The Spectra and Dynamics of Diatomic Molecules
Revised and Enlarged Edition
By: Helene Lefebvre-Brion, Robert W. Field
Paperback | 1 April 2004 | Edition Number 2
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800 Pages
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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 Techniques | p. 1 |
Rotation-Vibration-Electronic Spectra of Diatomic Molecules | p. 2 |
Rotation-Vibration-Electronic Energy Levels and Standard Notation | p. 3 |
Band Systems, Bands, and Branches | p. 6 |
Rotational Structure: Fortrat Parabola | p. 6 |
Some Strategies for Rotational Line Assignments | p. 11 |
Experimental Techniques of Diatomic Molecule Spectroscopy | p. 21 |
The Goals of a Spectroscopic Experiment | p. 21 |
What and How Much? | p. 22 |
Rotational Analysis of a Spectrum | p. 24 |
Spectroscopic Strategies: Access and Selectivity | p. 26 |
Classes of Spectroscopic Experiment | p. 27 |
One Photon Resonant: Upward (Absorption Spectra) | p. 27 |
One Photon Resonant: Downward (Emission Spectra) | p. 33 |
Multiple Resonance Spectra | p. 35 |
Photofragment and Coincidence Experiments | p. 39 |
Molecule Sources | p. 41 |
Frequency Calibration | p. 43 |
Detection Techniques | p. 45 |
Radiation Sources | p. 47 |
References | p. 55 |
Basic Models | p. 61 |
What Is a Perturbation? | p. 62 |
Structural Models | p. 69 |
Elementary Properties of Angular Momenta in Diatomic Molecules | p. 72 |
Angular Momentum Components Defined by Normal and Anomalous Commutation Rules | p. 73 |
Recipes for Evaluation of Molecule-Fixed Angular Momentum Matrix Elements | p. 79 |
Euler Angles, [vertical bar]JM[Omega right angle bracket] Basis Functions, Direction Cosines, and Phases | p. 81 |
Estimation of Parameters in a Model Hamiltonian | p. 83 |
Data Compilations | p. 84 |
References | p. 85 |
Terms Neglected in the Born-Oppenheimer Approximation | p. 87 |
The Born-Oppenheimer Approximation | p. 89 |
Potential Energy Curves | p. 90 |
Terms Neglected in the Born-Oppenheimer Approximation | p. 92 |
Electrostatic and Nonadiabatic Part of H | p. 92 |
Crossing or Diabatic Curves | p. 93 |
Noncrossing or Adiabatic Curves | p. 94 |
The Spin Part of H | p. 94 |
Rotational Part of H | p. 96 |
Basis Functions | p. 99 |
Hund's Cases | p. 101 |
Definition of Basis Sets | p. 103 |
Quantum Numbers, Level Patterns, and the Effects of Terms Excluded from H[superscript (0)] | p. 113 |
Intermediate Case Situations | p. 126 |
Introduction | p. 126 |
Examples | p. 127 |
Transformations Between Hund's Case Basis Sets | p. 130 |
Spectroscopic vs. Dynamical Hund's Cases | p. 136 |
Relationship between Noncommuting Terms in H and the Most Appropriate Hund's Case | p. 137 |
Symmetry Properties | p. 138 |
Symmetry Properties of Hund's Case (a) Basis Functions | p. 138 |
Symmetry Properties of non-Hund's Case (a) Basis Functions | p. 145 |
Molecular Electronic Wavefunctions | p. 148 |
Matrix Elements between Electronic Wavefunctions | p. 156 |
Electrostatic Perturbations | p. 161 |
Diabatic Curves | p. 163 |
Approximate Representation of the Diabatic Electronic Wavefunction | p. 165 |
Adiabatic Curves | p. 168 |
Choice between the Diabatic and Adiabatic Models | p. 172 |
Electromagnetic Field-Dressed Diabatic and Adiabatic Potential Energy Curves | p. 177 |
Spin Part of the Hamiltonian | p. 180 |
The Spin-Orbit Operator | p. 181 |
