Performance of numerical approximation on the calculation of overlap integrals with noninteger Slater-type orbitals

Bağcı, A.; Hoggan, Philip E.

doi:10.1103/physreve.89.053307

Cited by 22 publications

(36 citation statements)

References 32 publications

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“…In addition, the results given in Ref. [24] using the single-center expansion method determine the upper limit of summation to be N e = 250 and constitute numerical proof of the nonexistence of the single-center expansion method made in Refs. [25,26] as the total number of terms used in these calculations is ≈ 4 × 10 4 , which are overlap integrals over STOs and still show no satisfactory convergence.…”

Section: Introductionsupporting

confidence: 58%

“…[24,[55][56][57][58] for the details on the implementation of the procedure and information on the roots and singularities). The algorithm described in Eq.…”

Section: Resultsmentioning

confidence: 99%

“…Detailed investigations of both methods have been made recently for two-center overlap integrals (see Ref. [24]). The results of Ref.…”

Section: Introductionmentioning

confidence: 99%

“…The results of Ref. [24] show that it is impossible to calculate molecular integrals over NSTOs accurately by use of single-center methods. This reference gives benchmark values for the first time, using an approach similar to that extended here.…”

Section: Introductionmentioning

confidence: 99%

“…Afterwards, the highly accurate evaluation of Coulomb and hybrid integrals over STOs and NSTOs using the numerical global-adaptive method, specifically using the Gauss-Kronrod rule (please see Ref. [24] for details), is performed. A computer program is constructed in the MATHEMATICA programming language [48] with the numerical methods therein.…”

Section: Introductionmentioning

confidence: 99%

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Benchmark values for molecular two-electron integrals arising from the Dirac equation

Bağcı

Hoggan

2015

Phys. Rev. E

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The two-center two-electron Coulomb and hybrid integrals arising in relativistic and nonrelativistic ab initio calculations on molecules are evaluated. Compact, arbitrarily accurate expressions are obtained. They are expressed through molecular auxiliary functions and evaluated with the numerical Global-adaptive method for arbitrary values of parameters in the noninteger Slater-type orbitals. Highly accurate benchmark values are presented for these integrals. The convergence properties of new molecular auxiliary functions are investigated. The comparison for two-center two-electron integrals is made with results obtained from single center expansions by translation of the wave function to a single center with integer principal quantum numbers and results obtained from the Cuba numerical integration algorithm, respectively. The procedures discussed in this work are capable of yielding highly accurate two-center two-electron integrals for all ranges of orbital parameters.

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Section: Introductionsupporting

confidence: 58%

“…[24,[55][56][57][58] for the details on the implementation of the procedure and information on the roots and singularities). The algorithm described in Eq.…”

Section: Resultsmentioning

confidence: 99%

“…Detailed investigations of both methods have been made recently for two-center overlap integrals (see Ref. [24]). The results of Ref.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Benchmark values for molecular two-electron integrals arising from the Dirac equation

Bağcı

Hoggan

2015

Phys. Rev. E

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Analytical evaluation of relativistic molecular integrals. I. Auxiliary functions

Bağcı¹,

Hoggan²

2018

Rend. Fis. Acc. Lincei

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The Slater-type orbital basis with non-integer principal quantum numbers is a physically and mathematically motivated choice for molecular electronic structure calculations in both non-relativistic and relativistic theory. The non-analyticity of these orbitals at r = 0, however, requires analytical relations for multi-center integrals to be derived. This is nearly insurmountable. Previous papers by present authors eliminated this difficulty. Highly accurate results can be achieved by the procedure described in these papers, which place no restrictions on quantum numbers in all ranges of orbital parameters. The purpose of this work is to investigate computational aspects of the formulae given in the previous paper. It is to present a method which helps to increase computational efficiency. In terms of the processing time, evaluation of integrals over Slater-type orbitals with non-integer principal quantum numbers are competitive with those over Slater-type orbitals with integer principal quantum numbers.Keywords Slater-type orbitals · Multi-center integrals · Auxiliary functions 1 IntroductionIn the first paper [1] of aforementioned series, history and importance of usage the auxiliary function method was summarized. Applications in molecular calculations were briefly

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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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Performance of numerical approximation on the calculation of overlap integrals with noninteger Slater-type orbitals

Cited by 22 publications

References 32 publications

Benchmark values for molecular two-electron integrals arising from the Dirac equation

Benchmark values for molecular two-electron integrals arising from the Dirac equation

Analytical evaluation of relativistic molecular integrals. I. Auxiliary functions

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

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