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Beyond Born-Oppenheimer [[electronic resource] ] : electronic non-adiabatic coupling terms and conical intersections / / by Michael Baer
| Beyond Born-Oppenheimer [[electronic resource] ] : electronic non-adiabatic coupling terms and conical intersections / / by Michael Baer |
| Autore | Baer M (Michael), <1937-> |
| Pubbl/distr/stampa | Hoboken, N.J., : Wiley, c2006 |
| Descrizione fisica | 1 online resource (254 p.) |
| Disciplina |
539.758
541/.28 |
| Soggetto topico |
Molecular dynamics - Mathematics
Born-Oppenheimer approximation Adiabatic invariants |
| Soggetto genere / forma | Electronic books |
| ISBN |
1-280-41143-0
9786610411436 0-470-32705-7 0-471-78008-1 0-471-78007-3 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
BEYOND BORN-OPPENHEIMER; CONTENTS; PREFACE; ABBREVIATIONS; 1 MATHEMATICAL INTRODUCTION; 1.1 Hilbert Space; 1.1.1 Eigenfunction and Electronic Nonadiabatic Coupling Term; 1.1.2 Abelian and Non-Abelian Curl Equations; 1.1.3 Abelian and Non-Abelian Divergence Equations; 1.2 Hilbert Subspace; 1.3 Vectorial First-Order Differential Equation and Line Integral; 1.3.1 Vectorial First-Order Differential Equation; 1.3.1.1 Study of Abelian Case; 1.3.1.2 Study of Non-Abelian Case; 1.3.1.3 Orthogonality; 1.3.2 Integral Equation; 1.3.2.1 Integral Equation along an Open Contour
1.3.2.2 Integral Equation along a Closed Contour1.3.3 Solution of Differential Vector Equation; 1.4 Summary and Conclusions; Problem; References; 2 BORN-OPPENHEIMER APPROACH: DIABATIZATION AND TOPOLOGICAL MATRIX; 2.1 Time-Independent Treatment; 2.1.1 Adiabatic Representation; 2.1.2 Diabatic Representation; 2.1.3 Adiabatic-to-Diabatic Transformation; 2.1.3.1 Transformation for Electronic Basis Sets; 2.1.3.2 Transformation for Nuclear Wavefunctions; 2.1.3.3 Implications Due to Adiabatic-to-Diabatic Transformation; 2.1.3.4 Final Comments; 2.2 Application of Complex Eigenfunctions 2.2.1 Introducing Time-Independent Phase Factors2.2.1.1 Adiabatic Schrödinger Equation; 2.2.1.2 Adiabatic-to-Diabatic Transformation; 2.2.2 Introducing Time-Dependent Phase Factors; 2.3 Time-Dependent Treatment; 2.3.1 Time-Dependent Perturbative Approach; 2.3.2 Time-Dependent Nonperturbative Approach; 2.3.2.1 Adiabatic Time-Dependent Electronic Basis Set; 2.3.2.2 Adiabatic Time-Dependent Nuclear Schrödinger Equation; 2.3.2.3 Time-Dependent Adiabatic-to-Diabatic Transformation; 2.3.3 Summary; Problem; 2A Appendixes; 2A.1 Dressed Nonadiabatic Coupling Matrix 2A.2 Analyticity of Adiabatic-to-Diabatic Transformation Matrix à in Spacetime ConfigurationReferences; 3 MODEL STUDIES; 3.1 Treatment of Analytical Models; 3.1.1 Two-State Systems; 3.1.1.1 Adiabatic-to-Diabatic Transformation Matrix; 3.1.1.2 Topological (D) Matrix; 3.1.1.3 The Diabatic Potential Matrix; 3.1.2 Three-State Systems; 3.1.2.1 Adiabatic-to-Diabatic Transformation Matrix; 3.1.2.2 Topological Matrix; 3.1.3 Four-State Systems; 3.1.3.1 Adiabatic-to-Diabatic Transformation Matrix; 3.1.3.2 Topological Matrix; 3.1.4 Comments Related to General Case 4.3 Quantization of Nonadiabatic Coupling Matrix: Study of Ab Initio Molecular Systems |
| Record Nr. | UNINA-9910143416003321 |
Baer M (Michael), <1937->
|
||
| Hoboken, N.J., : Wiley, c2006 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Beyond Born-Oppenheimer [[electronic resource] ] : electronic non-adiabatic coupling terms and conical intersections / / by Michael Baer
| Beyond Born-Oppenheimer [[electronic resource] ] : electronic non-adiabatic coupling terms and conical intersections / / by Michael Baer |
| Autore | Baer M (Michael), <1937-> |
| Pubbl/distr/stampa | Hoboken, N.J., : Wiley, c2006 |
| Descrizione fisica | 1 online resource (254 p.) |
| Disciplina |
539.758
541/.28 |
| Soggetto topico |
Molecular dynamics - Mathematics
