Search NASA⌕ Search

SEARCH · Search NASA

Results for “explicit correlation”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2016

Algorithms for calculating mass-velocity and Darwin relativistic corrections with n-electron explicitly correlated Gaussians with shifted centers

Algorithms for calculating the leading mass-velocity (MV) and Darwin (D) relativistic corrections are derived for electronic wave functions expanded in terms of n-electron explicitly correlated Gaussian functions with shifted centers and without pre-exponential angular factors. The algorithms are implemented and tested in calculations of MV and D corrections for several points on the ground-state potential energy curves of the H{sub 2} and LiH molecules. The algorithms are general and can be applied in calculations of systems with an arbitrary number of electrons.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

High angular momentum states of lithium atom, studied with symmetry-projected explicitly correlated Gaussian lobe functions

Method of construction of wave functions approximating eigenfunctions of the L{sup ^2} operator is proposed for high angular momentum states of few-electron atoms. Basis functions are explicitly correlated Gaussian lobes, projected onto irreducible representations of finite point groups. Variational calculations have been carried out for the lowest states of lithium atom, with quantum number L in the range from 1 to 8. Nonrelativistic energies accurate to several dozens of nanohartree have been obtained. For 2{sup 2}P, 3{sup 2}D, and 4{sup 2}F states they agree well with the reference results. Transition frequencies have been computed and compared with available experimental data.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Direct non-Born-Oppenheimer variational calculations of all bound vibrational states corresponding to the first rotational excitation of D{sub 2} performed with explicitly correlated all-particle Gaussian functions

Direct variational calculations where the Born-Oppenheimer approximation is not assumed are done for all rovibrational states of the D{sub 2} molecule corresponding to first excited rotational level (the N = 1 states). All-particle explicitly correlated Gaussian basis functions are used in the calculations. The exponential parameters of the Gaussians are optimized with the aid of analytically calculated energy gradient determined with respect to these parameters. The results allow to determine the ortho-para spin isomerization energies as a function of the vibrational quantum number.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2014

Communication: Stochastic evaluation of explicitly correlated second-order many-body perturbation energy

A stochastic algorithm is proposed that can compute the basis-set-incompleteness correction to the second-order many-body perturbation (MP2) energy of a polyatomic molecule. It evaluates the sum of two-, three-, and four-electron integrals over an explicit function of electron-electron distances by a Monte Carlo (MC) integration at an operation cost per MC step increasing only quadratically with size. The method can reproduce the corrections to the MP2/cc-pVTZ energies of H{sub 2}O, CH{sub 4}, and C{sub 6}H{sub 6} within a few mE{sub h} after several million MC steps. It circumvents the resolution-of-the-identity approximation to the nonfactorable three-electron integrals usually necessary in the conventional explicitly correlated (R12 or F12) methods.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2012

Molecular structure calculations: A unified quantum mechanical description of electrons and nuclei using explicitly correlated Gaussian functions and the global vector representation

We elaborate on the theory for the variational solution of the Schroedinger equation of small atomic and molecular systems without relying on the Born-Oppenheimer paradigm. The all-particle Schroedinger equation is solved in a numerical procedure using the variational principle, Cartesian coordinates, parameterized explicitly correlated Gaussian functions with polynomial prefactors, and the global vector representation. As a result, non-relativistic energy levels and wave functions of few-particle systems can be obtained for various angular momentum, parity, and spin quantum numbers. A stochastic variational optimization of the basis function parameters facilitates the calculation of accurate energies and wave functions for the ground and some excited rotational-(vibrational-)electronic states of H{sub 2}{sup +} and H{sub 2}, three bound states of the positronium molecule, Ps{sub 2}, and the ground and two excited states of the {sup 7}Li atom.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Explicit correlation treatment of the potential energy surface of CO{sub 2} dimer

We present an extensive study of the four-dimensional potential energy surface (4D-PES) of the carbon dioxide dimer, (CO{sub 2}){sub 2}. This PES is developed over the set of intermolecular coordinates. The electronic computations are carried out at the explicitly correlated coupled cluster method with single, double, and perturbative triple excitations [CCSD(T)-F12] level of theory in connection with the augmented correlation-consistent aug-cc-pVTZ basis set. An analytic representation of the 4D-PES is derived. Our extensive calculations confirm that “Slipped Parallel” is the most stable form and that the T-shaped structure corresponds to a transition state. Later on, this PES is employed for the calculations of the vibrational energy levels of the dimer. Moreover, the temperature dependence of the dimer second virial coefficient and of the first spectral moment of rototranslational collision-induced absorption spectrum is derived. For both quantities, a good agreement is found between our values and the experimental data for a wide range of temperatures. This attests to the high quality of our PES. Generally, our PES and results can be used for modeling CO{sub 2} supercritical fluidity and examination of its role in planetary atmospheres. It can be also incorporated into dynamical computations of CO{sub 2} capture and sequestration. This allows deep understanding, at the microscopic level, of these processes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2014

