Symmetry of Intramolecular Quantum Dynamics.:
The main goal of this book is to give a systematic description of intramolecular quantum dynamics on the basis of only the symmetry principles. In this respect, the book has no analogs in the world literature. The obtained models lead to a simple, purely algebraic, scheme of calculation and are rigo...
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| Format: | Elektronisch E-Book |
| Sprache: | English Russian |
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Berlin :
De Gruyter,
2012.
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| Schriftenreihe: | De Gruyter studies in mathematical physics.
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| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | The main goal of this book is to give a systematic description of intramolecular quantum dynamics on the basis of only the symmetry principles. In this respect, the book has no analogs in the world literature. The obtained models lead to a simple, purely algebraic, scheme of calculation and are rigorous in the sense that their correctness is limited only to the correct choice of symmetry of the internal dynamics. The book is basically intended for scientists working in the field of molecular spectroscopy, quantum and structural chemistry. |
| Beschreibung: | 12.3 Internal geometric symmetry of the Hamiltonian. |
| Beschreibung: | 1 online resource (444 pages) |
| Bibliographie: | Includes bibliographical references and index. |
| ISBN: | 9783110267648 3110267640 3110267535 9783110267532 |
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| 300 | |a 1 online resource (444 pages) | ||
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| 490 | 1 | |a De Gruyter Studies in Mathematical Physics ; |v v. 11 | |
| 588 | 0 | |a Print version record. | |
| 505 | 0 | |a Preface; I Foundations of the mathematical apparatus; 1 Basic concepts of group theory; 1.1 The group postulates; 1.2 Subgroup, direct product of groups, isomorphism, and homomorphism; 1.3 Cosets. Semidirect product of groups; 1.4 Conjugacy classes; 2 Basic concepts of group representation theory; 2.1 Linear vector spaces; 2.2 Operators in configuration and function spaces; 2.3 Representations of groups; 2.4 Characters. Decomposition of reducible representations; 2.5 Direct product of representations. Symmetric power; 2.6 The Clebsch-Gordan coefficients. | |
| 505 | 8 | |a 2.7 Basis functions of irreducible representations2.8 Irreducible tensor operators. The Wigner-Eckart theorem; 3 The permutation group; 3.1 Operations in the permutation group. Classes; 3.2 Irreducible representations. The Young diagrams and tableaux; 3.3 Basis functions of irreducible representations; 3.4 The conjugate representation; 4 Continuous groups; 4.1 Compact Lie groups; 4.2 Lie group of linear transformations; 4.3 Lie algebra. Three-dimensional rotation group; 4.4 Irreducible representations of a three-dimensional rotation group; 5 Point groups; 5.1 Operations in point groups. | |
| 505 | 8 | |a 5.2 Discrete axial groups5.3 Cubic groups. Icosahedral groups; 5.4 Continuous axial groups; 6 Dynamic groups; 6.1 Invariant dynamic groups; 6.2 Noninvariant dynamic groups; II Qualitative intramolecular quantum dynamics; 7 The philosophy of using the symmetry properties of internal dynamics; 7.1 Symmetry groups of internal dynamics; 7.2 Significance of the analysis of symmetry properties; 7.3 On the domain of the point group; 7.4 The chain of symmetry groups; 7.5 The concept of the coordinate spin; 7.6 The influence of numerical methods on the overall description; 7.7 Conclusions. | |