Born-Oppenheimer approximation Adiabatic invariants |
| ISBN |
1-280-41143-0
9786610411436 0-470-32705-7 0-471-78008-1 0-471-78007-3 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
BEYOND BORN-OPPENHEIMER; CONTENTS; PREFACE; ABBREVIATIONS; 1 MATHEMATICAL INTRODUCTION; 1.1 Hilbert Space; 1.1.1 Eigenfunction and Electronic Nonadiabatic Coupling Term; 1.1.2 Abelian and Non-Abelian Curl Equations; 1.1.3 Abelian and Non-Abelian Divergence Equations; 1.2 Hilbert Subspace; 1.3 Vectorial First-Order Differential Equation and Line Integral; 1.3.1 Vectorial First-Order Differential Equation; 1.3.1.1 Study of Abelian Case; 1.3.1.2 Study of Non-Abelian Case; 1.3.1.3 Orthogonality; 1.3.2 Integral Equation; 1.3.2.1 Integral Equation along an Open Contour
1.3.2.2 Integral Equation along a Closed Contour1.3.3 Solution of Differential Vector Equation; 1.4 Summary and Conclusions; Problem; References; 2 BORN-OPPENHEIMER APPROACH: DIABATIZATION AND TOPOLOGICAL MATRIX; 2.1 Time-Independent Treatment; 2.1.1 Adiabatic Representation; 2.1.2 Diabatic Representation; 2.1.3 Adiabatic-to-Diabatic Transformation; 2.1.3.1 Transformation for Electronic Basis Sets; 2.1.3.2 Transformation for Nuclear Wavefunctions; 2.1.3.3 Implications Due to Adiabatic-to-Diabatic Transformation; 2.1.3.4 Final Comments; 2.2 Application of Complex Eigenfunctions 2.2.1 Introducing Time-Independent Phase Factors2.2.1.1 Adiabatic Schrödinger Equation; 2.2.1.2 Adiabatic-to-Diabatic Transformation; 2.2.2 Introducing Time-Dependent Phase Factors; 2.3 Time-Dependent Treatment; 2.3.1 Time-Dependent Perturbative Approach; 2.3.2 Time-Dependent Nonperturbative Approach; 2.3.2.1 Adiabatic Time-Dependent Electronic Basis Set; 2.3.2.2 Adiabatic Time-Dependent Nuclear Schrödinger Equation; 2.3.2.3 Time-Dependent Adiabatic-to-Diabatic Transformation; 2.3.3 Summary; Problem; 2A Appendixes; 2A.1 Dressed Nonadiabatic Coupling Matrix 2A.2 Analyticity of Adiabatic-to-Diabatic Transformation Matrix à in Spacetime ConfigurationReferences; 3 MODEL STUDIES; 3.1 Treatment of Analytical Models; 3.1.1 Two-State Systems; 3.1.1.1 Adiabatic-to-Diabatic Transformation Matrix; 3.1.1.2 Topological (D) Matrix; 3.1.1.3 The Diabatic Potential Matrix; 3.1.2 Three-State Systems; 3.1.2.1 Adiabatic-to-Diabatic Transformation Matrix; 3.1.2.2 Topological Matrix; 3.1.3 Four-State Systems; 3.1.3.1 Adiabatic-to-Diabatic Transformation Matrix; 3.1.3.2 Topological Matrix; 3.1.4 Comments Related to General Case 4.3 Quantization of Nonadiabatic Coupling Matrix: Study of Ab Initio Molecular Systems |
| Record Nr. | UNINA-9910830642703321 |
|
Baer M (Michael), <1937->
|
||
| Hoboken, N.J., : Wiley, c2006 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Beyond Born-Oppenheimer : electronic non-adiabatic coupling terms and conical intersections / / by Michael Baer
| Beyond Born-Oppenheimer : electronic non-adiabatic coupling terms and conical intersections / / by Michael Baer |
| Autore | Baer M (Michael), <1937-> |
| Pubbl/distr/stampa | Hoboken, N.J., : Wiley, c2006 |
| Descrizione fisica | 1 online resource (254 p.) |
| Disciplina | 541/.28 |
| Soggetto topico |
Molecular dynamics - Mathematics
Born-Oppenheimer approximation Adiabatic invariants |
| ISBN |
1-280-41143-0
9786610411436 0-470-32705-7 0-471-78008-1 0-471-78007-3 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
BEYOND BORN-OPPENHEIMER; CONTENTS; PREFACE; ABBREVIATIONS; 1 MATHEMATICAL INTRODUCTION; 1.1 Hilbert Space; 1.1.1 Eigenfunction and Electronic Nonadiabatic Coupling Term; 1.1.2 Abelian and Non-Abelian Curl Equations; 1.1.3 Abelian and Non-Abelian Divergence Equations; 1.2 Hilbert Subspace; 1.3 Vectorial First-Order Differential Equation and Line Integral; 1.3.1 Vectorial First-Order Differential Equation; 1.3.1.1 Study of Abelian Case; 1.3.1.2 Study of Non-Abelian Case; 1.3.1.3 Orthogonality; 1.3.2 Integral Equation; 1.3.2.1 Integral Equation along an Open Contour
