Page 11 - Essentials of physical chemistry

x Contents

Chapter 16 Approximate Methods and Linear Algebra............................................................. 345
Introduction ............................................................................................................. 345
Simple First-Order Perturbation Theory ................................................................. 345
Principles of Perturbation Theory ........................................................................... 347
Variation Method .................................................................................................... 348
Molecular Orbitals and the Secular Equation ......................................................... 350
Chemical Bonds of Ethylene................................................................................... 352
Elementary Linear Algebra ..................................................................................... 356
Unitary Similarity Diagonalization of a Square Hermitian Matrix......................... 359
Jacobi Algorithm for Diagonalization Using a Computer ...................................... 361
Order Matters! ......................................................................................................... 361
Summary.................................................................................................................. 362
Problems.................................................................................................................. 363
Testing, Grading, and Learning?............................................................................. 363
Study, Test, and Learn?........................................................................................... 365
References ............................................................................................................... 366

Chapter 17 Electronic Structure of Molecules........................................................................... 367
Introduction ............................................................................................................. 367
Hartree–Fock–Roothan LCAO Calculations........................................................... 367
Chemical Effects in Orbital Screening.................................................................... 368
Many-Electron Wave Functions.............................................................................. 370
Determinantal Wave Functions for Many-Electron Systems............................. 370
Atomic Units ........................................................................................................... 371
Roothaan’s LCAO Hartree–Fock Equation............................................................. 372
Electron Exchange Energy ................................................................................. 373
The Hartree–Fock–Roothaan Equations for 2n Electrons.................................. 374
Practical Implementation and Examples ................................................................. 375
SCF Iteration ...................................................................................................... 377
Gaussian Basis Sets............................................................................................ 377
Dipole Moment of BH ............................................................................................ 392
Excited States of BH............................................................................................... 392
Mesoionic Bond Orders .......................................................................................... 393
Summary.................................................................................................................. 399
Problems.................................................................................................................. 399
References ............................................................................................................... 401

Chapter 18 Point Group Theory and Electrospray Mass Spectrometry .................................... 403
Introduction ............................................................................................................. 403
Basic Point Group Theory....................................................................................... 403
Calculation of Molecular Vibrations....................................................................... 410
Future Development of Electrospray Mass Spectrometry?..................................... 412
‘‘Making Elephants Fly’’......................................................................................... 414
Summary.................................................................................................................. 419
Problems.................................................................................................................. 419
References ............................................................................................................... 420

Chapter 19 Essentials of Nuclear Magnetic Resonance ............................................................ 423
Introduction ............................................................................................................. 423
Early NMR Spectrometers ...................................................................................... 423