| 505 | 8 | |a 8 Internal dynamics of rigid molecules8.1 Nonlinear molecules without inversion center; 8.2 Nonlinear molecules with inversion center; 8.3 Linear molecules; 8.4 Description of quasidegenerate vibronic states; 8.5 Conclusions; 9 Molecules with torsional transitions of the exchange type; 9.1 Extended point groups. Intermediate configuration; 9.2 Methanol molecule CH3OH; 9.3 Ethane molecule C2H6; 9.4 The molecules of complex hydrides LiBH4 and NaBH4; 9.5 The molecules of dimethyl ether (CH3)2O and acetone (CH3)2CO; 9.6 Conclusions; 10 Molecules with pseudorotations of the exchange type. | |
| 505 | 8 | |a 10.1 Extended point groups10.2 Cyclobutane molecule C4H8; 10.3 Molecules of the XPF4 type; 10.4 Phosphorus pentafluoride molecule PF5; 10.5 The separation of internal motions; 10.6 Conclusions; 11 Molecules with transitions of the nonexchange type between equivalent configurations; 11.1 Extended point groups; 11.2 The ammonia molecule NH3; 11.3 The peroxide molecule HOOH; 11.4 The hydrazine molecule N2H4; 11.5 Conclusions; 12 On the meaning of the Born-Oppenheimer Approximation; 12.1 Nondegenerate electronic states; 12.2 Degenerate electronic states. | |
| 500 | |a 12.3 Internal geometric symmetry of the Hamiltonian. | ||
| 520 | |a The main goal of this book is to give a systematic description of intramolecular quantum dynamics on the basis of only the symmetry principles. In this respect, the book has no analogs in the world literature. The obtained models lead to a simple, purely algebraic, scheme of calculation and are rigorous in the sense that their correctness is limited only to the correct choice of symmetry of the internal dynamics. The book is basically intended for scientists working in the field of molecular spectroscopy, quantum and structural chemistry. | ||
| 504 | |a Includes bibliographical references and index. | ||
| 546 | |a English. | ||
| 650 | 0 | |a Molecular dynamics |x Mathematical models. | |
| 650 | 0 | |a Molecular spectra. |0 http://id.loc.gov/authorities/subjects/sh85086591 | |
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| 650 | 4 | |a Dynamics | |
| 650 | 4 | |a Intramolecular | |
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| 650 | 4 | |a Quantum | |
| 650 | 6 | |a Dynamique moléculaire |x Modèles mathématiques. | |
| 650 | 6 | |a Molécules |x Spectre. | |
| 650 | 7 | |a SCIENCE |x Physics |x Atomic & Molecular. |2 bisacsh | |
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| 700 | 1 | |a Krayev, Alexey Vissarionovich. | |
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| contents | Preface; I Foundations of the mathematical apparatus; 1 Basic concepts of group theory; 1.1 The group postulates; 1.2 Subgroup, direct product of groups, isomorphism, and homomorphism; 1.3 Cosets. Semidirect product of groups; 1.4 Conjugacy classes; 2 Basic concepts of group representation theory; 2.1 Linear vector spaces; 2.2 Operators in configuration and function spaces; 2.3 Representations of groups; 2.4 Characters. Decomposition of reducible representations; 2.5 Direct product of representations. Symmetric power; 2.6 The Clebsch-Gordan coefficients. 2.7 Basis functions of irreducible representations2.8 Irreducible tensor operators. The Wigner-Eckart theorem; 3 The permutation group; 3.1 Operations in the permutation group. Classes; 3.2 Irreducible representations. The Young diagrams and tableaux; 3.3 Basis functions of irreducible representations; 3.4 The conjugate representation; 4 Continuous groups; 4.1 Compact Lie groups; 4.2 Lie group of linear transformations; 4.3 Lie algebra. Three-dimensional rotation group; 4.4 Irreducible representations of a three-dimensional rotation group; 5 Point groups; 5.1 Operations in point groups. 