and its porting on last-generation massively parallel systems. The performance of the code is illustrated by some test calculations on several gold clusters of increasing size. The DKS self-consistent procedure has been explicitly converged for two representative clusters, namely Au20 and Au34, for which the density of electronic states is reported and discussed. The largest gold cluster uses more than 39k basis functions and DKS matrices of the order of 23 GB. PMID:26592273
Yao, Y. X.; Wang, C. Z.; Ho, K. M.
2010-06-16
A chemical bonding scheme is presented for the analysis of solid-state systems. The scheme is based on the intrinsic oriented quasiatomic minimal-basis-set orbitals (IO-QUAMBOs) previously developed by Ivanic and Ruedenberg for molecular systems. In the solid-state scheme, IO-QUAMBOs are generated by a unitary transformation of the quasiatomic orbitals located at each site of the system with the criteria of maximizing the sum of the fourth power of interatomic orbital bond order. Possible bonding and antibonding characters are indicated by the single particle matrix elements, and can be further examined by the projected density of states. We demonstrate the method by applications to graphene and (6,0) zigzag carbon nanotube. The oriented-orbital scheme automatically describes the system in terms of sp{sup 2} hybridization. The effect of curvature on the electronic structure of the zigzag carbon nanotube is also manifested in the deformation of the intrinsic oriented orbitals as well as a breaking of symmetry leading to nonzero single particle density matrix elements. In an additional study, the analysis is performed on the Al{sub 3}V compound. The main covalent bonding characters are identified in a straightforward way without resorting to the symmetry analysis. Our method provides a general way for chemical bonding analysis of ab initio electronic structure calculations with any type of basis sets.
Relaxation of Actinide Surfaces: An All Electron Study
NASA Astrophysics Data System (ADS)
Atta-Fynn, Raymond; Dholabhai, Pratik; Ray, Asok
2006-10-01
Fully relativistic full potential density functional calculations with a linearized augmented plane wave plus local orbitals basis (LAPW + lo) have been performed to investigate the relaxations of heavy actinide surfaces, namely the (111) surface of fcc δ-Pu and the (0001) surface of dhcp Am using WIEN2k. This code uses the LAPW + lo method with the unit cell divided into non-overlapping atom-centered spheres and an interstitial region. The APW+lo basis is used to describe all s, p, d, and f states and LAPW basis to describe all higher angular momentum states. Each surface was modeled by a three-layer periodic slab separated by 60 Bohr vacuum with four atoms per surface unit cell. In general, we have found a contraction of the interlayer separations for both Pu and Am. We will report, in detail, the electronic and geometric structures of the relaxed surfaces and comparisons with the respective non-relaxed surfaces.
Label-free all-electronic biosensing in microfluidic systems
NASA Astrophysics Data System (ADS)
Stanton, Michael A.
Label-free, all-electronic detection techniques offer great promise for advancements in medical and biological analysis. Electrical sensing can be used to measure both interfacial and bulk impedance changes in conducting solutions. Electronic sensors produced using standard microfabrication processes are easily integrated into microfluidic systems. Combined with the sensitivity of radiofrequency electrical measurements, this approach offers significant advantages over competing biological sensing methods. Scalable fabrication methods also provide a means of bypassing the prohibitive costs and infrastructure associated with current technologies. We describe the design, development and use of a radiofrequency reflectometer integrated into a microfluidic system towards the specific detection of biologically relevant materials. We developed a detection protocol based on impedimetric changes caused by the binding of antibody/antigen pairs to the sensing region. Here we report the surface chemistry that forms the necessary capture mechanism. Gold-thiol binding was utilized to create an ordered alkane monolayer on the sensor surface. Exposed functional groups target the N-terminus, affixing a protein to the monolayer. The general applicability of this method lends itself to a wide variety of proteins. To demonstrate specificity, commercially available mouse anti- Streptococcus Pneumoniae monoclonal antibody was used to target the full-length recombinant pneumococcal surface protein A, type 2 strain D39 expressed by Streptococcus Pneumoniae. We demonstrate the RF response of the sensor to both the presence of the surface decoration and bound SPn cells in a 1x phosphate buffered saline solution. The combined microfluidic sensor represents a powerful platform for the analysis and detection of cells and biomolecules.
Seijo, Luis; Barandiarán, Zoila
2004-10-01
We present a linear scaling method for the energy minimization step of semiempirical and first-principles Hartree-Fock and Kohn-Sham calculations. It is based on the self-consistent calculation of the optimum localized orbitals of any localization method of choice and on the use of orbital-specific basis sets. The full set of localized orbitals of a large molecule is seen as an orbital mosaic where each tessera is made of only a few of them. The orbital tesserae are computed out of a set of embedded cluster pseudoeigenvalue coupled equations which are solved in a building-block self-consistent fashion. In each iteration, the embedded cluster equations are solved independently of each other and, as a result, the method is parallel at a high level of the calculation. In addition to full system calculations, the method enables to perform simpler, much less demanding embedded cluster calculations, where only a fraction of the localized molecular orbitals are variational while the rest is frozen, taking advantage of the transferability of the localized orbitals of a given localization method between similar molecules. Monitoring single point energy calculations of large poly(ethylene oxide) molecules and three dimensional carbon monoxide clusters using an extended Huckel Hamiltonian are presented. PMID:15473725
NASA Astrophysics Data System (ADS)
Thomas, Patrick Ryan
Large simulation cell sizes, relativistic effects, and the need to correctly model excited state properties are major impediments to the accurate prediction of the optical properties of candidate materials for solid-state laser crystal and luminescent applications. To overcome these challenges, new methods must be created to improve the electron orbital wavefunction and interactions. In this work, a method has been developed to create new analytical four-component, fully-relativistic and single-component scalar relativistic descriptions of the atomic orbital wave functions from Grasp2K numerically represented atomic orbitals. In addition, adapted theory for the calculation of the relativistic kinetic energy contribution to Hamiltonian which bypasses directly solving the Dirac equation has been explicated. The orbital description improvements are tested against YAG, YBCO, SnO2 and BiF3. The improvements to the basis set reflect an improvement in both computational speed and accuracy.
NASA Astrophysics Data System (ADS)
Guan, Qingze; Blume, Doerte
2016-05-01
The explicit correlated Gaussian (ECG) basis set expansion approach is a variational approach that has been used in various areas, including molecular, nuclear, atomic, and chemical physics. In the world of cold atoms, e.g., the ECG approach has been used to calculate the eigenenergies and eigenstates of few-body systems governed by Efimov physics. Since the first experimental realization of synthesized gauge fields, few-body systems with spin-orbit coupling have attracted a great deal of attention. Here, the ECG approach is customized to few-body systems with both short-range interactions and spin-orbit couplings. Benchmark tests and a performance analysis will be presented. Support by the NSF is gratefully acknowledged.
Andrade, Xavier; Aspuru-Guzik, Alán
2013-10-01
We discuss the application of graphical processing units (GPUs) to accelerate real-space density functional theory (DFT) calculations. To make our implementation efficient, we have developed a scheme to expose the data parallelism available in the DFT approach; this is applied to the different procedures required for a real-space DFT calculation. We present results for current-generation GPUs from AMD and Nvidia, which show that our scheme, implemented in the free code Octopus, can reach a sustained performance of up to 90 GFlops for a single GPU, representing a significant speed-up when compared to the CPU version of the code. Moreover, for some systems, our implementation can outperform a GPU Gaussian basis set code, showing that the real-space approach is a competitive alternative for DFT simulations on GPUs. PMID:26589153
Cignetti, Fabien; Salvia, Emilie; Anton, Jean-Luc; Grosbras, Marie-Hélène; Assaiante, Christine
2016-01-01
Conventional analysis of functional magnetic resonance imaging (fMRI) data using the general linear model (GLM) employs a neural model convolved with a canonical hemodynamic response function (HRF) peaking 5 s after stimulation. Incorporation of a further basis function, namely the canonical HRF temporal derivative, accounts for delays in the hemodynamic response to neural activity. A population that may benefit from this flexible approach is children whose hemodynamic response is not yet mature. Here, we examined the effects of using the set based on the canonical HRF plus its temporal derivative on both first- and second-level GLM analyses, through simulations and using developmental data (an fMRI dataset on proprioceptive mapping in children and adults). Simulations of delayed fMRI first-level data emphasized the benefit of carrying forward to the second-level a derivative boost that combines derivative and nonderivative beta estimates. In the experimental data, second-level analysis using a paired t-test showed increased mean amplitude estimate (i.e., increased group contrast mean) in several brain regions related to proprioceptive processing when using the derivative boost compared to using only the nonderivative term. This was true especially in children. However, carrying forward to the second-level the individual derivative boosts had adverse consequences on random-effects analysis that implemented one-sample t-test, yielding increased between-subject variance, thus affecting group-level statistic. Boosted data also presented a lower level of smoothness that had implication for the detection of group average activation. Imposing soft constraints on the derivative boost by limiting the time-to-peak range of the modeled response within a specified range (i.e., 4–6 s) mitigated these issues. These findings support the notion that there are pros and cons to using the informed basis set with developmental data. PMID:27471441
NASA Technical Reports Server (NTRS)
Mackenzie, Anne I.; Baginski, Michael E.; Rao, Sadasiva M.
