Weniger, Ernst Joachim (2002) Addition theorems as three-dimensional Taylor expansions. II. B functions and other exponentially decaying functions. INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, 90 (1). pp. 92-104. ISSN 0020-7608
Full text not available from this repository.Abstract
Addition theorems can be constructed by doing three-dimensional Taylor expansions according to f(r + r') = exp(r' . del)f (r). Since, however, one is normally interested in addition theorems of irreducible spherical tensors, the application of the translation operator in its Cartesian form exp(x'partial derivative / partial derivativex) exp(y'partial derivative / partial derivativey) exp(z'partial derivative / partial derivativez) would lead to enormous technical problems. A better alternative consists in using a series expansion for the translation operator exp(r' . del) involving powers of the Laplacian del(2) and spherical tensor gradient operators y(l)(m/) (del), which are irreducible spherical tensors of ranks zero and l, respectively (Santos, F.D. Nucl Phys A 1973, 212, 341). In this way, it is indeed possible to derive addition theorems by doing three-dimensional Taylor expansions (Weniger, E. J. Int J Quantum Chem 2000, 76, 280). The application of the translation operator in its spherical form is particularly simple in the case of B functions and leads to an addition theorem with a comparatively compact structure. Since other exponentially decaying functions like Slater-type functions, bound-state hydrogenic eigenfunctions, and other functions based on generalized Laguerre polynomials can be expressed by simple finite sums of B functions, the addition theorems for these functions can be written down immediately. (C) 2002 Wiley Periodicals, Inc. Int.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | SLATER-TYPE ORBITALS; 3-CENTER NUCLEAR ATTRACTION; REDUCED BESSEL-FUNCTIONS; GAUSSIAN-TYPE FUNCTIONS; LOWDIN ALPHA-FUNCTION; MULTICENTER BIELECTRONIC INTEGRALS; CALCULATING MOLECULAR INTEGRALS; ELECTRON-REPULSION INTEGRALS; NONLINEAR D-TRANSFORMATIONS; REAL SPHERICAL-HARMONICS; addition theorems; Taylor expansions; spherical tensor gradient operator; B functions; other exponentially decaying functions |
| Subjects: | 500 Science > 540 Chemistry & allied sciences |
| Divisions: | Chemistry and Pharmacy > Institut für Physikalische und Theoretische Chemie |
| Depositing User: | Petra Gürster |
| Date Deposited: | 11 Jun 2021 06:36 |
| Last Modified: | 11 Jun 2021 06:36 |
| URI: | https://pred.uni-regensburg.de/id/eprint/39781 |
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