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...
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| Sprache: | English |
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Singapore ; Hackensack, NJ :
World Scientific,
©2012.
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| Zusammenfassung: | 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 resource (xi, 227 pages) : illustrations |
| Bibliographie: | Includes bibliographical references (pages 207-219) and index. |
| ISBN: | 9814350478 9789814350471 |
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| 100 | 1 | |a Avery, John, |d 1933- |1 https://id.oclc.org/worldcat/entity/E39PBJdCrg3ggGYF4gKMKRVt8C |0 http://id.loc.gov/authorities/names/n82252507 | |
| 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. |
| 260 | |a Singapore ; |a Hackensack, NJ : |b World Scientific, |c ©2012. | ||
| 300 | |a 1 online resource (xi, 227 pages) : |b illustrations | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 504 | |a Includes bibliographical references (pages 207-219) and index. | ||
| 505 | 0 | |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 -- 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. | |
| 520 | |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 | 0 | |a Algebras, Linear. |0 http://id.loc.gov/authorities/subjects/sh85003441 | |
| 650 | 0 | |a Symmetry (Physics) |0 http://id.loc.gov/authorities/subjects/sh85131443 | |
| 650 | 0 | |a Basis sets (Quantum mechanics) |0 http://id.loc.gov/authorities/subjects/sh85012107 | |
| 650 | 6 | |a Algèbre linéaire. | |
| 650 | 6 | |a Symétrie (Physique) | |
| 650 | 7 | |a SCIENCE |x Physics |x 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 | |
| 700 | 1 | |a Rettrup, Sten. | |
| 700 | 1 | |a Avery, James. | |
| 758 | |i has work: |a Symmetry-adapted basis sets (Text) |1 https://id.oclc.org/worldcat/entity/E39PCGChmw69gmp8xkgCykHkCP |4 https://id.oclc.org/worldcat/ontology/hasWork | ||
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Datensatz im Suchindex
| DE-BY-FWS_katkey | ZDB-4-EBA-ocn776990543 |
|---|---|
| _version_ | 1816881786590855168 |
| adam_text | |
| any_adam_object | |
| author | Avery, John, 1933- |
| author2 | Rettrup, Sten Avery, James |
| author2_role | |
| author2_variant | s r sr j a ja |
| author_GND | http://id.loc.gov/authorities/names/n82252507 |
| author_facet | Avery, John, 1933- Rettrup, Sten Avery, James |
| author_role | |
| author_sort | Avery, John, 1933- |
| author_variant | j a ja |
| building | Verbundindex |
| bvnumber | localFWS |
| callnumber-first | Q - Science |
| callnumber-label | QA184 |
| callnumber-raw | QA184.2 .A94 2012 |
| callnumber-search | QA184.2 .A94 2012 |
| callnumber-sort | QA 3184.2 A94 42012 |
| callnumber-subject | QA - Mathematics |
| collection | ZDB-4-EBA |
| 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. |
| ctrlnum | (OCoLC)776990543 |
| 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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ind1=" " ind2=" "><subfield code="a">Includes bibliographical references (pages 207-219) and index.</subfield></datafield><datafield tag="505" ind1="0" ind2=" "><subfield code="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 -- 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.</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="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.</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">Algebras, Linear.</subfield><subfield code="0">http://id.loc.gov/authorities/subjects/sh85003441</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">Symmetry (Physics)</subfield><subfield code="0">http://id.loc.gov/authorities/subjects/sh85131443</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">Basis sets (Quantum mechanics)</subfield><subfield code="0">http://id.loc.gov/authorities/subjects/sh85012107</subfield></datafield><datafield tag="650" ind1=" " ind2="6"><subfield code="a">Algèbre linéaire.</subfield></datafield><datafield tag="650" ind1=" " ind2="6"><subfield code="a">Symétrie (Physique)</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">SCIENCE</subfield><subfield code="x">Physics</subfield><subfield code="x">General.</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Algebras, Linear</subfield><subfield code="2">fast</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Basis sets (Quantum mechanics)</subfield><subfield code="2">fast</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Symmetry (Physics)</subfield><subfield code="2">fast</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Rettrup, Sten.