2008-01-01
In this work, we present an alternate set of basis functions, each defined over a pair of planar triangular patches, for the method of moments solution of electromagnetic scattering and radiation problems associated with arbitrarily-shaped, closed, conducting surfaces. The present basis functions are point-wise orthogonal to the pulse basis functions previously defined. The prime motivation to develop the present set of basis functions is to utilize them for the electromagnetic solution of dielectric bodies using a surface integral equation formulation which involves both electric and magnetic cur- rents. However, in the present work, only the conducting body solution is presented and compared with other data.
Oyeyemi, Victor B.; Pavone, Michele; Carter, Emily A.
2011-11-03
Quantum chemistry has become one of the most reliable tools for characterizing the thermochemical underpinnings of reactions, such as bond dissociation energies (BDEs). The accurate prediction of these particular properties (BDEs) are challenging for ab initio methods based on perturbative corrections or coupled cluster expansions of the single-determinant Hartree-Fock wave function: the processes of bond breaking and forming are inherently multi-configurational and require an accurate description of non-dynamical electron correlation. To this end, we present a systematic ab initio approach for computing BDEs that is based on three components: (1) multi-reference single and double excitation configuration interaction (MRSDCI) for the electronic energies; (2) a two-parameter scheme for extrapolating MRSDCI energies to the complete basis set limit; and (3) DFT-B3LYP calculations of minimumenergy structures and vibrational frequencies to account for zero point energy and thermal corrections. We validated our methodology against a set of reliable experimental BDE values of C*C and C*H bonds of hydrocarbons. The goal of chemical accuracy is achieved, on average, without applying any empirical corrections to the MRSDCI electronic energies. We then use this composite scheme to make predictions of BDEs in a large number of hydrocarbon molecules for which there are no experimental data, so as to provide needed thermochemical estimates for fuel molecules.
NASA Astrophysics Data System (ADS)
Blum, Volker
This talk describes recent advances of a general, efficient, accurate all-electron electronic theory approach based on numeric atom-centered orbitals; emphasis is placed on developments related to materials for energy conversion and their discovery. For total energies and electron band structures, we show that the overall accuracy is on par with the best benchmark quality codes for materials, but scalable to large system sizes (1,000s of atoms) and amenable to both periodic and non-periodic simulations. A recent localized resolution-of-identity approach for the Coulomb operator enables O (N) hybrid functional based descriptions of the electronic structure of non-periodic and periodic systems, shown for supercell sizes up to 1,000 atoms; the same approach yields accurate results for many-body perturbation theory as well. For molecular systems, we also show how many-body perturbation theory for charged and neutral quasiparticle excitation energies can be efficiently yet accurately applied using basis sets of computationally manageable size. Finally, the talk highlights applications to the electronic structure of hybrid organic-inorganic perovskite materials, as well as to graphene-based substrates for possible future transition metal compound based electrocatalyst materials. All methods described here are part of the FHI-aims code. VB gratefully acknowledges contributions by numerous collaborators at Duke University, Fritz Haber Institute Berlin, TU Munich, USTC Hefei, Aalto University, and many others around the globe.
NASA Astrophysics Data System (ADS)
Rivelino, Roberto; Malaspina, Thaciana; Fileti, Eudes E.
2009-01-01
We have investigated the stability, electronic properties, Rayleigh (elastic), and Raman (inelastic) depolarization ratios, infrared and Raman absorption vibrational spectra of fullerenols [C60(OH)n] with different degrees of hydroxylation by using all-electron density-functional-theory (DFT) methods. Stable arrangements of these molecules were found by means of full geometry optimizations using Becke’s three-parameter exchange functional with the Lee, Yang, and Parr correlation functional. This DFT level has been combined with the 6-31G(d,p) Gaussian-type basis set, as a compromise between accuracy and capability to treat highly hydroxylated fullerenes, e.g., C60(OH)36 . Thus, the molecular properties of fullerenols were systematically analyzed for structures with n=1 , 2, 3, 4, 8, 10, 16, 18, 24, 32, and 36. From the electronic structure analysis of these molecules, we have evidenced an important effect related to the weak chemical reactivity of a possible C60(OH)24 isomer. To investigate Raman scattering and the vibrational spectra of the different fullerenols, frequency calculations are carried out within the harmonic approximation. In this case a systematic study is only performed for n=1-4 , 8, 10, 16, 18, and 24. Our results give good agreements with the expected changes in the spectral absorptions due to the hydroxylation of fullerenes.
NASA Astrophysics Data System (ADS)
Maroulis, George
1998-06-01
A large (18s 13p 8d 5f / 12s 7p 3d 2f) basis set consisting of 256 uncontracted gaussian-type functions is expected to yield values near the Hartree-Fock limit for the static hyperpolarizability of H 2O: βzxx=-9.40, βzyy=-1.35, βzzz=-7.71 and β¯=-11.07 for βαβγ ( e3a03Eh-2) and γxxxx=569, γyyyy=1422, γzzzz=907, γxxyy=338, γyyzz=389, γzzxx=287 and γ¯=985 for γαβγδ ( e4a04Eh-3) at the experimental equilibrium geometry (with z as the C 2 axis, molecule on the xz plane). The respective electron correlation corrections obtained with the single, double and perturbatively linked triple excitations coupled-cluster method and a [9s 6p 6d 3f / 6s 4p 2d 1f] basis set are βzxx=-0.45, βzyy=-4.19, βzzz=-6.09, β¯=-6.44 and γxxxx=267, γyyyy=1228, γzzzz=574, γxxyy=295, γyyzz=322, γzzxx=152, γ¯=721 . For the static limit we propose β¯=-17.5±0.3 e3a03Eh-2 and γ¯=(171±6)×10 1e4a04Eh-3, in near agreement with the experimental findings of β¯=-19.2±0.9 e3a03Eh-2 and γ¯=1800±150 e4a04Eh-3 deduced from EFISH measurements at 1064 nm by Kaatz et al. [P. Kaatz, E.A. Donley, D.P. Shelton, J. Chem. Phys. 108 (1998) 849].
Mourik, Van Tonja; Wilson, Angela K.; Dunning, Thomas H.
1999-02-20
The potential energy curves of the rare gas dimers He2, Ne2, and Ar2 have been computed using correlation consistent basis sets ranging from singly augmented aug-cc-pVDZ sets through triply augmented t-aug-cc-pV6Z sets, with the augmented sextuple basis sets being reported herein. Several methods for including electron correlation were investigated, namely Moller Plesset perturbation theory (MP2, MP3 and MP4) and coupled cluster theory [CCSD and CCSD(T)].
