Global and Accurate Vibration Hamiltonians from High-Resolution Molecular Spectroscopy, Volume 108,9780471328438

Global and Accurate Vibration Hamiltonians from High-Resolution Molecular Spectroscopy, Volume 108

by ; ; ;
Edition: 1st
ISBN13: 9780471328438
ISBN10: 047132843X
Format: Hardcover
Pub. Date: 1999-03-30
Publisher(s): Wiley-Interscience
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Summary

The latest in a series providing chemical physicists with a forum for critical, authoritative evaluations of advances in every area of the discipline, this stand-alone volume focuses on using high resolution molecular spectroscopy to arrive at global and accurate Vibration Hamiltonians.

Author Biography

Michael Robert Herman was a French American mathematician. He was one of the leading experts on the theory of dynamical systems. Born in New York City, he was educated in France.

Jacques Lievin is the editor of Global and Accurate Vibration Hamiltonians from High-Resolution Molecular Spectroscopy, Volume 108, published by Wiley.

Table of Contents

Series Introduction xv
I. General Introduction 1(3)
II. The Forward Trip: From the Hamiltonian to the Vibration--Rotation Spectrum 4(91)
Introduction
4(1)
The Forward Trip: An Ab Initio Approach
5(51)
Exact Quantum Mechanical Formulation
5(20)
Full Molecular Hamiltonian
5(1)
Born--Oppenheimer Separation
6(2)
Translation-Free Hamiltonian
8(1)
Vibration--Rotation Separation
9(1)
Molecular Axis System (MAS)
9(1)
Rotation Coordinates
9(2)
Eckart Frame
11(1)
Vibration Coordinates
12(1)
Exact Vibration--Rotation Hamiltonian
12(1)
Vibration--Rotation Kinetic Energy Operator
12(1)
Potential-Energy Surface
12(1)
Exact Vibration--Rotation Schrodinger Equation
13(1)
Variational Resolution of the Vibration--Rotation Schrodinger equation
13(1)
Variational Principle
13(1)
Linear Variational Method
14(2)
Configuration Interaction Method
16(1)
Diagonalisation of the Vibration-Rotation Hamiltonian
16(1)
Energy Spectrum of the Vibration-Rotation Hamiltonian
17(2)
Vibration--Rotation Transition Energies
19(2)
Vibration--Rotation Lines Intensities
21(1)
Optical Vibration--Rotation Transition Probabilities
21(1)
Electric Dipole Transition Probabilities
22(2)
Dipole Moment Surface
24(1)
Full Ab Initio Forward Trip
25(1)
Towards a Converged Ab Initio Approach
25(31)
Setting the Ab Initio Approach
25(1)
Need for a Pes
25(1)
General Problems with Pes and DMS
26(1)
Choice of a Coordinate System
27(1)
Criteria
27(1)
Rectilinear Versus Curvilinear Coordinates
27(2)
Selected Curvilinear Coordinates
29(1)
Curvilinear Bond-Angle Coordinates
29(1)
Local-Mode Coordinates
29(1)
Heliocentric-Type Coordinates
30(1)
Adapted Stretching Coordinates
30(1)
Potential-Adapted Coordinates
30(2)
Adapted Bending Coordinates
32(1)
Optimised Coordinates
32(1)
Curvilinear Normal Coordinates
33(1)
Transformation of Coordinates
33(1)
Approximate PES from Quantum Chemistry
34(1)
Ab Initio Level of Calculation
34(4)
Analytical Expression for the Pes
38(1)
Adjustment of an Analytical Function to Ab Initio Calculated Points
39(3)
Analytical Versus Numerical Derivatives Calculations
42(2)
Ab Initio DVR Approach
44(1)
Ab initio Electric Dipole Moment Surfaces
44(1)
Variational Methods
45(1)
Contraction or Diagonalization-Truncation
45(2)
General Mean-Field Optimizations
47(2)
The Vibrational Multiconfigurational SCF Method
49(1)
Discrete-Variable Representation (DVR)
50(2)
Adiabatic Approaches
52(1)
Morse Oscillator Rigid Bender Internal Dynamics (MORBID) Approach
