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Symmetry-adapted basis sets : automatic generation for problems in chemistry and physics

Author: John Avery; Sten Rettrup; James Avery
Publisher: Singapore ; Hackensack, NJ : World Scientific, ©2012.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Database:WorldCat
Summary:
In theoretical physics, theoretical chemistry and engineering, one often wishes to solve partial differential equations subject to a set of boundary conditions. This gives rise to eigenvalue problems of which some solutions may be very difficult to find. For example, the problem of finding eigenfunctions and eigenvalues for the Hamiltonian of a many-particle system is usually so difficult that it requires  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: John Avery; Sten Rettrup; James Avery
ISBN: 9814350478 9789814350471
OCLC Number: 776990543
Description: 1 online resource (xi, 227 pages) : illustrations
Contents: 1. General considerations. 1.1 The need for symmetry-adapted basis functions. 1.2. Fundamental concepts. 1.3 Definition of invariant blocks. 1.4. Diagonalization of the invariant blocks. 1.5. Transformation of the large matrix to block-diagonal form. 1.6. Summary of the method --
2. Examples from atomic physics. 2.1. The Hartree-Fock-Roothaan method for calculating atomic orbitals. 2.2. Automatic generation of symmetry-adapted configurations. 2.3. Russell-Saunders states. 2.4. Some illustrative examples. 2.5. The Slater-Condon rules. 2.6. Diagonalization of invariant blocks using the Slater-Condon rules --
3. Examples from quantum chemistry. 3.1. The Hartree-Fock-Roothaan method applied to molecules. 3.2. Construction of invariant subsets. 3.3. The trigonal group C[symbol] the NH[symbol] molecule --
4. Generalized sturmians applied to atoms. 4.1. Goscinskian configurations. 4.2. Relativistic corrections. 4.3. The large-Z approximation: restriction of the basis set to an R-block. 4.4. Electronic potential at the nucleus in the large-Z approximation. 4.5. Core ionization energies. 4.6. Advantages and disadvantages of Goscinskian configurations. 4.7. R-blocks, invariant subsets and invariant blocks. 4.8. Invariant subsets based on subshells; Classification according to M[symbol] and M[symbol]. 4.9. An atom surrounded by point charges --
5. Molecular orbitals based on sturmians. 5.1. The one-electron secular equation. 5.2. Shibuya-Wulfman integrals and Sturmian overlap integrals evaluated in terms of hyperpherical harmonics. 5.3. Molecular calculations using the isoenergetic configurations. 5.4. Building T[symbol] and [symbol] from 1-electron components. 5.5. Interelectron repulsion integrals for molecular Sturmians from hyperspherical harmonics. 5.6. Many-center integrals treated by Gaussian expansions (Appendix E). 5.7. A pilot calculation. 5.8. Automatic generation of symmetry-adapted basis functions --
6. An example from acoustics. 6.1. The Helmholtz equation for a non-uniform medium. 6.2. Homogeneous boundary conditions at the surface of a cube. 6.3. Spherical symmetry of v(x); nonseparability of the Helmholtz equation. 6.4. Diagonalization of invariant blocks --
7. An example from heat conduction. 7.1. Inhomogeneous media . 7.2. A 1-dimensional example. 7.3. Heat conduction in a 3-dimensional inhomogeneous medium --
8. Symmetry-adapted solutions by iteration. 8.1. Conservation of symmetry under Fourier transformation. 8.2. The operator [symbol] and its Green's function. 8.3. Conservation of symmetry under iteration of the Schrodinger equation. 8.4. Evaluation of the integrals. 8.5. Generation of symmetry-adapted basis functions by iteration. 8.6. A simple example. 8.7. An alternative expansion of the Green's function that applies to the Hamiltonian formulation of physics.
Responsibility: John Scales Avery, Sten Rettrup, James Emil Avery.

Abstract:

In theoretical physics, theoretical chemistry and engineering, one often wishes to solve partial differential equations subject to a set of boundary conditions. This book describes an easier method  Read more...

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