COMPUTATION OF MULTICENTER NUCLEAR-ATTRACTION INTEGRALS OF INTEGER AND NONINTEGER n SLATER ORBITALS USING AUXILIARY FUNCTIONS

2002 ◽  
Vol 01 (01) ◽  
pp. 17-24 ◽  
Author(s):  
I. I. GUSEINOV ◽  
B. A. MAMEDOV
Keyword(s):  
Series Expansion ◽  
Slater Type Orbitals ◽  
Slater Type ◽  
Auxiliary Functions ◽  
Quantum Numbers ◽  
Slater Orbitals ◽  
Nuclear Attraction

A unified treatment of multicenter nuclear-attraction integrals with integer n and noninteger n* Slater-type orbitals (ISTOs and NISTOs) is described. Using different sets of series expansion formulas for NISTOs and their two-center distributions in terms of ISTOs at a displaced center obtained by one of the authors, the three-center nuclear-attraction integrals over NISTOs are expressed through the products of overlap and two-center nuclear-attraction integrals. The two-center overlap and nuclear-attraction integrals are calculated by the use of well-known auxiliary functions Aσ and Bk. Accuracy of the computer results is quite high for quantum numbers, screening constants, and location of orbitals.

Self-friction power series and their use for evaluation of atomic nuclear attraction integrals with noninteger indices of Slater orbitals and Coulomb–Yukawa-like potentials

2017 ◽  
Vol 16 (02) ◽  
pp. 1750017
Author(s):  
Israfil I. Guseinov ◽  
Gurkan Demirdak
Keyword(s):  
Power Series ◽  
Slater Type Orbitals ◽  
Slater Type ◽  
Friction Power ◽  
Quantum Numbers ◽  
Slater Orbitals ◽  
Computer Calculations ◽  
Nuclear Attraction

Using complete orthogonal [Formula: see text]-Self-Friction Polynomials ([Formula: see text]-SFPs) introduced by one of the authors, the analytical and power series formulas for SF atomic nuclear attraction integrals over [Formula: see text]-noninteger Slater type orbitals ([Formula: see text]-NISTOs) and [Formula: see text]-noninteger Coulomb–Yukawa-like potentials ([Formula: see text]-NICYPs) are presented, where [Formula: see text] are the integer ([Formula: see text] or noninteger ([Formula: see text] SF quantum numbers and [Formula: see text]. As an application, the computer calculations for dependence of the atomic nuclear attraction integrals over [Formula: see text]-NISTOs and [Formula: see text]-NICYPs functions are presented.

scholarly journals Evaluation of Self-Friction Three-Center Nuclear Attraction Integrals with Integer and Noninteger Principal Quantum Numbers n over Slater Type Orbitals

2017 ◽  
Vol 2017 ◽  
pp. 1-6 ◽  
Author(s):  
Ebru Çopuroğlu
Keyword(s):  
Addition Theorem ◽  
Slater Type Orbitals ◽  
Slater Type ◽  
Arbitrary Integer ◽  
New Approach ◽  
Quantum Numbers ◽  
Noninteger Principal Quantum Numbers ◽  
Exponential Type Orbitals ◽  
Analytical Expressions ◽  
Nuclear Attraction

We have proposed a new approach to evaluate self-friction (SF) three-center nuclear attraction integrals over integer and noninteger Slater type orbitals (STOs) by using Guseinov one-range addition theorem in standard convention. A complete orthonormal set of Guseinov ψα exponential type orbitals (ψα-ETOs, α=2,1,0,-1,-2,…) has been used to obtain the analytical expressions. The overlap integrals with noninteger quantum numbers occurring in SF three-center nuclear attraction integrals have been evaluated using Qnsq auxiliary functions. The accuracy of obtained formulas is satisfactory for arbitrary integer and noninteger principal quantum numbers.

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.

scholarly journals Use of lined-up auxiliary functions in the evaluation of overlap integrals over integer and non-integer n Slater type orbitals

2019 ◽  
Vol 12 ◽  
pp. 298-301
Author(s):  
Israfil I. Guseinov ◽  
Zekayi Andıç ◽  
Bahtiyar A. Mamedov ◽  
Nurşen Seçkin Görgün
Keyword(s):  
Slater Type Orbitals ◽  
Overlap Integrals ◽  
Slater Type ◽  
Auxiliary Functions

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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