Symmetry-adapted basis sets: automatic generation for problems in chemistry and physics
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| Sprache: | English |
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©2012
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| Beschreibung: | Includes bibliographical references (pages 207-219) and index 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 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 approximate methods, the most common of which is expansion of the eigenfunctions in terms of basis functions that obey the boundary conditions of the problem. The computational effort needed in such problems can be much reduced by making use of symmetry-adapted basis functions. The conventional method for generating symmetry-adapted basis sets is through the application of group theory, but this can be difficult. This book describes an easier method for generating symmetry-adapted basis sets automatically with computer techniques. The method has a wide range of applicability and can be used to solve difficult eigenvalue problems in a number of fields. The book is of special interest to quantum theorists, computer scientists, computational chemists and applied mathematicians |
| Beschreibung: | 1 Online-Ressource (xi, 227 pages) |
| ISBN: | 9789814350464 9789814350471 981435046X 9814350478 |
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| 245 | 1 | 0 | |a Symmetry-adapted basis sets |b automatic generation for problems in chemistry and physics |c John Scales Avery, Sten Rettrup, James Emil Avery |
| 264 | 1 | |a Singapore |b World Scientific |c ©2012 | |
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| 500 | |a Includes bibliographical references (pages 207-219) and index | ||
| 500 | |a 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 -- | ||
| 500 | |a - 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 -- | ||
| 500 | |a - 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 -- | ||
| 500 | |a - 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 | ||
| 500 | |a 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 approximate methods, the most common of which is expansion of the eigenfunctions in terms of basis functions that obey the boundary conditions of the problem. The computational effort needed in such problems can be much reduced by making use of symmetry-adapted basis functions. The conventional method for generating symmetry-adapted basis sets is through the application of group theory, but this can be difficult. This book describes an easier method for generating symmetry-adapted basis sets automatically with computer techniques. The method has a wide range of applicability and can be used to solve difficult eigenvalue problems in a number of fields. The book is of special interest to quantum theorists, computer scientists, computational chemists and applied mathematicians | ||
| 650 | 7 | |a SCIENCE / Physics / General |2 bisacsh | |
| 650 | 7 | |a Algebras, Linear |2 fast | |
| 650 | 7 | |a Basis sets (Quantum mechanics) |2 fast | |
| 650 | 7 | |a Symmetry (Physics) |2 fast | |
| 650 | 4 | |a Algebras, Linear | |
| 650 | 4 | |a Symmetry (Physics) | |
| 650 | 4 | |a Basis sets (Quantum mechanics) | |
| 700 | 1 | |a Rettrup, Sten |e Sonstige |4 oth | |
| 700 | 1 | |a Avery, James |e Sonstige |4 oth | |
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Datensatz im Suchindex
| _version_ | 1804175545897844736 |
|---|---|
| any_adam_object | |
| author | Avery, John |
| author_facet | Avery, John |
| author_role | aut |
| author_sort | Avery, John |
| author_variant | j a ja |
| building | Verbundindex |
| bvnumber | BV043118718 |
| collection | ZDB-4-EBA |
| ctrlnum | (OCoLC)776990543 (DE-599)BVBBV043118718 |
| dewey-full | 530.1 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.1 |
| dewey-search | 530.1 |
| dewey-sort | 3530.1 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
| format | Electronic eBook |
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| id | DE-604.BV043118718 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:18:00Z |
| institution | BVB |
| isbn | 9789814350464 9789814350471 981435046X 9814350478 |
| language | English |
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| spelling | Avery, John Verfasser aut Symmetry-adapted basis sets automatic generation for problems in chemistry and physics John Scales Avery, Sten Rettrup, James Emil Avery Singapore World Scientific ©2012 1 Online-Ressource (xi, 227 pages) txt rdacontent c rdamedia cr rdacarrier Includes bibliographical references (pages 207-219) and index 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 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 approximate methods, the most common of which is expansion of the eigenfunctions in terms of basis functions that obey the boundary conditions of the problem. The computational effort needed in such problems can be much reduced by making use of symmetry-adapted basis functions. The conventional method for generating symmetry-adapted basis sets is through the application of group theory, but this can be difficult. This book describes an easier method for generating symmetry-adapted basis sets automatically with computer techniques. The method has a wide range of applicability and can be used to solve difficult eigenvalue problems in a number of fields. The book is of special interest to quantum theorists, computer scientists, computational chemists and applied mathematicians SCIENCE / Physics / General bisacsh Algebras, Linear fast Basis sets (Quantum mechanics) fast Symmetry (Physics) fast Algebras, Linear Symmetry (Physics) Basis sets (Quantum mechanics) Rettrup, Sten Sonstige oth Avery, James Sonstige oth http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=521257 Aggregator Volltext |
| spellingShingle | Avery, John Symmetry-adapted basis sets automatic generation for problems in chemistry and physics SCIENCE / Physics / General bisacsh Algebras, Linear fast Basis sets (Quantum mechanics) fast Symmetry (Physics) fast Algebras, Linear Symmetry (Physics) Basis sets (Quantum mechanics) |
| title | Symmetry-adapted basis sets automatic generation for problems in chemistry and physics |
| title_auth | Symmetry-adapted basis sets automatic generation for problems in chemistry and physics |
| title_exact_search | Symmetry-adapted basis sets automatic generation for problems in chemistry and physics |
| title_full | Symmetry-adapted basis sets automatic generation for problems in chemistry and physics John Scales Avery, Sten Rettrup, James Emil Avery |
| title_fullStr | Symmetry-adapted basis sets automatic generation for problems in chemistry and physics John Scales Avery, Sten Rettrup, James Emil Avery |
| title_full_unstemmed | Symmetry-adapted basis sets automatic generation for problems in chemistry and physics John Scales Avery, Sten Rettrup, James Emil Avery |
| title_short | Symmetry-adapted basis sets |
| title_sort | symmetry adapted basis sets automatic generation for problems in chemistry and physics |
| title_sub | automatic generation for problems in chemistry and physics |
| topic | SCIENCE / Physics / General bisacsh Algebras, Linear fast Basis sets (Quantum mechanics) fast Symmetry (Physics) fast Algebras, Linear Symmetry (Physics) Basis sets (Quantum mechanics) |
| topic_facet | SCIENCE / Physics / General Algebras, Linear Basis sets (Quantum mechanics) Symmetry (Physics) |
| url | http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=521257 |
| work_keys_str_mv | AT averyjohn symmetryadaptedbasissetsautomaticgenerationforproblemsinchemistryandphysics AT rettrupsten symmetryadaptedbasissetsautomaticgenerationforproblemsinchemistryandphysics AT averyjames symmetryadaptedbasissetsautomaticgenerationforproblemsinchemistryandphysics |