Quantum mechanical tunneling in chemical physics:
"This text explores methodologies that can be usefully applied to various realistic problems in molecular spectroscopy and chemical dynamics. It covers the direct evaluation of reaction rate constants for both electronically adiabatic chemical reactions on a single adiabatic potential energy su...
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boca Raton
CRC Press, Taylor & Francis Group
2013
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Klappentext |
| Zusammenfassung: | "This text explores methodologies that can be usefully applied to various realistic problems in molecular spectroscopy and chemical dynamics. It covers the direct evaluation of reaction rate constants for both electronically adiabatic chemical reactions on a single adiabatic potential energy surface and non-adiabatic chemical reactions in which two or more adiabatic potential energy surfaces are involved. It also discusses the non-adiabatic tunneling phenomenon that represents one class of non-adiabatic transitions on which the authors have made an extensive research so far"-- |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | x, 215 pages illustrations 24 cm |
| ISBN: | 9781466507319 |
Internformat
MARC
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| 100 | 1 | |a Nakamura, Hiroki |e Verfasser |0 (DE-588)1021987271 |4 aut | |
| 245 | 1 | 0 | |a Quantum mechanical tunneling in chemical physics |c Hiroki Nakamura ; Gennady Mil'nikov |
| 264 | 1 | |a Boca Raton |b CRC Press, Taylor & Francis Group |c 2013 | |
| 300 | |a x, 215 pages |b illustrations |c 24 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Includes bibliographical references and index | ||
| 520 | 1 | |a "This text explores methodologies that can be usefully applied to various realistic problems in molecular spectroscopy and chemical dynamics. It covers the direct evaluation of reaction rate constants for both electronically adiabatic chemical reactions on a single adiabatic potential energy surface and non-adiabatic chemical reactions in which two or more adiabatic potential energy surfaces are involved. It also discusses the non-adiabatic tunneling phenomenon that represents one class of non-adiabatic transitions on which the authors have made an extensive research so far"-- | |
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Datensatz im Suchindex
| _version_ | 1804151360578387968 |
|---|---|
| adam_text | Contents
Preface
...................................................................ix
Chapter
1
Introduction
...................................................1
Chapter
2
One-Dimensional Theory
.......................................5
2.1
Exactly Solvable Cases
....................................5
2.1.1
Case of Delta-Function Barrier
.....................5
2.1.2
Case of Parabolic Potential Barrier
..................6
2.1.3
Case of
Eckart
Potential Barrier
....................8
2.2
WKB Approximation and Connection Formula
.............10
2.3
Comparison Equation Method
.............................11
2.4
Diagrammatic Technique
.................................13
2.5
Instanton
Theory and Modified WKB Method
..............16
2.5.1
Instanton
Theory
................................16
2.5.2
Modified WKB Method
..........................24
2.6
Energy Levels in a Double Well Potential
..................26
2.6.1
Asymmetric Double Well Potential
................26
2.6.2
Symmetric Double Well Potential
.................28
2.7
Decay of Metastable State
................................29
Chapter
3
Two-Dimensional Theory
......................................33
3.1
WKB Theory
............................................33
3.2
Instanton
Theory
........................................40
Chapter
4
Multidimensional Effects: Peculiar Phenomena
...................43
4.1
Effects of
Vibrati
on
al
Excitation on Tunneling Splitting
......43
4.1.1
Adiabatic and Sudden Approximations
.............43
4.1.2
Case of Symmetric Mode Coupling Potential
.......44
4.1.3
Case of Antisymmetric Mode Coupling Potential
... 49
4.1.4
Case of Squeezed (Sqz) Double Well Potential
......50
4.2
Insufficiency of Two-Dimensional Model
..................54
4.3
Proton Tunneling in Tropolone
............................54
4.3.1
Available Experimental Data
......................54
4.3.2
Tunneling Dynamics in the Ground X State
........56
4.3.3
Analysis of Tunneling Dynamics of the
Excited A State
..................................59
Chapter
5
Nonadiabatic Tunneling
.......................................61
5.1
Definition and Qualitative Explanation
.....................61
5.2
One-Dimensional Theory
.................................64
5.2.1
Case of
E
<
Et
.................................67
5.2.2
Case of Et
<
E
<
Eb
............................68
5.2.3
Case of Eb
<
E
.................................68
vi
Contents
Chapter
6
Multidimensional Theory of Tunneling Splitting
..................75
6.1
General Formulation
.....................................75
6.1.1
Multidimensional Extension of the
Instanton
Theory
................................75
6.1.2
WKB Approach in Cartesian Coordinates
..........82
6.1.3
WKB Approach in the Case of General
Hamiltonian in Curved Space
.....................85
6.2
How to Find
Instanton
Trajectory
..........................89
6.3
How to Use the Theory
...................................92
6.3.1
Evaluation of the Pre-Exponential Factor
...........92
6.3.2
Incorporation of High Level of
ab
init io
Quantum Chemical Calculations
...................95
6.4
Case of Low Vibrationally Excited States
...................96
6.4.1
One- and Two-Dimensional Cases
.................96
6.4.2
Multidimensional Case in Terms of
Cartesian Coordinates
............................99
6.4.3
Case of General Multidimensional
Curved Space
..................................103
Chapter
7
Numerical Applications to Polyatomic Molecules
...............109
7.1
jV-Dimensional Separable Potential Model
................109
7.2
Hydroperoxy Radical HO2
..............................
