Evaluation of Multicenter Electric Multipole Moment Integrals over Integer and Noninteger <i>n</i>‐STOs

Özdoğan, Telhat

doi:10.1002/jccs.200400003

Cited by 6 publications

(1 citation statement)

References 80 publications

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“…It was supposed that the results of calculations obtained with any of these approximations are accurate. Accordingly, these approximations applied for solution of various problems [86][87][88][89][90][91][92][93][94]. Finally, the benchmark results for two−, three−center one− and two−electron molecular integrals which have been demanded for years in order to test the accuracy of any analytical method to be derived, obtained via numerical global-adaptive method through Gauss-Kronrod numerical integration extension [95] by us [96][97][98] with 35 correct decimals.…”

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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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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Hartree‐Fock‐Roothaan calculations for ground states of some atoms using minimal basis sets of integer and noninteger n‐STOs

Gümüş

Özdoğan

2004

Chin. J. Chem.

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Hartree-Fock-Roothaan (HFR) calculations for ground states of some atoms, i.e. He, Be, Ne, Ar, and Kr have been performed using minimal basis sets of Slater type orbitals (STOs) with integer and noninteger principal quantum numbers (integer n-STOs and noninteger n-STOs). The obtained total energies for these atoms using minimal basis sets of integer n-STOs are in good agreement with those in the previous literature. On the other hand, for the case of minimal basis sets of noninteger n-STOs, although the calculated total energies of these atoms agree well with the results in Literature, some striking results have been obtained for atoms Ar and Kr. Our computational results for the energies of atoms Ar and Kr are slightly better than those in literature. by amount of 0.00222 and O.oooO54 a.u., respectively. The improvement in the energies of atoms Ar and Kr may result from the efficient calculations of one-center two-electron integrals over noninteger n-STOs. For some atomic ions in their ground state, HFR calculations have been canied out using minimal basis sets of noninteger n-STOs. The obtained total energies for these atomic ions are substantially lower than those available in literature.

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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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Evaluation of Multicenter Electric Multipole Moment Integrals over Integer and Noninteger n‐STOs

Cited by 6 publications

References 80 publications

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

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

Hartree‐Fock‐Roothaan calculations for ground states of some atoms using minimal basis sets of integer and noninteger n‐STOs

Translation of STO charge distributions

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