Fourier transform of spherical Laguerre Gaussian functions and its application in molecular integrals
✍ Scribed by Lue-Yung Chow Chiu; Mohammad Moharerrzadeh
- Publisher
- John Wiley and Sons
- Year
- 1999
- Tongue
- English
- Weight
- 296 KB
- Volume
- 73
- Category
- Article
- ISSN
- 0020-7608
No coin nor oath required. For personal study only.
✦ Synopsis
The Fourier transform of the spherical Laguerre Gaussian-type function 1 2 lq 2 l y␣ r 2 Ž . Ž . Ž . LGTF , L ␣r r Y r e , was derived. Applying the Fourier transform convolution n l m theorem, the basic two-center integrals over the general two-electron irregular solid Ž . Lq1 Ž harmonic operator, Y r rr which becomes Coulomb repulsion, spin᎐other-orbit LM 12 12
. interaction or spin᎐spin interaction when L s 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 threeand 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.