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Symmetry-adapted basis sets : automatic generation for problems in chemistry and physics /
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 eigenfunc...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Otros Autores: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Singapore ; Hackensack, NJ :
World Scientific,
©2012.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- 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.