Fast and stable algorithm for analytical evaluation of two‐center overlap integrals over Slater‐type orbitals with integer and noninteger principal quantum numbers

Özdoğan, Telhat

doi:10.1002/qua.20160

Cited by 9 publications

(3 citation statements)

References 73 publications

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“…The above expression has been extensively used by many authors [110,113,114] who presented explicit expressions for the coefficients B n a n b k (the so-called generalized binomial coefficients). We found it simpler to tabulate these coefficients as series of one-dimensional lookup tables.…”

Section: Preliminariesmentioning

confidence: 97%

Reexamination of the calculation of two-center, two-electron integrals over Slater-type orbitals. I. Coulomb and hybrid integrals

Lesiuk

Moszyński

2014

Phys. Rev. E

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In this paper, which constitutes the first part of the series, we consider calculation of two-center Coulomb and hybrid integrals over Slater-type orbitals. General formulas for these integrals are derived with no restrictions on the values of the quantum numbers and nonlinear parameters. Direct integration over the coordinates of one of the electrons leaves us with the set of overlaplike integrals which are evaluated by using two distinct methods. The first one is based on the transformation to the ellipsoidal coordinates system and the second utilizes a recursive scheme for consecutive increase of the angular momenta in the integrand. In both methods simple one-dimensional numerical integrations are used in order to avoid severe digital erosion connected with the straightforward use of the alternative analytical formulas. It is discussed that the numerical integration does not introduce a large computational overhead since the integrands are well-behaved functions, calculated recursively with decent speed. Special attention is paid to the numerical stability of the algorithms. Applicability of the resulting scheme over a large range of the nonlinear parameters is tested on examples of the most difficult integrals appearing in the actual calculations including, at most, 7i-type functions (l=6).

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Section: Preliminariesmentioning

confidence: 97%

Reexamination of the calculation of two-center, two-electron integrals over Slater-type orbitals. I. Coulomb and hybrid integrals

Lesiuk

Moszyński

2014

Phys. Rev. E

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“…In the late of 90s one more attempt was made by Mekelleche and Baba−Ahmed [70,71]. Due to lack of benchmark values for the integrals then, a tremendous number of papers were published (Mostly by Guseinov, his co−workers [72][73][74][75][76][77][78] and Ozdogan, his co−workers [79][80][81][82]. We only cite here, those that are noteworthy.…”

Section: Introductionmentioning

confidence: 99%

Analytical evaluation of relativistic molecular integrals. II: Method of computation for molecular auxiliary functions involved

Bağcı

Hoggan

Adak

2018

Rend. Fis. Acc. Lincei

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Fully analytical method for calculation of the molecular integrals over Slater−type orbitals with non−integer principal quantum numbers are proposed. These integrals are expressed through relativistic molecular auxiliary functions derived in our previous paper [Phys. Rev. E 91, 023303 (2015)]. The procedure for computation of the molecular auxiliary functions is detailed. It applies both in relativistic and non-relativistic electronic structure theory. It is capable of yielding highly accurate molecular integrals for all ranges of orbital parameters and quantum numbers.

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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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Fast and stable algorithm for analytical evaluation of two‐center overlap integrals over Slater‐type orbitals with integer and noninteger principal quantum numbers

Cited by 9 publications

References 73 publications

Reexamination of the calculation of two-center, two-electron integrals over Slater-type orbitals. I. Coulomb and hybrid integrals

Reexamination of the calculation of two-center, two-electron integrals over Slater-type orbitals. I. Coulomb and hybrid integrals

Analytical evaluation of relativistic molecular integrals. II: Method of computation for molecular auxiliary functions involved

Efficient calculation of integrals in mixed ramp-Gaussian basis sets

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