Weniger, Ernst Joachim (2000) Addition theorems as three-dimensional Taylor expansions. INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, 76 (2). pp. 280-295. ISSN 0020-7608
Full text not available from this repository.Abstract
A principal tool for the construction of the addition theorem of a function f is the translation operator e(r'.del), which generates f(r + r') by doing a three-dimensional Taylor expansion of f around r. In atomic and molecular quantum mechanics, one is usually interested in irreducible spherical tensors. In such a case, the application of the translation operator in its Cartesian form e(x'partial derivative)/(partial derivative x)e(y'partial derivative)/(partial derivative y)e(z'partial derivative)/(partial derivative z) leads to serious technical problems. A much more promising approach consists of the use of an operator expansion for e(r'.del) which contains exclusively irreducible spherical tensors. This expansion contains as differential operators the Laplacian del(2) and the spherical tensor gradient operator y(l)(m)(del), which is an irreducible spherical tensor of rank l. Thus, if y(l)(m)(del) is applied to another spherical tensor, the angular part of the resulting expression is completely determined by angular momentum coupling, whereas the radial part is obtained by differentiating the radial part of the spherical tensor with respect to r. Consequently, the systematic use of the spherical tensor gradient operator leads to a considerable technical simplification. In this way, the originally three-dimensional expansion problem in x, y, and z is reduced to an essentially one-dimensional expansion problem in y. The practical usefulness of this approach is demonstrated by constructing the Laplace expansion of the Coulomb potential as well as the addition theorems of the regular and irregular solid harmonics and of the Yukawa potential. (C) 2000 John Wiley & Sons, Inc.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | 3-BODY ATOMIC WAVEFUNCTIONS; GAUSSIAN-TYPE FUNCTIONS; INTERELECTRONIC DISTANCE FUNCTION; HYLLERAAS-TYPE CALCULATIONS; REDUCED BESSEL FUNCTIONS; SLATER-TYPE ORBITALS; MOLECULAR INTEGRALS; 3-ELECTRON INTEGRALS; ANALYTIC EXPANSIONS; SPHERICAL-HARMONICS; |
| Subjects: | 500 Science > 540 Chemistry & allied sciences |
| Divisions: | Chemistry and Pharmacy > Institut für Physikalische und Theoretische Chemie |
| Depositing User: | Petra Gürster |
| Date Deposited: | 28 Apr 2021 06:55 |
| Last Modified: | 28 Apr 2021 06:55 |
| URI: | https://pred.uni-regensburg.de/id/eprint/42894 |
Actions (login required)
 |
View Item |
