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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 |
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| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
World Scientific,
2011.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Preface; 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 rules3. 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 C3v; the NH3 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 blocks4.8 Invariant subsets based on subshells; Classification according to ML and Ms; 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 Tvv(N) and vv(N) 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 ITERATION8.1 Conservation of symmetry under Fourier transformation; 8.2 The operator
- + p2k 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; Appendix A REPRESENTATION THEORY OF FINITE GROUPS; A.1 Basic definitions; A.2 Representations of geometrical symmetry groups.