5.2 Discrete axial groups5.3 Cubic groups. Icosahedral groups; 5.4 Continuous axial groups; 6 Dynamic groups; 6.1 Invariant dynamic groups; 6.2 Noninvariant dynamic groups; II Qualitative intramolecular quantum dynamics; 7 The philosophy of using the symmetry properties of internal dynamics; 7.1 Symmetry groups of internal dynamics; 7.2 Significance of the analysis of symmetry properties; 7.3 On the domain of the point group; 7.4 The chain of symmetry groups; 7.5 The concept of the coordinate spin; 7.6 The influence of numerical methods on the overall description; 7.7 Conclusions. 8 Internal dynamics of rigid molecules8.1 Nonlinear molecules without inversion center; 8.2 Nonlinear molecules with inversion center; 8.3 Linear molecules; 8.4 Description of quasidegenerate vibronic states; 8.5 Conclusions; 9 Molecules with torsional transitions of the exchange type; 9.1 Extended point groups. Intermediate configuration; 9.2 Methanol molecule CH3OH; 9.3 Ethane molecule C2H6; 9.4 The molecules of complex hydrides LiBH4 and NaBH4; 9.5 The molecules of dimethyl ether (CH3)2O and acetone (CH3)2CO; 9.6 Conclusions; 10 Molecules with pseudorotations of the exchange type. 10.1 Extended point groups10.2 Cyclobutane molecule C4H8; 10.3 Molecules of the XPF4 type; 10.4 Phosphorus pentafluoride molecule PF5; 10.5 The separation of internal motions; 10.6 Conclusions; 11 Molecules with transitions of the nonexchange type between equivalent configurations; 11.1 Extended point groups; 11.2 The ammonia molecule NH3; 11.3 The peroxide molecule HOOH; 11.4 The hydrazine molecule N2H4; 11.5 Conclusions; 12 On the meaning of the Born-Oppenheimer Approximation; 12.1 Nondegenerate electronic states; 12.2 Degenerate electronic states. |
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Semidirect product of groups; 1.4 Conjugacy classes; 2 Basic concepts of group representation theory; 2.1 Linear vector spaces; 2.2 Operators in configuration and function spaces; 2.3 Representations of groups; 2.4 Characters. Decomposition of reducible representations; 2.5 Direct product of representations. Symmetric power; 2.6 The Clebsch-Gordan coefficients.</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">2.7 Basis functions of irreducible representations2.8 Irreducible tensor operators. The Wigner-Eckart theorem; 3 The permutation group; 3.1 Operations in the permutation group. Classes; 3.2 Irreducible representations. The Young diagrams and tableaux; 3.3 Basis functions of irreducible representations; 3.4 The conjugate representation; 4 Continuous groups; 4.1 Compact Lie groups; 4.2 Lie group of linear transformations; 4.3 Lie algebra. 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Icosahedral groups; 5.4 Continuous axial groups; 6 Dynamic groups; 6.1 Invariant dynamic groups; 6.2 Noninvariant dynamic groups; II Qualitative intramolecular quantum dynamics; 7 The philosophy of using the symmetry properties of internal dynamics; 7.1 Symmetry groups of internal dynamics; 7.2 Significance of the analysis of symmetry properties; 7.3 On the domain of the point group; 7.4 The chain of symmetry groups; 7.5 The concept of the coordinate spin; 7.6 The influence of numerical methods on the overall description; 7.7 Conclusions.</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">8 Internal dynamics of rigid molecules8.1 Nonlinear molecules without inversion center; 8.2 Nonlinear molecules with inversion center; 8.3 Linear molecules; 8.4 Description of quasidegenerate vibronic states; 8.5 Conclusions; 9 Molecules with torsional transitions of the exchange type; 9.1 Extended point groups. Intermediate configuration; 9.2 Methanol molecule CH3OH; 9.3 Ethane molecule C2H6; 9.4 The molecules of complex hydrides LiBH4 and NaBH4; 9.5 The molecules of dimethyl ether (CH3)2O and acetone (CH3)2CO; 9.6 Conclusions; 10 Molecules with pseudorotations of the exchange type.