Use of Recursion and Analytical Relations in Evaluation of Hypergeometric Functions Arising in Multicenter Integrals with Noninteger n Slater Type Orbitals

2005 ◽  
Vol 38 (4) ◽  
pp. 511-517 ◽  
Author(s):  
I. I. Guseinov ◽  
B. A. Mamedov
Keyword(s):  
Hypergeometric Functions ◽  
Slater Type Orbitals ◽  
Slater Type ◽  
Multicenter Integrals ◽  
Analytical Relations

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.

COMBINED THEORY OF NONRELATIVISTIC AND QUASIRELATIVISTIC ATOMIC INTEGRALS OVER INTEGER AND NONINTEGER N-SLATER-TYPE ORBITALS

2009 ◽  
Vol 08 (01) ◽  
pp. 47-56 ◽  
Author(s):  
I. I. GUSEINOV
Keyword(s):  
Slater Type Orbitals ◽  
Slater Type ◽  
Quantum Numbers ◽  
Slater Orbitals ◽  
Basic Functions ◽  
Analytical Relations

One- and two-electron nonrelativistic and quasirelativistic basic functions are introduced. The combined analytical relations in terms of these basic functions are derived for the non- and quasi-relativistic atomic integrals over integer and noninteger n-Slater-type orbitals. The relationships obtained are valid for the arbitrary values of principal quantum numbers and screening constants of Slater orbitals.

Unified treatment of overlap integrals with integer and noninteger n Slater-type orbitals using translational and rotational transformations for spherical harmonics

2004 ◽  
Vol 82 (3) ◽  
pp. 205-211 ◽  
Author(s):  
I I Guseinov ◽  
B A Mamedov
Keyword(s):  
Spherical Harmonics ◽  
Large Integer ◽  
Series Expansions ◽  
Slater Type Orbitals ◽  
Overlap Integrals ◽  
Addition Theorems ◽  
Slater Type ◽  
Quantum Numbers ◽  
Noninteger Principal Quantum Numbers ◽  
Analytical Relations

A unified treatment of two-center overlap integrals over Slater-type orbitals (STO) with integer and noninteger values of the principal quantum numbers is described. Using translation and rotation formulas for spherical harmonics, the overlap integrals with integer and noninteger n Slater-type orbitals are expressed through the basic overlap integrals and spherical harmonics. The basic overlap integrals are calculated using auxiliary functions Aσ and Bk. The analytical relations obtained in this work are especially useful for the calculation of overlap integrals for large integer and noninteger principal quantum numbers. The formulas established in this study for overlap integrals can be used for the construction of series expansions based on addition theorems. PACS Nos.: 31.15.–p, 31.20.Ej

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