Quantum mechanics in chemistry:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Mineola, N.Y.
Dover Publications
2002
|
| Ausgabe: | 1. publ., slightly corrected, unabridged republication of the work orig.. publ. in 1993 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | xix, 361 p. ill. |
| ISBN: | 0486420035 |
Internformat
MARC
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| 100 | 1 | |a Schatz, George C. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Quantum mechanics in chemistry |c George C. Schatz, Mark A. Ratner |
| 250 | |a 1. publ., slightly corrected, unabridged republication of the work orig.. publ. in 1993 | ||
| 264 | 1 | |a Mineola, N.Y. |b Dover Publications |c 2002 | |
| 300 | |a xix, 361 p. |b ill. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
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| 650 | 7 | |a Kwantummechanica |2 gtt | |
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| 650 | 4 | |a Quantum chemistry | |
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| 700 | 1 | |a Ratner, Mark A. |e Sonstige |4 oth | |
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Datensatz im Suchindex
| _version_ | 1804129302585802752 |
|---|---|
| adam_text | Contents
Preface
xvii
1 Review
of
Basic
Concepts
in Quantum
Mechanics I
1.1 Fundamental
Definitions
1
1.2
Eigenvalues and Eigenfunctions
3
1.3
Approximate Methods
5
1.3.1
Time-Independent Perturbation Theory
5
1.3.2
Variational Theory
б
1.4
Raising and Lowering Operators
7
1.4.1
Harmonic Oscillator
7
1.4.2
Angular Momentum Operators
9
1.5
Two-Body Problems
11
1.5.1
Relative-Motion
Schrödinger
Equation
11
1.5.2
Hydrogen Atom
12
1.6
Electronic Structure of Atoms and Molecules
13
1.6.1
Many-Electron Hamiltanian; Born-Oppenheimer
Approximation
13
vii
1.6.2 Pauli
Principle; Hartree-Fock Theory
15
1.6.3
LCAO-MO-SCF
17
1.6.4
Electronic
Structure Methods
18 .
Bibliography for Chapter
1 18
Problems for Chapter
1 19
Symmetry Considerations: Point Groups and Electronic
Structure
21
2.1
Group Theory for Point Groups
21
2.1.1
Symmetry Operations
22
2.1.2
Representations
22
2.1.3
Similarity Transformations
23
2.1.4
Irreducible Representations
23
2.1.5
Character Tables
24
2.1.6
Direct {or Tensor) Products
25
2.1.7
Clebsch-Gordan Series
26
2.2
Applications of Group Theory to Quantum
Mechanics
27
2.2.1
Symmetry-Adapted Linear Combinations
27
2.2.2
Constructions ofSALCs
28
2.2.3 Hückel
Theory Applications
30
2.2.4
Shortcuts
33
2.2.5
Energy Eigenvalues
34
2.3
Symmetry Properties of Many-Electron
Wavefunctions
36
2.3.1
Many-Electron Configurations and Terms
36
2.3.2
Application to C3H3
36
2.3.3
Incorporation of the
Pauli
Principle
37
2.3.4
Optical Spectrum:
Dipole
Selection Rules
39
Bibliography for Chapter
2 40
Problems for Chapter
2 40
viii
Contents
3
Symmetry Considerations: Continuous Groups and
Rotations
43
3.1
Introduction
43
3.2
Continuous Groups; The Electronic Structure of Linear
Molecules
43
3.2.1
Two-Dimensional Rotation Group
43
3.2.2
Cav Group
45
3.2.3
D„h
Group
45
3.2.4
Simple Example: O2
46
3.3
Three-Dimensional Rotation Group; Angular Momentum
Addition
50
3.3.1
Angular Momentum Addition; Clebsch-Gordan
Coefficients
50
3.3.2
Properties of Clebsch-Gordan Coefficients
51
3.3.3
Worked Examples
53
3.3.4
3-j and Higher Symbols
54
Bibliography for Chapter
3 55
Problems for Chapter
3 55
4
Time-Dependent Quantum Mechanics
57
4.1
Introduction
57
4.2
Time-Dependent
Schrödinger
Equation: Basis-Set
Solution
57
4.3
Time-Dependent Perturbation Theory
59
4.3.1
First-Order Time-Dependent Perturbation Theory
59
4.3.2
Example: Collision-Induced Excitation of a Diatomic
Molecule
59
4.3.3
Second-Order Perturbation Theory
63
4.3.4
Simplifications and Extensions to Higher Order
63
4.3.5
Time-Ordering Operators
64
4.4
Representations in Quantum Mechanics
65
4.4.1 Schrödinger
Representation
66
4.4.2 Heisenberg
Representation
67
4.4
J
Interaction Representation
69
Contents
ix
4.5
Transition
Probabilities per Unit Time
70
4.5.1
Perturbation Theory for a Constant Interaction
Potential
70
4.5.2
Fermi s Golden Rule
72
4.5.3
State-to-State Form of Fermi s Golden Rule
73
4.5.4
Treatment of Periodic Interactions
75
Bibliography for Chapter
4 74
Problems for Chapter
4 75
5
Interaction of Radiation with Matter
78
5.1
Introduction
78
5.2
Electromagnetic Fields
78
5.2.1
Vector Potentials and Wave Equations
78
