A FOURIER TRANSFORM APPROACH FOR TWO-CENTER OVERLAP-LIKE QUANTUM SIMILARITY INTEGRALS OVER SLATER TYPE ORBITALS

2004 ◽  
Vol 03 (02) ◽  
pp. 257-267 ◽  
Author(s):  
LILIAN BERLU
Keyword(s):  
Fourier Transform ◽  
Angular Momentum ◽  
Range Expansion ◽  
Expansion Method ◽  
Slater Type Orbitals ◽  
Quantum Similarity ◽  
Overlap Integrals ◽  
Slater Type ◽  
Transform Method ◽  
The Fourier Transform

In previous work,1 we presented a one center two range expansion method for the evaluation of the two-center overlap-like quantum similarity integrals over Slater type orbitals which are four orbitals overlap integrals. In this work, to improve the accuracy and to reduce the calculation times, the above integrals are developed using the Fourier transform approach and the so-called B functions. With the help of angular momentum selection rules, two-center overlap-like quantum similarity integrals are expressed as combinations of usual overlap integrals (e.g. two-orbitals) which could be evaluated very accurately using the Fourier transform method combinated with B functions.

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.

Useful Integrals for Ab-Initio Molecular Quantum Similarity Measurements Using Slater Type Atomic Orbitals

2003 ◽  
Vol 02 (02) ◽  
pp. 147-161 ◽  
Author(s):  
Lilian Berlu ◽  
Philip Hoggan
Keyword(s):  
Ab Initio ◽  
Similarity Function ◽  
Slater Type Orbitals ◽  
Quantum Similarity ◽  
Overlap Integrals ◽  
Single Center ◽  
Slater Type ◽  
Atomic Orbitals ◽  
Dirac Delta ◽  
Molecular Quantum Similarity

Molecular quantum similarity measurements are based on a quantitative comparison of the one-electron densities of two molecules superposed and aligned to optimize a well-defined similarity function. In most previous work the densities have been related using a Dirac delta leading to the overlap-like quantum similarity function. The densities for the two molecules compared have generally been approximated often with a simple LCAO of s-gaussian functions. In this work, we present a one center two range expansion method for the evaluation of the overlap integrals involved in the overlap-like quantum similarity function over Slater type orbitals (STO). The single center and three types of two-center overlap integrals (involving four atomic orbitals; two in each molecule) have led to finite sums using a single center approach combined with selection rules obtained by analysis of orbital angular momentum (conservation). The three- and four-center integrals are also obtained analytically but involve infinite sums which require further study before leading to a complete set of integral codes for ab-initio quantum similarity.

A unified formula for the Fourier transform of Slater-type orbitals

1989 ◽  
Vol 39 (2) ◽  
pp. 226-229 ◽  
Author(s):  
Dževad Belkić ◽  
Howard S Taylor
Keyword(s):  
Fourier Transform ◽  
Slater Type Orbitals ◽  
Slater Type ◽  
The Fourier Transform

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.

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