An algorithm for nonrelativistic quantum-mechanical finite-nuclear-mass variational calculations of nitrogen atom in L = 0, M = 0 states using all-electrons explicitly correlated Gaussian basis functions

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 {sup 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.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Explicitly correlated second-order Møller-Plesset perturbation theory in a Divide-Expand-Consolidate (DEC) context

We present the DEC-RIMP2-F12 method where we have augmented the Divide Expand-Consolidate resolution-of-the-identity second-order Møller-Plesset perturbation theory method (DEC-RIMP2) [P. Baudin et al., J. Chem. Phys. 144, 054102 (2016)] with an explicitly correlated (F12) correction. Here, the new method is linear-scaling, massively parallel, and it corrects for the basis set incompleteness error in an efficient manner. In addition, we observe that the F12 contribution decreases the domain error of the DEC-RIMP2 correlation energy by roughly an order of magnitude. An important feature of the DEC scheme is the inherent error control defined by a single parameter, and this feature is also retained for the DEC-RIMP2-F12 method. In this paper we present the working equations for the DEC-RIMP2-F12 method and proof of concept numerical results for a set of test molecules.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2012

Explicitly correlated Gaussian calculations of the {sup 2}D Rydberg states of the boron atom

Accurate non-relativistic variational calculations are performed for the seven lowest members of the {sup 2}D Rydberg series (1s{sup 2}2s2p{sup 2}, and 1s{sup 2}2s{sup 2}nd, n= 3, Horizontal-Ellipsis , 8) of the boron atom. The wave functions of the states are expanded in terms of all-electron explicitly correlated Gaussian basis functions and the effect of the finite nuclear mass is directly included in the calculations allowing for determining the isotopic shifts of the energy levels. The Gaussian basis is optimized independently for each state with the aid of the analytic energy gradient with respect to the Gaussian parameters. The calculations represent the highest accuracy level currently achievable for the considered states. The computed energies are compared with the available experimental data.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2013

Charge asymmetry in rovibrationally excited HD{sup +} determined using explicitly correlated all-particle Gaussian functions

Very accurate non-Born-Oppenheimer quantum-mechanical calculations are performed to determine the average values of the interparticle distances and the proton-deuteron density function for the rovibrationally excited HD{sup +} ion. The states corresponding to excitations to all bound vibrational states (v = 0, …, 22) and simultaneously excited to the first excited rotational state (N = 1) are considered. To describe each state up to 8000 explicitly correlated all-particle Gaussian functions are used. The nonlinear parameters of the Gaussians are variationally optimized using a procedure that employs the analytical energy gradient determined with respect to these parameters. The results show an increasing asymmetry in the electron distribution with the vibrational excitation as the electron density shifts towards deuteron and away from the proton.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2013

Linear-scaling explicitly correlated treatment of solids: Periodic local MP2-F12 method

Theory and implementation of the periodic local MP2-F12 method in the 3*A fixed-amplitude ansatz is presented. The method is formulated in the direct space, employing local representation for the occupied, virtual, and auxiliary orbitals in the form of Wannier functions (WFs), projected atomic orbitals (PAOs), and atom-centered Gaussian-type orbitals, respectively. Local approximations are introduced, restricting the list of the explicitly correlated pairs, as well as occupied, virtual, and auxiliary spaces in the strong orthogonality projector to the pair-specific domains on the basis of spatial proximity of respective orbitals. The 4-index two-electron integrals appearing in the formalism are approximated via the direct-space density fitting technique. In this procedure, the fitting orbital spaces are also restricted to local fit-domains surrounding the fitted densities. The formulation of the method and its implementation exploits the translational symmetry and the site-group symmetries of the WFs. Test calculations are performed on LiH crystal. The results show that the periodic LMP2-F12 method substantially accelerates basis set convergence of the total correlation energy, and even more so the correlation energy differences. The resulting energies are quite insensitive to the resolution-of-the-identity domain sizes and the quality of the auxiliary basis sets. The convergence with the orbital domain size is somewhat slower, but still acceptable. Moreover, inclusion of slightly more diffuse functions, than those usually used in the periodic calculations, improves the convergence of the LMP2-F12 correlation energy with respect to both the size of the PAO-domains and the quality of the orbital basis set. At the same time, the essentially diffuse atomic orbitals from standard molecular basis sets, commonly utilized in molecular MP2-F12 calculations, but problematic in the periodic context, are not necessary for LMP2-F12 treatment of crystals.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2011

{sup 1}D states of the beryllium atom: Quantum mechanical nonrelativistic calculations employing explicitly correlated Gaussian functions

