Comment on ‘‘Molecular overlap integrals with exponential‐type orbitals’’

1987 ◽  
Vol 87 (6) ◽  
pp. 3709-3711 ◽  
Author(s):  
E. Joachim Weniger ◽  
E. Otto Steinborn
Keyword(s):  
Exponential Type ◽  
Overlap Integrals ◽  
Exponential Type Orbitals

scholarly journals EXPANSION FORMULAE FOR ONE- AND TWO-CENTER CHARGE DENSITIES OVER COMPLETE ORTHONORMAL SETS OF EXPONENTIAL TYPE ORBITALS AND THEIR USE IN EVALUATION OF MULTICENTER–MULTIELECTRON INTEGRALS

2009 ◽  
Vol 08 (04) ◽  
pp. 597-602 ◽  
Author(s):  
I. I. GUSEINOV
Keyword(s):  
Exponential Type ◽  
Overlap Integrals ◽  
Charge Densities ◽  
Hartree Fock ◽  
Expansion Formulae ◽  
Multicenter Multielectron Integrals ◽  
Explicitly Correlated ◽  
Explicitly Correlated Methods ◽  
Exponential Type Orbitals ◽  
The One

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.

Molecular overlap integrals with exponential‐type orbitals

1986 ◽  
Vol 84 (3) ◽  
pp. 1598-1605 ◽  
Author(s):  
A. K. Bhattacharya ◽  
S. C. Dhabal
Keyword(s):  
Exponential Type ◽  
Overlap Integrals ◽  
Exponential Type Orbitals

COMPUTATION OF THREE-CENTER OVERLAP INTEGRALS OVER NONINTEGER n SLATER TYPE ORBITALS USING Ψα-ETO

2007 ◽  
Vol 06 (03) ◽  
pp. 641-646 ◽  
Author(s):  
I. I. GUSEINOV ◽  
B. A. MAMEDOV
Keyword(s):  
Exponential Type ◽  
Slater Type Orbitals ◽  
Overlap Integrals ◽  
Slater Type ◽  
Interaction Potentials ◽  
Quantum Numbers ◽  
Noninteger Principal Quantum Numbers ◽  
Multicenter Multielectron Integrals ◽  
Exponential Type Orbitals

Using complete orthonormal sets of Ψα-exponential type orbitals (Ψα- ETO , α = 1, 0, -1, -2,…), the three-center overlap integrals over noninteger n STO (NISTO) appearing in the evaluation of multicenter–multielectron integrals of central and noncentral interaction potentials are calculated. The final results are expressed in terms of one- or two-center overlap integrals between NISTO and integer n STO (ISTO). The formulas obtained are valid for arbitrary noninteger principal quantum numbers, screening parameters, and location of NSTO.

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

2005 ◽  
Vol 16 (06) ◽  
pp. 837-842 ◽  
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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