Magnetic susceptibility of semiconductors by an all-electron first-principles approach
Ohno, K. |; Mauri, F.; Louie, S.G. |
1997-07-01
The magnetic susceptibility ({chi}) of the semiconductors (diamond, Si, GaAs, and GaP) and of the inert-gas solids (Ne, Ar, and Kr) are evaluated within density-functional theory in the local-density approximation, using a mixed-basis all-electron approach. In Si, GaAs, GaP, Ar, and Kr, the contribution of core electrons to {chi} is comparable to that of valence electrons. However, our results show that the contribution associated with the core states is independent of the chemical environment and can be computed from the isolated atoms. Moreover, our results indicate that the use of a {open_quotes}scissor operator{close_quotes} does not improve the agreement of the theoretical {chi} with experiments. {copyright} {ital 1997} {ital The American Physical Society}
NASA Astrophysics Data System (ADS)
Yang, Yanchao; Jiang, Hong; Liu, Congbin; Lan, Zhongli
2013-03-01
Cognitive radio (CR) is an intelligent wireless communication system which can dynamically adjust the parameters to improve system performance depending on the environmental change and quality of service. The core technology for CR is the design of cognitive engine, which introduces reasoning and learning methods in the field of artificial intelligence, to achieve the perception, adaptation and learning capability. Considering the dynamical wireless environment and demands, this paper proposes a design of cognitive engine based on the rough sets (RS) and radial basis function neural network (RBF_NN). The method uses experienced knowledge and environment information processed by RS module to train the RBF_NN, and then the learning model is used to reconfigure communication parameters to allocate resources rationally and improve system performance. After training learning model, the performance is evaluated according to two benchmark functions. The simulation results demonstrate the effectiveness of the model and the proposed cognitive engine can effectively achieve the goal of learning and reconfiguration in cognitive radio.
NASA Astrophysics Data System (ADS)
Mohr, Stephan; Genovese, Luigi; Ratcliff, Laura; Masella, Michel
The quantum mechanics/molecular mechanis (QM/MM) method is a popular approach that allows to perform atomistic simulations using different levels of accuracy. Since only the essential part of the simulation domain is treated using a highly precise (but also expensive) QM method, whereas the remaining parts are handled using a less accurate level of theory, this approach allows to considerably extend the total system size that can be simulated without a notable loss of accuracy. In order to couple the QM and MM regions we use an approximation of the electrostatic potential based on a multipole expansion. The multipoles of the QM region are determined based on the results of a linear scaling Density Functional Theory (DFT) calculation using a set of adaptive, localized basis functions, as implemented within the BigDFT software package. As this determination comes at virtually no extra cost compared to the QM calculation, the coupling between QM and MM region can be done very efficiently. In this presentation I will demonstrate the accuracy of both the linear scaling DFT approach itself as well as of the approximation of the electrostatic potential based on the multipole expansion, and show some first QM/MM applications using the aforementioned approach.
Teodoro, Tiago Quevedo; da Silva, Albérico Borges Ferreira; Haiduke, Roberto Luiz Andrade
2014-09-01
This study reports a new relativistic prolapse-free Gaussian basis set series of quadruple-ζ quality, RPF-4Z, and an augmented version that includes extra diffuse functions, aug-RPF-4Z, for all the s- and p-block elements. The relativistic adapted Gaussian basis sets (RAGBSs), which are free of variational prolapse, were used as the starting primitive sets. Exponents of correlating/polarization functions were taken from a polynomial version of the generator coordinate Dirac-Fock (p-GCDF) method, in which the previously optimized RAGBS parameters are applied. By using such procedure we aimed to reduce the computational demand of these sets in comparison with fully optimized ones. The effect of these basis set increments on the correlation energy was evaluated by atomic multireference configuration interaction calculations with single and double excitations out of the valence shell. Finally, atomic and molecular calculations of fundamental properties (bond lengths, vibrational frequencies, dipole moments and electron affinities) corroborate the quadruple-ζ quality of these new sets that are also about half-time-consuming than the correspondent Dyall's v4z sets. The read-to use format of these (aug-)RPF-4Fz sets are available as Supporting Information files and can also be found at http://basis-sets.iqsc.usp.br/ . PMID:26588525
Gulans, Andris; Kontur, Stefan; Meisenbichler, Christian; Nabok, Dmitrii; Pavone, Pasquale; Rigamonti, Santiago; Sagmeister, Stephan; Werner, Ute; Draxl, Claudia
2014-09-10
Linearized augmented planewave methods are known as the most precise numerical schemes for solving the Kohn-Sham equations of density-functional theory (DFT). In this review, we describe how this method is realized in the all-electron full-potential computer package, exciting. We emphasize the variety of different related basis sets, subsumed as (linearized) augmented planewave plus local orbital methods, discussing their pros and cons and we show that extremely high accuracy (microhartrees) can be achieved if the basis is chosen carefully. As the name of the code suggests, exciting is not restricted to ground-state calculations, but has a major focus on excited-state properties. It includes time-dependent DFT in the linear-response regime with various static and dynamical exchange-correlation kernels. These are preferably used to compute optical and electron-loss spectra for metals, molecules and semiconductors with weak electron-hole interactions. exciting makes use of many-body perturbation theory for charged and neutral excitations. To obtain the quasi-particle band structure, the GW approach is implemented in the single-shot approximation, known as G(0)W(0). Optical absorption spectra for valence and core excitations are handled by the solution of the Bethe-Salpeter equation, which allows for the description of strongly bound excitons. Besides these aspects concerning methodology, we demonstrate the broad range of possible applications by prototypical examples, comprising elastic properties, phonons, thermal-expansion coefficients, dielectric tensors and loss functions, magneto-optical Kerr effect, core-level spectra and more. PMID:25135665
The route to MBxNyCz molecular wheels: II. Results using accurate functionals and basis sets
NASA Astrophysics Data System (ADS)
Güthler, A.; Mukhopadhyay, S.; Pandey, R.; Boustani, I.
2014-04-01
Applying ab initio quantum chemical methods, molecular wheels composed of metal and light atoms were investigated. High quality basis sets 6-31G*, TZPV, and cc-pVTZ as well as exchange and non-local correlation functionals B3LYP, BP86 and B3P86 were used. The ground-state energy and structures of cyclic planar and pyramidal clusters TiBn (for n = 3-10) were computed. In addition, the relative stability and electronic structures of molecular wheels TiBxNyCz (for x, y, z = 0-10) and MBnC10-n (for n = 2 to 5 and M = Sc to Zn) were determined. This paper sustains a follow-up study to the previous one of Boustani and Pandey [Solid State Sci. 14 (2012) 1591], in which the calculations were carried out at the HF-SCF/STO3G/6-31G level of theory to determine the initial stability and properties. The results show that there is a competition between the 2D planar and the 3D pyramidal TiBn clusters (for n = 3-8). Different isomers of TiB10 clusters were also studied and a structural transition of 3D-isomer into 2D-wheel is presented. Substitution boron in TiB10 by carbon or/and nitrogen atoms enhances the stability and leads toward the most stable wheel TiB3C7. Furthermore, the computations show that Sc, Ti and V at the center of the molecular wheels are energetically favored over other transition metal atoms of the first row.
NASA Astrophysics Data System (ADS)
Betzinger, Markus; Friedrich, Christoph; Görling, Andreas; Blügel, Stefan
2012-06-01
The optimized-effective-potential method is a special technique to construct local Kohn-Sham potentials from general orbital-dependent energy functionals. In a recent publication [M. Betzinger, C. Friedrich, S. Blügel, A. Görling, Phys. Rev. BPRBMDO1098-012110.1103/PhysRevB.83.045105 83, 045105 (2011)] we showed that uneconomically large basis sets were required to obtain a smooth local potential without spurious oscillations within the full-potential linearized augmented-plane-wave method. This could be attributed to the slow convergence behavior of the density response function. In this paper, we derive an incomplete-basis-set correction for the response, which consists of two terms: (1) a correction that is formally similar to the Pulay correction in atomic-force calculations and (2) a numerically more important basis response term originating from the potential dependence of the basis functions. The basis response term is constructed from the solutions of radial Sternheimer equations in the muffin-tin spheres. With these corrections the local potential converges at much smaller basis sets, at much fewer states, and its construction becomes numerically very stable. We analyze the improvements for rock-salt ScN and report results for BN, AlN, and GaN, as well as the perovskites CaTiO3, SrTiO3, and BaTiO3. The incomplete-basis-set correction can be applied to other electronic-structure methods with potential-dependent basis sets and opens the perspective to investigate a broad spectrum of problems in theoretical solid-state physics that involve response functions.
TiCl, TiH and TiH+ Bond Energies, a Test of a Correlation Consistent Ti Basis Set
NASA Technical Reports Server (NTRS)
Bauschlicher, Charles W., Jr.; Arnold, James O. (Technical Monitor)
1999-01-01
Correlation consistent basis sets are developed for Ti atom. The polarization functions are optimized for the average of the 3F and 5F states. One series of correlation consistent basis sets is for 3d and 4s correlation, while the second series includes 3s and 3p correlation as well as 3d and 4s correlation. These basis sets are tested using the Ti 3F-5F separation and the dissociation energies of TiCl X4Phi, TiH X4Phi, and TiH(+) X3Phi. The CCSD(T) complete basis set limit values are determined by extrapolation. The Douglas Kroll approach is used to compute the scalar relativistic effect. Spin-orbit effects are taken from experiment and/or computed at the CASSCF level. The Ti 3F-5F separation is in excellent agreement with experiment, while the TiCl, TiH, and TiH(+) bond energies are in good agreement with experiment. Extrapolation with the valence basis set is consistent with other atoms, while including 3s and 3p correlation appears to make extrapolation.
