Evaluation of two‐center, three‐ and four‐electron integrals over Slater‐type orbitals in elliptical coordinates

Budziński, Jan

doi:10.1002/qua.10801

Cited by 11 publications

(2 citation statements)

References 44 publications

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“…Interestingly enough, there has been a significant progress on this issue in recent years. In fact, looking at only the past 15 years, there are many notable works of Bouferguene et al [10][11][12][13], Rico et al [14][15][16][17][18][19][20][21][22][23][24], Hoggan et al [25][26][27][28][29][30], Pachucki [31][32][33][34][35], and others [36][37][38][39][40][41][42][43][44][45][46][47][48][49][50][51][52]. In particular, for the diatomic systems STOs can be now used routinely [51].…”

Section: Introductionmentioning

confidence: 99%

Combining Slater-type orbitals and effective core potentials

2017

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We present a general methodology to evaluate matrix elements of the effective core potentials (ECPs) within one-electron basis set of Slater-type orbitals (STOs). The scheme is based on translation of individual STO distributions in the framework of Barnett-Coulson method. We discuss different types of integrals which naturally appear and reduce them to few basic quantities which can be calculated recursively or purely numerically. Additionally, we consider evaluation of the STOs matrix elements involving the core polarisation potentials (CPP) and effective spin-orbit potentials. Construction of the STOs basis sets designed specifically for use with ECPs is discussed and differences in comparison with all-electron basis sets are briefly summarised. We verify the validity of the present approach by calculating excitation energies, static dipole polarisabilities and valence orbital energies for the alkaline earth metals (Ca, Sr, Ba). Finally, we evaluate interaction energies, permanent dipole moments and ionisation energies for barium and strontium hydrides, and compare them with the best available experimental and theoretical data.

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Section: Introductionmentioning

confidence: 99%

Combining Slater-type orbitals and effective core potentials

2017

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“…It is well known that the evaluation of molecular integrals over χ-STOs has attracted continuous attention [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26]. To our knowledge, although many improvements have been made in previous years by the use of computers, an efficient program for the calculation of molecular integrals, particularly for the three-center nuclear attraction integral of χ-STOs, is not yet available in the literature.…”

Section: Introductionmentioning

confidence: 99%

On the fast evaluation of three-center nuclear attraction integrals using one-range addition theorems for Slater functions

Görgün¹

2013

Phys. Scr.

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Using one-range addition theorems, the three-center nuclear attraction integrals are expressed through the overlap integrals containing χand χ α -Slater-type orbitals (χ -STOs andFor the fast calculation, the partial summation is utilized for some indices of series expansion relations which correspond to progressively increasing upper limits. The binomial coefficients are stored in the memory of the computer. The convergence and accuracy of series are tested by calculating concrete cases. The best values are obtained for α = 0.

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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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Evaluation of two‐center, three‐ and four‐electron integrals over Slater‐type orbitals in elliptical coordinates

Abstract: An

Cited by 11 publications

References 44 publications

Combining Slater-type orbitals and effective core potentials

Combining Slater-type orbitals and effective core potentials

On the fast evaluation of three-center nuclear attraction integrals using one-range addition theorems for Slater functions

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

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