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Spectroscopy and Dynamics of Diatomic Molecules : Revised and Enlarged Edition - Helene Lefebvre-Brion

Spectroscopy and Dynamics of Diatomic Molecules

Revised and Enlarged Edition


Published: 15th April 2004
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This book is written for graduate students just beginning research, for theorists curious about what experimentalists actually can and do measure, and for experimentalists bewildered by theory. It is a guide for potential users of spectroscopic data, and uses language and concepts that bridge the frequency-and time-domain spectroscopic communities.

Key topics, concepts, and techniques include: the assignment of simple spectra, basic experimental techniques, definition of Born-Oppenheimer and angular momentum basis sets and the associated spectroscopic energy level patterns (Hund's cases), construction of effective Hamiltonian matrices to represent both spectra and dynamics, terms neglected in the Born-Oppenheimer approximation (situations intermediate between Hund's cases, spectroscopic perturbations), nonlinear least squares fitting, calculation and interpretation of coupling terms, semi-classical (WKB) approximation, transition intensities and interference effects, direct photofragmentation (dissociation and ionization) and indirect photofragmentation (predissociation and autoionization) processes, visualization of intramolecular dynamics, quantum beats and wavepackets, treatment of decaying quasi-eigenstates using a complex Heff model, and concluding with some examples of polyatomic molecule dynamics.

Students will discover that there is a fascinating world of cause-and-effect localized dynamics concealed beyond the reduction of spectra to archival molecular constants and the exact ab initio computation of molecular properties. Professional spectroscopists, kinetics, ab initio theorists will appreciate the practical, simplified-model, and rigorous theoretical approaches discussed in this book.

Key Features:

- A fundamental reference for all spectra of small, gas-phase molecules.

- It is the most up-to-date and comprehensive book on the electronic spectroscopy and dynamics of diatomic molecules.

- The authors pioneered the development of many of the experimental methods, concepts, models, and computational schemes described in this book.

- A fundamental reference for all spectra of small, gas-phase molecules.
- Emphasizes the role of perturbations in understanding the dynamics of isolated molecules.
- Includes new applications of interest to researchers in all areas of chemistry and materials science.

