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At least 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Removing Basis Set Incompleteness Error in Finite-Temperature Electronic Structure Calculations: Two-Electron Systems

We investigate the basis-set-size dependence for quantities related to interacting electrons in the canonical ensemble. Calculations are performed using exact diagonalization (finite temperature full configuration interaction method) on two-electron model systems–the uniform electron gas (UEG) and the helium atom. Our data reproduce previous observations of a competition for how the internal energy converges between the ground-state correlation energy and the high-temperature kinetic energy. We explore how this can be related to component parts of the internal energy including kinetic, exchange, and correlation energies and show there is surprising nuance in how this can be broken down into mostly monotonically converging quantities. We also show that separation of the free energy into a free energy with/without correlation allows for monotonic convergence with basis set size due to the variational principle. We find that the free energy convergence matches the previously observed convergence properties of the internal energy. We discuss the free energy divergence that happens when converging a finite basis analytical hydrogen atom to the complete basis set limit and compare this to the energies of a helium atom in a large periodic box. Reducing the box size, we saw convergence trends for the helium atom that were similar to the UEG.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Efficient Calculation of NMR Shielding Constants Using Composite Method Approximations and Locally Dense Basis Sets

This paper presents a systematic study of applying composite method approximations with locally dense basis sets (LDBS) to efficiently calculate NMR shielding constants in small and medium-sized molecules. The pcSseg-n series of basis sets are shown to have similar accuracy to the pcS-n series when n ≥ 1 and can slightly reduce computational costs. We identify two different LDBS partition schemes that perform very effectively for density functional calculations. Here, we select a large subset of the recent NS372 database containing 290 H, C, N, and O shielding values evaluated by reference methods on 106 molecules to carefully assess methods of the high, medium, and low computational costs to make practical recommendations. Our assessment covers conventional electronic structure methods (density functional theory and wave function) with global basis calculations, as well as their use in one of the satisfactory LDBS approaches, and a range of composite approaches, also with and without LDBS. Altogether 99 methods are evaluated. On this basis, we recommend different methods to reach three different levels of accuracy and time requirements across the four nuclei considered.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Influence of the complete basis set approximation, tight weighted-core, and diffuse functions on the DLPNO-CCSD(T1) atomization energies of neutral H,C,O-compounds

The impact of complete basis set extrapolation schemes (CBS), diffuse functions, and tight weighted core functions on enthalpies of formation predicted via the DLPNO-CCSD(T1) reduced Feller Peterson-Dixon approach has been examined for neutral H,C,O-compounds. All tested three-point (TZ/QZ/5Z) extrapolation schemes result in mean unsigned deviation (MUD) below 2 kJ mol -1 relative to the experiment. Here, the two-point QZ/5Z and TZ/QZ CBS 1/$l^3_{max}$ extrapolation schemes are inferior to their inverse power counterpart (1/($l_{max}$ + 1/2) 4 ) by 1.3 and 4.3 kJ mol -1 . The CBS extrapolated frozen core atomization energies are insensitive (within 1 kJ mol -1 ) to augmentation of the basis set with tight weighted core functions. The core-valence correlation effects converge already at triple-ζ, although double- ζ/triple- ζ CBS extrapolation performs better and is recommended. The effect of diffuse function augmentation converges slowly, and cannot be reproduced with double- ζ or triple- ζ calculations as these are plagued with basis set superposition and incompleteness errors.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Single-Point Extrapolation to the Complete Basis Set Limit through Deep Learning

Machine learning (ML) offers an attractive method for making predictions about molecular systems while circumventing the need to run expensive electronic structure calculations. Once trained on ab initio data, the promise of ML is to deliver accurate predictions of molecular properties that were previously computationally infeasible. In this work, we develop and train a graph neural network model to correct the basis set incompleteness error (BSIE) between a small and large basis set at the RHF and B3LYP levels of theory. Our results show that, when compared to fitting to the total potential, an ML model fitted to correct the BSIE is better at generalizing to systems not seen during training. We test this ability by training on single molecules while evaluating on molecular complexes. We also show that ensemble models yield better behaved potentials in situations where the training data is insufficient. However, even when only fitting to the BSIE, acceptable performance is only achieved when the training data sufficiently resemble the systems one wants to make predictions on. As a result, the test error of the final model trained to predict the difference between the cc-pVDZ and cc-pV5Z potential is 0.184 kcal/mol for the B3LYP density functional, and the ensemble model accurately reproduces the large basis set interaction energy curves on the S66x8 dataset.