</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">10.1 Extended point groups10.2 Cyclobutane molecule C4H8; 10.3 Molecules of the XPF4 type; 10.4 Phosphorus pentafluoride molecule PF5; 10.5 The separation of internal motions; 10.6 Conclusions; 11 Molecules with transitions of the nonexchange type between equivalent configurations; 11.1 Extended point groups; 11.2 The ammonia molecule NH3; 11.3 The peroxide molecule HOOH; 11.4 The hydrazine molecule N2H4; 11.5 Conclusions; 12 On the meaning of the Born-Oppenheimer Approximation; 12.1 Nondegenerate electronic states; 12.2 Degenerate electronic states.</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">12.3 Internal geometric symmetry of the Hamiltonian.</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">The main goal of this book is to give a systematic description of intramolecular quantum dynamics on the basis of only the symmetry principles. 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| id | ZDB-4-EBA-ocn826479663 |
| illustrated | Not Illustrated |
| indexdate | 2024-11-27T13:25:09Z |
| institution | BVB |
| isbn | 9783110267648 3110267640 3110267535 9783110267532 |
| language | English Russian |
| oclc_num | 826479663 |
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| owner | MAIN DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource (444 pages) |
| psigel | ZDB-4-EBA |
| publishDate | 2012 |
| publishDateSearch | 2012 |
| publishDateSort | 2012 |
| publisher | De Gruyter, |
| record_format | marc |
| series | De Gruyter studies in mathematical physics. |
| series2 | De Gruyter Studies in Mathematical Physics ; |
| spelling | Burenin, Alexander V. Symmetry of Intramolecular Quantum Dynamics. Berlin : De Gruyter, 2012. 1 online resource (444 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier De Gruyter Studies in Mathematical Physics ; v. 11 Print version record. Preface; I Foundations of the mathematical apparatus; 1 Basic concepts of group theory; 1.1 The group postulates; 1.2 Subgroup, direct product of groups, isomorphism, and homomorphism; 1.3 Cosets. Semidirect product of groups; 1.4 Conjugacy classes; 2 Basic concepts of group representation theory; 2.1 Linear vector spaces; 2.2 Operators in configuration and function spaces; 2.3 Representations of groups; 2.4 Characters. Decomposition of reducible representations; 2.5 Direct product of representations. Symmetric power; 2.6 The Clebsch-Gordan coefficients. 2.7 Basis functions of irreducible representations2.8 Irreducible tensor operators. The Wigner-Eckart theorem; 3 The permutation group; 3.1 Operations in the permutation group. Classes; 3.2 Irreducible representations. The Young diagrams and tableaux; 3.3 Basis functions of irreducible representations; 3.4 The conjugate representation; 4 Continuous groups; 4.1 Compact Lie groups; 4.2 Lie group of linear transformations; 4.3 Lie algebra. Three-dimensional rotation group; 4.4 Irreducible representations of a three-dimensional rotation group; 5 Point groups; 5.1 Operations in point groups. 5.2 Discrete axial groups5.3 Cubic groups. Icosahedral groups; 5.4 Continuous axial groups; 6 Dynamic groups; 6.1 Invariant dynamic groups; 6.2 Noninvariant dynamic groups; II Qualitative intramolecular quantum dynamics; 7 The philosophy of using the symmetry properties of internal dynamics; 7.1 Symmetry groups of internal dynamics; 7.2 Significance of the analysis of symmetry properties; 7.3 On the domain of the point group; 7.4 The chain of symmetry groups; 7.5 The concept of the coordinate spin; 7.6 The influence of numerical methods on the overall description; 7.7 Conclusions. 