Formulas for three-center exchange integrals by computer implementation of the L�wdin ?-function method

Jones, Herbert W.

doi:10.1002/qua.560260810

Int. J. Quantum Chem.

1984

DOI: 10.1002/qua.560260810

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Formulas for three-center exchange integrals by computer implementation of the L�wdin ?-function method

Herbert W. Jones

Abstract: By use of computer algebra and expansions of orbitals about a single center in spherical harmonics with a matrix representation for the a-function coefficients it is possible to produce formulas for each term of an infinite series that represents the value of a three-center exchange integral. Only seven terms are required to get six decimal digits for triatomic hydrogen. This method is readily generalized to solve all three-center exchange integrals over Slater-type orbitals.

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1986

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Cited by 6 publications

References 13 publications

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Calculation of the one‐electron two‐center integrals with STOS using recurrence‐based algorithms

1988

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We present a new algorithm for the calculation of two‐center one‐electron integrals with STOS based on two sets of recurrence relations. The first one enables us to calculate any of these integrals in terms of a few “basic integrals.” Furthermore, these basic integrals are written in terms of certain auxiliary functions which can be obtained through the second set of relations from only two starting values. We give also simple formulas for these starting quantities. Finally, the numerical stability, accuracy, and speed of the different steps of the algorithm are analyzed.

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Calculation of the one‐electron two‐center integrals with STOS using recurrence‐based algorithms

1988

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Computer‐generated formulas for four‐center integrals over slater‐type orbitals

Jones

1986

Int J of Quantum Chemistry

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A triple infinite sum of formulas is generated by a computer algebra implementation of the Lijwdin afunction method (supplemented by a C matrix with integer elements that characterize an orbital) for a fourcenter two-electron repulsion integral over 1s Siater-type orbitals, with screening constants of 1. In this example, one orbital is placed at the origin and the others at equal distances along the x, y , and z axes.Surprisingly few terms are needed for five figure accuracy. There should be no problem in generalizing these methods to all cases of four-center integrals.

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Developments in multicenter molecular integrals over STOs using expansions in spherical harmonics

Jones

1994

Int J of Quantum Chemistry

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The strategy of using expansions in spherical harmonics of displaced Slater-type orbitals for the evaluation of multicenter molecular integrals is reviewed and projected. Our Lowdin a-function method is augmented by computer algebra and C, E, and F matrices with rational elements. This permits exact evaluations of each term in an infinite sum using a commercial computer algebra program to investigate the three-center nuclear attraction integral. Each term (harmonic potential) is important for proposed use in numerical evaluations of multicenter integrals. 0

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Formulas for three-center exchange integrals by computer implementation of the L�wdin ?-function method

Cited by 6 publications

References 13 publications

Calculation of the one‐electron two‐center integrals with STOS using recurrence‐based algorithms

Calculation of the one‐electron two‐center integrals with STOS using recurrence‐based algorithms

Computer‐generated formulas for four‐center integrals over slater‐type orbitals

Developments in multicenter molecular integrals over STOs using expansions in spherical harmonics

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