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

Localized basis set for plutonium

The implementation of optimal strictly localized atomic orbitals basis for plutonium (Pu) using norm-conserving pseudopotential density-functional theory (DFT) is presented. The basis set was applied to the α, β, γ, δ, δ', and ε phases of Pu, δ-Pu surface, and δ-PuGa alloys. The computed properties of the Pu phases and δ-Pu surface were in good agreement with both available experimental data and prior DFT calculations based on plane-wave methodologies. Results for the δ-PuGa alloys were also in good agreement with experimental data. Finally, the reliability of the basis set was further demonstrated by using ab initio molecular dynamics to model the diffusion coefficient and activation barrier for atomic diffusion in a δ-PuGa alloy.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Kohn–Sham Density in a Slater Orbital Basis Set

Finite, atom-centered Slater basis sets are used to determine approximate Kohn–Sham molecular orbitals. This is achieved by minimizing the kinetic energy plus the sum-squared difference between the Kohn–Sham density and the full configuration interaction density. As a result of the finite basis, a weight factor is introduced to balance the two minimization components. Results herein show that this can be done systematically, without sensitive dependence on the choice of scaling factor. In addition, the algorithm is applied to the LiH diatomic for fractional electron counts, where stretching the bond introduces significant reorganization of the electron density. As a result, the analysis will show the correct KS orbital structure and reveal the effects of correlation and electron locality on the KS solutions.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2025

Many-Body Basis Set Amelioration Method for Incremental Full Configuration Interaction

Incremental full configuration interaction (iFCI) is a polynomial-cost electronic structure method that systematically approaches the FCI limit by employing the method of increments to solve the Schrödinger equation through a many-body expansion. This article introduces the many-body basis set amelioration (MBBSA) method, which is designed to allow iFCI to be applicable to larger atomic orbital basis sets. MBBSA uses a series of inexpensive iFCI calculations to approximate the correlation energy that would be found using a more expensive, highly accurate iFCI calculation. Here, when compared to standard iFCI computations on smaller molecules in triple-zeta and larger basis sets, MBBSA provides approximations to the total and relative energies within chemical accuracy. MBBSA exhibits a reduced cost of between 60-92% when compared to standard iFCI calculations, with larger systems experiencing the largest benefit. Tests of MBBSA on two reactions that involve highly correlated systems, the automerization of cyclobutadiene and a Criegee intermediate reaction, show that MBBSA has practical utility for studying realistic chemistries.

Basis sets↗
NASA NTRS1994

Large Atomic Natural Orbital Basis Sets for the First Transition Row Atoms

Large atomic natural orbital (ANO) basis sets are tabulated for the Sc to Cu. The primitive sets are taken from the large sets optimized by Partridge, namely (21s 13p 8d) for Sc and Ti and (20s 12p 9d) for V to Cu. These primitive sets are supplemented with three p, one d, six f, and four g functions. The ANO sets are derived from configuration interaction density matrices constructed as the average of the lowest states derived from the 3d(sup n)4s(sup 2) and 3d(sup n+1)4s(sup 1) occupations. For Ni, the 1S(3d(sup 10)) state is included in the averaging. The choice of basis sets for molecular calculations is discussed.

Bauschlicher, Charles W., Jr.↗
NASA NTRS1996

On the Use of a Mixed Gaussian/Finite-Element Basis Set for the Calculation of Rydberg States

Configuration-interaction studies are reported for the Rydberg states of the helium atom using mixed Gaussian/finite-element (GTO/FE) one particle basis sets. Standard Gaussian valence basis sets are employed, like those, used extensively in quantum chemistry calculations. It is shown that the term values for high-lying Rydberg states of the helium atom can be obtained accurately (within 1 cm -1), even for a small GTO set, by augmenting the n-particle space with configurations, where orthonormalized interpolation polynomials are singly occupied.

Thuemmel, Helmar T.↗
DOE OSTI2023

Accurate Hellmann–Feynman forces from density functional calculations with augmented Gaussian basis sets

The Hellmann–Feynman (HF) theorem provides a way to compute forces directly from the electron density, enabling efficient force calculations for large systems through machine learning (ML) models for the electron density. The main issue holding back the general acceptance of the HF approach for atom-centered basis sets is the well-known Pulay force which, if naively discarded, typically constitutes an error upward of 10 eV/Å in forces. In this work, we demonstrate that if a suitably augmented Gaussian basis set is used for density functional calculations, the Pulay force can be suppressed, and HF forces can be computed as accurately as analytical forces with state-of-the-art basis sets, allowing geometry optimization and molecular dynamics to be reliably performed with HF forces. Our results pave a clear path forward for the accurate and efficient simulation of large systems using ML densities and the HF theorem.

