Premium
Fourier transform of spherical Laguerre Gaussian functions and its application in molecular integrals
Author(s) -
Chiu LueYung Chow,
Moharerrzadeh Mohammad
Publication year - 1999
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/(sici)1097-461x(1999)73:3<265::aid-qua1>3.0.co;2-7
Subject(s) - laguerre polynomials , fourier transform , type (biology) , spherical harmonics , slater integrals , convolution (computer science) , wave function , physics , gaussian , coulomb , quantum mechanics , electron , mathematical physics , mathematical analysis , mathematics , ecology , machine learning , artificial neural network , computer science , biology
The Fourier transform of the spherical Laguerre Gaussian‐type function (LGTF), L n l +½(α r 2 ) r l Y lm ( r̂ ) e −α r 2, was derived. Applying the Fourier transform convolution theorem, the basic two‐center integrals over the general two‐electron irregular solid harmonic operator, Y LM ( r̂ 12 )/ r 12 L +1(which becomes Coulomb repulsion, spin–other‐orbit interaction or spin–spin interaction when L =0, 1, or 2, respectively) as well as the overlap were evaluated analytically. These basic integral results generate the two‐electron integrals of the Coulomb type, hybrid type, and exchange type as well as that of three‐ and four‐center. The formulas obtained, which are general for electronic wave functions of unrestricted quantum numbers n , l , and m , are expressed explicitly in terms of nuclear spherical LGTFs of internuclear geometrical variables. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 73: 265–273, 1999