Unified analytical treatment of one- and two-electron multicenter integrals with Slater-type orbitals

1988 ◽  
Vol 37 (7) ◽  
pp. 2314-2317 ◽  
Author(s):  
I. I. Guseinov
Keyword(s):  
Slater Type Orbitals ◽  
Slater Type ◽  
Analytical Treatment ◽  
Multicenter Integrals

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.

scholarly journals Berechnung von Eigensdiaften zweiatomiger Moleküle Ein- und Zweizentrenintegrale mit Slater-Funktionen / Calculation of Properties of Diatomic Molecules. One and Two Center Integrals Using Slater Type Orbitals

1973 ◽  
Vol 28 (2) ◽  
pp. 142-173
Author(s):  
Otto Hell ◽  
Hans Knof
Keyword(s):  
Computer Program ◽  
Numerical Integration ◽  
Computer Programs ◽  
Slater Type Orbitals ◽  
Slater Type ◽  
Analytical Treatment ◽  
Program Logic ◽  
Modern Computer ◽  
Numerical Integrations ◽  
The One

The methods for evaluation of two center integrals by use of Slater functions originate from the time of desk calculators, although they were later adapted to computers. This paper gives an analytical treatment of these integrals, in preparation for a modern computer program. The sixfold two electron two center integrals require only one numerical integration in case of the exchange integrals, and in case of the Coulomb and hybrid integrals two numerical integrations are required. The one center integrals and all the one electron integrals are solved fully analytically. This makes the analysis and program logic more lucid.All the special conditions arising during evaluation of the integrals are described in detail so that this paper should suffice as a basis for writing computer programs to evaluate such integrals.

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