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NASA NTRS1987

Near Hartree-Fock quality GTO basis sets for the second-row atoms

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.

Partridge, Harry↗

NASA NTRS1987

Near Hartree-Fock quality GTO basis sets for the second-row atoms

Partridge, Harry↗

NASA NTRS1992

On the performance of large Gaussian basis sets for the computation of total atomization energies

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.

Martin, J. M. L.↗

NASA NTRS1990

Dynamical basis sets for algebraic variational calculations in quantum-mechanical scattering theory

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.

Sun, Yan↗

DOE OSTI2026

Reducing the Cost of CCSD Basis Set Extrapolation in Ab Initio Computational Thermochemistry

Here, a series of approximations to CCSD contributions in computational model chemistries is presented in the context of kcal mol –1 , kJ mol –1 , and 20 cm –1 theoretical predictions of total atomization energies, benchmarked within the HEAT+CH 4 test suite. A specific set of circumstances where MP2, without empirical scaling, may be used as an effective intermediate in the first two of these accuracy ranges was determined. However, SDQ-MP4, a method long used in pursuit of kcal mol –1 accuracy but relatively unstudied in the subchemical accuracy community, offers significant improvement over the quality of MP2 as a basis-set intermediate at significantly reduced cost compared to CCSD. Given this, we argue for SDQ-MP4 as the de facto CCSD basis-set intermediate in sub-chemical accuracy calculations when CCSD in a desired basis set becomes unaffordable. We additionally report on a “CBS-like” scheme, where MP2 and SDQ-MP4 are used in conjunction to create a “cheap” three-part approximation of large CCSD basis set limits. The data for the CCSD approximation schemes are organized in such a way that model chemistry developers can locate an analog of their current approach for the CCSD basis set limit and explore alternative intermediates that either decrease computational cost or increase computational accuracy. We also show, for a handful of molecules, that SDQ-MP4 shows promise as an effective basis-set intermediate for harmonic and fundamental frequency computations, allowing for zero-point corrections of nearly CCSD(T)/ANO1 quality using simple composite methods that only require CCSD(T)/ANO0.

Thorpe, James H. [Argonne National Laboratory (ANL↗

DOE OSTI2020

Electronic couplings for singlet fission: Orbital choice and extrapolation to the complete basis set limit

Abstract For the search for promising singlet fission candidates, the calculation of the effective electronic coupling, which is required to estimate the singlet fission rate between the initially excited state (S 0 S 1 ) and the multiexcitonic state ( 1 TT, two triplets on neighboring molecules, coupled into a singlet), should be sufficiently reliable and fast enough to explore the configuration space. We propose here to modify the calculation of the effective electronic coupling using a nonorthogonal configuration interaction approach by: (a) using only one set of orbitals, optimized for the triplet state of the molecules, to describe all molecular electronic states, and (b) only taking the leading configurations into consideration. Furthermore, we also studied the basis set convergence of the electronic coupling, and we found, by comparison to the complete basis set limit obtained using the cc‐pV n Z series of basis sets, that both the aug‐cc‐pVDZ and 6–311++G** basis sets are a good compromise between accuracy and computational feasibility. The proposed approach enables future work on larger clusters of molecules than dimers.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

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 OSTI2021

On the Finite Nuclear Effect and Gaussian Basis Sets for Four-Component Dirac Hartree-Fock Calculations

In this perspective we describe an overview of Dirac Hartree-Fock theory, which is the foundation of relativistic quantum chemistry methods vital in the molecular modeling of heavy element chemistry and physics. A special emphasis was placed upon the physical connection between the finite nuclear model and the kinetic-balance condition between the large and small components. Additionally, we review the consequences of basis set choices for Dirac Hartree-Fock calculations in the restricted kinetic balance formalism, and show that the basis set limit does not have a hard lower bound due to the nature of the Hamiltonian, referred to in the literature as prolapse. Standard Gaussian basis set contraction schemes can break down in Dirac Hartree-Fock calculations, and special care must be taken for the description of core orbitals near the nucleus. The phenomena described in this perspective are vital for theoreticians and practitioners to understand when selecting a basis set for heavy element quantum chemical calculations using Dirac Hartree-Fock theory.

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↗