Baranowska-Łączkowska, Angelika; Fernández, Berta
2014-01-30
In order to obtain efficient basis sets for the evaluation of van der Waals complex intermolecular potentials, we carry out systematic basis set studies. For this, interaction energies at representative geometries on the potential energy surfaces are evaluated using the CCSD(T) correlation method and large polarized LPol-n and augmented polarization-consistent aug-pc-2 basis sets extended with different sets of midbond functions. On the basis of the root mean square errors calculated with respect to the values for the most accurate potentials available, basis sets are selected for fitting the corresponding interaction energies and getting analytical potentials. In this work, we study the Ne-N2 van der Waals complex and after the above procedure, the aug-pc-2-3321 and the LPol-ds-33221 basis set results are fitted. The obtained potentials are characterized by T-shaped global minima at distances between the Ne atom and the N2 center of mass of 3.39 Å, with interaction energies of -49.36 cm(-1) for the aug-pc-2-3321 surface and -50.28 cm(-1) for the LPol-ds-33221 surface. Both sets of results are in excellent agreement with the reference surface. To check the potentials further microwave transition frequencies are calculated that agree well with the experimental and the aV5Z-33221 values. The success of this study suggests that it is feasible to carry out similar accurate calculations of interaction energies and ro-vibrational spectra at reduced cost for larger complexes than has been possible hitherto. PMID:24375320
Shrivastava, ManishKumar B.; Fast, Jerome D.; Easter, Richard C.; Gustafson, William I.; Zaveri, Rahul A.; Jimenez, Jose L.; Saide, Pablo; Hodzic, Alma
2011-07-13
The Weather Research and Forecasting model coupled with chemistry (WRF-Chem) is modified to include a volatility basis set (VBS) treatment of secondary organic aerosol formation. The VBS approach, coupled with SAPRC-99 gas-phase chemistry mechanism, is used to model gas-particle partitioning and multiple generations of gas-phase oxidation of organic vapors. In addition to the detailed 9-species VBS, a simplified mechanism using 2 volatility species (2-species VBS) is developed and tested for similarity to the 9-species VBS in terms of both mass and oxygen-to-carbon ratios of organic aerosols in the atmosphere. WRF-Chem results are evaluated against field measurements of organic aerosols collected during the MILAGRO 2006 campaign in the vicinity of Mexico City. The simplified 2-species mechanism reduces the computational cost by a factor of 2 as compared to 9-species VBS. Both ground site and aircraft measurements suggest that the 9-species and 2-species VBS predictions of total organic aerosol mass as well as individual organic aerosol components including primary, secondary, and biomass burning are comparable in magnitude. In addition, oxygen-to-carbon ratio predictions from both approaches agree within 25%, providing evidence that the 2-species VBS is well suited to represent the complex evolution of organic aerosols. Model sensitivity to amount of anthropogenic semi-volatile and intermediate volatility (S/IVOC) precursor emissions is also examined by doubling the default emissions. Both the emission cases significantly under-predict primary organic aerosols in the city center and along aircraft flight transects. Secondary organic aerosols are predicted reasonably well along flight tracks surrounding the city, but are consistently over-predicted downwind of the city. Also, oxygen-to-carbon ratio predictions are significantly improved compared to prior studies by adding 15% oxygen mass per generation of oxidation; however, all modeling cases still under
NASA Astrophysics Data System (ADS)
Lowe, D.; Topping, D. O.; Archer-Nicholls, S.; Darbyshire, E.; Morgan, W.; Liu, D.; Allan, J. D.; Coe, H.; McFiggans, G.
2015-12-01
The burning of forests in the Amazonia region is a globally significant source of carbonaceous aerosol, containing both absorbing and scattering components [1]. In addition biomass burning aerosol (BBA) are also efficient cloud condensation nuclei (CCN), modifying cloud properties and influencing atmospheric circulation and precipitation tendencies [2]. The impacts of BBA are highly dependent on their size distribution and composition. A bottom-up emissions inventory, the Brazilian Biomass Burning Emissions Model (3BEM) [3], utilising satellite products to generate daily fire emission maps is used. Injection of flaming emissions within the atmospheric column is simulated using both a sub-grid plume-rise parameterisation [4], and simpler schemes, within the Weather Research and Forecasting Model with Chemistry (WRF-Chem, v3.4.1) [5]. Aerosol dynamics are simulated using the sectional MOSAIC scheme [6], incorporating a volatility basis set (VBS) treatment of organic aerosol [7]. For this work we have modified the 9-bin VBS to use the biomass burning specific scheme developed by May et al. [8]. The model has been run for September 2012 over South America (at a 25km resolution). We will present model results evaluating the modelled aerosol vertical distribution, size distribution, and composition against measurements taken by the FAAM BAe-146 research aircraft during the SAMBBA campaign. The main focus will be on investigating the factors controlling the vertical gradient of the organic mass to black carbon ratio of the measured aerosol. This work is supported by the Nature Environment Research Council (NERC) as part of the SAMBBA project under grant NE/J010073/1. [1] D. G. Streets et al., 2004, J. Geophys. Res., 109, D24212. [2] M. O. Andreae et al., 2004, Science, 303, 1337-1342. [3] K. Longo et al., 2010, Atmos. Chem. Phys., 10, 5,785-5,795. [4] S. Freitas et al., 2007, Atmos. Chem. Phys., 7, 3,385-3,398. [5] S. Archer-Nicholls et al., 2015, Geosci. Model Dev., 8
Kaprálová-Žďánská, Petra Ruth; Šmydke, Jan; Department of Radiation and Chemical Physics, Institute of Physics, Academy of Sciences of the Czech Republic, Na Slovance 2, 182 21 Prague 8 ; Civiš, Svatopluk
2013-09-14
Recently optimized exponentially tempered Gaussian basis sets [P. R. Kapralova-Zdanska and J. Smydke, J. Chem. Phys. 138, 024105 (2013)] are employed in quantitative simulations of helium absorption cross-sections and two-photon excitation yields of doubly excited resonances. Linearly polarized half-infinite and Gaussian laser pulses at wavelengths 38–58 nm and large intensities up to 100 TW/cm{sup 2} are considered. The emphasis is laid on convergence of the results with respect to the quality of the Gaussian basis sets (typically limited by a number of partial waves, density, and spatial extent of the basis functions) as well as to the quality of the basis set of field-free states (typically limited by the maximum rotational quantum number and maximum excitation of the lower electron). Particular attention is paid to stability of the results with respect to varying complex scaling parameter. Moreover, the study of the dynamics is preceded by a thorough check of helium energies and oscillator strengths as they are obtained with the exponentially tempered Gaussian basis sets, being also compared with yet unpublished emission wavelengths measured in electric discharge experiments.
Teodoro, Tiago Quevedo; Haiduke, Roberto Luiz Andrade
2013-10-15
Accurate relativistic adapted Gaussian basis sets (RAGBSs) for 87 Fr up to 118 Uuo atoms without variational prolapse were developed here with the use of a polynomial version of the Generator Coordinate Dirac-Fock method. Two finite nuclear models have been used, the Gaussian and uniform sphere models. The largest RAGBS error, with respect to numerical Dirac-Fock results, is 15.4 miliHartree for Ununoctium with a basis set size of 33s30p19d14f functions. PMID:23913741
Pinheiro, J.C.; Jorge, F.E.; Castro, E.V.R. de
2000-05-15
Accurate Gaussian basis sets (18s for Li and Be and 20s11p for the atoms from B to Ne) for the first-row atoms, generated with an improved generator coordinate Hartree-Fock method, were contracted and enriched with polarization functions. These basis sets were tested for B{sub 2}, C{sub 2}, BeO, Cn{sup {minus}}, LiF, N{sub 2}, CO, BF, NO{sup +}, O{sub 2}, and F{sub 2}. At the Hartree-Fock (HP), second-order Moeller-Plesset (MP2), fourth-order Moeller-Plesset (MP4), and density functional theory (DFT) levels, the dipole moments, bond lengths, and harmonic vibrational frequencies were studied, and at the MP2, MP4, and DFT levels, the dissociation energies were evaluated and compared with the corresponding experimental values and with values obtained using other contracted Gaussian basis sets and numerical HF calculations. For all diatomic molecules studied, the differences between the total energies, obtained with the largest contracted basis set [6s5p3d1f], and those calculated with the numerical HF methods were always less than 3.2 mhartree.
