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.

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.

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

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.

scholarly journals On the accurate Evaluation of Overlap Integrals over Slater Type Orbitals Using Analytical and Recurrence Relations

2007 ◽  
Vol 62 (9) ◽  
pp. 467-470 ◽  
Author(s):  
Israfil I. Guseinov ◽  
Bahtiyar A. Mamedov
Keyword(s):  
Recurrence Relations ◽  
Evaluation Procedure ◽  
Complete Agreement ◽  
Slater Type Orbitals ◽  
Overlap Integrals ◽  
Slater Type ◽  
Computational Accuracy ◽  
Accurate Evaluation ◽  
Program Language ◽  
Internuclear Distances

In this study, using the analytical and recurrence relations suggested by the authors in previous works, the new efficient and reliable program procedure for the overlap integrals over Slater type orbitals is presented. The proposed procedure guarantees a highly accurate evaluation of the overlap integrals with arbitrary values of quantum numbers, screening constants and internuclear distances. It is demonstrated that the computational accuracy of the proposed procedure is not only dependent on the efficiency of formulas, as has been discussed previously, but also on a number of other factors including the used program language package and solvent properties. The numerical results obtained, using the algorithm described in the present work, are in complete agreement with those obtained using the alternative evaluation procedure. We notice that the program works without any restrictions and in all ranges of integral parameters.

ANALYTICAL DEVELOPMENT OF MULTICENTER OVERLAP-LIKE QUANTUM SIMILARITY INTEGRALS OVER SLATER TYPE ORBITALS AND NUMERICAL EVALUATION

2005 ◽  
Vol 04 (03) ◽  
pp. 787-801 ◽  
Author(s):  
LILIAN BERLU ◽  
HASSAN SAFOUHI
Keyword(s):  
Fourier Transform ◽  
Linear Combination ◽  
Slater Type Orbitals ◽  
Quantum Similarity ◽  
Overlap Integrals ◽  
Slater Type ◽  
Atomic Orbitals ◽  
Dirac Delta ◽  
Electronic Densities ◽  
The Fourier Transform

Molecular overlap-like quantum similarity measurements imply the evaluation of overlap integrals of two molecular electronic densities related by the Dirac delta function. When the electronic densities are expanded over atomic orbitals using the usual LCAO (Linear Combination of Atomic Orbitals) scheme, overlap-like quantum similarity integrals could be expressed as a linear combination of four-center overlap integrals. In previous works, we showed that the one-center two-range expansion method leads to very complicated analytic expressions for three- and four-center terms. This is why its use has been prevented even for two-center integrals. We also showed that the use of the Fourier transform approach, combined with the so-called B functions, leads to great simplifications in both analytical and numerical development of overlap-like quantum similarity integrals over Slater type functions. In this work, a unified analytical treatment of multicenter overlap-like quantum similarity integrals over Slater type functions is described. The Fourier transform and nonlinear transformation methods are used. The numerical results section shows that the approach described in the present work can be applied to two-, three- and four-center integrals whatever nucleus positions might be.

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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