Page 10 - Essentials of physical chemistry

Contents ix

Chapter 13 The Quantized Rigid Rotor and the Vib-Rotor....................................................... 277
Introduction ............................................................................................................. 277
Three-Dimensional Particle-in-a-Box...................................................................... 277
Rigid Rotor.............................................................................................................. 279
Key Step!............................................................................................................ 281
Rigid Rotor Wave Functions.............................................................................. 283
Rigid Rotor Results............................................................................................ 285
Angular Wave Functions......................................................................................... 285
Angular Momentum ................................................................................................ 286
Rotational Spectrum of CO..................................................................................... 289
Fourier Transform Spectrometry............................................................................. 291
FT-IR Imaging and Microscopy.............................................................................. 292
Dipole Requirement ................................................................................................ 294
Vib-Rotor Infrared Spectroscopy ............................................................................ 295
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Bond Length of H- Cl ........................................................................................... 302
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Summary.................................................................................................................. 303
Problems.................................................................................................................. 304
References ............................................................................................................... 305

Chapter 14 The Schrödinger Hydrogen Atom........................................................................... 307
Introduction ............................................................................................................. 307
Strategy to Solve the Problem................................................................................. 307
Associated Laguerre Polynomials........................................................................... 310
Interpretation ........................................................................................................... 311
Pictures of Angular Orbitals.................................................................................... 316
Powell Equivalent d-Orbitals .................................................................................. 319
Unsöld’s Theorem ................................................................................................... 323
Aufbau Principle and the Scaled H Atom............................................................... 323
Term Symbols and Spin Angular Momentum........................................................ 324
Hund’s Rule............................................................................................................. 325
jL, S z i versus jJ, J z i Coupling................................................................................. 326
Summary.................................................................................................................. 328
Problems.................................................................................................................. 329
References ............................................................................................................... 329

Chapter 15 Quantum Thermodynamics ..................................................................................... 331
Introduction ............................................................................................................. 331
(Energy) Partition Function..................................................................................... 333
Average Translation Energy in One Dimension..................................................... 334
Average Rotational Energy of a Diatomic Molecule.............................................. 334
Average Vibrational Energy.................................................................................... 335
High-Temperature Limit for Vibrational Heat Capacity......................................... 337
Heat Capacity of a Polyatomic Species: Water ...................................................... 337
Combining Partition Functions ............................................................................... 339
Statistical Formulas for Other Thermodynamic Functions..................................... 340
Statistical Formula for S(T)..................................................................................... 340
Sakur–Tetrode Formula for Absolute Entropy of a Gas......................................... 341
Summary.................................................................................................................. 343
Problems.................................................................................................................. 344
References ............................................................................................................... 344