Fundamentals of molecular symmetry / Philip R. Bunker, Per Jensen.

Format:

Book

Author/Creator:

Bunker, Philip R.

Contributor:

Jensen, Per, 1956-

Series:

Series in chemical physics

Language:

English

Subjects (All):

Molecular theory.

Symmetry (Physics).

Group theory.

Physical Description:

xiii, 358 pages : illustrations ; 24 cm.

Place of Publication:

Bristol ; Philadelphia : Institute of Physics, [2005]

Contents:

Part 1 Spectroscopy and the quantum states of molecules 1

1 Molecular spectroscopy 3

1.1 Molecular spectra 3

1.2 The energies of molecules in the gas phase 6

1.3 The positions of spectral lines 9

1.4 The intensities of spectral lines 11

1.5 The shapes of spectral lines 12

1.6 Raman spectra 14

2 Quantum mechanics 17

2.1 The Schrodinger equation 17

2.2 The postulates of quantum mechanics 18

2.2.1 Operators and eigenfunctions 19

2.3 Diagonalizing the Hamiltonian matrix 21

2.4 The molecular Schrodinger equation 26

2.5 The separation of translational energy 26

2.5.1 The translational Schrodinger equation 29

2.6 The rovibronic Schrodinger equation 32

2.7 The angular momentum operator 34

2.8 The dipole moment operator and line strengths 35

2.9 Matrices and matrix algebra 37

3 Electronic states 42

3.1 The Born-Oppenheimer approximation 42

3.2 Spin and the Pauli exclusion principle 46

3.3 Electronic wavefunctions and energies 48

3.3.1 The Slater determinant 49

3.3.2 The Hartree-Fock approximation and molecular orbitals 50

3.3.3 MOs as linear combinations of atomic orbitals 52

3.3.4 Configuration interaction 52

3.4 Molecular orbital theory 53

3.4.1 Bonding and antibonding orbitals 54

3.4.2 Hybridization 57

3.4.3 The Huckel approximation and benzene 61

3.4.4 Polyene chain molecules 62

4 Vibrational states 68

4.1 Space-fixed and molecule-fixed axes 68

4.2 The vibrational Hamiltonian 70

4.3 Vibrational wavefunctions and energies 72

4.4 Anharmonicity 78

4.5 Tunnelling 81

5 Rotational states 89

5.1 The Euler angles 89

5.2 The principal moments of inertia 90

5.3 The rigid-rotor Hamiltonian 92

5.3.1 Symmetric top molecules 92

5.3.2 Linear molecules 94

5.3.3 Spherical top molecules 95

5.3.4 Asymmetric top molecules 95

5.4 Rovibronic wavefunctions 96

5.5 The Hamiltonian and wavefunctions in detail 97

5.5.1 The derivation of the rigid-rotor Hamiltonian 97

5.5.2 The Euler angles and angular momentum 99

5.5.3 The symmetric top wavefunctions 101

5.5.4 The asymmetric top wavefunctions and energies 101

Part 2 Symmetry and symmetry groups 111

6 Geometrical symmetry 113

6.1 Geometrical symmetry operations 113

6.2 Geometrical symmetry groups: Point groups 117

6.3 The point group symmetry of molecules 122

7 The symmetry of the Hamiltonian 126

7.1 Hamiltonian symmetry operations 126

7.2 Nuclear permutations and the inversion E* 127

7.3 Symmetry labels 132

7.4 Symmetry groups 133

7.5 The vanishing integral rule 136

7.5.1 Proof of the vanishing integral rule for the water molecule 138

7.6 Selection rules 139

7.7 The rovibronic symmetry label J 140

7.8 Diagonalizing the Hamiltonian matrix using symmetry 141

7.9 The Stark effect 142

7.10 The symmetry of H[subscript 3] 143

7.11 Group theory 149

8 The symmetry groups of rigid molecules 158

8.1 The CNPI group 158

8.2 The molecular symmetry (MS) group 162

8.3 The MS group and the point group 164

8.3.1 The H[subscript 2]O molecule 164

8.3.2 The H[subscript 3] molecule 168

8.3.3 General rules for rigid molecule symmetry groups 171

8.3.4 Linear rigid molecules 172

8.3.5 The ethylene molecule C[subscript 2]H[subscript 4] 173

Part 3 Applications of symmetry 177

9 Nuclear spin, statistical weights and hyperfine structure 179

9.1 The fifth postulate of quantum mechanics 179

9.2 Statistical weights 180

9.3 Missing levels 184

9.3.1 CO[subscript 2] 184

9.3.2 H[superscript + subscript 3] 185

9.4 Statistical weights for CH[subscript 3]F 186

9.5 Nuclear spin hyperfine structure 187

10 The symmetry of electronic wavefunctions 193

10.1 The water molecule 193

10.2 The benzene molecule 197

10.3 The butadiene molecule 205

10.4 Conservation of orbital symmetry 207

10.5 The non-crossing rule 217

10.6 The C[subscript 6] and [sigma subscript v] operations for benzene 218

11 The symmetry of rotation-vibration wavefunctions 222

11.1 The transformation properties of the Euler angles 222

11.2 The symmetry of rotational wavefunctions 224

11.2.1 H[superscript + subscript 3] 226

11.2.2 H[subscript 2]O 229

11.3 The symmetry of normal coordinates 230

11.3.1 H[subscript 2]O 232

11.3.2 Benzene 233

11.4 The symmetry of vibrational wavefunctions 236

11.4.1 H[subscript 2]O 236

11.4.2 H[superscript + subscript 3] 236

11.5 Rotation-vibration coupling 238

12 Symmetry selection rules for optical transitions 245

12.1 Forbidden and allowed transitions 245

12.2 Zero-order transition moment integrals 247

12.3 Transitions within an electronic state 249

12.3.1 Vibrational transition moments and Honl-London factors 249

12.3.2 The rotational spectrum of the CO molecule 255

12.3.3 Parallel and perpendicular bands of CH[subscript 3]F 255

12.3.4 Rotation-vibration interaction 261

12.4 Transitions between electronic states 264

12.5 Raman transitions 266

13 The symmetry groups of non-rigid molecules 274

13.1 The MS group of a non-rigid molecule 274

13.2 The ammonia molecule 275

13.3 Torsionally tunnelling ethylene 278

13.4 Intensity alternations for HSSH and DSSD 280

13.5 The water dimer and the water trimer 282

13.5.1 Water dimer 282

13.5.2 Water trimer 287

13.6 Ethylene and its Raman spectrum 288

Part 4 Other symmetries and symmetry violation 291

14 Other symmetries 293

14.1 The fourth postulate of quantum mechanics 293

14.2 Conservation laws 294

14.3 Electron permutation symmetry 295

14.4 Translational symmetry 296

14.5 Rotational symmetry 301

14.6 Charge conjugation 304

14.7 Parity 305

14.8 Time reversal 308

15 Symmetry violation 310

15.1 The electroweak Hamiltonian 310

15.2 Parity (P) violation 311

15.3 CP violation 313

15.4 T violation 315

15.5 Testing for CPT violation 316

15.6 Testing for permutation symmetry violation 316.

Notes:

Includes bibliographical references (pages 352-353) and index.

ISBN:

0750309415

OCLC:

56807393