Very accurate finite-nuclear-mass variational nonrelativistic calculations are performed for the lowest five {sup 1}D states (1s{sup 2} 2p{sup 2}, 1s{sup 2} 2s{sup 1} 3d{sup 1}, 1s{sup 2} 2s{sup 1} 4d{sup 1}, 1s{sup 2} 2s{sup 1} 5d{sup 1}, and 1s{sup 2} 2s{sup 1} 6d{sup 1}) of the beryllium atom ({sup 9}Be). The wave functions of the states are expanded in terms of all-electron explicitly correlated Gaussian functions. The exponential parameters of the Gaussians are optimized using the variational method with the aid of the analytical energy gradient determined with respect to those parameters. The calculations exemplify the level of accuracy that is now possible with Gaussians in describing bound states of a four-electron system where some of the electrons are excited into higher angular states.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2012

Explicitly correlated Gaussian calculations of the {sup 2}P{sup o} Rydberg spectrum of the lithium atom

Accurate quantum-mechanical nonrelativistic variational calculations are performed for the nine lowest members of the {sup 2}P{sup o} Rydberg series (1s{sup 2}np{sup 1}, n= 2, ..., 10) of the lithium atom. The effect of the finite nuclear mass is included in the calculations allowing for determining the isotopic shifts of the energy levels. The wave functions of the states are expanded in terms of all-electron explicitly correlated Gaussian functions. The exponential parameters of the Gaussians are variationally optimized with the aid of the analytical energy gradient determined with respect to those parameters. The calculated state energies are compared with the available experimental data.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2014

Appointing silver and bronze standards for noncovalent interactions: A comparison of spin-component-scaled (SCS), explicitly correlated (F12), and specialized wavefunction approaches

A systematic examination of noncovalent interactions as modeled by wavefunction theory is presented in comparison to gold-standard quality benchmarks available for 345 interaction energies of 49 bimolecular complexes. Quantum chemical techniques examined include spin-component-scaling (SCS) variations on second-order perturbation theory (MP2) [SCS, SCS(N), SCS(MI)] and coupled cluster singles and doubles (CCSD) [SCS, SCS(MI)]; also, method combinations designed to improve dispersion contacts [DW-MP2, MP2C, MP2.5, DW-CCSD(T)-F12]; where available, explicitly correlated (F12) counterparts are also considered. Dunning basis sets augmented by diffuse functions are employed for all accessible ζ-levels; truncations of the diffuse space are also considered. After examination of both accuracy and performance for 394 model chemistries, SCS(MI)-MP2/cc-pVQZ can be recommended for general use, having good accuracy at low cost and no ill-effects such as imbalance between hydrogen-bonding and dispersion-dominated systems or non-parallelity across dissociation curves. Moreover, when benchmarking accuracy is desirable but gold-standard computations are unaffordable, this work recommends silver-standard [DW-CCSD(T**)-F12/aug-cc-pVDZ] and bronze-standard [MP2C-F12/aug-cc-pVDZ] model chemistries, which support accuracies of 0.05 and 0.16 kcal/mol and efficiencies of 97.3 and 5.5 h for adenine·thymine, respectively. Choice comparisons of wavefunction results with the best symmetry-adapted perturbation theory [T. M. Parker, L. A. Burns, R. M. Parrish, A. G. Ryno, and C. D. Sherrill, J. Chem. Phys. 140, 094106 (2014)] and density functional theory [L. A. Burns, Á. Vázquez-Mayagoitia, B. G. Sumpter, and C. D. Sherrill, J. Chem. Phys. 134, 084107 (2011)] methods previously studied for these databases are provided for readers' guidance.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Monte Carlo Explicitly Correlated Second-Order Many-Body Green’s Function Calculations of Semiconductor Band Gaps

A systematically converging series of ab initio, post-density-functional, size-consistent, electron-correlated approximations is desired for predictive computing of felectronic band structures of insulating, semiconducting, and metallic solids. A series that meets all of these desiderata (except the applicability to metals) is ab initio many-body Green's function theory based on Gaussian-type-orbital (GTO) basis sets. Here, its leading-order approximation, the second-order Green's function (GF2) method in the diagonal and frequency-independent approximations with the aug-cc-pVDZ basis set, is applied to the fundamental band gaps of three semiconductors (diamond, silicon, and silicon carbide in the zincblende structure) using cluster models. Corrections are made to the basis-set-incompleteness errors by the explicit-correlation (F12) ansatz (GF2-F12) for the valence band edges. The crystals are modeled as surface-passivated clusters of increasing sizes, whose wave functions are expanded by up to 2709 GTO basis functions. Immense computational costs of these calculations are overcome by the highly scalable stochastic algorithm of the Monte Carlo GF2-F12 method, whose operation cost per state increases only as a cubic power of system size, which has a tiny memory footprint and easily achieves near-perfect parallel efficiency on thousands of CPUs or on hundreds of GPUs. The correlated, F12-corrected highest-occupied and lowest-unoccupied molecular-orbital energy (HOMO-LUMO) gap is 5.78 ± 0.07 eV for C 87 H 76 as compared with the experimental value of the fundamental (indirect) band gap of bulk diamond at 5.48 eV. The correlated, F12-corrected HOMO-LUMO gaps for Si 75 H 76 and Si 32 C 43 H 76 are 2.56 ± 0.15 eV and 3.50 ± 0.12 eV, respectively, which are expected to decrease further with increasing cluster sizes. As a result, the experimental fundamental (indirect) band gaps of bulk silicon and silicon carbide are 1.17 eV and 2.42 eV, respectively.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2016

