Rational approximants to evaluate four-center electron repulsion integrals for 1s hydrogen Slater type functions

Cesco, Juan Carlos; Pérez, Jorge Enrique Romero; Denner, Claudia C.; Giubergia, G; Rosso, Ana

doi:10.1016/j.apnum.2005.02.003

Cited by 8 publications

(8 citation statements)

References 23 publications

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“…Previous work on separation of integration variables is difficult to apply, in contrast to the case for Gaussians [28] cf. [29].…”

Section: Avoiding Eto Translations For Two-electron Integrals Over 3 mentioning

confidence: 93%

Four‐center Slater‐type orbital molecular integrals without orbital translations

Hoggan

2009

Int J of Quantum Chemistry

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ABSTRACT:This article advocates the use of atomic orbitals which have direct physical interpretation, i.e., hydrogen-like orbitals. They are exponential-type orbitals (ETOs). Convenient nodeless linear combinations are used, namely Slater-type orbitals (STOs), with a product of a single power of r and an exponential as radial factor. Until 2008, such orbital products on different atoms were difficult to manipulate for the evaluation of two-electron integrals. The difficulty was mostly due to cumbersome orbital translations involving slowly convergent infinite sums. These are completely eliminated using Coulomb resolutions. They provide an excellent approximation that reduces these integrals to a sum of one-electron overlap-like integral products that each involve orbitals on at most two centers. Such two-center integrals are separable in prolate spheroidal coordinates. They are thus readily evaluated. Only these integrals need to be re-evaluated to change basis functions. The above is still valid or three-center integrals. In four-center integrals, the resolutions require translating one potential term per product. This is outlined here and detailed elsewhere. Numerical results are reported for the H 2 dimer.

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“…Previous work on separation of integration variables is difficult to apply, in contrast to the case for Gaussians [28] cf. [29].…”

Section: Avoiding Eto Translations For Two-electron Integrals Over 3 mentioning

confidence: 93%

Four‐center Slater‐type orbital molecular integrals without orbital translations

Hoggan

2009

Int J of Quantum Chemistry

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“…for gaussians [30] cf [31]. Recent work by Gill and coworkers [32] proposes a resolution of the Coulomb operator, in terms of potential functions φ i , which are characterized by examining Poisson's equation.…”

Section: Avoiding Eto Translations For Two-electron Integrals Over 3 mentioning

confidence: 99%

General two‐electron exponential type orbital integrals in polyatomics without orbital translations

Hoggan

2009

Int J of Quantum Chemistry

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ABSTRACT:This article advocates the use of atomic orbitals which have direct physical interpretation, i.e., hydrogen-like orbitals. They are exponential type orbitals (ETOs). Convenient nodeless linear combinations are used, namely Slater type orbitals (STOs) (with a product of a single power of r and an exponential as radial factor). Until 2008, such orbital products on different atoms were difficult to manipulate for the evaluation of two-electron integrals. The difficulty was mostly due to cumbersome orbital translations involving slowly convergent infinite sums. These are completely eliminated using Coulomb resolutions. They provide an excellent approximation that reduces these integrals to a sum of one-electron overlap-like integral products that each involve orbitals on at most two centers. Such two-center integrals are separable in prolate spheroidal coordinates. They are thus readily evaluated. Only these integrals need to be re-evaluated to change basis functions. The above is still valid or three-center integrals. In four-center integrals, the resolutions require translating one potential term per product. This is outlined here and detailed elsewhere. Numerical results are reported for the H 2 dimer and CH 3 F molecule.

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“…The usefulness of non-Gaussian basis sets with improved cusp properties is illustrated most starkly by considering the current use 18 of Slater basis sets [19][20][21] for specific purposes despite the very long integral evaluation times, 22,23 as well as more generally in the Amsterdam Density Functional (ADF) program. 24 Thus, despite more than 80 yr of investigation, [25][26][27][28] research is still undertaken [29][30][31][32][33][34][35][36][37][38][39][40][41] to improve integral evaluation for Slatertype orbitals to make these calculations competitive with all-Gaussian calculations. Given this, mixed ramp-Gaussian basis sets arguably encapsulate the best of both worlds: characteristics similar to all-Slater basis sets with the potential to match or better all-Gaussian calculation speeds.…”

Section: Introductionmentioning

confidence: 99%

Efficient calculation of integrals in mixed ramp-Gaussian basis sets

McKemmish

2015

The Journal of Chemical Physics

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Algorithms for the efficient calculation of two-electron integrals in the newly developed mixed ramp-Gaussian basis sets are presented, alongside a Fortran90 implementation of these algorithms, RampItUp. These new basis sets have significant potential to (1) give some speed-up (estimated at up to 20% for large molecules in fully optimised code) to general-purpose Hartree-Fock (HF) and density functional theory quantum chemistry calculations, replacing all-Gaussian basis sets, and (2) give very large speed-ups for calculations of core-dependent properties, such as electron density at the nucleus, NMR parameters, relativistic corrections, and total energies, replacing the current use of Slater basis functions or very large specialised all-Gaussian basis sets for these purposes. This initial implementation already demonstrates roughly 10% speed-ups in HF/R-31G calculations compared to HF/6-31G calculations for large linear molecules, demonstrating the promise of this methodology, particularly for the second application. As well as the reduction in the total primitive number in R-31G compared to 6-31G, this timing advantage can be attributed to the significant reduction in the number of mathematically complex intermediate integrals after modelling each ramp-Gaussian basis-function-pair as a sum of ramps on a single atomic centre.

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Rational approximants to evaluate four-center electron repulsion integrals for 1s hydrogen Slater type functions

Cited by 8 publications

References 23 publications

Four‐center Slater‐type orbital molecular integrals without orbital translations

Four‐center Slater‐type orbital molecular integrals without orbital translations

General two‐electron exponential type orbital integrals in polyatomics without orbital translations

Efficient calculation of integrals in mixed ramp-Gaussian basis sets

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