Alam, T.M.
1998-09-01
The influence of changes in the contracted Gaussian basis set used for ab initio calculations of nuclear magnetic resonance (NMR) phosphorous chemical shift anisotropy (CSA) tensors was investigated. The isotropic chemical shitl and chemical shift anisotropy were found to converge with increasing complexity of the basis set at the Hartree-Fock @IF) level. The addition of d polarization function on the phosphorous nucIei was found to have a major impact of the calculated chemical shi~ but diminished with increasing number of polarization fimctions. At least 2 d polarization fimctions are required for accurate calculations of the isotropic phosphorous chemical shift. The introduction of density fictional theory (DFT) techniques through tie use of hybrid B3LYP methods for the calculation of the phosphorous chemical shift tensor resulted in a poorer estimation of the NMR values, even though DFT techniques result in improved energy and force constant calculations. The convergence of the W parametem with increasing basis set complexity was also observed for the DFT calculations, but produced results with consistent large deviations from experiment. The use of a HF 6-31 l++G(242p) basis set represents a good compromise between accuracy of the simulation and the complexity of the calculation for future ab initio calculations of 31P NMR parameters in larger complexes.
Friese, Daniel H.; Törk, Lisa; Hättig, Christof
2014-11-21
We present scaling factors for vibrational frequencies calculated within the harmonic approximation and the correlated wave-function methods coupled cluster singles and doubles model (CC2) and Møller-Plesset perturbation theory (MP2) with and without a spin-component scaling (SCS or spin-opposite scaling (SOS)). Frequency scaling factors and the remaining deviations from the reference data are evaluated for several non-augmented basis sets of the cc-pVXZ family of generally contracted correlation-consistent basis sets as well as for the segmented contracted TZVPP basis. We find that the SCS and SOS variants of CC2 and MP2 lead to a slightly better accuracy for the scaled vibrational frequencies. The determined frequency scaling factors can also be used for vibrational frequencies calculated for excited states through response theory with CC2 and the algebraic diagrammatic construction through second order and their spin-component scaled variants.
NASA Astrophysics Data System (ADS)
Rybczyński, Józef
2011-02-01
This paper presents the results of computer simulation of bearing misalignment defects in a power turbogenerator. This malfunction is typical for great multi-rotor and multi-bearing rotating machines and very common in power turbo-sets. Necessary calculations were carried out by the computer code system MESWIR, developed and used at the IFFM in Gdansk for calculating dynamics of rotors supported on oil bearings. The results are presented in the form of a set of journal and bush trajectories of all turbo-set bearings. Our analysis focuses on the vibrational effects of displacing the two most vulnerable machine bearings in horizontal and vertical directions by the maximum acceptable range calculated with regard to bearing vibration criterion. This assumption required preliminary assessment of the maximum values for the permissible bearing dislocations. We show the relations between the attributes of the particular bearing trajectories and the bearing displacements in relation to their base design position. The shape and dimensions of bearing trajectories are interpreted based on the theory of hydrodynamic lubrication of oil bearings. It was shown that the relative journal trajectories and absolute bush trajectories carry much important information about the dynamic state of the machine, indicating also the way in which bearings are loaded. Therefore, trajectories can be a source of information about the position and direction of bearing misalignments. This article indicates the potential of using trajectory patterns for diagnosing misalignment defects in rotating machines and suggests including sets of trajectory patterns to the knowledge base of a machine diagnostic system.
ERIC Educational Resources Information Center
Grebennikov, I. V.
1978-01-01
Maintains that lack of pedagogical training of parents in the Soviet Union leads to errors in the education of children in the family setting. Methods to increase parents' pedagogical sophistication include media presentations about social education, community education clubs for young families, parent teacher conferences, and training sessions…
Sure, Rebecca; Brandenburg, Jan Gerit; Grimme, Stefan
2016-04-01
In quantum chemical computations the combination of Hartree-Fock or a density functional theory (DFT) approximation with relatively small atomic orbital basis sets of double-zeta quality is still widely used, for example, in the popular B3LYP/6-31G* approach. In this Review, we critically analyze the two main sources of error in such computations, that is, the basis set superposition error on the one hand and the missing London dispersion interactions on the other. We review various strategies to correct those errors and present exemplary calculations on mainly noncovalently bound systems of widely varying size. Energies and geometries of small dimers, large supramolecular complexes, and molecular crystals are covered. We conclude that it is not justified to rely on fortunate error compensation, as the main inconsistencies can be cured by modern correction schemes which clearly outperform the plain mean-field methods. PMID:27308221
Sure, Rebecca; Brandenburg, Jan Gerit
2015-01-01
Abstract In quantum chemical computations the combination of Hartree–Fock or a density functional theory (DFT) approximation with relatively small atomic orbital basis sets of double‐zeta quality is still widely used, for example, in the popular B3LYP/6‐31G* approach. In this Review, we critically analyze the two main sources of error in such computations, that is, the basis set superposition error on the one hand and the missing London dispersion interactions on the other. We review various strategies to correct those errors and present exemplary calculations on mainly noncovalently bound systems of widely varying size. Energies and geometries of small dimers, large supramolecular complexes, and molecular crystals are covered. We conclude that it is not justified to rely on fortunate error compensation, as the main inconsistencies can be cured by modern correction schemes which clearly outperform the plain mean‐field methods. PMID:27308221
Song, Y Z; Varandas, A J C
2009-04-01
A single-sheeted potential energy surface is reported for the electronic ground-state of H(2)S by fitting accurate multireference configuration interaction energies calculated using aug-cc-pVTZ and aug-cc-pVQZ basis sets with extrapolation of the electron correlation energy to the complete basis set limit, plus extrapolation to the complete basis set limit of the complete-active-space self-consistent field energy. A switching function formalism has been used to warrant the correct behavior at the H(2)(X (1)Sigma(g) (+))+S((1)D) and SH(X (2)Pi)+H((2)S) dissociation limits. The topographical features of the novel global potential energy surface are examined in detail, with the former being used for exploratory quasiclassical trajectory calculations of the thermal rate constant for the S((1)D)+H(2), S((1)D)+D(2), and S((1)D)+HD reactions at room temperature. A comparison with other available potential energy surfaces as well as kinetics data is also provided. PMID:19355742
Petersson, George A; Malick, David K; Frisch, Michael J; Braunstein, Matthew
2006-07-28
Examination of the convergence of full valence complete active space self-consistent-field configuration interaction including all single and double excitation (CASSCF-CISD) energies with expansion of the one-electron basis set reveals a pattern very similar to the convergence of single determinant energies. Calculations on the lowest four singlet states and the lowest four triplet states of N(2) with the sequence of n-tuple-zeta augmented polarized (nZaP) basis sets (n=2, 3, 4, 5, and 6) are used to establish the complete basis set limits. Full configuration-interaction (CI) and core electron contributions must be included for very accurate potential energy surfaces. However, a simple extrapolation scheme that has no adjustable parameters and requires nothing more demanding than CAS(10e(-),8orb)-CISD/3ZaP calculations gives the R(e), omega(e), omega(e)X(e), T(e), and D(e) for these eight states with rms errors of 0.0006 Angstrom, 4.43 cm(-1), 0.35 cm(-1), 0.063 eV, and 0.018 eV, respectively. PMID:16942134
NASA Astrophysics Data System (ADS)
Kobus, J.; Moncrieff, D.; Wilson, S.
