Application of combined open shell Hartree–Fook–Roothaan theory to molecules using symmetrical one-range addition theorems of Slater type orbitals

2009 ◽  
Vol 47 (1) ◽  
pp. 295-304 ◽  
Author(s):  
I. I. Guseinov ◽  
B. A. Mamedov ◽  
Z. Andıç
Keyword(s):  
Open Shell ◽  
Slater Type Orbitals ◽  
Addition Theorems ◽  
Slater Type

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.

scholarly journals A Hartree - Fock Program for Atomic Structure Calculations

1999 ◽  
Vol 52 (6) ◽  
pp. 973 ◽  
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.

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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