Off‐center Gaussian functions: Applications toward larger basis sets, post‐second‐order correlation treatment, and truncated virtual orbital space in investigations of noncovalent interactions

Melichercik, M.; Suchá, Denisa; Neogrády, Pavel; Pitoňák, Michal

doi:10.1002/qua.25580

Cited by 6 publications

(7 citation statements)

References 25 publications

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“…to account for dispersion energy. [20][21][22] The result shows the importance of adding customized ghost orbitals in the NCI region, saying that such technique improves the accuracy of the dispersion part significantly. However, adding ghost orbitals is equivalent to using a larger basis set with diffusion, and the customization part introduces artificial error.…”

Section: Composite Sapt Methodsmentioning

confidence: 94%

The composite method of symmetry adapted perturbation theory

Li¹,

Deng²,

Liu³

et al. 2022

Preprint

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In symmetry-adapted perturbation theory (SAPT), accurate calculations on non-covalent interaction for large complexes with more than 50 atoms are impractical using a large basis set. The more efficient with a smaller basis set, however, usually results in poor prediction in terms of dispersion and overall energies. In this study, we propose a composite method with a baseline calculated at SAPT2/aug-cc-pVTZ with dispersion term corrected at SAPT2+ level with a smaller basis set at the canonical limit using extrapolation techniques. Two point and three point extrapolation schemes are discussed, and we showed that our composite methods perform better than the previously ranked silver standard and can even compete with gold standard with the computational cost in between the latter and former's.

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Section: Composite Sapt Methodsmentioning

confidence: 94%

The composite method of symmetry adapted perturbation theory

Li¹,

Deng²,

Liu³

et al. 2022

Preprint

View full text Add to dashboard Cite

show abstract

“…The procedure could especially be combined with the Gaussian cell model, [35][36][37][38] which has been recently resuggested as the off-center Gaussian model. 39,40 In addition, the decomposition procedure could also be used with auxiliary basis sets for resolution of identity approaches. 41 Although only fixed geometries have been considered in the present work, the extension to geometry optimization and potential energy surfaces is straightforward.…”

Section: Summary and Discussionmentioning

confidence: 99%

Curing basis set overcompleteness with pivoted Cholesky decompositions

Lehtola

2019

The Journal of Chemical Physics

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The description of weakly bound electronic states is especially difficult with atomic orbital basis sets. The diffuse atomic basis functions that are necessary to describe the extended electronic state generate significant linear dependencies in the molecular basis set, which may make the electronic structure calculations illconvergent. We propose a method where the over-complete molecular basis set is pruned by a pivoted Cholesky decomposition of the overlap matrix, yielding an optimal low-rank approximation that is numerically stable; the pivot indices determining a reduced basis set that is complete enough to describe all the basis functions in the original over-complete basis. The method can be implemented either by a simple modification to the usual canonical orthogonalization procedure, which hides the excess functions and yields fewer efficiency benefits, or by generating custom basis sets for all the atoms in the system, yielding significant cost reductions in electronic structure calculations. The pruned basis sets from the latter choice allow accurate calculations to be performed at a lower cost even at the self-consistent field level, as illustrated on a solvated (H 2 O) -24 anion. Our results indicate that the Cholesky procedure allows one to perform calculations with accuracies close to standard augmented basis sets with cost savings which increase with the size of the basis set, ranging from 9% fewer functions in single-ζ basis sets to 28% fewer functions in triple-ζ basis sets.

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“…A general approach for avoiding the problems with linear dependencies that arise from diffuse functions in a molecular setting has, however, been suggested. In this approach, diffuse functions are modeled by a large number of non‐diffuse functions placed all around the system . The use of such lattices of Gaussian functions is an old idea, originally proposed as the “Gaussian cell model” by Murrell and coworkers .…”

Section: Lcao Approachesmentioning

confidence: 99%

“…The authors of Refs. 253 and 254 appear to have been unaware of the work by Murrell, Wilson, and coworkers. Nonetheless, the Gaussian cell model is but an imitation of proper real‐space methods: the use of a grid of spherically symmetric Gaussians clearly cannot yield the same amount of accuracy or convenience as a true real‐space approach that employs a set of systematically convergent basis functions with finite support.…”

Section: Lcao Approachesmentioning

confidence: 99%

“…In this approach, diffuse functions are modeled by a large number of non-diffuse functions placed all around the system. 253,254 The use of such lattices of Gaussian functions is an old idea, originally proposed as the "Gaussian cell model" by Murrell and coworkers. 255 The Gaussian cell model was later revisited by Wilson and coworkers, who showed that much better results can be obtained by supplementing the lattice basis set with AO functions on the nuclei.…”

Section: Deficiencies Of Lcao Approachesmentioning

confidence: 99%

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A review on non‐relativistic, fully numerical electronic structure calculations on atoms and diatomic molecules

Lehtola

2019

Int J of Quantum Chemistry

102

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The need for accurate calculations on atoms and diatomic molecules is motivated by the opportunities and challenges of such studies. The most commonly used approach for all-electron electronic structure calculations in general-the linear combination of atomic orbitals (LCAO) method-is discussed in combination with Gaussian, Slater a.k.a. exponential, and numerical radial functions. Even though LCAO calculations have major benefits, their shortcomings motivate the need for fully numerical approaches based on, for example, finite differences, finite elements, or the discrete variable representation, which are also briefly introduced. Applications of fully numerical approaches for general molecules are briefly reviewed, and their challenges are discussed. It is pointed out that the high level of symmetry present in atoms and diatomic molecules can be exploited to fashion more efficient fully numerical approaches for these special cases, after which it is possible to routinely perform allelectron Hartree-Fock and density functional calculations directly at the basis set limit on such systems. Applications of fully numerical approaches to calculations on atoms as well as diatomic molecules are reviewed. Finally, a summary and outlook is given.atomic calculations, density functional theory, diatomic calculations, fully numerical electronic structure theory, Hartree-Fock | INTRODUCTIONThanks to decades of development in approximate density functionals and numerical algorithms, density functional theory [1,2] (DFT) is now one of the cornerstones of computational chemistry and solid-state physics. [3][4][5] Since atoms are the basic building block of molecules, a number of popular density functionals [6][7][8][9][10] have been parametrized using ab initio data on noble gas atoms; these functionals have been used in turn as the starting point for the development of other functionals. A comparison of the results of density-functional calculations to accurate ab initio data on atoms has, however, recently sparked controversy on the accuracy of a number of recently published, commonly used density functionals. [11][12][13][14][15][16][17][18][19][20][21] This underlines that there is still room for improvement in DFT even for the relatively simple case of atomic studies.The development and characterization of new density functionals require the ability to perform accurate atomic calculations. Because atoms are the simplest chemical systems, atomic calculations may seem simple; however, they are in fact sometimes surprisingly challenging. For instance, a long-standing discrepancy between the theoretical and experimental electron affinity and ionization potential of gold has been resolved only very recently with high-level ab initio calculations. [22] Atomic calculations can also be used to formulate efficient starting guesses for molecular electronic structure calculations via either the atomic density [23,24] or the atomic potential as discussed in Ref. [25].

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Off‐center Gaussian functions: Applications toward larger basis sets, post‐second‐order correlation treatment, and truncated virtual orbital space in investigations of noncovalent interactions

Cited by 6 publications

References 25 publications

The composite method of symmetry adapted perturbation theory

The composite method of symmetry adapted perturbation theory

Curing basis set overcompleteness with pivoted Cholesky decompositions

A review on non‐relativistic, fully numerical electronic structure calculations on atoms and diatomic molecules

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