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

, by Herman, Michel; Lievin, Jacques; Vander Auwera, Jean; Campargue, Alain

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ISBN: 9780471328438 | 047132843X
Cover: Hardcover
Copyright: 3/30/1999

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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.

Series Introduction

I. General Introduction

(3)

II. The Forward Trip: From the Hamiltonian to the Vibration--Rotation Spectrum

(91)

Introduction

(1)

The Forward Trip: An Ab Initio Approach

(51)

Exact Quantum Mechanical Formulation

(20)

Full Molecular Hamiltonian

(1)

Born--Oppenheimer Separation

(2)

Translation-Free Hamiltonian

(1)

Vibration--Rotation Separation

(1)

Molecular Axis System (MAS)

(1)

Rotation Coordinates

(2)

Eckart Frame

(1)

Vibration Coordinates

(1)

Exact Vibration--Rotation Hamiltonian

(1)

Vibration--Rotation Kinetic Energy Operator

(1)

Potential-Energy Surface

(1)

Exact Vibration--Rotation Schrodinger Equation

(1)

Variational Resolution of the Vibration--Rotation Schrodinger equation

(1)

Variational Principle

(1)

Linear Variational Method

(2)

Configuration Interaction Method

(1)

Diagonalisation of the Vibration-Rotation Hamiltonian

(1)

Energy Spectrum of the Vibration-Rotation Hamiltonian

(2)

Vibration--Rotation Transition Energies

(2)

Vibration--Rotation Lines Intensities

(1)

Optical Vibration--Rotation Transition Probabilities

(1)

Electric Dipole Transition Probabilities

(2)

Dipole Moment Surface

(1)

Full Ab Initio Forward Trip

(1)

Towards a Converged Ab Initio Approach

(31)

Setting the Ab Initio Approach

(1)

Need for a Pes

(1)

General Problems with Pes and DMS

(1)

Choice of a Coordinate System

(1)

Criteria

(1)

Rectilinear Versus Curvilinear Coordinates

(2)

Selected Curvilinear Coordinates

(1)

Curvilinear Bond-Angle Coordinates

(1)

Local-Mode Coordinates

(1)

Heliocentric-Type Coordinates

(1)

Adapted Stretching Coordinates

(1)

Potential-Adapted Coordinates

(2)

Adapted Bending Coordinates

(1)

Optimised Coordinates

(1)

Curvilinear Normal Coordinates

(1)

Transformation of Coordinates

(1)

Approximate PES from Quantum Chemistry

(1)

Ab Initio Level of Calculation

(4)

Analytical Expression for the Pes

(1)

Adjustment of an Analytical Function to Ab Initio Calculated Points

(3)

Analytical Versus Numerical Derivatives Calculations

(2)

Ab Initio DVR Approach

(1)

Ab initio Electric Dipole Moment Surfaces

(1)

Variational Methods

(1)

Contraction or Diagonalization-Truncation

(2)

General Mean-Field Optimizations

(2)

The Vibrational Multiconfigurational SCF Method

(1)

Discrete-Variable Representation (DVR)

(2)

Adiabatic Approaches

(1)

Morse Oscillator Rigid Bender Internal Dynamics (MORBID) Approach

(1)

Perturbation Theory Methods

(1)

Basic Formulas

(1)

Treatment of Resonating States

(1)

High Order Canonical Van Vleck Perturbation Theory (CVPT)

(2)

Acetylene: A Laboratory for Intramolecular Advances

(39)

The Acetylene Molecule

(17)

Both Simple and Complex

(1)

Symmetry Properties

(1)

Topology of the Ground-State PES

(4)

Calculated Properties

(1)

Coordinate Systems

(1)

9D Systems

(1)

6D Systems

(3)

Symmetry-Adapted Coordinates

(1)

Rectilinear Normal Coordinates

(1)

Planar 5D Systems

(1)

Vibration--Rotation Hamiltonian for Acetylene

(1)

Choice of a Coordinate System

(2)

Kinetic-Energy Operator

(2)

Potential-Energy Surface

(2)

Forward and Backward Trips Applied to Acetylene

(22)

Refined Quartic Force Fields in Valence Internal Coordinates

(1)

Refinement From Second-Order Perturbation Theory: The Strey--Mills Potential

(1)

Variational Calculations with a Modified SM Potential

(1)

Sixth-Order CVPT with the SM Potential

(1)

Refinement from Variational Calculations: The Bramley--Carter--Handy--Mills Potential

(2)

Variational Calculations with the BCHM Potential

(1)

Ab initio Quartic Force Fields

(1)

SCF Quartic Force Field from Analytical Derivatives

(1)

SD(Q)CI Quartic Force Field and SDCI Cubic Electric Field from Grid Calculations

(1)

Testing the Quality of the SDCI and SD(Q)CI Force Fields

(1)

Overtone Spectrum of Stretching Modes

(6)

Analysis of Stretch--Bend Interactions from the Vcasscf Approach

(1)

CCSD(T) Quartic Force Field from Numerical Differences

(2)

Bending Dynamics

(1)

DVR Variational Calculations

(2)

Adiabatic Variational Refinement

(1)

Classical and Semiclassical Approaches of Intramolecular Dynamics

(1)

Classical Trajectories

(1)

Semiclassical Approach

(1)

Normal, Local, and Precessional Bending Modes

(1)

Algebraic Approaches

(1)

III. The Backward Trip: From the Vibration-Rotation Data to the Hamiltonian

(158)

Introduction

(7)

Strategy

(3)

Aim

(1)

Selection of Coordinates

(1)

Matrix Image of the Molecule

(1)

Matrix Treatment

(1)

Watsonian

(4)

General Form

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

Summary

Author Biography

Table of Contents

Supplemental Materials