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Angular dependence of Gaussian-Lobe orbitals. I. Analysis of standard p- and d-orbitals

✍ Scribed by H. Le Rouzo; B. Silvi

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

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✦ Synopsis

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 average‐square values of multipole components are related to a unique orbital parameter λ. The numerical values of p‐ and d‐components are given for selected λ and the choice of this parameter is discussed on the basis of symmetry and computational arguments. The transferability of optimized atomic exponents from harmonic (or Cartesian) functions to lobe functions is established so that the possibility of applying the Gaussian‐lobe orbital approach in chemical studies is greatly extended.

📜 SIMILAR VOLUMES

Angular dependence of Gaussian-Lobe orbi
Angular dependence of Gaussian-Lobe orbitals. II. Set of axial Gaussian-Lobe orbitals
✍ H. Le Rouzo; B. Silvi 📂 Article 📅 1978 🏛 John Wiley and Sons 🌐 English ⚖ 642 KB

## 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 usin

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## 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.

On the use of Gaussian shell type basis
On the use of Gaussian shell type basis orbitals for single-center expansions. I. Evaluation of integrals
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## Abstract Formulas are derived for all Hamiltonian integrals required for molecular computations using a novel basis for single‐center expansions. The basis orbitals depend exponentially upon α(__r__ − ρ)^2^ where __r__ and ρ are the distance from center to electron and to a variationally scaled

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## Abstract __Ab initio__ double‐zeta quality molecular orbital calculations have been carried out on an extensive series of ten‐electron hydrides. The Edmiston–Ruedenberg energy‐localized molecular orbitals were calculated and the total molecular and localized orbital densities analyzed in terms o

Torsional Angular Dependence of 1J(Se,Se
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## Abstract ^__n__^__J__(Se,Se) (__n__=1–4) nuclear couplings between Se atoms were analyzed by using molecular orbital (MO) theory as the first step to investigating the nature of bonded and nonbonded ^__n__^__J__(Se,Se) interactions between Se atoms. The values were calculated by employing Slater