On the combination of two methods for the calculation of multicenter integrals using exponential-type orbitals

The series expansion formulae are established for the one- and two-center charge densities over complete orthonormal sets of Ψα-exponential type orbitals (Ψα-ETO α = 1,0,-1,-2,…) introduced by the author. Three-center overlap integrals of Ψα appearing in these relations are expressed through the two-center overlap integrals between Ψα-orbitals. The general formulae obtained for the charge densities are utilized for the evaluation of arbitrary multicenter–multielectron integrals occurring when the complete orthonormal sets of Ψα-ETO are used as basis functions in the Hartree–Fock–Roothaan and explicitly correlated methods. The relationships for charge densities and multicenter–multielectron integrals obtained are valid for the arbitrary quantum numbers, screening constants, and location of Ψα-orbitals.

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New methods for accelerating the convergence of molecular electronic integrals over exponential type orbitals

Molecular Physics ◽

10.1080/0026897021000026809 ◽

2003 ◽

Vol 101 (1-2) ◽

pp. 19-31 ◽

Cited By ~ 16

Author(s):

HASSAN SAFOUHI ◽

PHILIP HOGGAN

Keyword(s):

Exponential Type ◽

Molecular Electronic ◽

New Methods ◽

Exponential Type Orbitals

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Application of Complete Orthonormal Sets of Ψ α -Exponential-Type Orbitals to Accurate Ground and Excited States Calculations of One-Electron Diatomic Molecules Using Single-Zeta Approximation

Chinese Physics Letters ◽

10.1088/0256-307x/25/8/030 ◽

2008 ◽

Vol 25 (8) ◽

pp. 2841-2844 ◽

Cited By ~ 2

Author(s):

I Guseinov ◽

R Aydιn ◽

A Bağcι

Keyword(s):

Excited States ◽

Exponential Type ◽

Diatomic Molecules ◽

Exponential Type Orbitals

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EVALUATION OF ONE- AND TWO-ELECTRON MULTICENTER INTEGRALS OF YUKAWA-LIKE SCREENED CENTRAL AND NONCENTRAL INTERACTION POTENTIALS OVER SLATER ORBITALS USING ADDITION THEOREMS

International Journal of Modern Physics C ◽

10.1142/s0129183105007534 ◽

2005 ◽

Vol 16 (06) ◽

pp. 837-842 ◽

Cited By ~ 1

Author(s):

I. I. GUSEINOV ◽

B. A. MAMEDOV

Keyword(s):

Numerical Stability ◽

Slater Type Orbitals ◽

Overlap Integrals ◽

Slater Type ◽

Interaction Potentials ◽

Multicenter Integrals ◽

Expansion Formulae ◽

Slater Orbitals ◽

Exponential Type Orbitals ◽

The One

By the use of complete orthonormal sets of Ψα-exponential type orbitals (Ψα-ETOs, where α =1, 0, -1, -2, …), the series expansion formulae are established for the one- and two-electron multicenter integrals of arbitrary Yukawa-like screened central and noncentral interaction potentials (YSCPs and YSNCPs) in terms of two- and three-center overlap integrals of three Slater type orbitals (STOs). The convergence of the series is tested by the concrete cases of parameters. The formulae given in this study for the evaluation of one- and two-electron multicenter integrals of YSCPs and YSNCPs show good rate of convergence and numerical stability.

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