Calculation of One-Electron Multicenter Integrals of Slater Type Orbitals and Coulomb–Yukawa Like Correlated Interaction Potentials with Integer and Noninteger Indices Using Unsymmetrical One-Range Addition Theorems

2010 ◽  
Vol 83 (9) ◽  
pp. 1047-1051 ◽  
Author(s):  
I. I. Guseinov ◽  
B. A. Mamedov
Keyword(s):  
Slater Type Orbitals ◽  
Addition Theorems ◽  
Slater Type ◽  
Interaction Potentials ◽  
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 UNSYMMETRICAL AND SYMMETRICAL ONE-RANGE ADDITION THEOREMS FOR SLATER TYPE ORBITALS AND COULOMB–YUKAWA-LIKE CORRELATED INTERACTION POTENTIALS OF INTEGER AND NONINTEGER INDICES

2008 ◽  
Vol 07 (02) ◽  
pp. 257-262 ◽  
Author(s):  
I. I. GUSEINOV
Keyword(s):  
Basis Functions ◽  
Slater Type Orbitals ◽  
Addition Theorems ◽  
Slater Type ◽  
Interaction Potentials ◽  
Hartree Fock ◽  
Quantum Numbers ◽  
Noninteger Principal Quantum Numbers ◽  
Multicenter Multielectron Integrals ◽  
Exponential Type Orbitals

Using one-center expansion relations for the Slater type orbitals (STOs) of noninteger principal quantum numbers in terms of integer nSTOs derived in this study with the help of ψa-exponential type orbitals (ψa-ETOs, a = 1, 0, -1, -2,…), the general formulas through the integer nSTOs are established for the unsymmetrical and symmetrical one-range addition theorems for STOs and Coulomb–Yukawa-like correlated interaction potentials (CIPs) with integer and noninteger indices. The final results are especially useful for the computations of arbitrary multicenter multielectron integrals that arise in the Hartree–Fock–Roothaan (HFR) approximation and also in the correlated methods based upon the use of STOs as basis functions.

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