scholarly journals Unified Treatment for Two-Center One-Electron Molecular Integrals Over Slater Type Orbitals with Integer and Noninteger Principal Quantum Numbers

2004 ◽  
Vol 59 (11) ◽  
pp. 743-749
Author(s):  
Telhat Özdoğan
Keyword(s):  
Slater Type Orbitals ◽  
Legendre Functions ◽  
Slater Type ◽  
Expansion Formula ◽  
Good Convergence ◽  
Quantum Numbers ◽  
Noninteger Principal Quantum Numbers ◽  
Wide Range ◽  
Internuclear Distances ◽  
Molecular Integrals

A unified expression has been obtained for two-center one-electron molecular integrals over Slater type orbitals with integer and noninteger principal quantum numbers by the use of the expansion formula for the product of two normalized associated Legendre functions. The presented expression for two-center one-electron molecular integrals contains the expansion coefficients akk' us and Mulliken integrals An and Bn. The efficiency of the presented calculation has been compared with that of other methods, indicating good convergence and great numerical stability for a wide range of quantum numbers, orbital exponents and internuclear distances

On The Computation Of Two-Center Coulomb Integrals Over Slater Type Orbitals Using The Poisson Equation

2005 ◽  
Vol 60 (7) ◽  
pp. 477-483 ◽  
Author(s):  
Sedat Gümüş
Keyword(s):  
Poisson Equation ◽  
Analytical Formula ◽  
Slater Type Orbitals ◽  
Slater Type ◽  
Quantum Numbers ◽  
The Poisson Equation ◽  
Wide Range ◽  
Internuclear Distances ◽  
Coulomb Integrals ◽  
Orbital Exponents

In this paper, a new analytical formula has been derived for the two-center Coulomb integrals over Slater type orbitals using the Poisson equation. The obtained results from constructed computer program for the presented formula have been compared with the available literature and it is seen that the efficiency of the presented algorithm for a wide range of quantum numbers, orbital exponents and internuclear distances is satisfactory.

Evaluation of Two-Center Overlap Integrals Over Slater-Type Orbitals Using Fourier Transform Convolution Theorem

2004 ◽  
Vol 69 (2) ◽  
pp. 279-291 ◽  
Author(s):  
Telhat Özdogan
Keyword(s):  
Fourier Transform ◽  
Convolution Theorem ◽  
Slater Type Orbitals ◽  
Overlap Integrals ◽  
Slater Type ◽  
Quantum Numbers ◽  
Wide Range ◽  
Internuclear Distances ◽  
Analytical Expressions ◽  
Orbital Exponents

Analytical expressions are presented for two-center overlap integrals over Slater-type orbitals using Fourier transform convolution theorem. The efficiency of calculation of these expressions is compared with those of other methods and good rate of convergence and great numerical stability is obtained for wide range of quantum numbers, orbital exponents and internuclear distances.

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 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.

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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