Pathak, Shivesh (ORCID:0000000172798195)↗
DOE OSTI2024

Benchmarking Correlation-Consistent Basis Sets for Frequency-Dependent Polarizabilities with Multiresolution Analysis

This paper presents the first converged frequency-dependent HF polarizability results for general molecules, on a set of 89 closed-shell atoms and molecules. The solver employs multiresolution analysis (MRA) in a multiwavelet basis to compute both ground and response states to a guaranteed precision, which are validated against independent numerical grid calculations on atoms and linear molecules. The MRA ground-state energies and response properties are used to evaluate results in correlation-consistent basis sets up to 5Z augmented with either single or double diffuse functions and core-polarization functions. Systematic trends are revealed through consideration of chemical composition as well as the use of machine learning to cluster convergence trends, the latter suggesting the possibility of learning and correcting basis-set error.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1993

Atomic Natural Orbital Basis Sets for Transition Metals

We show that atomic natural orbitals are an excellent way to contract transition-metal basis sets, even though the different low-lying electronic states may have very different basis set requirements.

Bauschlicher, Charles W., Jr.↗
NASA NTRS1990

Polyatomic molecular Dirac-Hartree-Fock calculations with Gaussian basis sets

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.

Dyall, Kenneth G.↗
DOE OSTI2022

KSSOLV 2.0: An efficient MATLAB toolbox for solving the Kohn-Sham equations with plane-wave basis set

KSSOLV (Kohn-Sham Solver) is a MATLAB toolbox for performing Kohn-Sham density functional theory (DFT) calculations with a plane-wave basis set. KSSOLV 2.0 preserves the design features of the original KSSOLV software to allow users and developers to easily set up a problem and perform ground-state calculations as well as to prototype and test new algorithms. Furthermore, it includes new functionalities such as new iterative diagonalization algorithms, k-point sampling for electron band structures, geometry optimization and advanced algorithms for performing DFT calculations with local, semi-local, and hybrid exchange-correlation functionals. It can be used to study the electronic structures of both molecules and solids. So, we describe these new capabilities in this work through a few use cases. We also demonstrate the numerical accuracy and computational efficiency of KSSOLV on a variety of examples.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1987

Small Al clusters. I - The effect of basis set and correlation on the geometry of small Al clusters

A detailed study is presented of the basis set requirements and effects of correlation on the geometry and structure of small Al(n) clusters n = 2, 4, and 13. An effective core potential (ECP) is developed from the Huzinaga basis which accurately reproduces the all-electron results. It is found that depolarization functions are very important in computing the bond length, and that the bond contraction obtained is about as large for a 13-atom cluster as for the Al(4) rhombus structure. With d functions on each center in Al(13), a bond distance shorter than the bulk is obtained, as expected. The inclusion of correlation in Al(4) is found to be less important than the addition of polarization functions for determining the bond length, but increases substantially the calculated atomization energy. These calibration calculations allow an accurate treatment for Al(n) clusters to be designed.

Bauschlicher, Charles W., Jr.↗
NASA NTRS1989

Near Hartree-Fock quality GTO basis sets for the first- and third-row atoms

Energy-optimized Gaussian-type-orbital (GTO) basis sets of accuracy approaching that of numerical Hartree-Fock computations are compiled for the elements of the first and third rows of the periodic table. The methods employed in calculating the sets are explained; the applicability of the sets to electronic-structure calculations is discussed; and the results are presented in tables and briefly characterized.

Partridge, Harry↗
NASA NTRS1982

Perturbation corrections to Koopmans' theorem. V - A study with large basis sets

The vertical ionization potentials of N2, F2 and H2O were calculated by perturbation corrections to Koopmans' theorem using six different basis sets. The largest set used includes several sets of polarization functions. Comparison is made with measured values and with results of computations using Green's functions.

Chong, D. P.↗
NASA NTRS1990

General contraction of Gaussian basis sets. II - Atomic natural orbitals and the calculation of atomic and molecular properties

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.

Almlof, Jan↗