Ill
7.3
Vinyl Radical C2H3
.....................................120
7.4
Malonaldehyde C3O2H4
.................................128
7.5
Formic Acid Dimer (DCOOH^
..........................139
Chapter
8
Decay of Metastable States
...................................149
8.1
General Formulation
....................................149
8.1.1
Determination of
Instanton
Trajectory
............149
8.1.2
Formulation in Terms of Cartesian Coordinates
.... 151
8.1.3
General Canonically Invariant Formulation
........154
8.2
Numerical Application
..................................158
Chapter
9
Tunneling in Chemical Reactions
..............................163
9.1
Determination of Caustics and Propagation in
Tunneling Region
......................................163
9.1.1
Caustics in Chaotic Henon-
Heiles
System
.........166
9.1.2
Caustics in Chemical Reaction Dynamics
.........167
9.2
Direct Evaluation of Reaction Rate Constant
..............174
9.2.1
Adiabatic Chemical Reaction
....................174
9.2.2
Nonadiabatic Chemical Reaction
.................178
Chapter
10
Concluding Remarks and Future Perspectives
..................183
Contents vü
Appendix
A Proofs of Equation
(2.95)
and Equation
(2.110)...............185
Appendix
В
Derivation of Equation
(6.80)...............................187
Appendix
С
Herring Formula in Curved Space
...........................189
Appendix
D
Derivation of Equation
(6.97)...............................
І
9
1
Appendix
E
Computer Code to Calculate
Instanton
Trajectory
..............193
Appendix
F
Derivation of Some Equations in Section
6.4.2................201
Bibliography
............................................................205
Index
...................................................................213
CHEMICAL
PHYSICS
Quantum Mechanical Tunneling
in Chemical Physics
Quantum mechanical tunneling plays important roles in a wide range of natural
sciences, from nuclear and solid-state physics to proton transfer and chemical reactions
in chemistry and biology. Responding to the need for further understanding of
multidimensional tunneling, the authors have recently developed practical methods that
can be applied to multidimensional systems. Quantum Mechanical Tunneling in Chemical
Physics presents basic theories, as well as original ones developed by the authors. It also
provides methodologies and numerical applications to real molecular systems.
The book offers information so readers can understand the basic concepts and dynamics
of multidimensional tunneling phenomena and use the described methods for various
molecular spectroscopy and chemical dynamics problems. The text focuses on three
tunneling phenomena:
(1)
energy splitting, or tunneling splitting, in symmetric double
well potential,
(2)
decay of metastable state through tunneling, and
(3)
tunneling
effects in chemical reactions. Incorporating mathematics to explain basic theories, the
text requires readers to have graduate-level math to grasp the concepts presented.
The book reviews low-dimensional theories and clarifies their insufficiency conceptually and
numerically. It also examines the phenomenon of nonadiabatic tunneling, which is common
in molecular systems. The book describes applications to real polyatomic molecules, such
as vinyl radicals and malonaldehyde, demonstrating the high efficiency and accuracy
of the method. It discusses tunneling in chemical reactions, including theories for direct
evaluation of reaction rate constants for both electronically adiabatic and nonadiabatic
chemical reactions. In the final chapter, the authors touch on future perspectives.
CRC
Press
Тау
¡or &t Francis Group
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informa business
6000
Srofcen Sound Parkway, NW
Suite 3OO, Boca Raton, FL
3 3487
711
Third Avenue
NewYortc, NY
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Park Square, Milton Park
Abingdon, Oxon OX14 4RN, UK WWW
ISBN:
Ч7а-1-ЧЬЬ5-07Э1-с!
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|
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| id | DE-604.BV041294577 |
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| indexdate | 2024-07-10T00:53:35Z |
| institution | BVB |
| isbn | 9781466507319 |
| language | English |
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| spelling | Nakamura, Hiroki Verfasser (DE-588)1021987271 aut Quantum mechanical tunneling in chemical physics Hiroki Nakamura ; Gennady Mil'nikov Boca Raton CRC Press, Taylor & Francis Group 2013 x, 215 pages illustrations 24 cm txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and index "This text explores methodologies that can be usefully applied to various realistic problems in molecular spectroscopy and chemical dynamics. It covers the direct evaluation of reaction rate constants for both electronically adiabatic chemical reactions on a single adiabatic potential energy surface and non-adiabatic chemical reactions in which two or more adiabatic potential energy surfaces are involved. It also discusses the non-adiabatic tunneling phenomenon that represents one class of non-adiabatic transitions on which the authors have made an extensive research so far"-- Tunneleffekt (DE-588)4136216-0 gnd rswk-swf Tunneleffekt (DE-588)4136216-0 s DE-604 Mil'nikov, Gennady Verfasser aut Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026743493&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026743493&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Nakamura, Hiroki Mil'nikov, Gennady Quantum mechanical tunneling in chemical physics Tunneleffekt (DE-588)4136216-0 gnd |
| subject_GND | (DE-588)4136216-0 |
| title | Quantum mechanical tunneling in chemical physics |
| title_auth | Quantum mechanical tunneling in chemical physics |
| title_exact_search | Quantum mechanical tunneling in chemical physics |
| title_full | Quantum mechanical tunneling in chemical physics Hiroki Nakamura ; Gennady Mil'nikov |
| title_fullStr | Quantum mechanical tunneling in chemical physics Hiroki Nakamura ; Gennady Mil'nikov |
| title_full_unstemmed | Quantum mechanical tunneling in chemical physics Hiroki Nakamura ; Gennady Mil'nikov |
| title_short | Quantum mechanical tunneling in chemical physics |
| title_sort | quantum mechanical tunneling in chemical physics |
| topic | Tunneleffekt (DE-588)4136216-0 gnd |
| topic_facet | Tunneleffekt |
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