5.2.2
Plane Waves
80
5.2.3
Energy and Photon Number Density
81
5.3
Interaction between Matter and Field
82
5.3.1
Classical Theory
82
5.3.2
Derivation of Classical Hamiltonian
82
5.3.3
Quantum Hamiltonian for a Particle in an Electromagnetic
Field
83
5.4
Absorption and Emission of Light
86
5.4.1
Application of Fermi s Golden Rule
86
5.4.2
Dipole
Approximation
87
5.4.3
Photon Density of States
88
5.4.4
Emission Rate
88
5.4.5
Absorption Rate
90
5.4.6
Einstein A and
В
Coefficients
90
5.4.7
Oscillator Strengths
92
5.4.8
Electric Quadrupole
,
Magnetic
Dipole
Mechanisms
92
5.4.9
Molecular Transitions: Franck-Condon Factors
95
5.5
Light Scattering
99
5.5.1
Qualitative Description of Light Scattering
99
5.5.2
Simplification of Electric
Dipole
Interaction
99
5.5.3
Interaction between Field and Induced
Dipole;
Two-Photon Process
100
5.5.4
Raman Scattering
102
5.5.5
Evaluation
ofa^,: Kramers-Heisenberg Formula
104
X Contents
Bibliography for Chapter
5 108
Problems for Chapter
5 108
6
Occupation Number Representations 111
6.1
Introduction
111
6.2
Occupation Number Representation for Harmonic
Molecular Vibrations and Quantized Radiation
Fields
112
6.2.1
Single Harmonic Oscillator
112
6.2.2
Normal Modes
113
6.2.3
Quantized Radiation Fields
115
6.2.4
Coupling of Radiation to Matter Using Second
Quantization
117
6.2.5
Applications of Fermi s Golden Rule
118
6.3
Occupation Number Representations for Electrons
119
6.3.1
Fermion Creation and Destruction Operators
119
6.3.2
Slater Determinants and Electron Creation Operators
121
6.3.3
Manipulation of Fermion Operators; Commutators and
Anticommutators
125
6.3.4
Arbitrary Electronic Operators in the Occupation Number
Representation
126
6.4
Fermion Field Operators and Second Quantization
132
6.5
Molecular Electronic Structure: Model Hamiltonians and
Occupation Number Representations
135
6.5.1
Model Hamiltonians: Basis Set and Matrix Elements
135
6.5.2
Noninteracting Electrons: Hiickel, Extended Hiickel, and
Free-Electron Models
137
6.5.3
Molecular
Orbitals
for Noninteracting Electrons
139
6.6
Treatment of Interacting Electrons
142
6.6.1
Model Hamiltonians
142
6.6.2
Self-Consistent Field (SCF) Solution
145
6.6.3
Example: SCF Solution for the Two-Center, Two-Orbital
Problem
147
Bibliography for Chapter
6 148
Problems for Chapter
6 149
Contents
xi
7
Quantum
Scattering Theory
153
7.1
Introduction
153
7.2
One-Dimensional Scattering
154
7.2.1
Introduction
154
7.2.2
Wavepackets in One Dimension
155
7.2.3
Wavepackets for the Complete Scattering Problem
157
7.2.4
Fluxes and Probabilities
158
7.2.5
Time-Independent Approach to Scattering
159
7.2.6
Scattering Matrix
161
7.2.7
Green
s
Functions for Scattering
163
7.2.8
Born Approximation
166
7.3
Semiclassical Theory
167
7.3.1
WKB Approximation
167
7.3.2
Semiclassical Wavepackets
173
7.4
Scattering in Three Dimensions
175
Bibliography for Chapter
7 178
Problems for Chapter
7 179
8
Theories of Reaction Rates
182
8.1
Introduction
182
8.2
Rate Constants for Bimolecular Reactions: Cumulative
Reaction Probabilities
182
8.3
Transition-State Theory
184
8.4
RRKM Theory
185
8.5
Formal Expression for Rates in Terms of Flux
Operators
186
8.6
Additional Expressions for Rate Constant
189
8.7
Flux-Flux Autocorrelation Functions
192
8.8
Evaluation of Propagator Matrix Elements Using Path
Integrals
194
xii
Contents
Bibliography for Chapter
8 197
Problems for Chapter
8 197
9
Time-Dependent Approach to Spectroscopy: Electronic,
Vibrational, and Rotational Spectra
199
9.1
Introduction
199
9.2
Thermal Averages and Imaginary Time Propagation
200
9.3
Electronic Spectra from Time Correlation Functions
201
9.4
Electronic Spectra: Time Development of the
Correlation Functions
202
9.5
Optical Spectra with Narrow-Line or Wide-Line
Excitations: Time-Dependent Picture
209
9.6
Vibrational Spectra: Correlation Function Approach
214
9.7
Rotational, Raman, and Magnetic Resonance
Spectra
220
9.8
Motional Narrowing and Stochastic Motion
225
Bibliography for Chapter
9 227
Problems for Chapter
9 227
10
Correlation Functions and Dynamical Processes:
Nonadiabatic Intramolecular Electron Transfer
231
10.1
Introduction
231
10.2
Electron Transfer: Some Generalities
232
10.3
Molecular Crystal Model
237
10.4
Rate Processes with Vibronic Coupling: Canonical
Transformations and Franck-Condon Factors
240
Contents
xiii
10.5
Steepest-Descents Evaluation of Franck-Condon