1.3.2.2 Integral Equation along a Closed Contour1.3.3 Solution of Differential Vector Equation; 1.4 Summary and Conclusions; Problem; References; 2 BORN-OPPENHEIMER APPROACH: DIABATIZATION AND TOPOLOGICAL MATRIX; 2.1 Time-Independent Treatment; 2.1.1 Adiabatic Representation; 2.1.2 Diabatic Representation; 2.1.3 Adiabatic-to-Diabatic Transformation; 2.1.3.1 Transformation for Electronic Basis Sets; 2.1.3.2 Transformation for Nuclear Wavefunctions; 2.1.3.3 Implications Due to Adiabatic-to-Diabatic Transformation; 2.1.3.4 Final Comments; 2.2 Application of Complex Eigenfunctions 2.2.1 Introducing Time-Independent Phase Factors2.2.1.1 Adiabatic Schrödinger Equation; 2.2.1.2 Adiabatic-to-Diabatic Transformation; 2.2.2 Introducing Time-Dependent Phase Factors; 2.3 Time-Dependent Treatment; 2.3.1 Time-Dependent Perturbative Approach; 2.3.2 Time-Dependent Nonperturbative Approach; 2.3.2.1 Adiabatic Time-Dependent Electronic Basis Set; 2.3.2.2 Adiabatic Time-Dependent Nuclear Schrödinger Equation; 2.3.2.3 Time-Dependent Adiabatic-to-Diabatic Transformation; 2.3.3 Summary; Problem; 2A Appendixes; 2A.1 Dressed Nonadiabatic Coupling Matrix 2A.2 Analyticity of Adiabatic-to-Diabatic Transformation Matrix à in Spacetime ConfigurationReferences; 3 MODEL STUDIES; 3.1 Treatment of Analytical Models; 3.1.1 Two-State Systems; 3.1.1.1 Adiabatic-to-Diabatic Transformation Matrix; 3.1.1.2 Topological (D) Matrix; 3.1.1.3 The Diabatic Potential Matrix; 3.1.2 Three-State Systems; 3.1.2.1 Adiabatic-to-Diabatic Transformation Matrix; 3.1.2.2 Topological Matrix; 3.1.3 Four-State Systems; 3.1.3.1 Adiabatic-to-Diabatic Transformation Matrix; 3.1.3.2 Topological Matrix; 3.1.4 Comments Related to General Case 4.3 Quantization of Nonadiabatic Coupling Matrix: Study of Ab Initio Molecular Systems |
| Record Nr. | UNINA-9910877235603321 |
|
Baer M (Michael), <1937->
|
||
| Hoboken, N.J., : Wiley, c2006 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Molecular propagation through electron energy level crossings / / George A. Hagedorn
| Molecular propagation through electron energy level crossings / / George A. Hagedorn |
| Autore | Hagedorn George A (George Allan), <1953-> |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 1994 |
| Descrizione fisica | 1 online resource (142 p.) |
| Disciplina | 539/.6 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Born-Oppenheimer approximation
Molecular dynamics - Mathematics Energy levels (Quantum mechanics) - Mathematics |
| Soggetto genere / forma | Electronic books. |
| ISBN | 1-4704-0115-0 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Table of Contents""; ""1. Introduction""; ""2. Generic Minimal Multiplicity Quantum Eigenvalue Crossings""; ""3. Technical Preliminaries""; ""3A. Semiclassical Wave Packets""; ""3B. Adiabatic Electronic States""; ""3C. Rigorous Error Estimates from Formal Calculations""; ""4. Born-Oppenheimer Propagation Away from Crossings""; ""4A. The Multiplicity 1 Case""; ""4B. The Multiplicity 2 Case""; ""5. Codimension 1 Crossings""; ""5A. Crossings of Types A and C""; ""5B. Crossings of Types F and G""; ""5C. Crossings of Types D, E, and H""; ""6. Codimension 2 Crossings""
""7. Codimension 3 Crossings""""8. Codimension 5 Crossings""; ""References"" |
| Record Nr. | UNINA-9910480195003321 |
|
Hagedorn George A (George Allan), <1953->
|
||
| Providence, Rhode Island : , : American Mathematical Society, , 1994 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Molecular propagation through electron energy level crossings / / George A. Hagedorn
| Molecular propagation through electron energy level crossings / / George A. Hagedorn |
| Autore | Hagedorn George A (George Allan), <1953-> |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 1994 |