Simple Spectra and Standard Experimental Techniquesp. 1
Rotation-Vibration-Electronic Spectra of Diatomic Moleculesp. 2
Rotation-Vibration-Electronic Energy Levels and Standard Notationp. 3
Band Systems, Bands, and Branchesp. 6
Rotational Structure: Fortrat Parabolap. 6
Some Strategies for Rotational Line Assignmentsp. 11
Experimental Techniques of Diatomic Molecule Spectroscopyp. 21
The Goals of a Spectroscopic Experimentp. 21
What and How Much?p. 22
Rotational Analysis of a Spectrump. 24
Spectroscopic Strategies: Access and Selectivityp. 26
Classes of Spectroscopic Experimentp. 27
One Photon Resonant: Upward (Absorption Spectra)p. 27
One Photon Resonant: Downward (Emission Spectra)p. 33
Multiple Resonance Spectrap. 35
Photofragment and Coincidence Experimentsp. 39
Molecule Sourcesp. 41
Frequency Calibrationp. 43
Detection Techniquesp. 45
Radiation Sourcesp. 47
Referencesp. 55
Basic Modelsp. 61
What Is a Perturbation?p. 62
Structural Modelsp. 69
Elementary Properties of Angular Momenta in Diatomic Moleculesp. 72
Angular Momentum Components Defined by Normal and Anomalous Commutation Rulesp. 73
Recipes for Evaluation of Molecule-Fixed Angular Momentum Matrix Elementsp. 79
Euler Angles, [vertical bar]JM[Omega right angle bracket] Basis Functions, Direction Cosines, and Phasesp. 81
Estimation of Parameters in a Model Hamiltonianp. 83
Data Compilationsp. 84
Referencesp. 85
Terms Neglected in the Born-Oppenheimer Approximationp. 87
The Born-Oppenheimer Approximationp. 89
Potential Energy Curvesp. 90
Terms Neglected in the Born-Oppenheimer Approximationp. 92
Electrostatic and Nonadiabatic Part of Hp. 92
Crossing or Diabatic Curvesp. 93
Noncrossing or Adiabatic Curvesp. 94
The Spin Part of Hp. 94
Rotational Part of Hp. 96
Basis Functionsp. 99
Hund's Casesp. 101
Definition of Basis Setsp. 103
Quantum Numbers, Level Patterns, and the Effects of Terms Excluded from H[superscript (0)]p. 113
Intermediate Case Situationsp. 126
Introductionp. 126
Examplesp. 127
Transformations Between Hund's Case Basis Setsp. 130
Spectroscopic vs. Dynamical Hund's Casesp. 136
Relationship between Noncommuting Terms in H and the Most Appropriate Hund's Casep. 137
Symmetry Propertiesp. 138
Symmetry Properties of Hund's Case (a) Basis Functionsp. 138
Symmetry Properties of non-Hund's Case (a) Basis Functionsp. 145
Molecular Electronic Wavefunctionsp. 148
Matrix Elements between Electronic Wavefunctionsp. 156
Electrostatic Perturbationsp. 161
Diabatic Curvesp. 163
Approximate Representation of the Diabatic Electronic Wavefunctionp. 165
Adiabatic Curvesp. 168
Choice between the Diabatic and Adiabatic Modelsp. 172
Electromagnetic Field-Dressed Diabatic and Adiabatic Potential Energy Curvesp. 177
Spin Part of the Hamiltonianp. 180
The Spin-Orbit Operatorp. 181
Expression of Spin-Orbit Matrix Elements in Terms of One-Electron Molecular Spin-Orbit Parametersp. 183
Matrix Elements of the l[subscript zi] - s[subscript zi] Termp. 183
Diagonal Matrix Elementsp. 184
Off-Diagonal Matrix Elementsp. 187
Matrix Elements of the (l[superscript + subscript i]s[superscript - subscript i] + l[superscript - subscript i]s[superscript + subscript i]) Part of H[superscript SO]p. 190
The Spin-Rotation Operatorp. 191
The Spin-Spin Operatorp. 196
Diagonal Matrix Elements of H[superscript SS]: Calculation of the Direct Spin-spin Parameterp. 196
Calculation of Second-Order Spin-Orbit Effectsp. 199
[pi superscript 2] Configurationp. 201
[pi superscript 3 pi]' (or [pi superscript 3 pi]'[superscript 3] and [pi pi]') Configurationsp. 201
Off-Diagonal Matrix Elementsp. 202
Tensorial Operatorsp. 203
Rotational Perturbationsp. 210
Spin-Electronic Homogeneous Perturbationsp. 210
The S-Uncoupling Operatorp. 212
The L-Uncoupling Operatorp. 213
[superscript 2 Pi] - [superscript 2 Sigma superscript +] Interactionp. 217
Referencesp. 227
Methods of Deperturbationp. 233
Variational Calculationsp. 234
The Van Vleck Transformation and Effective Hamiltoniansp. 237
Approximate Solutionsp. 243
Graphical Methods for Deperturbationp. 243
Direct Diagonalization Versus Algebraic Approachesp. 247
Exact Solutionsp. 248