Behavior: Energy Sharing
247
10.6
Solvent Contributions to Electron Transfer Rates
251
10.7
Electron Transfer Reactions: Qualitative Remarks
253
Bibliography for Chapter
10 256
Problems for Chapter
10 256
11
Density Matrices
262
11.1
Introduction
262
11.2
Density Operators and Density Matrices: Definitions and
Averages
263
11.2.1
Wavefunctions and the Pure State Density Operator
263
11.2.2
Density Operators for Mixed States
264
11.3
Representations and Equations of Motion
266
11.4
Example: Spin-i Particles
267
11.4.1
Representation of Density Matrix Using
Pauli
Spin
Matrices
269
11.4.2
Crude Description of Dephasing in Two-Site Systems
269
11.5
Reduced Density Matrices
272
11.5.1
Reduced Density Matrices and Electronic Structure
273
11.5.2
Hartree-Fock Density Matrices; Natural
Orbitals 275
11.6
Reduced Density Matrices for Dynamical Statistical
Systems
277
11.6.1
Reduced Density Matrices for Subsystems
278
11.6.2
Zero-Order Density Matrix: Equilibrium
281
11.6.3
First-Order Expressions for the Density Matrix: Linear
Response Theory
281
11.6.4
Second-Order Response and the Density Matrix: Redfield
Equations and Relaxation Processes
284
11.6.5
Example: Relaxation and Dephasing in a Simple Spin
System
289
11.6.6
Second-Order Corrections to the Density: Application to
Molecular Nonlinear Optics
295
xiv
Contents
11.7
Higher-Order Corrections to the Density Matrix: Pulsed
Spectroscopy
298
11.7.1
Spins: Rotations and Angular Momentum
299
11.7.2
Rotating Frame Transformation
300
11.7.3
Simple Pulse Experiment: Carr-Purcell Spin Echo for
Uncoupled Spins
301
11.7.4
Average Hamiltonian Theory for Multiple-Pulse NMR
304
Bibliography for Chapter
11 310
Problems for Chapter
11 311
Appendix A: Dirac Delta Function
315
Appendix
В
:
Laplace Tranf
orms
317
Appendix C: Solutions to Problems
319
Index
355
Contents
xv
|
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| id | DE-604.BV014470294 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T19:02:59Z |
| institution | BVB |
| isbn | 0486420035 |
| language | English |
| lccn | 2001047374 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009878088 |
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| physical | xix, 361 p. ill. |
| publishDate | 2002 |
| publishDateSearch | 2002 |
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| publisher | Dover Publications |
| record_format | marc |
| spelling | Schatz, George C. Verfasser aut Quantum mechanics in chemistry George C. Schatz, Mark A. Ratner 1. publ., slightly corrected, unabridged republication of the work orig.. publ. in 1993 Mineola, N.Y. Dover Publications 2002 xix, 361 p. ill. txt rdacontent n rdamedia nc rdacarrier Kwantumchemie gtt Kwantummechanica gtt Quantentheorie Quantum chemistry Quantum theory Quantenmechanik (DE-588)4047989-4 gnd rswk-swf Quantenchemie (DE-588)4047979-1 gnd rswk-swf Quantenmechanik (DE-588)4047989-4 s DE-604 Quantenchemie (DE-588)4047979-1 s Ratner, Mark A. Sonstige oth Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009878088&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Schatz, George C. Quantum mechanics in chemistry Kwantumchemie gtt Kwantummechanica gtt Quantentheorie Quantum chemistry Quantum theory Quantenmechanik (DE-588)4047989-4 gnd Quantenchemie (DE-588)4047979-1 gnd |
| subject_GND | (DE-588)4047989-4 (DE-588)4047979-1 |
| title | Quantum mechanics in chemistry |
| title_auth | Quantum mechanics in chemistry |
| title_exact_search | Quantum mechanics in chemistry |
| title_full | Quantum mechanics in chemistry George C. Schatz, Mark A. Ratner |
| title_fullStr | Quantum mechanics in chemistry George C. Schatz, Mark A. Ratner |
| title_full_unstemmed | Quantum mechanics in chemistry George C. Schatz, Mark A. Ratner |
| title_short | Quantum mechanics in chemistry |
| title_sort | quantum mechanics in chemistry |
| topic | Kwantumchemie gtt Kwantummechanica gtt Quantentheorie Quantum chemistry Quantum theory Quantenmechanik (DE-588)4047989-4 gnd Quantenchemie (DE-588)4047979-1 gnd |
| topic_facet | Kwantumchemie Kwantummechanica Quantentheorie Quantum chemistry Quantum theory Quantenmechanik Quantenchemie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009878088&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT schatzgeorgec quantummechanicsinchemistry AT ratnermarka quantummechanicsinchemistry |