Expression of Spin-Orbit Matrix Elements in Terms of One-Electron Molecular Spin-Orbit Parameters | p. 183 |
Matrix Elements of the l[subscript zi] - s[subscript zi] Term | p. 183 |
Diagonal Matrix Elements | p. 184 |
Off-Diagonal Matrix Elements | p. 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 Operator | p. 191 |
The Spin-Spin Operator | p. 196 |
Diagonal Matrix Elements of H[superscript SS]: Calculation of the Direct Spin-spin Parameter | p. 196 |
Calculation of Second-Order Spin-Orbit Effects | p. 199 |
[pi superscript 2] Configuration | p. 201 |
[pi superscript 3 pi]' (or [pi superscript 3 pi]'[superscript 3] and [pi pi]') Configurations | p. 201 |
Off-Diagonal Matrix Elements | p. 202 |
Tensorial Operators | p. 203 |
Rotational Perturbations | p. 210 |
Spin-Electronic Homogeneous Perturbations | p. 210 |
The S-Uncoupling Operator | p. 212 |
The L-Uncoupling Operator | p. 213 |
[superscript 2 Pi] - [superscript 2 Sigma superscript +] Interaction | p. 217 |
References | p. 227 |
Methods of Deperturbation | p. 233 |
Variational Calculations | p. 234 |
The Van Vleck Transformation and Effective Hamiltonians | p. 237 |
Approximate Solutions | p. 243 |
Graphical Methods for Deperturbation | p. 243 |
Direct Diagonalization Versus Algebraic Approaches | p. 247 |
Exact Solutions | p. 248 |
Least-Squares Fitting | p. 248 |
Linear Least-Squares Fitting | p. 248 |
Nonlinear Least-Squares Fitting | p. 251 |
Practical Considerations | p. 255 |
Least Squares vs. Robust Estimator Fitting | p. 257 |
Types of Programs | p. 258 |
Comparison Between Effective and True Parameters | p. 261 |
Coupled Equations | p. 264 |
Typical Examples of Fitted Perturbations | p. 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 Molecule | p. 269 |
References | p. 272 |
Interpretation of the Perturbation Matrix Elements | p. 275 |
Calculation of the Vibrational Factor | p. 278 |
Semiclassical Approximation | p. 279 |
Model Potentials | p. 285 |
Numerical Potentials and Vibrational Wavefunctions | p. 288 |
Some Remarks about "Borrowed" Computer Programs | p. 291 |
Vibrational Assignment by the Matrix Element Method | p. 293 |
Homogeneous vs. Heterogeneous Perturbations | p. 305 |
Order of Magnitude of Electrostatic Perturbation Parameters: Interactions Between Valence and Rydberg States of the Same Symmetry | p. 307 |
Valence and Rydberg States | p. 308 |
Different Classes of Valence-Rydberg Mixing | p. 310 |
Electrostatic Perturbations Between Valence and Rydberg States | p. 312 |
Electrostatic Perturbations between Rydberg States Converging to Different States of the Ion | p. 314 |
Order of Magnitude of Spin Parameters | p. 315 |
Diagonal Spin-Orbit Parameters | p. 318 |
Off-Diagonal Spin-Orbit Parameters | p. 322 |
Spin-Spin Parameters | p. 323 |
Magnitudes of Rotational Perturbation Parameters | p. 325 |
Pure Precession Approximation | p. 327 |
R-Dependence of the Spin Interaction Parameters | p. 333 |
Beyond the Single-Configuration Approximation | p. 340 |
Identification and Location of Metastable States by Perturbation Effects | p. 341 |
References | p. 342 |
Transition Intensities and Special Effects | p. 347 |
Intensity Factors | p. 348 |
Interrelationships between Intensity Factors | p. 348 |
General Formulas for One-Photon and Multi-Photon Transition Strengths | p. 355 |
One-Photon Transitions | p. 356 |