| Descrizione fisica | 1 online resource (142 p.) |
| Disciplina | 539/.6 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Born-Oppenheimer approximation
Molecular dynamics - Mathematics Energy levels (Quantum mechanics) - Mathematics |
| ISBN | 1-4704-0115-0 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Table of Contents""; ""1. Introduction""; ""2. Generic Minimal Multiplicity Quantum Eigenvalue Crossings""; ""3. Technical Preliminaries""; ""3A. Semiclassical Wave Packets""; ""3B. Adiabatic Electronic States""; ""3C. Rigorous Error Estimates from Formal Calculations""; ""4. Born-Oppenheimer Propagation Away from Crossings""; ""4A. The Multiplicity 1 Case""; ""4B. The Multiplicity 2 Case""; ""5. Codimension 1 Crossings""; ""5A. Crossings of Types A and C""; ""5B. Crossings of Types F and G""; ""5C. Crossings of Types D, E, and H""; ""6. Codimension 2 Crossings""
""7. Codimension 3 Crossings""""8. Codimension 5 Crossings""; ""References"" |
| Record Nr. | UNINA-9910788755903321 |
|
Hagedorn George A (George Allan), <1953->
|
||
| Providence, Rhode Island : , : American Mathematical Society, , 1994 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Molecular propagation through electron energy level crossings / / George A. Hagedorn
| Molecular propagation through electron energy level crossings / / George A. Hagedorn |
| Autore | Hagedorn George A (George Allan), <1953-> |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 1994 |
| Descrizione fisica | 1 online resource (142 p.) |
| Disciplina | 539/.6 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Born-Oppenheimer approximation
Molecular dynamics - Mathematics Energy levels (Quantum mechanics) - Mathematics |
| ISBN | 1-4704-0115-0 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Table of Contents""; ""1. Introduction""; ""2. Generic Minimal Multiplicity Quantum Eigenvalue Crossings""; ""3. Technical Preliminaries""; ""3A. Semiclassical Wave Packets""; ""3B. Adiabatic Electronic States""; ""3C. Rigorous Error Estimates from Formal Calculations""; ""4. Born-Oppenheimer Propagation Away from Crossings""; ""4A. The Multiplicity 1 Case""; ""4B. The Multiplicity 2 Case""; ""5. Codimension 1 Crossings""; ""5A. Crossings of Types A and C""; ""5B. Crossings of Types F and G""; ""5C. Crossings of Types D, E, and H""; ""6. Codimension 2 Crossings""
""7. Codimension 3 Crossings""""8. Codimension 5 Crossings""; ""References"" |
| Record Nr. | UNINA-9910828267603321 |
|
Hagedorn George A (George Allan), <1953->
|
||
| Providence, Rhode Island : , : American Mathematical Society, , 1994 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Twisted pseudodifferential calculus and application to the quantum evolution of molecules / / André Martinez, Vania Sordoni
| Twisted pseudodifferential calculus and application to the quantum evolution of molecules / / André Martinez, Vania Sordoni |
| Autore | Martinez André |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2009 |
| Descrizione fisica | 1 online resource (96 p.) |
| Disciplina | 515/.7242 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Pseudodifferential operators
Born-Oppenheimer approximation Wave packets Evolution equations Evolution (Biology) - Mathematical models Quantum theory - Mathematics |
| Soggetto genere / forma | Electronic books. |
| ISBN | 1-4704-0550-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Contents""; ""Chapter 1. Introduction""; ""Chapter 2. Assumptions and Main Results""; ""Chapter 3. A Modified Operator""; ""Chapter 4. Twisted h-Admissible Operators""; ""Chapter 5. Twisted Partial Differential Operators""; ""Chapter 6. Construction of a Quasi-Invariant Subspace""; ""Chapter 7. Decomposition of the Evolution for the Modified Operator""; ""Chapter 8. Proof of Theorem 2.1""; ""Chapter 9. Proof of Corollary 2.6""; ""Chapter 10. Computing the Effective Hamiltonian""; ""Chapter 11. Propagation of Wave-Packets""; ""Chapter 12. Application to Polyatomic Molecules""