Least-Squares Fittingp. 248
Linear Least-Squares Fittingp. 248
Nonlinear Least-Squares Fittingp. 251
Practical Considerationsp. 255
Least Squares vs. Robust Estimator Fittingp. 257
Types of Programsp. 258
Comparison Between Effective and True Parametersp. 261
Coupled Equationsp. 264
Typical Examples of Fitted Perturbationsp. 267
An Indirect Heterogeneous Perturbation: NO B[superscript 2 Pi] - C[superscript 2 Pi] - D[superscript 2] [Sigma superscript +]p. 267
A Strong Multistate Interaction in the NO Moleculep. 269
Referencesp. 272
Interpretation of the Perturbation Matrix Elementsp. 275
Calculation of the Vibrational Factorp. 278
Semiclassical Approximationp. 279
Model Potentialsp. 285
Numerical Potentials and Vibrational Wavefunctionsp. 288
Some Remarks about "Borrowed" Computer Programsp. 291
Vibrational Assignment by the Matrix Element Methodp. 293
Homogeneous vs. Heterogeneous Perturbationsp. 305
Order of Magnitude of Electrostatic Perturbation Parameters: Interactions Between Valence and Rydberg States of the Same Symmetryp. 307
Valence and Rydberg Statesp. 308
Different Classes of Valence-Rydberg Mixingp. 310
Electrostatic Perturbations Between Valence and Rydberg Statesp. 312
Electrostatic Perturbations between Rydberg States Converging to Different States of the Ionp. 314
Order of Magnitude of Spin Parametersp. 315
Diagonal Spin-Orbit Parametersp. 318
Off-Diagonal Spin-Orbit Parametersp. 322
Spin-Spin Parametersp. 323
Magnitudes of Rotational Perturbation Parametersp. 325
Pure Precession Approximationp. 327
R-Dependence of the Spin Interaction Parametersp. 333
Beyond the Single-Configuration Approximationp. 340
Identification and Location of Metastable States by Perturbation Effectsp. 341
Referencesp. 342
Transition Intensities and Special Effectsp. 347
Intensity Factorsp. 348
Interrelationships between Intensity Factorsp. 348
General Formulas for One-Photon and Multi-Photon Transition Strengthsp. 355
One-Photon Transitionsp. 356
Two-Photon Transitionsp. 359
Three-Photon Transitionsp. 366
Comparisons between Excitation Schemes Involving Different Numbers of Photonsp. 367
Intensity Borrowingp. 368
Perturbations by States with "Infinite" Radiative Lifetime; Simple Intensity Borrowingp. 368
Multistate Deperturbation; The NO [superscript 2 Pi] Statesp. 375
Interference Effectsp. 378
Perturbations between States of the Same Symmetry; Vibrational-Band Intensity Anomaliesp. 380
[Delta Lambda] = [plus or minus]1 Perturbations; Rotational-Branch Intensity Anomaliesp. 386
Assignments Based on Pattern-Forming Rotational Quantum Numbersp. 403
[Sigma superscript +] - [Sigma subscript -] Perturbations; Subband Intensity Anomalies in [Sigma] [left and right arrow] [Pi] Transitionsp. 404
F[subscript 1] vs. F[subscript 2] Intensity Anomalies in [superscript 2 Sigma] Statesp. 405
Forbidden Transitions; Intensity Borrowing by Mixing with a Remote Perturberp. 406
Special Effectsp. 415
Differential Power Broadeningp. 416
Effects of Magnetic and Electric Fields on Perturbationsp. 418
Anticrossing, Quantum-Beat, and Double-Resonance Experimentsp. 427
Rydberg States and the Zeeman Effectp. 439
Nonthermal Population Distributions; Chemical and Collisional Effectsp. 445
"Deperturbation" at High Pressure and in Matricesp. 455
Matrix Effectsp. 458
Referencesp. 460
Photodissociation Dynamicsp. 469
Photofragmentationp. 470
Direct Dissociationp. 471
Photodissociation: Wigner-Witmer Rulesp. 471
Photodissociation Cross Sectionsp. 476
Photofragment Branching Ratios for Photodissociationp. 485
Photofragment Angular Distributionp. 486
Alignment of the Photofragmentp. 491
Introduction to Predissociationp. 493
Experimental Aspects of Predissociationp. 495
Measurement of Lifetimesp. 496
Measurement of Linewidthsp. 498
Energy Shiftsp. 503
Detection of Fragmentsp. 505
Theoretical Expressions for Widths and Level Shiftsp. 505
The Vibrational Factorp. 510
Mulliken's Classification of Predissociationsp. 514
The Electronic Interaction Strengthp. 518
Electrostatic Predissociationp. 519
Spin-Orbit Predissociationp. 520
Rotational or Gyroscopic Predissociationp. 521
