Use of auxiliary functions $${Q_{ns}^q}$$ and $${G_{-ns}^q}$$ in evaluation of multicenter integrals over integer and noninteger n-Slater type orbitals arising in Hartree–Fock–Roothaan equations for molecules

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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Computation of molecular integrals over Slater-type orbitals. V. Calculation of multicenter electron-repulsion integrals using auxiliary functions

Journal of Molecular Structure THEOCHEM ◽

10.1016/s0166-1280(99)00499-6 ◽

2000 ◽

Vol 528 (1-3) ◽

pp. 245-253 ◽

Cited By ~ 7

Author(s):

I.I. Guseinov ◽

B.A. Mamedov

Keyword(s):

Slater Type Orbitals ◽

Slater Type ◽

Auxiliary Functions ◽

Electron Repulsion ◽

Molecular Integrals ◽

Electron Repulsion Integrals

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

Journal of Theoretical and Computational Chemistry ◽

10.1142/s0219633602000130 ◽

2002 ◽

Vol 01 (01) ◽

pp. 17-24 ◽

Cited By ~ 28

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.

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UNSYMMETRICAL AND SYMMETRICAL ONE-RANGE ADDITION THEOREMS FOR SLATER TYPE ORBITALS AND COULOMB–YUKAWA-LIKE CORRELATED INTERACTION POTENTIALS OF INTEGER AND NONINTEGER INDICES

Journal of Theoretical and Computational Chemistry ◽

10.1142/s0219633608003691 ◽

2008 ◽

Vol 07 (02) ◽

pp. 257-262 ◽

Cited By ~ 16

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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A Hartree - Fock Program for Atomic Structure Calculations

Australian Journal of Physics ◽

10.1071/ph99042 ◽

1999 ◽

Vol 52 (6) ◽

pp. 973 ◽

Cited By ~ 26

Author(s):

J. Mitroy

Keyword(s):

Open Shell ◽

Fortran Program ◽

Basis Functions ◽

Slater Type Orbitals ◽

Matrix Equations ◽

Slater Type ◽

Hartree Fock ◽

The Matrix ◽

Atomic Structure Calculations ◽

Structure Calculations

The Hartree–Fock equations for a general open shell atom are described. The matrix equations that result when the single particle orbitals are written in terms of a linear combination of analytic basis functions are derived. Attention is paid to the complexities that occur when open shells are present. The specifics of a working FORTRAN program which is available for public use are described. The program has the flexibility to handle either Slater-type orbitals or Gaussian-type orbitals.

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