Evaluation of two‐center, two‐ and three‐electron integrals involving correlation factors over Slater‐type orbitals. II. Kinetic and potential energy integrals and examples of numerical results

Budziński, Jan; Firszt, M.; Woźnicki, W.

doi:10.1002/qua.560410210

Cited by 12 publications

(9 citation statements)

References 22 publications

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“…The numerical tests performed [16] give positive results justifying the usefulness of that method in practical applications.…”

Section: Introductionmentioning

confidence: 64%

“…( 2 3 ) . The s o-c a l l e d c ompa r i s on v a l u e s a r e t he c ompu t a t i on r e s u l t s obt a i ne d by means of the method presented in [15,16], based on the Neumann expansion. In our opinion, they are rather accurate.…”

Section: Numerical Results and Conclusionmentioning

confidence: 99%

“…Analytical formulas for evaluating the twocenter, two-and three-electron integrals in prolate spherical coordinates [14,15] as well as the two and three-electron integrals with the one-electron operator [16] have been obtained. The numerical tests performed [16] give positive results justifying the usefulness of that method in practical applications.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Application of Laguerre Polynomials to Evaluation of Two-Center, Two- and Three-Electron Integrals in the Basis of Slater-Type Orbitals - Algorithm and Numerical Results

1994

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“…The numerical tests performed [16] give positive results justifying the usefulness of that method in practical applications.…”

Section: Introductionmentioning

confidence: 64%

Section: Numerical Results and Conclusionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Application of Laguerre Polynomials to Evaluation of Two-Center, Two- and Three-Electron Integrals in the Basis of Slater-Type Orbitals - Algorithm and Numerical Results

1994

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“…The wavefuctions Ψ in spherical, parabolic and prolate spheroidal coordinates are then distinguished by the corresponding quantum numbers.) By solving (31) and (32), we get the normalized wavefunction…”

Section: Parabolic Basismentioning

confidence: 99%

“…[28][29][30][31][32][33][34] for a nonhexhaustive list of papers showing the interest of spheroidal coordinates in quantum chemistry).…”

Section: Introductionmentioning

confidence: 99%

On a generalized Kepler–Coulomb system: Interbasis expansions

Kibler

Mardoyan

Pogosyan

1994

Int J of Quantum Chemistry

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This paper deals with a dynamical system that generalizes the Kepler-Coulomb system and the Hartmann system. It is shown that the Schrödinger equation for this generalized KeplerCoulomb system can be separated in prolate spheroidal coordinates. The coefficients of the interbasis expansions between three bases (spherical, parabolic and spheroidal) are studied in detail. It is found that the coefficients for the expansion of the parabolic basis in terms of the spherical basis, and vice-versa, can be expressed through the Clebsch-Gordan coefficients for the group SU(2) analytically continued to real values of their arguments. The coefficients for the expansions of the spheroidal basis in terms of the spherical and parabolic bases are proved to satisfy three-term recursion relations.

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Addition theorems as three-dimensional Taylor expansions

Weniger

2000

Int. J. Quant. Chem.

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A principal tool for the construction of the addition theorem of a r Ји١Ž . function f is the translation operator e , which generates f r q rЈ by doing a threedimensional Taylor expansion of f around r. In atomic and molecular quantum mechanics, one is usually interested in irreducible spherical tensors. In such a case, the application of the translation operator in its Cartesian form e xЈѨ rѨ x e yЈѨ rѨ y e zЈѨ rѨ z leads to serious technical problems. A much more promising approach consists of the use of an operator expansion for e r Ји١ which contains exclusively irreducible spherical tensors. This expansion contains as differential operators the Laplacian ٌ 2 and the spherical tensor m Ž . gradient operator Y Y ٌ , which is an irreducible spherical tensor of rank l. Thus, if l m Ž . Y Y ٌ is applied to another spherical tensor, the angular part of the resulting expression l is completely determined by angular momentum coupling, whereas the radial part is obtained by differentiating the radial part of the spherical tensor with respect to r. Consequently, the systematic use of the spherical tensor gradient operator leads to a considerable technical simplification. In this way, the originally three-dimensional expansion problem in x, y, and z is reduced to an essentially one-dimensional expansion problem in r. The practical usefulness of this approach is demonstrated by constructing the Laplace expansion of the Coulomb potential as well as the addition theorems of the regular and irregular solid harmonics and of the Yukawa potential.

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Evaluation of two‐center, two‐ and three‐electron integrals involving correlation factors over Slater‐type orbitals. II. Kinetic and potential energy integrals and examples of numerical results

Cited by 12 publications

References 22 publications

Application of Laguerre Polynomials to Evaluation of Two-Center, Two- and Three-Electron Integrals in the Basis of Slater-Type Orbitals - Algorithm and Numerical Results

Application of Laguerre Polynomials to Evaluation of Two-Center, Two- and Three-Electron Integrals in the Basis of Slater-Type Orbitals - Algorithm and Numerical Results

On a generalized Kepler–Coulomb system: Interbasis expansions

Addition theorems as three-dimensional Taylor expansions

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