2001-12-01
A comparison is made of the accuracy by which the electric dipole polarizability αzz and hyperpolarizability βzzz can be calculated by using the finite basis set approach (the algebraic approximation) and finite difference method in calculations employing the Hartree-Fock model. The numerical and algebraic methods were tested on the ground states of H2, LiH, BH and FH molecules at their respective experimental equilibrium geometries. For the FH molecule at its experimental equilibrium geometry, a sequence of distributed universal even-tempered basis sets have been used to explore the convergence pattern of the total energy, dipole moment and polarizabilities. The comparison of finite difference and finite basis set methods is extended to geometries for which the nuclear separation, RFH, lies in the range 1.5-2.2 b. The methods give consistent results to within 1% or better. In the case of the FH molecule the dependence of truncation errors of the total energy, dipole moment and polarizabilities on the geometry have been studied and are shown to be negligible.
NASA Astrophysics Data System (ADS)
Balabin, Roman M.
2008-10-01
In this paper, an extra error source for high-quality ab initio calculation of conformation equilibrium in normal alkanes—intramolecular basis set superposition error (BSSE)—is discussed. Normal butane (n-butane) and normal hexane (n-hexane) are used as representative examples. Single-point energy difference and BSSE values of trans and gauche conformations for n-butane (and trans-trans-trans and gauche-gauche-gauche conformations for n-hexane) were calculated using popular electron correlation methods: The second-order Moller-Plesset (MP2), the fourth-order Moller-Plesset (MP4), and coupled cluster with single and double substitutions with noniterative triple excitation [CCSD(T)] levels of theory. Extrapolation to the complete basis set is applied. The difference between BSSE-corrected and uncorrected relative energy values ranges from ˜100 cal/mol (in case of n-butane) to more than 1000 cal/mol (in case of n-hexane). The influence of basis set type (Pople or Dunning) and size [up to 6-311G(3df,3pd) and aug-cc-pVQZ] is discussed.
Cheng, Lan Stanton, John F.; Gauss, Jürgen
2015-06-14
A systematic relativistic coupled-cluster study is reported on the harmonic vibrational frequencies of the O{sub h}, C{sub 3v}, and C{sub 2v} conformers of XeF{sub 6}, with scalar-relativistic effects efficiently treated using the spin-free exact two-component theory in its one-electron variant (SFX2C-1e). Atomic natural orbital type basis sets recontracted for the SFX2C-1e scheme have been shown to provide rapid basis-set convergence for the vibrational frequencies. SFX2C-1e as well as complementary pseudopotential based computations consistently predicts that both O{sub h} and C{sub 3v} structures are local minima on the potential energy surface, while the C{sub 2v} structure is a transition state. Qualitative disagreement between the present results for the O{sub h} structure and those from CCSD(T)-F12b calculations [Peterson et al., J. Phys. Chem. A 116, 9777 (2012)], which yielded a triply degenerate imaginary frequency for the O{sub h} structure, is attributed here to the high sensitivity of the computed harmonic frequencies of the t{sub 1u} bending modes to the basis-set effects of triples contributions.
Chitwood, Daniel H.; Kumar, Ravi; Headland, Lauren R.; Ranjan, Aashish; Covington, Michael F.; Ichihashi, Yasunori; Fulop, Daniel; Jiménez-Gómez, José M.; Peng, Jie; Maloof, Julin N.; Sinha, Neelima R.
2013-01-01
Introgression lines (ILs), in which genetic material from wild tomato species is introgressed into a domesticated background, have been used extensively in tomato (Solanum lycopersicum) improvement. Here, we genotype an IL population derived from the wild desert tomato Solanum pennellii at ultrahigh density, providing the exact gene content harbored by each line. To take advantage of this information, we determine IL phenotypes for a suite of vegetative traits, ranging from leaf complexity, shape, and size to cellular traits, such as stomatal density and epidermal cell phenotypes. Elliptical Fourier descriptors on leaflet outlines provide a global analysis of highly heritable, intricate aspects of leaf morphology. We also demonstrate constraints between leaflet size and leaf complexity, pavement cell size, and stomatal density and show independent segregation of traits previously assumed to be genetically coregulated. Meta-analysis of previously measured traits in the ILs shows an unexpected relationship between leaf morphology and fruit sugar levels, which RNA-Seq data suggest may be attributable to genetically coregulated changes in fruit morphology or the impact of leaf shape on photosynthesis. Together, our results both improve upon the utility of an important genetic resource and attest to a complex, genetic basis for differences in leaf morphology between natural populations. PMID:23872539
Influence of a strong magnetic field on the hydrogen molecular ion using B-spline-type basis-sets
NASA Astrophysics Data System (ADS)
Zhang, Yue-Xia; Xiao-Long, Zhang
2015-12-01
As an improvement on our previous work [J. Phys. B: At. Mol. Opt. Phys. 45 085101 (2012)], an accurate method combining the spheroidal coordinates and B-spline basis is applied to study the ground state 1σg and low excited states 1σu, 1πg,u,1δg,u,2σg of the in magnetic fields ranging from 109 Gs (1 Gs = 10-4 T) to 4.414 × 1013 Gs. Comparing the one-center method used in our previous work, the present method has a higher precision with a shorter computing time. Equilibrium distances of the states of the in strong magnetic fields were found to be accurate to 3˜5 significant digits (s.d.) and the total energies 6˜11 s.d., even for some antibonding state, such as 1πg, which is difficult for the one-center method to give reliable results while the field strength is B ≥ 1013 Gs. For the large disagreement in previous works, such as the equilibrium distances of the 1πg state at B = 109 Gs, the present data may be used as a reference. Further, the potential energy curves (PECs) and the electronic probability density distributions (EPDDs) of the bound states 1σg, 1πu, 1δg and antibonding states 1σu, 1πg, 1δu for B = 1, 10, 100, 1000 a.u. (atomic unit) are compared, so that the different influences of the magnetic fields on the chemical bonds of the bound states and antibonding states are discussed in detail. Project supported by the National Natural Science Foundation of China (Grant No. 11204389) and the Natural Science Foundation Project of Chongqing (Grant Nos. CSTC2012jjA50015 and CSTC2012jjA00012).
Kruse, Holger; Grimme, Stefan
2012-04-21
A semi-empirical counterpoise-type correction for basis set superposition error (BSSE) in molecular systems is presented. An atom pair-wise potential corrects for the inter- and intra-molecular BSSE in supermolecular Hartree-Fock (HF) or density functional theory (DFT) calculations. This geometrical counterpoise (gCP) denoted scheme depends only on the molecular geometry, i.e., no input from the electronic wave-function is required and hence is applicable to molecules with ten thousands of atoms. The four necessary parameters have been determined by a fit to standard Boys and Bernadi counterpoise corrections for Hobza's S66×8 set of non-covalently bound complexes (528 data points). The method's target are small basis sets (e.g., minimal, split-valence, 6-31G*), but reliable results are also obtained for larger triple-ζ sets. The intermolecular BSSE is calculated by gCP within a typical error of 10%-30% that proves sufficient in many practical applications. The approach is suggested as a quantitative correction in production work and can also be routinely applied to estimate the magnitude of the BSSE beforehand. The applicability for biomolecules as the primary target is tested for the crambin protein, where gCP removes intramolecular BSSE effectively and yields conformational energies comparable to def2-TZVP basis results. Good mutual agreement is also found with Jensen's ACP(4) scheme, estimating the intramolecular BSSE in the phenylalanine-glycine-phenylalanine tripeptide, for which also a relaxed rotational energy profile is presented. A variety of minimal and double-ζ basis sets combined with gCP and the dispersion corrections DFT-D3 and DFT-NL are successfully benchmarked on the S22 and S66 sets of non-covalent interactions. Outstanding performance with a mean absolute deviation (MAD) of 0.51 kcal/mol (0.38 kcal/mol after D3-refit) is obtained at the gCP-corrected HF-D3/(minimal basis) level for the S66 benchmark. The gCP-corrected B3LYP-D3/6-31G* model
NASA Astrophysics Data System (ADS)
Legler, C. R.; Brown, N. R.; Dunbar, R. A.; Harness, M. D.; Nguyen, K.; Oyewole, O.; Collier, W. B.
