《Molecular vibrations the theory of infrared and raman vibrational spectra.》求取 ⇩

CHAPTER 1.INTRODUCTION1

1-1.Infrared Spectra1

1-2.Raman Spectra3

1-3.The Molecular Model4

1-4.Classical Theory of Vibrational and Rotational Spectra6

1-5.The Quantum Viewpoint7

1-6.Applications9

CHAPTER 2.THE VIERATION OF MOLECULES11

2-1.Separation of Rotation and Vibration11

2-2.Small Vibrations in Classical Mechanics14

2-3.Normal Modes of Vibration17

2-4.Normal Coordinates19

2-5.Modes of Motion with Zero Frequency22

2-6.Other Types of Coordinates25

2-7.An Illustration27

2-8.Linear Molecules31

CHAPTER 3.WAVE MECHANICS AND THE VIBRATION OF MOLECULES34

3-1.The Wave Equation for the Vibration of the Harmonic Oscillator Model34

3-2.Description of the Energy Levels of the Harmonic Oscillator35

3-3.Nature of the Wave Functions37

3-4.Selection Rules in Wave Mechanics38

3-5.Infrared Selection Rules and Intensities for the Harmonic Oscillator Model39

3-6.Classical Intensities of Radiation from an Induced Dipole43

3-7.Quantum-mechanical Theory of Raman Intensities48

CHAPTER 4.MORE ADVANCED METRODS OF STUDYING VIBRATIONS54

4-1.Internal Coordinates and Their Relation to Atomic Displacements54

4-2.Construction and Properties of the G Matrix61

4-3.The Secular Equation in Terms of Internal Coordinates63

4-4.A Form of the Secular Equation Convenient for Machine Solution65

4-5.Direct Expansion of the Secular Equation68

4-6.An Example:The Nonlinear Triatomic Molecule69

4-7.Determination of Normal Coordinates71

4-8.Approximate Separation of High and Low Frequencies74

CHAPTER 5.SYMMETRY CONSIDERATIONS77

5-1.The Symmetry of Molecules78

5-2.Groups of Symmetry Operations80

5-3.The Symmetry Point Groups82

5-4.Symmetrically Equivalent Atoms and Subgroups85

5-5.Symmetry of the Potential and Kinetic Energies87

5-6.Representations88

5-7.Symmetry of Normal Coordinates92

5-8.Irreducible Representations97

5-9.Classes of Symmetry Operations99

CHAPTER 6.APPLICATIONS OF GROUP THEORY TO THE ANALYSIS OF MOLECULAR VIBRATIONS102

6-1.Determination of the Characters XR102

6-2.Symmetry and Degeneracy of the Normal Modes106

6-3.Factoring of the Secular Equation113

6-4.Construction of Internal Symmetry Coordinates117

6-5.External Symmetry Coordinates125

6-6.The Potential and Kinetic Energies in Terms of Symmetry Coordinates127

6-7.Correlation Tables and the Treatment of Internal Coordinate Sets in which n(r)＞1135

6-8.Removal of Redundant Coordinates140

CHAPTER 7.VIBRATIONAL SELECTION RULES AND INTENSITIES146

7-1.Symmetry of Wave Functions147

7-2.Symmetry of Combination Levels148

7-3.Symmetry Species of Overtone Levels151

7-4.Symmetry Species of a General Vibrational Level155

7-5.Symmetry of the Components of the Electric Moment156

7-6.The Transformation Properties of the Components of the Polarizability157

7-7.Determination of Selection Rules for Infrared Absorption159

7-8.Selection Rules for the Raman Effect161

7-9.Absolute Infrared Absorption Intensities of Fundamentals162

CHAPTER 8.POTENTIAL FUNCTIONS169

8-1.The General Quadratic Potential Function169

8-2.The Approximation of Central Forces173

8-3.The Approximation of Valence Forces174

8-4.Modification of the Simple Force Functions177

8-5.The Isotope Effect182

8-6.Anharmonic Terms in the Potential Energy193

8-7.Quantum-mechanical Resonance197

8-8.Vibrations of Molecules with Several Equilibrium Positions200

8-9.Molecules with Internal Rotation202

CHAPR 9.METHODS OF SOLVING THE SECULAR DETERMINANT208

9-1.Characteristic Values and Characteristic Vectors209

9-2.Symmetrization of the Secular Determinant211

9-3.Solution by Direct Expansion of the Secular Determinant214

9-4.Indirect Expansion of the Secular Determinant215

9-5.Solution by Evaluation of the Determinant218

9-6.Rayleigh’s Principle218

9-7.Solution of the Simultaneous Equations222

9-8.Matrix Iteration Methods226

9-9.Perturbation Methods229

9-10.Use of Electric Circuit Analogues232

CHAPTER 10.A SAMPLE VIBRATIONAL ANALYSIS:THE BENZENE MOLECULE240

10-1.Structure and Symmetry of the Benzene Molecule240

10-2.Symmetry Species of Normal Coordinates and Internal Coordinates241

10-3.Selection Rules244

10-4.Isotopically Substituted Benzene and the Product Rule248

10-5.Assignment of Observed Frequencies251

10-6.Potential and Kinetic Energy in Internal Coordinates253

10-7.Symmetry Coordinates257

10-8.Factored Potential and Kinetic Energy Matrices260

10-9.Expansion of Secular Equation265

10-10.Calculation of Some Force Constants and Frequencies265

CHAPTER 11.THE SEPARATION OF ROTATION AND VIBRATION273

11-1.Classical Kinetic Energy273

11-2.Hamiltonian Form of Kinetic Energy277

11-3.A General Theorem Concerning Quantum-mechanical Hamiltonians279

11-4.The Quantum-mechanical Hamiltonian for a Molecul281

11-5.Practical Approximations283

APPENDIXES285

Ⅰ.Coordinate Systems and Eulerian Angles285

Ⅱ.Justification of the Procedure used in Section 2-2 for Obtaining Normal Vibrations287

Ⅲ.Hermite Polynomials and Some Integrals Involving the Harmonic Oscillator Wave Functions289

Ⅳ.Averages of Direction Cosines Over All Orientations292

Ⅴ.A Summary of Matrix Notation293

Ⅵ.A Tabulation of G Matrix Elements303

Ⅶ.Connection Between G Matrix and Kinetic Energy307

Ⅷ.Matrix Treatment of Normal Coordinate Problem309

Ⅸ.The Separation of High and Low Frequencies311

Ⅹ.Some Properties of Group Representations;Character Tables and Correlation Tables312

Ⅹ-1.Derivation of Characters for the Cyclic Groups,en312

Ⅹ-2.Character Orthogonality Relations313

Ⅹ-3.Characters of the Dihedral Groups,Dn316

Ⅹ-4.Isomorphic and Direct Product Groups320

Ⅹ-5.Species Notation322

Ⅹ-6.Symmetry Species of Combinations:Direct Products of Ineducible Representations331

Ⅹ-7.Overtones of Degenerate Fundamentals332

Ⅹ-8.Correlation Tables333

Ⅺ.Orthogonality of Irreducible Representation Matrices341

Ⅻ.Proof of the Factoring of the Secalar Determinant347

ⅩⅢ.Reduction of an Irreducible Representation in a Subgroup350

ⅩⅣ.Symmetry Species for the Overtones of Degenerate Fundamentals352

ⅩⅤ.Transformation of the Polarizability Components,axx,axv,etc.359

ⅩⅥ.Rotational Energies and Selection Rules361

INDEX371