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Angular dependence of Gaussian-Lobe orbitals. II. Set of axial Gaussian-Lobe orbitals

✍ Scribed by H. Le Rouzo; B. Silvi

Publisher
John Wiley and Sons
Year
1978
Tongue
English
Weight
642 KB
Volume
13
Category
Article
ISSN
0020-7608

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✦ Synopsis

Abstract

The topological properties of real spherical harmonic representations on the unit sphere have been found to provide a convenient tool to infer the lobe edifices which mimic these orbitals. The prohibitive number of lobes required in such an approach for l > 2, can be avoided in using only axial Gaussian‐lobe orbitals (AGLO). It is proved that 2__l__ + 1 independent Y~lo~‐like functions correctly span the relevant Y~lm~ (m = βˆ’l,l) subspace. The multipolar component analysis of any spatial arrangement of lobes is derived, and allows the optimization of the angular dependence of AGLOS. The cases of d‐ and f‐orbitals are studied in detail and accurate optimized functions are proposed. This method can be easily extended to obtain the atomic orbitals of any azimuthal quantum number l‐subspace.

πŸ“œ SIMILAR VOLUMES

Angular dependence of Gaussian-Lobe orbi
Angular dependence of Gaussian-Lobe orbitals. III. Polyhedric lobe edifices
✍ H. Le Rouzo; B. Silvi πŸ“‚ Article πŸ“… 1978 πŸ› John Wiley and Sons 🌐 English βš– 224 KB

## Abstract An analysis is presented that shows how the angular symmetry defects of lobe orbitals constructed from a polyhedric edifice can be accurately evaluated, and how these lobe orbitals can be related to harmonic Gaussian functions, the exponents being tranferred by a scale factor procedure.

Angular dependence of Gaussian-Lobe orbi
Angular dependence of Gaussian-Lobe orbitals. I. Analysis of standard p- and d-orbitals
✍ H. Le Rouzo; B. Silvi πŸ“‚ Article πŸ“… 1978 πŸ› John Wiley and Sons 🌐 English βš– 590 KB

## Abstract Multipole expansions of Gaussian‐lobe atomic orbitals around their centers are theoretically investigated in order to study the exact angular dependence of such functions. Analytical expressions of the multipole coefficients are derived for standard lobe orbitals. It is shown that the a

Axial gaussian-lobe orbitals: Optimizati
Axial gaussian-lobe orbitals: Optimization of highly angularly dependent functions
✍ H. Le Rouzo πŸ“‚ Article πŸ“… 1981 πŸ› John Wiley and Sons 🌐 English βš– 697 KB

## Abstract Highly angularly dependent axial Gaussian‐lobe orbitals (AGLO) (up to __L__ = 5) are presented. The angular and radial optimizations of these functions have been realized on the ground of theoretical frameworks, previously reported in the literature and somewhat extended here. The numer

Spherically symmetric axial Gaussian lob
Spherically symmetric axial Gaussian lobe 3d and 4f orbitals
✍ Donald D. Shillady; David B. Talley πŸ“‚ Article πŸ“… 1982 πŸ› John Wiley and Sons 🌐 English βš– 444 KB

## Abstract The axial Gaussian lobe orbital (AGLO) representations of 3__d__ and 4__f__ orbitals proposed by LeRouzo and Silvi have been angularly optimized to ensure spherical symmetry of filled 3__d__ and 4__f__ shells. The functions have been tested on the hydrogen atom in the presence of high q