8 Internal dynamics of rigid molecules8.1 Nonlinear molecules without inversion center; 8.2 Nonlinear molecules with inversion center; 8.3 Linear molecules; 8.4 Description of quasidegenerate vibronic states; 8.5 Conclusions; 9 Molecules with torsional transitions of the exchange type; 9.1 Extended point groups. Intermediate configuration; 9.2 Methanol molecule CH3OH; 9.3 Ethane molecule C2H6; 9.4 The molecules of complex hydrides LiBH4 and NaBH4; 9.5 The molecules of dimethyl ether (CH3)2O and acetone (CH3)2CO; 9.6 Conclusions; 10 Molecules with pseudorotations of the exchange type. 10.1 Extended point groups10.2 Cyclobutane molecule C4H8; 10.3 Molecules of the XPF4 type; 10.4 Phosphorus pentafluoride molecule PF5; 10.5 The separation of internal motions; 10.6 Conclusions; 11 Molecules with transitions of the nonexchange type between equivalent configurations; 11.1 Extended point groups; 11.2 The ammonia molecule NH3; 11.3 The peroxide molecule HOOH; 11.4 The hydrazine molecule N2H4; 11.5 Conclusions; 12 On the meaning of the Born-Oppenheimer Approximation; 12.1 Nondegenerate electronic states; 12.2 Degenerate electronic states. 12.3 Internal geometric symmetry of the Hamiltonian. The main goal of this book is to give a systematic description of intramolecular quantum dynamics on the basis of only the symmetry principles. In this respect, the book has no analogs in the world literature. The obtained models lead to a simple, purely algebraic, scheme of calculation and are rigorous in the sense that their correctness is limited only to the correct choice of symmetry of the internal dynamics. The book is basically intended for scientists working in the field of molecular spectroscopy, quantum and structural chemistry. Includes bibliographical references and index. English. Molecular dynamics Mathematical models. Molecular spectra. http://id.loc.gov/authorities/subjects/sh85086591 Biomolecules Dynamics Intramolecular Proteins Quantum Dynamique moléculaire Modèles mathématiques. Molécules Spectre. SCIENCE Physics Atomic & Molecular. bisacsh Molecular dynamics Mathematical models fast Molecular spectra fast Molekülsystem gnd http://d-nb.info/gnd/4507233-4 Intramolekulare Wechselwirkung gnd http://d-nb.info/gnd/4336499-8 Quantenmechanisches System gnd Krayev, Alexey Vissarionovich. Print version: Burenin, Alexander V. Symmetry of Intramolecular Quantum Dynamics. Berlin : De Gruyter, ©2012 9783110267532 De Gruyter studies in mathematical physics. http://id.loc.gov/authorities/names/no2012028823 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=530550 Volltext 240-00/Zsym Simmetri�i�a kvantovo�i vnutrimolekul�i�arno�i dinamiki. English |
| spellingShingle | Burenin, Alexander V. Symmetry of Intramolecular Quantum Dynamics. De Gruyter studies in mathematical physics. Preface; I Foundations of the mathematical apparatus; 1 Basic concepts of group theory; 1.1 The group postulates; 1.2 Subgroup, direct product of groups, isomorphism, and homomorphism; 1.3 Cosets. Semidirect product of groups; 1.4 Conjugacy classes; 2 Basic concepts of group representation theory; 2.1 Linear vector spaces; 2.2 Operators in configuration and function spaces; 2.3 Representations of groups; 2.4 Characters. Decomposition of reducible representations; 2.5 Direct product of representations. Symmetric power; 2.6 The Clebsch-Gordan coefficients. 2.7 Basis functions of irreducible representations2.8 Irreducible tensor operators. The Wigner-Eckart theorem; 3 The permutation group; 3.1 Operations in the permutation group. Classes; 3.2 Irreducible representations. The Young diagrams and tableaux; 3.3 Basis functions of irreducible representations; 3.4 The conjugate representation; 4 Continuous groups; 4.1 Compact Lie groups; 4.2 Lie group of linear transformations; 4.3 Lie algebra. Three-dimensional rotation group; 4.4 Irreducible representations of a three-dimensional rotation group; 5 Point groups; 5.1 Operations in point groups. 