Page 10 - Modern physical chemistry

Contents xi

10.4 Translational Motion in a General 12.2 Schrodinger Equation for the Harmonic
Direction 245 Oscillator 312
10.5 Diffraction Experiments Revisited 246 12.3 Quantization of the Harmonic
10.6 Rectangularly Symmetric Free Motion 246 Oscillator 313
10.7 Translational Energy of the Molecules in 12.4 Nodeless Solutions 315
an Ideal Gas 248 12.5 Acceptable Wavy Solutions 317
10.8 Enumerating and Filling Translational 12.6 Partition Function for a Vibrational
States 251 Mode 317
10.9 Normalization and Orthogonality 12.7 Selection Rules 320
Conditions 254 12.8 Vibration-Rotation Spectra 321
10.10 Standing-Wave Translational 12.9 Raman Spectra 324
Functions 256 12.10 Bond Anharmonicity and its Effect 325
10.11 Confined Rectangularly Symmetric 12.11 Asymptotic Solutions for the Central
Motion 257 Field 330
10.12 Attenuated Motion 259 12.12 Radial State Functions for a Hydrogenlike
10.13 Joining Different Constant-Potential Atom 331
Regions 260 12.13 Electronic Spectrum of a Hydrogenlike
10.14 A Differential Equation for Multidirectional Atom 334
Propagation 263 12.14 Multiparticle Systems 334
10.15 The Schrodinger Equations 265 12.15 Multielectron Uninuclear Structures 337
10.16 Suitable Solutions 266 12.16 Combining Angular Momenta 338
10.17 Expressing V 2 in Orthogonal Generalized Questions 341
Coordinates 266 Problems 342
Questions 269 References 344
Problems 270
References 272 Chapter 13
Analyzing Organized Structures 347
Chapter 11 13.1 The General Behavior of Bases 347
Free Rotational and Angular Motion 275 13.2 Representing Nondistortive
11.1 introduction 275 Operations 347
11.2 Classical Rotational Kinetic Energy 277 13.3 Symmetry Operations 350
11.3 Quantized Angular Momentum States of a 13.4 Pertinent Permutation Matrices 352
Linear Rotator 278 13.5 Other Transformation Matrices 353
11.4 Energy Levels for the Linear Rotator 279 13.6 Classifying Operations 358
11.5 Rotational Spectrum of a Linear 13.7 Character Vectors 359
Molecule 281 13.8 Symmetry Species 361
11.6 Broadening of Spectral Lines 284 13.9 Selection Rules 363
11. 7 Quantization of Cylindrically Symmetric 13.10 The Orthogonality Condition 364
Rotators 284 13.11 Generating Primitive Symmetry
11.8 The Asymmetric Rotator 285 Species 365
11.9 Rotational Partition Functions and the Questions 368
Resulting Energies 287 Problems 369
11.10 independence of the Angular References 371
Factor Yea, 4» 290
11.11 A Multiaxial Formula for Yea, 4» 291 Chapter 14
11.12 Directional Behavior of the Standard States of Molecular Electrons 373
Rotational State Functions 292 14.1 introduction 373
11.13 Normalization and Orthogonality 14.2 The Hydrogen Molecule Ion Model 373
Conditions Revisited 298 14.3 Correlations with Atomic Structures 375
11.14 Magnetic Energy Associated with Angular 14.4 Bonding between Two Equivalent
Momentum 300 Atoms 376
11.15 Observing Spatial Quantization in a 14.5 Symmetric Three-Center Bonds 380
Beam 303 14.6 Symmetric Six-Center Bonds 385
11.16 Spin States 304 14.7 Conventional Resonance Energy and the
Questions 305 True Delocalization Energy 389
Problems 306 14.8 The Variation Theorem 391
References 308 14.9 Linear Variation Functions 392
14.10 Bonding between Two Nonequivalent
Chapter 12 Atoms 394
Vibrational and Radial Motion 309 14.11 Pi Bonding in Fulvene 396
12.1 Pertinent Potentials 309 Questions 400