Calculation of nuclear‐attraction and modified overlap integrals using Gegenbauer coefficients*

Öztekin, Emin; Özcan, Selda; Orbay, Metin; Yavuz, Metin

doi:10.1002/qua.983

Cited by 9 publications

(1 citation statement)

References 58 publications

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“…here 𝐹 𝑙 (𝑛) are the binomial coefficients and 𝐶 𝑛 𝜆 (𝑥) is Gegenbauer polynomial defined by the following relation [57,58];…”

Section: General Formulasmentioning

confidence: 99%

Slater Tipi Orbitaller Bazında Bir- ve İki-Merkezli Coulomb İntegrallerinin Özellikleri

Akdemir

2022

Süleyman Demirel Üniversitesi Fen Edebiyat Fakültesi Fen Dergisi

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In this study, two-electron one- and two-center Coulomb integrals with the same and different screening parameters are investigated numerically in the real Slater type orbital (STO) basis using Fourier transform method. In momentum space firstly, for atomic, i.e. one-center, Coulomb integrals are calculated, and analytical expressions are obtained in terms of binomial coefficients. Then, the solutions of the two-center Coulomb integrals are made with the modified Bessel function of second kind and the results are expressed in terms of binomial and Gaunt coefficients, irregular solid harmonics, and finite sum of STOs. A computer program is written in the MATHEMATICA language to determine the accuracy of the analytical expressions that are highly suitable for programming. The numerical results obtained from the program are given in the tables, and it is shown that the results agree with the literature.

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“…here 𝐹 𝑙 (𝑛) are the binomial coefficients and 𝐶 𝑛 𝜆 (𝑥) is Gegenbauer polynomial defined by the following relation [57,58];…”

Section: General Formulasmentioning

confidence: 99%

Slater Tipi Orbitaller Bazında Bir- ve İki-Merkezli Coulomb İntegrallerinin Özellikleri

Akdemir

2022

Süleyman Demirel Üniversitesi Fen Edebiyat Fakültesi Fen Dergisi

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Efficiency of the algorithms for the calculation of Slater molecular integrals in polyatomic molecules

et al. 2004

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The performances of the algorithms employed in a previously reported program for the calculation of integrals with Slater-type orbitals are examined. The integrals are classified in types and the efficiency (in terms of the ratio accuracy/cost) of the algorithm selected for each type is analyzed. These algorithms yield all the one- and two-center integrals (both one- and two-electron) with an accuracy of at least 12 decimal places and an average computational time of very few microseconds per integral. The algorithms for three- and four-center electron repulsion integrals, based on the discrete Gauss transform, have a computational cost that depends on the local symmetry of the molecule and the accuracy of the integrals, standard efficiency being in the range of eight decimal places in hundreds of microseconds.

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Translation of STO charge distributions

et al. 2005

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Barnett and Coulson's zeta-function method (M. P. Barnett and C. A. Coulson, Philos. Trans. R. Soc., Lond. A 1951, 243, 221) is one of the main sources of algorithms for the solution of multicenter integrals with Slater-type orbitals. This method is extended here from single functions to two-center charge distributions, which are expanded at a third center in terms of spherical harmonics times analytical radial factors. For s-s distributions, the radial factors are given by a series of factors corresponding to the translation of s-type orbitals. For distributions with higher quantum numbers, they are obtained from those of the s-s distributions by recurrence. After analyzing the convergence of the series, a computational algorithm is proposed and its practical efficiency is tested in three-center (AB/CC) repulsion integrals. In cases of large basis sets, the procedure yields about 12 correct significant figures with a computational cost of a few microseconds per integral.

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Calculation of nuclear‐attraction and modified overlap integrals using Gegenbauer coefficients*

Cited by 9 publications

References 58 publications

Slater Tipi Orbitaller Bazında Bir- ve İki-Merkezli Coulomb İntegrallerinin Özellikleri

Slater Tipi Orbitaller Bazında Bir- ve İki-Merkezli Coulomb İntegrallerinin Özellikleri

Efficiency of the algorithms for the calculation of Slater molecular integrals in polyatomic molecules

Translation of STO charge distributions

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