5.2 Discrete axial groups5.3 Cubic groups. Icosahedral groups; 5.4 Continuous axial groups; 6 Dynamic groups; 6.1 Invariant dynamic groups; 6.2 Noninvariant dynamic groups; II Qualitative intramolecular quantum dynamics; 7 The philosophy of using the symmetry properties of internal dynamics; 7.1 Symmetry groups of internal dynamics; 7.2 Significance of the analysis of symmetry properties; 7.3 On the domain of the point group; 7.4 The chain of symmetry groups; 7.5 The concept of the coordinate spin; 7.6 The influence of numerical methods on the overall description; 7.7 Conclusions. 8 Internal dynamics of rigid molecules8.1 Nonlinear molecules without inversion center; 8.2 Nonlinear molecules with inversion center; 8.3 Linear molecules; 8.4 Description of quasidegenerate vibronic states; 8.5 Conclusions; 9 Molecules with torsional transitions of the exchange type; 9.1 Extended point groups. Intermediate configuration; 9.2 Methanol molecule CH3OH; 9.3 Ethane molecule C2H6; 9.4 The molecules of complex hydrides LiBH4 and NaBH4; 9.5 The molecules of dimethyl ether (CH3)2O and acetone (CH3)2CO; 9.6 Conclusions; 10 Molecules with pseudorotations of the exchange type. 10.1 Extended point groups10.2 Cyclobutane molecule C4H8; 10.3 Molecules of the XPF4 type; 10.4 Phosphorus pentafluoride molecule PF5; 10.5 The separation of internal motions; 10.6 Conclusions; 11 Molecules with transitions of the nonexchange type between equivalent configurations; 11.1 Extended point groups; 11.2 The ammonia molecule NH3; 11.3 The peroxide molecule HOOH; 11.4 The hydrazine molecule N2H4; 11.5 Conclusions; 12 On the meaning of the Born-Oppenheimer Approximation; 12.1 Nondegenerate electronic states; 12.2 Degenerate electronic states. Molecular dynamics Mathematical models. Molecular spectra. http://id.loc.gov/authorities/subjects/sh85086591 Biomolecules Dynamics Intramolecular Proteins Quantum Dynamique moléculaire Modèles mathématiques. Molécules Spectre. SCIENCE Physics Atomic & Molecular. bisacsh Molecular dynamics Mathematical models fast Molecular spectra fast Molekülsystem gnd http://d-nb.info/gnd/4507233-4 Intramolekulare Wechselwirkung gnd http://d-nb.info/gnd/4336499-8 Quantenmechanisches System gnd |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85086591 http://d-nb.info/gnd/4507233-4 http://d-nb.info/gnd/4336499-8 |
| title | Symmetry of Intramolecular Quantum Dynamics. |
| title_auth | Symmetry of Intramolecular Quantum Dynamics. |
| title_exact_search | Symmetry of Intramolecular Quantum Dynamics. |
| title_full | Symmetry of Intramolecular Quantum Dynamics. |
| title_fullStr | Symmetry of Intramolecular Quantum Dynamics. |
| title_full_unstemmed | Symmetry of Intramolecular Quantum Dynamics. |
| title_short | Symmetry of Intramolecular Quantum Dynamics. |
| title_sort | symmetry of intramolecular quantum dynamics |
| topic | Molecular dynamics Mathematical models. Molecular spectra. http://id.loc.gov/authorities/subjects/sh85086591 Biomolecules Dynamics Intramolecular Proteins Quantum Dynamique moléculaire Modèles mathématiques. Molécules Spectre. SCIENCE Physics Atomic & Molecular. bisacsh Molecular dynamics Mathematical models fast Molecular spectra fast Molekülsystem gnd http://d-nb.info/gnd/4507233-4 Intramolekulare Wechselwirkung gnd http://d-nb.info/gnd/4336499-8 Quantenmechanisches System gnd |
| topic_facet | Molecular dynamics Mathematical models. Molecular spectra. Biomolecules Dynamics Intramolecular Proteins Quantum Dynamique moléculaire Modèles mathématiques. Molécules Spectre. SCIENCE Physics Atomic & Molecular. Molecular dynamics Mathematical models Molecular spectra Molekülsystem Intramolekulare Wechselwirkung Quantenmechanisches System |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=530550 |
| work_keys_str_mv | AT bureninalexanderv symmetryofintramolecularquantumdynamics AT krayevalexeyvissarionovich symmetryofintramolecularquantumdynamics |