.

0 (hodnocen0 x )

BK

First published

New York : Dover Publications, Inc., 1980

xi, 388 stran : ilustrace ; 22 cm

ISBN 978-0-486-63941-3 (brožováno)

Dover books on physics

Obsahuje bibliografie a rejstříky

Reprint vydání z roku 1955 (McGraw-Hill Book Company, Inc.)

001462193

CONTENTS // Preface... // Chapter 1. Introduction... 1 // Infrared Spectra... // 1-2. Raman Spectra... // 1-3. The Molecular Model... // 1-4 Classical Theory of Vibrational and Rotational Spectra // 1-5. The Quantum Viewpoint... // 1-6. Applications... // Chapter 2. The Vibration of Molecules...11 // 2-1. Separation of Rotation and Vibration...11 // 2-2. Small Vibrations in Classical Mechanics...14 // 2-3. Normal Modes of Vibration...17 // 2-4. Normal Coordinates...19 // 2-5. Modes of Motion with Zero Frequency...22 // 2-6. Other Types of Coordinates...25 // 2-7. An Illustration...27 // 2- 8. Linear Molecules...31 // Chapter 3. Wave Mechanics and the Vibration of Molecules . 34 // 3- 1. The Wave Equation for the Vibration of the Harmonic Oscillator Model 34 // 3-2. Description of the Energy Levels of the Harmonic Oscillator... 35 // 3-3. Nature of the Wave Functions...37 // 3-4. Selection Rules in Wave Mechanics...38 // 3-5. Infrared Selection Rules and Intensities for the Harmonic Oscillator // Model...39 // 3-6. Classical Intensities of Radiation from an Induced Dipole ... 43 // 3- 7. Quantum-mechanical Theory of Raman Intensities...48 // Chapter 4. More Advanced Methods of Studying Vibrations. . 54 // 4- 1. Internal Coordinates and Their Relation to Atomic Displacements . . 54 // 4-2. Construction and Properties of the G Matrix...61 // 4-3. The Secular Equation in Terms of Internal Coordinates...63 // 4-4. A Form of the Secular Equation Convenient for Machine Solution . . 65

// 4-5. Direct Expansion of the Secular Equation...68 // 4-6. An Example: The Nonlinear Triatomic Molecule...69 // 4-7. Determination of Normal Coordinates...71 // 4- 8. Approximate Separation of High and Low Frequencies...74 // Chapter 5. Symmetry Considerations...77 // 5- 1. The Symmetry of Molecules...78 // 5-2. Groups of Symmetry Operations . 80 // 5-3. The Symmetry Point Groups ...82 // ix // «? ? ?» ?. w // X CONTENTS // 5-4. Symmetrically Equivalent Atoms and Subgroups...85 // 5-5. Symmetry of the Potential and Kinetic Energies...87 // 5-6. Representations...88 // 5-7. Symmetry of Normal Coordinates...92 // 5-8. Irreducible Representations...97 // 5- 9. Classes of Symmetry Operations...99 // Chapter 6. Applications of Group Theory to the Analysis of Molecular Vibrations...102 // 6- 1. Determination of the Characters x«...102 // 6-2. Symmetry and Degeneracy of the Normal Modes ... 106 // 6-3. Factoring of the Secular Equation... 113 // 6-4. Construction of Internal Symmetry Coordinates...117 // 6-5. External Symmetry Coordinates...125 // 6-6. The Potential and Kinetic Energies in Terms of Symmetry Coordinates 127 // 6-7. Correlation Tables and the Treatment of Internal Coordinate Sets in // which n™ >1...135 // 6- 8. Removal of Redundant Coordinates...140 // Chapter 7. Vibrational Selection Rules and Intensities ... 146 // 7- 1. Symmetry of Wave Functions...147 // 7-2. Symmetry of Combination Levels...148 // 7-3. Symmetry Species of Overtone Levels...151 // 7-4. Symmetry