Two-Photon Transitions | p. 359 |
Three-Photon Transitions | p. 366 |
Comparisons between Excitation Schemes Involving Different Numbers of Photons | p. 367 |
Intensity Borrowing | p. 368 |
Perturbations by States with "Infinite" Radiative Lifetime; Simple Intensity Borrowing | p. 368 |
Multistate Deperturbation; The NO [superscript 2 Pi] States | p. 375 |
Interference Effects | p. 378 |
Perturbations between States of the Same Symmetry; Vibrational-Band Intensity Anomalies | p. 380 |
[Delta Lambda] = [plus or minus]1 Perturbations; Rotational-Branch Intensity Anomalies | p. 386 |
Assignments Based on Pattern-Forming Rotational Quantum Numbers | p. 403 |
[Sigma superscript +] - [Sigma subscript -] Perturbations; Subband Intensity Anomalies in [Sigma] [left and right arrow] [Pi] Transitions | p. 404 |
F[subscript 1] vs. F[subscript 2] Intensity Anomalies in [superscript 2 Sigma] States | p. 405 |
Forbidden Transitions; Intensity Borrowing by Mixing with a Remote Perturber | p. 406 |
Special Effects | p. 415 |
Differential Power Broadening | p. 416 |
Effects of Magnetic and Electric Fields on Perturbations | p. 418 |
Anticrossing, Quantum-Beat, and Double-Resonance Experiments | p. 427 |
Rydberg States and the Zeeman Effect | p. 439 |
Nonthermal Population Distributions; Chemical and Collisional Effects | p. 445 |
"Deperturbation" at High Pressure and in Matrices | p. 455 |
Matrix Effects | p. 458 |
References | p. 460 |
Photodissociation Dynamics | p. 469 |
Photofragmentation | p. 470 |
Direct Dissociation | p. 471 |
Photodissociation: Wigner-Witmer Rules | p. 471 |
Photodissociation Cross Sections | p. 476 |
Photofragment Branching Ratios for Photodissociation | p. 485 |
Photofragment Angular Distribution | p. 486 |
Alignment of the Photofragment | p. 491 |
Introduction to Predissociation | p. 493 |
Experimental Aspects of Predissociation | p. 495 |
Measurement of Lifetimes | p. 496 |
Measurement of Linewidths | p. 498 |
Energy Shifts | p. 503 |
Detection of Fragments | p. 505 |
Theoretical Expressions for Widths and Level Shifts | p. 505 |
The Vibrational Factor | p. 510 |
Mulliken's Classification of Predissociations | p. 514 |
The Electronic Interaction Strength | p. 518 |
Electrostatic Predissociation | p. 519 |
Spin-Orbit Predissociation | p. 520 |
Rotational or Gyroscopic Predissociation | p. 521 |
Hyperfine Predissociation | p. 521 |
Fano Lineshape | p. 522 |
Isotope Effects | p. 526 |
Examples of Predissociation | p. 528 |
Examples of Spin-Orbit Predissociation | p. 528 |
Examples of Nonadiabatic Predissociation | p. 531 |
Case of Intermediate Coupling Strength | p. 535 |
Indirect (Accidental) Predissociation and Interference Effects | p. 538 |
Some Recipes for Interpretation | p. 543 |
References | p. 545 |
Photoionization Dynamics | p. 551 |
Direct Ionization | p. 552 |
Photoelectron Spectroscopy | p. 552 |
ZEKE Spectroscopy | p. 557 |
Shape resonances | p. 559 |
Cooper minima | p. 561 |
Experimental Aspects of Autoionization | p. 564 |
The Nature of Autoionized States | p. 568 |
Autoionization Widths | p. 569 |
Rotational Autoionization | p. 572 |
Vibrational Autoionization | p. 576 |
Spin-Orbit Autoionization | p. 581 |
Electronic (or Electrostatic) Autoionization | p. 586 |
Validity of the Approximations | p. 588 |
Influence of Autoionization on ZEKE Peak Intensities | p. 591 |
