An Application of the Gaussian Transform for Approximating Some Bessel Functions and Multicenter Integrals Involving 1s Slater-Type Orbitals

2016 ◽  
pp. 139-144
Author(s):  
Philip E. Hoggan ◽  
Jorge E. Pérez ◽  
Ahmed Bouferguene
Keyword(s):  
Bessel Functions ◽  
Slater Type Orbitals ◽  
Slater Type ◽  
Multicenter Integrals ◽  
Gaussian Transform

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.

Unified treatment of electronic attraction, electric field, and electric-field gradient multicenter integrals of reened and nonscreened Coulomb potentials using overlap integrals for Slater orbitals

2004 ◽  
Vol 82 (10) ◽  
pp. 819-825 ◽  
Author(s):  
I I Guseinov
Keyword(s):  
Electric Field ◽  
Electric Field Gradient ◽  
Field Gradient ◽  
Slater Type Orbitals ◽  
Overlap Integrals ◽  
Slater Type ◽  
Multicenter Integrals ◽  
Slater Orbitals ◽  
Rotational Transformation ◽  
Coulomb Potentials

A unified treatment of multicenter electronic attraction (EA), electric field (EF), and electric-field gradient (EFG) integrals of Yukawa-like screened and nonscreened Coulomb potentials with Slater-type orbitals (STOs) is described. Using different sets of series expansion formulas of two-center distributions for STOs in terms of STOs at a displaced center the EA, EF, and EFG integrals over STOs are expressed through the overlap integrals between potentials or their derivatives and STOs. These two-center overlap integrals are evaluated by the use of rotational transformation for overlap integrals established by the author. The final results expressed through the overlap integrals of STOs with the same screening constants are valid for the arbitrary parameters of STOs and potentials. PACS No.: 31.15.–p

Sign in / Sign up

Export Citation Format

Share Document