2015-06-01
The Scaled Quantum Mechanical (SQM) method of scaling calculated force constants to predict theoretically calculated vibrational frequencies is expanded to include a broad array of polarized and augmented basis sets based on the split valence 6-31G and 6-311G basis sets with the B3LYP density functional. Pulay's original choice of a single polarized 6-31G(d) basis coupled with a B3LYP functional remains the most computationally economical choice for scaled frequency calculations. But it can be improved upon with additional polarization functions and added diffuse functions for complex molecular systems. The new scale factors for the B3LYP density functional and the 6-31G, 6-31G(d), 6-31G(d,p), 6-31G+(d,p), 6-31G++(d,p), 6-311G, 6-311G(d), 6-311G(d,p), 6-311G+(d,p), 6-311G++(d,p), 6-311G(2d,p), 6-311G++(2d,p), 6-311G++(df,p) basis sets are shown. The double d polarized models did not perform as well and the source of the decreased accuracy was investigated. An alternate system of generating internal coordinates that uses the out-of plane wagging coordinate whenever it is possible; makes vibrational assignments via potential energy distributions more meaningful. Automated software to produce SQM scaled vibrational calculations from different molecular orbital packages is presented.
A Core Gene Set Describes the Molecular Basis of Mutualism and Antagonism in Epichloë spp.
Eaton, Carla J; Dupont, Pierre-Yves; Solomon, Peter; Clayton, William; Scott, Barry; Cox, Murray P
2015-03-01
Beneficial plant-fungal interactions play an important role in the ability of plants to survive changing environmental conditions. In contrast, phytopathogenic fungi fall at the opposite end of the symbiotic spectrum, causing reduced host growth or even death. In order to exploit beneficial interactions and prevent pathogenic ones, it is essential to understand the molecular differences underlying these alternative states. The association between the endophyte Epichloë festucae and Lolium perenne (perennial ryegrass) is an excellent system for studying these molecular patterns due to the existence of several fungal mutants that have an antagonistic rather than a mutualistic interaction with the host plant. By comparing gene expression in a wild-type beneficial association with three mutant antagonistic associations disrupted in key signaling genes, we identified a core set of 182 genes that show common differential expression patterns between these two states. These gene expression changes are indicative of a nutrient-starvation response, as supported by the upregulation of genes encoding degradative enzymes, transporters, and primary metabolism, and downregulation of genes encoding putative small-secreted proteins and secondary metabolism. These results suggest that disruption of a mutualistic symbiotic interaction may lead to an elevated uptake and degradation of host-derived nutrients and cell-wall components, reminiscent of phytopathogenic interactions. PMID:25496592
NASA Astrophysics Data System (ADS)
Glushkov, V. N.; Kobus, J.; Wilson, S.
2008-10-01
Within the Hartree-Fock approximation, distributed basis sets of s-type Gaussian functions are used to compute those portions of the ground-state potential energy curves of the H2, LiH and BH molecules for which the model is appropriate. The exponents are generated using the even-tempered prescription and an anharmonic model is employed to distribute the basis functions. For few-electron diatomic systems, this approach is known to support sub-μHartree accuracy for electronic energies. For the molecules studied in the present work, matrix Hartree-Fock energy expectation values are compared with finite difference Hartree-Fock calculations carried out at the same geometries and using grids designed to support an accuracy of at least 1 nanoHartree. The distributed basis sets developed in this work support matrix Hartree-Fock energies which differ from the corresponding finite difference energies by 0.41, 0.58 and 0.68 μHartree, respectively, for the ground states of the H2, LiH and BH molecules at their equilibrium geometries. For each of these systems, a sub-μHartree level of accuracy is supported for a range of geometries.
NASA Astrophysics Data System (ADS)
Li, Yong-Qing; Song, Yu-Zhi; Joaquim de Campos Varandas, António
2015-01-01
An accurate single-sheeted double many-body expansion potential energy surface is reported for the title system. It is obtained by using the aug-cc-pVTZ and aug-cc-pVQZ basis sets with extrapolation of the electron correlation energy to the complete basis set limit, plus extrapolation to the complete basis set limit of the complete-active-space self-consistent field energy. The collinear and bending barrier heights of the new global potential energy surface is 2.301 and 1.768 kcal mol-1, in very good agreement with the values of 2.222 and 1.770 kcal mol-1 from the current best potential energy surface. In particular, the new potential energy surface describes well the important van der Waals interactions which is very useful for investigating the dynamics of the title system. Thus, the new potential energy surface can both be recommended for dynamics studies of the F + H2 reaction and as building block for constructing the potential energy surfaces of larger fluorine/hydrogen containing systems. Based on the new potential energy surface, a preliminary theoretical study of the reaction F(2P) + H2 (X1 Σg+) → FH(X1Σ+) + H(2S) has been carried out with the methods of quasi-classical trajectory and quantum mechanical. The results have shown that the new PES is suitable for any kind of dynamics studies. Supplementary material in the form of one pdf file available from the Journal web page at http://dx.doi.org/10.1140/epjd/e2014-50445-3
NASA Astrophysics Data System (ADS)
Varandas, A. J. C.; Pansini, F. N. N.
2014-12-01
A method previously suggested to calculate the correlation energy at the complete one-electron basis set limit by reassignment of the basis hierarchical numbers and use of the unified singlet- and triplet-pair extrapolation scheme is applied to a test set of 106 systems, some with up to 48 electrons. The approach is utilized to obtain extrapolated correlation energies from raw values calculated with second-order Møller-Plesset perturbation theory and the coupled-cluster singles and doubles excitations method, some of the latter also with the perturbative triples corrections. The calculated correlation energies have also been used to predict atomization energies within an additive scheme. Good agreement is obtained with the best available estimates even when the (d, t) pair of hierarchical numbers is utilized to perform the extrapolations. This conceivably justifies that there is no strong reason to exclude double-zeta energies in extrapolations, especially if the basis is calibrated to comply with the theoretical model.
Varandas, A. J. C.; Pansini, F. N. N.
2014-12-14
A method previously suggested to calculate the correlation energy at the complete one-electron basis set limit by reassignment of the basis hierarchical numbers and use of the unified singlet- and triplet-pair extrapolation scheme is applied to a test set of 106 systems, some with up to 48 electrons. The approach is utilized to obtain extrapolated correlation energies from raw values calculated with second-order Møller-Plesset perturbation theory and the coupled-cluster singles and doubles excitations method, some of the latter also with the perturbative triples corrections. The calculated correlation energies have also been used to predict atomization energies within an additive scheme. Good agreement is obtained with the best available estimates even when the (d, t) pair of hierarchical numbers is utilized to perform the extrapolations. This conceivably justifies that there is no strong reason to exclude double-zeta energies in extrapolations, especially if the basis is calibrated to comply with the theoretical model.
NASA Astrophysics Data System (ADS)
Gutsev, G. L.; Levin, A. A.
1980-10-01
A self-consistent version of the discrete variational method is described based on the use of numerical LCAO basis functions obtained as solutions of the Hartree—Fock equations for free atoms. Sets of single-zeta Slater functions are applied to approximate atomic densities further employed in the calculations of the Coulomb potential. The computer programs realizing this approach have been written and utilized to calculate electronic structures of molybdenum, tungsten and uranium hexafluorides. The ionization potentials calculated are in good quantitative agreement with experimental data. The deviations of the calculated valence state IP's from those determined by photoelectron spectroscopy do not exceed 1 eV.
Zhao, Bin; Wang, Shuxiao; Donahue, Neil M; Chuang, Wayne; Hildebrandt Ruiz, Lea; Ng, Nga L; Wang, Yangjun; Hao, Jiming
2015-02-17
We evaluate the one-dimensional volatility basis set (1D-VBS) and two-dimensional volatility basis set (2D-VBS) in simulating the aging of SOA derived from toluene and α-pinene against smog-chamber experiments. If we simulate the first-generation products with empirical chamber fits and the subsequent aging chemistry with a 1D-VBS or a 2D-VBS, the models mostly overestimate the SOA concentrations in the toluene oxidation experiments. This is because the empirical chamber fits include both first-generation oxidation and aging; simulating aging in addition to this results in double counting of the initial aging effects. If the first-generation oxidation is treated explicitly, the base-case 2D-VBS underestimates the SOA concentrations and O:C increase of the toluene oxidation experiments; it generally underestimates the SOA concentrations and overestimates the O:C increase of the α-pinene experiments. With the first-generation oxidation treated explicitly, we could modify the 2D-VBS configuration individually for toluene and α-pinene to achieve good model-measurement agreement. However, we are unable to simulate the oxidation of both toluene and α-pinene with the same 2D-VBS configuration. We suggest that future models should implement parallel layers for anthropogenic (aromatic) and biogenic precursors, and that more modeling studies and laboratory research be done to optimize the "best-guess" parameters for each layer. PMID:25581402
Zen, Andrea; Luo, Ye; Sorella, Sandro; Guidoni, Leonardo
2014-01-01
Quantum Monte Carlo methods are accurate and promising many body techniques for electronic structure calculations which, in the last years, are encountering a growing interest thanks to their favorable scaling with the system size and their efficient parallelization, particularly suited for the modern high performance computing facilities. The ansatz of the wave function and its variational flexibility are crucial points for both the accurate description of molecular properties and the capabilities of the method to tackle large systems. In this paper, we extensively analyze, using different variational ansatzes, several properties of the water molecule, namely, the total energy, the dipole and quadrupole momenta, the ionization and atomization energies, the equilibrium configuration, and the harmonic and fundamental frequencies of vibration. The investigation mainly focuses on variational Monte Carlo calculations, although several lattice regularized diffusion Monte Carlo calculations are also reported. Through a systematic study, we provide a useful guide to the choice of the wave function, the pseudopotential, and the basis set for QMC calculations. We also introduce a new method for the computation of forces with finite variance on open systems and a new strategy for the definition of the atomic orbitals involved in the Jastrow-Antisymmetrised Geminal power wave function, in order to drastically reduce the number of variational parameters. This scheme significantly improves the efficiency of QMC energy minimization in case of large basis sets. PMID:24526929
NASA Astrophysics Data System (ADS)
Balabanov, Nikolai B.; Peterson, Kirk A.