Photoelectron Angular Distribution, Photoion Alignment, and Spin Polarization | p. 595 |
Photoelectron Angular Distribution | p. 595 |
Photoion Alignment | p. 600 |
Spin-Polarization | p. 602 |
Competition between Autoionization and Predissociation | p. 604 |
Superexcited State Decay Pathways | p. 604 |
Theoretical Treatment | p. 608 |
Coherent Control of Photofragmentation Product Branching Ratios | p. 609 |
References | p. 615 |
Dynamics | p. 621 |
Dynamical Concepts, Tools, and Terminology | p. 622 |
The Time-Dependent Picture: Terminology | p. 623 |
Solution of the Time-Dependent Schrodinger Equation | p. 624 |
Frequency Domain Spectra Treated as the Fourier Transform of the Autocorrelation Function | p. 626 |
Dynamical Quantities | p. 635 |
General Density Matrix Formulation of a Dynamical Experiment: Excitation, Evolution, and Detection Matrices | p. 639 |
Particle (Photon) vs. Wave Pictures of Spectroscopy | p. 643 |
Motion of the Center of the Wavepacket | p. 644 |
Equations of Motion for Resonance Operators | p. 646 |
The One-Color Pump-Probe Experiment | p. 649 |
Crafted Pulses for Detailed Manipulation of Molecular Dynamics | p. 655 |
From Quantum Beats to Wavepackets | p. 656 |
Polarization Quantum Beats | p. 657 |
Population Quantum Beats | p. 658 |
Nuclear Wavepackets | p. 659 |
Vibrational Wavepackets | p. 661 |
Rotational Wavepackets | p. 667 |
Rydberg Wavepackets: Kepler and Precessional Periods | p. 668 |
Relaxation into a Quasi-Continuum: A Tool for Dimensionality Reduction | p. 671 |
The Complex-Energy Effective Hamiltonian | p. 672 |
Treatment of Two-State Interaction by Nondegenerate Perturbation Theory | p. 674 |
Treatment by Quasidegenerate Perturbation Theory: 2 x 2 Diagonalization | p. 675 |
Quantum Beats Between Two Decaying Quasi-Eigenstates | p. 679 |
The Use of the Complex H[superscript eff] in Reduced-Dimension Models | p. 681 |
Beyond the Spectra and Dynamics of Diatomic Molecules | p. 683 |
Basis States | p. 683 |
What is Deperturbation Anyway? | p. 684 |
Visualization of Dynamics | p. 685 |
Beyond Diatomic Molecules: Polyatomic Molecule Vibrational Dynamics | p. 687 |
Polyads | p. 689 |
Creation and Annihilation Operators | p. 690 |
Dynamics in State Space | p. 692 |
Number Operator | p. 693 |
Resonance Energy and Energy Transfer Rate Operators | p. 694 |
The Use of Expectation Values of Resonance Operators to Visualize Dynamic Processes | p. 697 |
Q and P | p. 700 |
Transformation Between Local and Normal Mode Limits | p. 702 |
Classical Mechanical Treatment | p. 703 |
The Morse Oscillator | p. 705 |
Quantum Mechanical Minimal Model for Two Anharmonically Coupled Local Stretch Morse Oscillators | p. 706 |
Transformation between 4-Parameter Forms of the Normal and Local Mode Basis Sets | p. 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 Dynamics | p. 733 |
Inter-System Crossing, Internal Conversion, and Intramolecular Vibrational Distribution | p. 733 |
References | p. 736 |
Table of Contents provided by Rittenhouse. All Rights Reserved. |
ISBN: 9780124414563
ISBN-10: 0124414567
Published: 1st April 2004
Format: Paperback
Language: English
Number of Pages: 800
Audience: Professional and Scholarly
Publisher: Elsevier Science Publishing Co Inc
Country of Publication: US
Edition Number: 2
Dimensions (cm): 22.9 x 15.2 x 3.51
Weight (kg): 1.46
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