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Transferable integrals in a deformation density approach to crystal orbital calculations. IV. Evaluation of angular integrals by a vector-pairing method

✍ Scribed by John Avery; Per-Johan ørmen

Publisher
John Wiley and Sons
Year
1980
Tongue
English
Weight
676 KB
Volume
18
Category
Article
ISSN
0020-7608

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✦ Synopsis

Abstract

A general method for performing angular integrations is presented. The method depends on the fact that the integral must be invariant under rotations of the coordinate system, and it also makes use of combinatorial analysis. In most cases the method presented is computationally much faster than alternative methods of angular integration using Condon–Shortley coefficients. Applications to charge density analysis and Fourier transforms are discussed, and a general formula for the action of angular momentum projection operators on functions of the Cartesian coordinates is derived. A general angular integration formula for an m‐dimensional space is also given.

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Transferable integrals in a deformation-density approach to crystal orbital calculations. I
✍ John Avery 📂 Article 📅 1979 🏛 John Wiley and Sons 🌐 English ⚖ 499 KB

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## Abstract A new method for calculating crystal orbitals in the Hartree‐Fock‐Slater approximation is proposed. The method makes use of x‐ray crystallographic measurements of the deformation density, and uses transferable integrals to treat the neutral–atom potentials. Methods for evaluating matrix

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Transferable integrals in a deformation density approach to crystal calculations. I. Crystal harmonics and their properties
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## Abstract The term “crystal harmonic” is introduced to denote a symmetrized plane wave in the special case where the wave vector is a reciprocal lattice vector. Crystal harmonics, thus defined, have the translational symmetry of the lattice, and they also have the transformation properties of the