Species of a General Vibrational Level...155 // 7-5. Symmetry of the Components of the Electric Moment...156 // 7-6. The Transformation Properties of the Components of the Polarizability 157 // 7-7. Determination of Selection Rules for Infrared Absorption ... 159 // 7-8. Selection Rules for the Raman Effect...161 // 7- 9. Absolute Infrared Absorption Intensities of Fundamentals ... 162 // Chapter 8. Potential Functions ... *...169 // 8- 1. The General Quadratic Potential Function...169 // 8-2. The Approximation of Central Forces...173 // 8-3. The Approximation of Valence Forces...174 // 8-4. Modification of the Simple Force Functions...177 // 8-5. The Isotope Effect...182 // 8-6. Anharmonic Terms in the Potential Energy...193 // 8-7. Quantum-mechanical Resonance...197 // 8-8. Vibrations of Molecules with Several Equilibrium Positions ... 200 // 8- 9. Molecules with Internal Rotation...202 // Chapter 9. Methods of Solving the Secular Determinant . . 208 // 9- 1. Characteristic Values and Characteristic Vectors...209 // 9-2. Symmetrization of the Secular Determinant...211 // 9-3. Solution by Direct Expansion of the Secular Determinant ... 214 // 9-4. Indirect Expansion of the Secular Determinant...215 // 9-5. Solution by Evaluation of the Determinant...218 // 9-6. Rayleigh’s Principle...218 // 9-7. Solution of the Simultaneous Equations...222 // 9-8. Matrix Iteration Methods...226 // 9-9. Perturbation Methods... 229 // 9-10. Use of Electric Circuit Analogues...232 // CONTENTS

// xi // 10-1. // 10-2. // 10-3. // 10-4. // 10-5. // 10-6. // 10-7. // 10-8. // 10-9. // 10-10. // 11-1. 11-2. 11-3. 11-4. J1-5. // Chapter 10. A Sample Vibrational Analysis: The Benzene // Molecule...240 // Structure and Symmetry of the Benzene Molecule...240 // Symmetry Species of Normal Coordinates and Internal Coordinates . 241 // Selection Rules...244 // Isotopically Substituted Benzene and the Product Rule...248 // Assignment of Observed Frequencies...251 // Potential and Kinetic Energy in Internal Coordinates...253 // Symmetry Coordinates...257 // Factored Potential and Kinetic Energy Matrices...260 // Expansion of Secular Equation...265 // Calculation of Some Force Constants and Frequencies...265 // Chapter 11. The Separation of Rotation and Vibration . . . 273 // Classical Kinetic Energy...273 // Hamiltonian Form of Kinetic Energy...277 // A General Theorem Concerning Quantum-mechanical Hamiltonians . 279 // The Quantum-mechanical Hamiltonian for a Molecule...281 // Practical Approximations...283 // Appendixes...285 // 1. Coordinate Systems and Eulerian Angles...285 // II. Justification of the Procedure used in Section 2-2 for Obtaining Normal Vibrations...287 // III. Hermite Polynomials and Some Integrals Involving the Harmonic // Oscillator Wave Functions...289 // IV. Averages of Direction Cosines Over All Orientations...292 // V. A Summary of Matrix Notation...293 // VI. A Tabulation of G Matrix Elements...303 // VII. Connection Between G Matrix and Kinetic Energy...307

// VIII. Matrix Treatment of Normal Coordinate Problem...309 // IX. The Separation of High and Low Frequencies...311 // X. Some Properties of Group Representations; Character Tables and Correlation Tables...312 // X-l. Derivation of Characters for the Cyclic Groups, en...312 // X-2. Character Orthogonality Relations...313 // X-3. Characters of the Dihedral Groups, Dn...316 // X-4. Isomorphic and Direct Product Groups...320 // X-5. Species Notation...322 // X-6. Symmetry Species of Combinations: Direct Products of Irreducible // Representations...331 // X-7. Overtones of Degenerate Fundamentals...332 // X-8. Correlation Tables...333 // I. Orthogonality of Irreducible Representation Matrices...341 // Y ’  ro°f the Factoring of the Secular Determinant...347 // ?, ’ eduction of an Irreducible Representation in a Subgroup ... 350 // XV l,ymmetry Species for the Overtones of Degenerate Fundamentals . . 352 // XVi‘ ;ransformation of the Polarizability Components, a«, etc. ... 359 // • Rotational Energies and Selection Rules...361 // Index. // 371