Monte Carlo explicitly correlated second-order many-body perturbation theory

A stochastic algorithm is proposed and implemented that computes a basis-set-incompleteness (F12) correction to an ab initio second-order many-body perturbation energy as a short sum of 6- to 15-dimensional integrals of Gaussian-type orbitals, an explicit function of the electron-electron distance (geminal), and its associated excitation amplitudes held fixed at the values suggested by Ten-no. The integrals are directly evaluated (without a resolution-of-the-identity approximation or an auxiliary basis set) by the Metropolis Monte Carlo method. Applications of this method to 17 molecular correlation energies and 12 gas-phase reaction energies reveal that both the nonvariational and variational formulas for the correction give reliable correlation energies (98% or higher) and reaction energies (within 2 kJ mol -1 with a smaller statistical uncertainty) near the complete-basis-set limits by using just the aug-cc-pVDZ basis set. The nonvariational formula is found to be 2–10 times less expensive to evaluate than the variational one, though the latter yields energies that are bounded from below and is, therefore, slightly but systematically more accurate for energy differences. Being capable of using virtually any geminal form, the method confirms the best overall performance of the Slater-type geminal among 6 forms satisfying the same cusp conditions. Lastly, not having to precompute lower-dimensional integrals analytically, to store them on disk, or to transform them in a nonscalable dense-matrix-multiplication algorithm, the method scales favorably with both system size and computer size; the cost increases only as O(n 4 ) with the number of orbitals (n), and its parallel efficiency reaches 99.9% of the ideal case on going from 16 to 4096 computer processors.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

Toward a W4-F12 approach: Can explicitly correlated and orbital-based ab initio CCSD(T) limits be reconciled?

In the context of high-accuracy computational thermochemistry, the valence coupled cluster with all singles and doubles (CCSD) correlation component of molecular atomization energies presents the most severe basis set convergence problem, followed by the (T) component. In the present paper, we make a detailed comparison, for an expanded version of the W4-11 thermochemistry benchmark, between, on the one hand, orbital-based CCSD/AV{5,6}Z + d and CCSD/ACV{5,6}Z extrapolation, and on the other hand CCSD-F12b calculations with cc-pVQZ-F12 and cc-pV5Z-F12 basis sets. This latter basis set, now available for H–He, B–Ne, and Al–Ar, is shown to be very close to the basis set limit. Apparent differences (which can reach 0.35 kcal/mol for systems like CCl{sub 4}) between orbital-based and CCSD-F12b basis set limits disappear if basis sets with additional radial flexibility, such as ACV{5,6}Z, are used for the orbital calculation. Counterpoise calculations reveal that, while total atomization energies with V5Z-F12 basis sets are nearly free of BSSE, orbital calculations have significant BSSE even with AV(6 + d)Z basis sets, leading to non-negligible differences between raw and counterpoise-corrected extrapolated limits. This latter problem is greatly reduced by switching to ACV{5,6}Z core-valence basis sets, or simply adding an additional zeta to just the valence orbitals. Previous reports that all-electron approaches like HEAT (high-accuracy extrapolated ab-initio thermochemistry) lead to different CCSD(T) limits than “valence limit + CV correction” approaches like Feller-Peterson-Dixon and Weizmann-4 (W4) theory can be rationalized in terms of the greater radial flexibility of core-valence basis sets. For (T) corrections, conventional CCSD(T)/AV{Q,5}Z + d calculations are found to be superior to scaled or extrapolated CCSD(T)-F12b calculations of similar cost. For a W4-F12 protocol, we recommend obtaining the Hartree-Fock and valence CCSD components from CCSD-F12b/cc-pV{Q,5}Z-F12 calculations, but the (T) component from conventional CCSD(T)/aug’-cc-pV{Q,5}Z + d calculations using Schwenke’s extrapolation; post-CCSD(T), core-valence, and relativistic corrections are to be obtained as in the original W4 theory. W4-F12 is found to agree slightly better than W4 with ATcT (active thermochemical tables) data, at a substantial saving in computation time and especially I/O overhead. A W4-F12 calculation on benzene is presented as a proof of concept.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