52(1)
Perturbation Theory Methods
53(1)
Basic Formulas
53(1)
Treatment of Resonating States
54(1)
High Order Canonical Van Vleck Perturbation Theory (CVPT)
54(2)
Acetylene: A Laboratory for Intramolecular Advances
56(39)
The Acetylene Molecule
56(17)
Both Simple and Complex
56(1)
Symmetry Properties
57(1)
Topology of the Ground-State PES
58(4)
Calculated Properties
62(1)
Coordinate Systems
63(1)
9D Systems
63(1)
6D Systems
63(3)
Symmetry-Adapted Coordinates
66(1)
Rectilinear Normal Coordinates
66(1)
Planar 5D Systems
67(1)
Vibration--Rotation Hamiltonian for Acetylene
67(1)
Choice of a Coordinate System
67(2)
Kinetic-Energy Operator
69(2)
Potential-Energy Surface
71(2)
Forward and Backward Trips Applied to Acetylene
73(22)
Refined Quartic Force Fields in Valence Internal Coordinates
73(1)
Refinement From Second-Order Perturbation Theory: The Strey--Mills Potential
73(1)
Variational Calculations with a Modified SM Potential
74(1)
Sixth-Order CVPT with the SM Potential
75(1)
Refinement from Variational Calculations: The Bramley--Carter--Handy--Mills Potential
76(2)
Variational Calculations with the BCHM Potential
78(1)
Ab initio Quartic Force Fields
79(1)
SCF Quartic Force Field from Analytical Derivatives
79(1)
SD(Q)CI Quartic Force Field and SDCI Cubic Electric Field from Grid Calculations
80(1)
Testing the Quality of the SDCI and SD(Q)CI Force Fields
80(1)
Overtone Spectrum of Stretching Modes
81(6)
Analysis of Stretch--Bend Interactions from the Vcasscf Approach
87(1)
CCSD(T) Quartic Force Field from Numerical Differences
87(2)
Bending Dynamics
89(1)
DVR Variational Calculations
89(2)
Adiabatic Variational Refinement
91(1)
Classical and Semiclassical Approaches of Intramolecular Dynamics
92(1)
Classical Trajectories
92(1)
Semiclassical Approach
93(1)
Normal, Local, and Precessional Bending Modes
93(1)
Algebraic Approaches
94(1)
III. The Backward Trip: From the Vibration-Rotation Data to the Hamiltonian 95(158)
Introduction
95(7)
Strategy
95(3)
Aim
95(1)
Selection of Coordinates
95(1)
Matrix Image of the Molecule
96(1)
Matrix Treatment
97(1)
Watsonian
98(4)
General Form
98(4)
Fractionation
102(1)
Vibrational Terms
102(40)
Basic Features
102(3)
Diagonal Terms
105(10)
The Harmonic Oscillator (Hhar)
105(3)
The Anharmonic Oscillator (vHvanhdiag)
108(1)
One Dimensional Dunham Expansion
109(4)
Multidimensional Dunham Expansion
113(2)
Off-Diagonal Terms
115(13)
Anharmonic Resonances (Hvanhoff-diag)
115(1)
Terminology
115(2)
Matrix Elements
117(1)
Bright and Dark States
118(4)
Quartic Resonances
122(1)
Detailed Content
122(1)
x--K Relations
123(3)
Unusual Quartic Resonances
126(2)
Linear Tops
128(14)
General Features
128(1)
Diagonal Terms
129(1)
Harmonic Contributions (Hvhar(lin))
129(2)
l Sublevels
131(2)
Diagonal Anharmonic Terms
133(2)
Off-Diagonal Terms (Hvanhar(lin)off-diag)
135(1)
l Resonance
135(1)
Anharmonic Resonances
136(3)
Anharmonic and l Resonances
139(3)
Level Clustering
142(23)
Vibrational Polyads
142(5)
One-Resonance Polyads
142(1)
Multiresonance Polyads
142(3)
Pseudo--Quantum Numbers
145(1)
Constants of the Motion
145(1)
General Procedure
145(2)
Examples
147(13)
Introduction
147(1)
Nitrous Oxide
148(1)
Level Clustering
148(1)
Band Intensities
149(2)
Acetylene
151(1)
Anharmonic Resonances
151(1)
Cluster Structure
152(4)
Parameters
156(1)
12C2D2
157(1)
Ethylene
157(3)
Giant Clusters
160(5)
V/l-Clusters
160(1)
Quantum Numbers
160(1)
Spectra
161(1)
V/l/C-Clusters
161(4)
Vibration-Rotation Terms
165(33)