""Appendix A. Smooth Pseudodifferential Calculus with Operator-Valued Symbol""""Appendix B. Propagation of the Support""; ""Appendix C. Two Technical Lemmas""; ""Bibliography"" |
| Record Nr. | UNINA-9910480500803321 |
|
Martinez André
|
||
| Providence, Rhode Island : , : American Mathematical Society, , 2009 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Twisted pseudodifferential calculus and application to the quantum evolution of molecules / / André Martinez, Vania Sordoni
| Twisted pseudodifferential calculus and application to the quantum evolution of molecules / / André Martinez, Vania Sordoni |
| Autore | Martinez André |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2009 |
| Descrizione fisica | 1 online resource (96 p.) |
| Disciplina | 515/.7242 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Pseudodifferential operators
Born-Oppenheimer approximation Wave packets Evolution equations Evolution (Biology) - Mathematical models Quantum theory - Mathematics |
| ISBN | 1-4704-0550-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Contents""; ""Chapter 1. Introduction""; ""Chapter 2. Assumptions and Main Results""; ""Chapter 3. A Modified Operator""; ""Chapter 4. Twisted h-Admissible Operators""; ""Chapter 5. Twisted Partial Differential Operators""; ""Chapter 6. Construction of a Quasi-Invariant Subspace""; ""Chapter 7. Decomposition of the Evolution for the Modified Operator""; ""Chapter 8. Proof of Theorem 2.1""; ""Chapter 9. Proof of Corollary 2.6""; ""Chapter 10. Computing the Effective Hamiltonian""; ""Chapter 11. Propagation of Wave-Packets""; ""Chapter 12. Application to Polyatomic Molecules""
""Appendix A. Smooth Pseudodifferential Calculus with Operator-Valued Symbol""""Appendix B. Propagation of the Support""; ""Appendix C. Two Technical Lemmas""; ""Bibliography"" |
| Record Nr. | UNINA-9910788855503321 |
|
Martinez André
|
||
| Providence, Rhode Island : , : American Mathematical Society, , 2009 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Twisted pseudodifferential calculus and application to the quantum evolution of molecules / / André Martinez, Vania Sordoni
| Twisted pseudodifferential calculus and application to the quantum evolution of molecules / / André Martinez, Vania Sordoni |
| Autore | Martinez André |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2009 |
| Descrizione fisica | 1 online resource (96 p.) |
| Disciplina | 515/.7242 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Pseudodifferential operators
Born-Oppenheimer approximation Wave packets Evolution equations Evolution (Biology) - Mathematical models Quantum theory - Mathematics |
| ISBN | 1-4704-0550-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Contents""; ""Chapter 1. Introduction""; ""Chapter 2. Assumptions and Main Results""; ""Chapter 3. A Modified Operator""; ""Chapter 4. Twisted h-Admissible Operators""; ""Chapter 5. Twisted Partial Differential Operators""; ""Chapter 6. Construction of a Quasi-Invariant Subspace""; ""Chapter 7. Decomposition of the Evolution for the Modified Operator""; ""Chapter 8. Proof of Theorem 2.1""; ""Chapter 9. Proof of Corollary 2.6""; ""Chapter 10. Computing the Effective Hamiltonian""; ""Chapter 11. Propagation of Wave-Packets""; ""Chapter 12. Application to Polyatomic Molecules""
""Appendix A. Smooth Pseudodifferential Calculus with Operator-Valued Symbol""""Appendix B. Propagation of the Support""; ""Appendix C. Two Technical Lemmas""; ""Bibliography"" |
| Record Nr. | UNINA-9910829177103321 |
|
Martinez André
|
||
| Providence, Rhode Island : , : American Mathematical Society, , 2009 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