2006-08-01
Recently developed correlation consistent basis sets for the first row transition metal elements Sc-Zn have been utilized to determine complete basis set (CBS) scalar relativistic electron affinities, ionization potentials, and 4s23dn -2-4s1dn -1 electronic excitation energies with single reference coupled cluster methods [CCSD(T), CCSDT, and CCSDTQ] and multireference configuration interaction with three reference spaces: 3d4s, 3d4s4p, and 3d4s4p3d'. The theoretical values calculated with the highest order coupled cluster techniques at the CBS limit, including extrapolations to full configuration interaction, are well within 1kcal/mol of the corresponding experimental data. For the early transition metal elements (Sc-Mn) the internally contracted multireference averaged coupled pair functional method yielded excellent agreement with experiment; however, the atomic properties for the late transition metals (Mn-Zn) proved to be much more difficult to describe with this level of theory, even with the largest reference function of the present work.
Hybrid functionals within the all-electron FLAPW method: Implementation and applications of PBE0
NASA Astrophysics Data System (ADS)
Betzinger, Markus; Friedrich, Christoph; Blügel, Stefan
2010-05-01
We present an efficient implementation of the Perdew-Burke-Ernzerhof hybrid functional PBE0 within the full-potential linearized augmented-plane-wave (FLAPW) method. The Hartree-Fock exchange term, which is a central ingredient of hybrid functionals, gives rise to a computationally expensive nonlocal potential in the one-particle Schrödinger equation. The matrix elements of this exchange potential are calculated with the help of an auxiliary basis that is constructed from products of FLAPW basis functions. By representing the Coulomb interaction in this basis the nonlocal exchange term becomes a Brillouin-zone sum over vector-matrix-vector products. The Coulomb matrix is calculated only once at the beginning of a self-consistent-field cycle. We show that it can be made sparse by a suitable unitary transformation of the auxiliary basis, which accelerates the computation of the vector-matrix-vector products considerably. Additionally, we exploit spatial and time-reversal symmetry to identify the nonvanishing exchange matrix elements in advance and to restrict the k summations for the nonlocal potential to an irreducible set of k points. Favorable convergence of the self-consistent-field cycle is achieved by a nested density-only and density-matrix iteration scheme. We discuss the convergence with respect to the parameters of our numerical scheme and show results for a variety of semiconductors and insulators, including the oxides ZnO, EuO, Al2O3 , and SrTiO3 , where the PBE0 hybrid functional improves the band gaps and the description of localized states in comparison with the PBE functional. Furthermore, we find that in contrast to conventional local exchange-correlation functionals ferromagnetic EuO is correctly predicted to be a semiconductor.
NASA Astrophysics Data System (ADS)
Löptien, U.; Dietze, H.
2014-12-01
The Baltic Sea is a seasonally ice-covered, marginal sea in central northern Europe. It is an essential waterway connecting highly industrialised countries. Because ship traffic is intermittently hindered by sea ice, the local weather services have been monitoring sea ice conditions for decades. In the present study we revisit a historical monitoring data set, covering the winters 1960/1961 to 1978/1979. This data set, dubbed Data Bank for Baltic Sea Ice and Sea Surface Temperatures (BASIS) ice, is based on hand-drawn maps that were collected and then digitised in 1981 in a joint project of the Finnish Institute of Marine Research (today the Finnish Meteorological Institute (FMI)) and the Swedish Meteorological and Hydrological Institute (SMHI). BASIS ice was designed for storage on punch cards and all ice information is encoded by five digits. This makes the data hard to access. Here we present a post-processed product based on the original five-digit code. Specifically, we convert to standard ice quantities (including information on ice types), which we distribute in the current and free Network Common Data Format (NetCDF). Our post-processed data set will help to assess numerical ice models and provide easy-to-access unique historical reference material for sea ice in the Baltic Sea. In addition we provide statistics showcasing the data quality. The website http://www.baltic-ocean.org hosts the post-processed data and the conversion code. The data are also archived at the Data Publisher for Earth & Environmental Science, PANGAEA (doi:10.1594/PANGAEA.832353).
NASA Astrophysics Data System (ADS)
Löptien, U.; Dietze, H.
2014-06-01
The Baltic Sea is a seasonally ice-covered, marginal sea, situated in central northern Europe. It is an essential waterway connecting highly industrialised countries. Because ship traffic is intermittently hindered by sea ice, the local weather services have been monitoring sea ice conditions for decades. In the present study we revisit a historical monitoring data set, covering the winters 1960/1961. This data set, dubbed Data Bank for Baltic Sea Ice and Sea Surface Temperatures (BASIS) ice, is based on hand-drawn maps that were collected and then digitised 1981 in a joint project of the Finnish Institute of Marine Research (today Finish Meteorological Institute (FMI)) and the Swedish Meteorological and Hydrological Institute (SMHI). BASIS ice was designed for storage on punch cards and all ice information is encoded by five digits. This makes the data hard to access. Here we present a post-processed product based on the original five-digit code. Specifically, we convert to standard ice quantities (including information on ice types), which we distribute in the current and free Network Common Data Format (NetCDF). Our post-processed data set will help to assess numerical ice models and provide easy-to-access unique historical reference material for sea ice in the Baltic Sea. In addition we provide statistics showcasing the data quality. The website www.baltic-ocean.org hosts the post-prossed data and the conversion code. The data are also archived at the Data Publisher for Earth & Environmental Science PANGEA (doi:10.1594/PANGEA.832353).
Evaluation of the vibration-rotation-tunneling dynamics at the basis set superposition error corrected global minimum geometry of the ammonia dimer
NASA Astrophysics Data System (ADS)
Muguet, Francis F.; Robinson, G. Wilse; Bassez-Muguet, M. Palmyre
1995-03-01
With the help of a new scheme to correct for the basis set superposition error (BSSE), we find that an eclipsed nonlinear geometry becomes energetically favored over the eclipsed linear hydrogen-bonded geometry. From a normal mode analysis of the potential energy surface (PES) in the vicinity of the nonlinear geometry, we suggest that several dynamical interchange pathways must be taken into account. The minimal molecular symmetry group to be considered should be the double group of G36, but still larger multiple groups may be required. An interpretation of experimental vibration-rotation-tunneling (VRT) data in terms of the G144 group, which implies monomer inversions, may not be the only alternative. It appears that group theoretical considerations alone are insufficient for understanding the complex VRT dynamics of the ammonia dimer.
NASA Astrophysics Data System (ADS)
Last, Isidore; Baer, Michael
1992-01-01
Recently we introduced a time-independent approach to treat reactive collisions employing the negative imaginary absorbing potentials and L 2 basis sets. The application of these potentials led to the formulation of a method whereby only one arrangement channel has to be considered in a given calculation. In the present work we further extend this approach. (a) We show how this method is capable of yielding reactive state-to-state S-matrix elements. (In the previous versions of this method, these could not be obtained.) (b) We show that by employing contracted vibrational adiabatic and translational Gaussian functions the number of algebraic equations to be solved within this approach is significantly reduced (by a factor of four).