Hyperfine Predissociationp. 521
Fano Lineshapep. 522
Isotope Effectsp. 526
Examples of Predissociationp. 528
Examples of Spin-Orbit Predissociationp. 528
Examples of Nonadiabatic Predissociationp. 531
Case of Intermediate Coupling Strengthp. 535
Indirect (Accidental) Predissociation and Interference Effectsp. 538
Some Recipes for Interpretationp. 543
Referencesp. 545
Photoionization Dynamicsp. 551
Direct Ionizationp. 552
Photoelectron Spectroscopyp. 552
ZEKE Spectroscopyp. 557
Shape resonancesp. 559
Cooper minimap. 561
Experimental Aspects of Autoionizationp. 564
The Nature of Autoionized Statesp. 568
Autoionization Widthsp. 569
Rotational Autoionizationp. 572
Vibrational Autoionizationp. 576
Spin-Orbit Autoionizationp. 581
Electronic (or Electrostatic) Autoionizationp. 586
Validity of the Approximationsp. 588
Influence of Autoionization on ZEKE Peak Intensitiesp. 591
Photoelectron Angular Distribution, Photoion Alignment, and Spin Polarizationp. 595
Photoelectron Angular Distributionp. 595
Photoion Alignmentp. 600
Spin-Polarizationp. 602
Competition between Autoionization and Predissociationp. 604
Superexcited State Decay Pathwaysp. 604
Theoretical Treatmentp. 608
Coherent Control of Photofragmentation Product Branching Ratiosp. 609
Referencesp. 615
Dynamicsp. 621
Dynamical Concepts, Tools, and Terminologyp. 622
The Time-Dependent Picture: Terminologyp. 623
Solution of the Time-Dependent Schrodinger Equationp. 624
Frequency Domain Spectra Treated as the Fourier Transform of the Autocorrelation Functionp. 626
Dynamical Quantitiesp. 635
General Density Matrix Formulation of a Dynamical Experiment: Excitation, Evolution, and Detection Matricesp. 639
Particle (Photon) vs. Wave Pictures of Spectroscopyp. 643
Motion of the Center of the Wavepacketp. 644
Equations of Motion for Resonance Operatorsp. 646
The One-Color Pump-Probe Experimentp. 649
Crafted Pulses for Detailed Manipulation of Molecular Dynamicsp. 655
From Quantum Beats to Wavepacketsp. 656
Polarization Quantum Beatsp. 657
Population Quantum Beatsp. 658
Nuclear Wavepacketsp. 659
Vibrational Wavepacketsp. 661
Rotational Wavepacketsp. 667
Rydberg Wavepackets: Kepler and Precessional Periodsp. 668
Relaxation into a Quasi-Continuum: A Tool for Dimensionality Reductionp. 671
The Complex-Energy Effective Hamiltonianp. 672
Treatment of Two-State Interaction by Nondegenerate Perturbation Theoryp. 674
Treatment by Quasidegenerate Perturbation Theory: 2 x 2 Diagonalizationp. 675
Quantum Beats Between Two Decaying Quasi-Eigenstatesp. 679
The Use of the Complex H[superscript eff] in Reduced-Dimension Modelsp. 681
Beyond the Spectra and Dynamics of Diatomic Moleculesp. 683
Basis Statesp. 683
What is Deperturbation Anyway?p. 684
Visualization of Dynamicsp. 685
Beyond Diatomic Molecules: Polyatomic Molecule Vibrational Dynamicsp. 687
Polyadsp. 689
Creation and Annihilation Operatorsp. 690
Dynamics in State Spacep. 692
Number Operatorp. 693
Resonance Energy and Energy Transfer Rate Operatorsp. 694
The Use of Expectation Values of Resonance Operators to Visualize Dynamic Processesp. 697
Q and Pp. 700
Transformation Between Local and Normal Mode Limitsp. 702
Classical Mechanical Treatmentp. 703
The Morse Oscillatorp. 705
Quantum Mechanical Minimal Model for Two Anharmonically Coupled Local Stretch Morse Oscillatorsp. 706
Transformation between 4-Parameter Forms of the Normal and Local Mode Basis Setsp. 710
Transformation between 6-Parameter Forms of the Normal Mode and Local Mode H[superscript eff]p. 714
From Quantum Mechanical H[superscript eff] to Classical Mechanical H(Q, P)p. 717
Polyatomic Molecule Dynamicsp. 733
Inter-System Crossing, Internal Conversion, and Intramolecular Vibrational Distributionp. 733
Referencesp. 736
Table of Contents provided by Rittenhouse. All Rights Reserved.

ISBN: 9780124414563
ISBN-10: 0124414567
Audience: General
Format: Paperback
Language: English
Number Of Pages: 786
Published: 15th April 2004
Publisher: Elsevier Science Publishing Co Inc
Country of Publication: NL
Dimensions (cm): 23.98 x 16.41  x 3.51
Weight (kg): 1.46
Edition Number: 2