General Picture
165(1)
Rigid Rotor Hamiltonian (Hrrig)
166(12)
Symmetric Tops
166(1)
Asymmetric Tops
167(4)
Linear Tops
171(1)
l Doubling
171(2)
e/f Levels
173(5)
Vibration--Rotation Hamiltonian
178(10)
General Picture
178(1)
Diatomic Species
179(2)
Linear Polyatomic Species
181(2)
Asymmetric Tops
183(1)
Coriolis Coupling
184(1)
Asymmetric Tops
184(3)
Acetylene
187(1)
Vibration--Rotation Fits in Acetylene
188(10)
MIME for Lower Bending Levels in 12C2H2
188(5)
Vibration--Rotation Wavefunctions in 12C2H2
193(1)
Lower-Energy Bending Energy Levels
193(2)
Fundamental CH Stretching Vibration, v3
195(1)
Lower Bending Levels in 12C2D2
195(2)
Rotational Constants in 12C2H2 Overtone Levels
197(1)
Molecular Vibration-Rotation Spectra
198(55)
Spectral Intensity
198(1)
Transition Probabilities
199(1)
Light Absorption
200(11)
Absorption Induced by Electric Dipole Interactions
200(2)
Absorption Coefficient: Beer's Law
202(1)
Absorption Line Shape
203(2)
Line Intensity
205(2)
Population Factors
207(1)
Thermal Distribution over the Energy Levels
207(1)
Total Internal Partition Function
207(1)
Degeneracy of the Levels
208(1)
Statistical Weight of the Rovibronic Levels
209(1)
Integrated Absorption Coefficient and Cross Section
209(2)
Emission
211(1)
Dipole Moment Matrix Elements for Vibration-Rotation Transitions
212(1)
Molecular Symmetry
213(1)
Vibrational Spectra
214(8)
Harmonic Selection Rules
214(1)
Non Degenerate Vibrations
214(2)
Degenerate Vibrations
216(1)
Vibrational Bands in the Harmonic Oscillator Approximation
217(2)
Application to Linear Molecules
219(1)
Vibrational Bands for the Anharmonic Oscillator
220(1)
Influence of Mechanical Anharmonicity
220(1)
Resonances and Intensity Borrowing
221(1)
Vibration--Rotation Spectra
222(31)
Rigid Rotor Selection Rules
222(1)
Vibration--Rotation Transitions
223(1)
Symmetric Top
223(6)
Asymmetric Top
229(5)
Linear Molecule
234(9)
Vibration--Rotation Interaction
243(1)
The Effective Dipole Moment Operator
243(3)
Influence of Vibration--Rotation Resonances on Intensities
246(2)
Herman--Wallis Effects in Linear Molecules
248(5)
IV. Experimental Overtone Spectroscopy 253(39)
Introduction
253(2)
Fourier Transform Spectroscopy (FTS)
255(7)
Introduction
255(2)
Overtone Spectroscopy Using FTS
257(5)
Laser Overtone Spectroscopy
262(30)
Frequency Modulation with Diode Lasers (FMDL)
263(2)
Method
263(1)
Application of FMDL to Spectroscopy
264(1)
Cavity Ringdown Spectroscopy (CRDS)
265(6)
Pulsed CRDS
265(2)
CW-CRDS
267(3)
Capabilities of CRDS
270(1)
Spectroscopy
270(1)
Diagnostics
270(1)
Intracavity Laser Absorption Spectroscopy (ICLAS)
271(10)
Principles
271(3)
Sensitivity Limitations
274(1)
Seeding Noise
275(1)
Spectral Resolution and Calibration
276(1)
Capabilities of ICLAS
277(1)
Overtone Spectroscopy
278(2)
Diagnostics
280(1)
Optoacoustic (OA) Spectroscopy
281(3)
Basic Principles
281(1)
Application to Overtone Spectroscopy
282(2)
Optothermal (OT) Spectroscopy
284(1)
Comparison of FMDL, CRDS, ICLAS, and OA Methods
285(3)
Other Laser Investigations of Vibration--Rotation Levels
288(4)
Laser Labelling
289(1)
Photofragment Spectroscopy
290(1)
Stimulated Emission Pumping and Dispersed Fluorescence
290(2)
Acknowledgments 292(1)
References 293(38)
Appendix A. Abbreviations and Symbols 331(9)
Appendix B. Bibliography on acetylene in the ground electronic state 340(23)
Appendix C. Vibrational Energy Levels of 12C2H2(X1Σ+g) 363(26)
Author Index 389(26)
Subject Index 415

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