A rigorous and optimized strategy for the evaluation of the Boys function kernel in molecular electronic structure theory

Weiss, Alexander K. H.; Ochsenfeld, Christian

doi:10.1002/jcc.23935

Cited by 10 publications

(10 citation statements)

References 15 publications

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“…For computing F (n max , z), instead of tabulating this function as it is done for real argument in e.g. 2,5,7,9 , we use nonlinear approximation of the integrand in (1) (see 11 ) leading an approximation of the Boys function valid for the complex argument Re (z) ≥ 0 with tight error estimates. Based on these approximations, we develop two algorithms, for real and complex valued arguments.…”

Section: S (Y) =mentioning

confidence: 99%

“…appears in problems of computing Gaussian integrals and, over the years, there were many algorithms proposed for its evaluation, see e.g. [2][3][4][5][6][7][8][9][10] . The Boys function is related to a number of special functions, for example the error function, the incomplete Gamma function as well as (for pure imaginary argument) to the Fresnel integrals.…”

Section: Introductionmentioning

confidence: 99%

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A fast algorithm for computing the Boys function

Beylkin

Sharma

2021

The Journal of Chemical Physics

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Section: S (Y) =mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A fast algorithm for computing the Boys function

Beylkin

Sharma

2021

The Journal of Chemical Physics

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“…[113][114][115][116] and references therein). Accurate and efficient methods for calculation of F n (T ) are available and there is no reason for us to elaborate on this issue.…”

Section: B Basic Integral and Derivativesmentioning

confidence: 99%

Calculation of Araki-Sucher correction for many-electron systems

2017

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In this paper we consider the evaluation of the Araki-Sucher correction for arbitrary many-electron atomic and molecular systems. This contribution appears in the leading order quantum electrodynamics corrections to the energy of a bound state. The conventional one-electron basis set of Gaussian-type orbitals (GTOs) is adopted; this leads to two-electron matrix elements which are evaluated with help of generalised the McMurchie-Davidson scheme. We also consider the convergence of the results towards the complete basis set. A rigorous analytic result for the convergence rate is obtained and verified by comparing with independent numerical values for the helium atom. Finally, we present a selection of numerical examples and compare our results with the available reference data for small systems. In contrast with other methods used for the evaluation of the Araki-Sucher correction, our method is not restricted to few-electron atoms or molecules. This is illustrated by calculations for several many-electron atoms and molecules.

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“…The evaluation of the Boys function had a recent renewed interest and was the subject of recent publications [12,13]. A different algorithm was developed for this work and will be discussed in a forthcoming paper.…”

Section: Theoretical Backgroundmentioning

confidence: 99%

Fast calculation of two-electron-repulsion integrals: a numerical approach

Lopes

2017

Theor Chem Acc

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An alternative methodology to evaluate two-electron-repulsion integrals based on numerical approximation is proposed. Computational chemistry has branched into two major fields with methodologies based on quantum mechanics and classical force fields. However, there are significant shadowy areas not covered by any of the available methods. Many relevant systems are often too big for traditional quantum chemical methods while being chemically too complex for classical force fields. Examples include systems in nanomedicine, studies of metalloproteins, etc. There is an urgent need to develop fast quantum chemical methods able to study large and complex systems. This work is a proof-of-concept on the numerical techniques required to develop accurate and computationally efficient algorithms for the fast calculation of electron-repulsion integrals, one of the most significant bottlenecks in the extension of quantum chemistry to large systems. All concepts and calculations were developed for the three-center integral (p xA p xB |p xC p xC ) with all atoms being carbon. Starting with the analytical formulae, convenient decompositions were tested to provide smooth two-dimensional surfaces that were easily fitted. The approximating algorithm consisted of a multilayered approach based on multiple fittings of two-dimensional surfaces. An important aspect of the new method is its independence on the number of contracted Gaussian primitives. The basis set of choice was STO-6G. In future developments, larger basis sets will be developed. This work is part of a large effort aimed at improving the inadequacies of existing computational chemistry methods, both based on quantum mechanics and classical force fields, in particular in describing large and heterogeneous systems (ex. metalloproteins).

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A rigorous and optimized strategy for the evaluation of the Boys function kernel in molecular electronic structure theory

Cited by 10 publications

References 15 publications

A fast algorithm for computing the Boys function

A fast algorithm for computing the Boys function

Calculation of Araki-Sucher correction for many-electron systems

Fast calculation of two-electron-repulsion integrals: a numerical approach

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