</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Avery, James.</subfield></datafield><datafield tag="758" ind1=" " ind2=" "><subfield code="i">has work:</subfield><subfield code="a">Symmetry-adapted basis sets (Text)</subfield><subfield code="1">https://id.oclc.org/worldcat/entity/E39PCGChmw69gmp8xkgCykHkCP</subfield><subfield code="4">https://id.oclc.org/worldcat/ontology/hasWork</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Print version:</subfield><subfield code="z">9789814350464</subfield><subfield code="z">981435046X</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="l">FWS01</subfield><subfield code="p">ZDB-4-EBA</subfield><subfield code="q">FWS_PDA_EBA</subfield><subfield code="u">https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=521257</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">ebrary</subfield><subfield code="b">EBRY</subfield><subfield code="n">ebr10529384</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">EBSCOhost</subfield><subfield code="b">EBSC</subfield><subfield code="n">521257</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">YBP Library Services</subfield><subfield code="b">YANK</subfield><subfield code="n">7223088</subfield></datafield><datafield tag="994" ind1=" " ind2=" "><subfield code="a">92</subfield><subfield code="b">GEBAY</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-4-EBA</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-863</subfield></datafield></record></collection> |
| id | ZDB-4-EBA-ocn776990543 |
| illustrated | Illustrated |
| indexdate | 2024-11-27T13:18:15Z |
| institution | BVB |
| isbn | 9814350478 9789814350471 |
| language | English |
| oclc_num | 776990543 |
| open_access_boolean | |
| owner | MAIN DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource (xi, 227 pages) : illustrations |
| psigel | ZDB-4-EBA |
| publishDate | 2012 |
| publishDateSearch | 2012 |
| publishDateSort | 2012 |
| publisher | World Scientific, |
| record_format | marc |
| spelling | Avery, John, 1933- https://id.oclc.org/worldcat/entity/E39PBJdCrg3ggGYF4gKMKRVt8C http://id.loc.gov/authorities/names/n82252507 Symmetry-adapted basis sets : automatic generation for problems in chemistry and physics / John Scales Avery, Sten Rettrup, James Emil Avery. Singapore ; Hackensack, NJ : World Scientific, ©2012. 1 online resource (xi, 227 pages) : illustrations text txt rdacontent computer c rdamedia online resource 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. Algebras, Linear. http://id.loc.gov/authorities/subjects/sh85003441 Symmetry (Physics) http://id.loc.gov/authorities/subjects/sh85131443 Basis sets (Quantum mechanics) http://id.loc.gov/authorities/subjects/sh85012107 Algèbre linéaire. Symétrie (Physique) SCIENCE Physics General. bisacsh Algebras, Linear fast Basis sets (Quantum mechanics) fast Symmetry (Physics) fast Rettrup, Sten. Avery, James. has work: Symmetry-adapted basis sets (Text) https://id.oclc.org/worldcat/entity/E39PCGChmw69gmp8xkgCykHkCP https://id.oclc.org/worldcat/ontology/hasWork Print version: 9789814350464 981435046X FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=521257 Volltext |
| spellingShingle | Avery, John, 1933- Symmetry-adapted basis sets : automatic generation for problems in chemistry and physics / 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. Algebras, Linear. http://id.loc.gov/authorities/subjects/sh85003441 Symmetry (Physics) http://id.loc.gov/authorities/subjects/sh85131443 Basis sets (Quantum mechanics) http://id.loc.gov/authorities/subjects/sh85012107 Algèbre linéaire. Symétrie (Physique) SCIENCE Physics General. bisacsh Algebras, Linear fast Basis sets (Quantum mechanics) fast Symmetry (Physics) fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85003441 http://id.loc.gov/authorities/subjects/sh85131443 http://id.loc.gov/authorities/subjects/sh85012107 |
| 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 | Algebras, Linear. http://id.loc.gov/authorities/subjects/sh85003441 Symmetry (Physics) http://id.loc.gov/authorities/subjects/sh85131443 Basis sets (Quantum mechanics) http://id.loc.gov/authorities/subjects/sh85012107 Algèbre linéaire. Symétrie (Physique) SCIENCE Physics General. bisacsh Algebras, Linear fast Basis sets (Quantum mechanics) fast Symmetry (Physics) fast |
| topic_facet | Algebras, Linear. Symmetry (Physics) Basis sets (Quantum mechanics) Algèbre linéaire. Symétrie (Physique) SCIENCE Physics General. Algebras, Linear |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=521257 |
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