Useful introductory course covers origins of quantum theory, Schrouml;dinger wave equation, quantum mechanics of simple systems, electron spin and many-electron systems, the quantum states of atoms, the Hartree-Fock self-consistent field method, the electronic structure of molecules, semiempirical molecular orbital methods, more. Appendices. Indexes.

Frank L. Pilar received B.S. and M.S. degrees from the University of Nebraska (Lincoln) in 1951 and 1953, respectively, and a Ph.D. from the University of Cincinnati in 1957. Between 1953 and 1955 he was a research chemist at the Standard Oil Company (Indiana), where he worked on Ziegler-Natta olefin polymerization. Since 1957 he taught at the University of New Hampshire and served as chairman of the chemistry department from 1982 to his retirement in 1992. Since retirement he has devoted his activities to town government and to volunteer trail work with the Appalachian Mountain Club.

Preface

xv

Origins of the Quantum Theory

1

(20)

The Spectral Shape of Blackbody Radiation

2

(3)

The Photoelectric Effect

5

(3)

Line Spectra of Atoms

8

(3)

The Bohr-Rutherford Model of the One-Electron Atom

11

(4)

Wave-Particle Duality

15

(3)

The Uncertainty Principle

18

(3)

The Schrodinger Wave Equation

21

(32)

Wave Mechanics

22

(2)

Probabilistic Interpretation of the Function ψ

24

(2)

The Time-Independent Wave Equation

26

(4)

Vector Interpretation of Wavefunctions

30

(2)

Orthonormality of Wavefunctions

32

(4)

Hermitian Operators

36

(6)

Normal Operators

42

(2)

Expectation Values in Quantum Mechanics

44

(2)

Construction of Quantum Mechanical Operators

46

(2)

The Generalized Uncertainty Principle

48

(1)

Constants of the Motion

49

(1)

The Quantum Mechanical Virial Theorem

50

(3)

The Quantum Mechanics of Some Simple Systems

53

(37)

Interaction of Matter and Radiation

53

(7)

The Free Particle

60

(2)

The Particle in a Box

62

(8)

Spectroscopy of the Particle in a Box

70

(3)

The Tunneling Effect

73

(5)

The Harmonic Oscillator

78

(1)

Spectroscopy of the Harmonic Oscillator

78

(12)

Quantum Theory of Angular Momentum: The Rigid Rotator

90

(27)

Review of Classical Angular Momentum

90

(2)

Commutation Properties of the Angular Momentum Operators

92

(2)

Angular Momentum in Spherical Polar Coordinates

94

(2)

Ladder Operators for Angular Momentum

96

(2)

The Eigenvalues of Lz and L2

98

(3)

The Simultaneous Eigenfunctions of Lz and L2

101

(4)

The Spherical Harmonics in Real Form

105

(3)

Recurrence Relations for Legendre Polynomials and Associated Legendre Functions

108

(1)

The Rigid Rotator

109

(8)

The Hydrogen Atom

117

(30)

Schrodinger Treatment of the One-Electron Atom

117

(8)

Wavefunctions of the One-Electron Atom

125

(12)

Selection Rules for One-Electron Atoms

137

(1)

Spin Angular Momentum in One-Electron Atoms: A Relativistic Effect

138

(6)

The Zeeman Effect

144

(3)

Approximate Solutions to the Schrodinger Equation

147

(44)

The Variation Method

148

(7)

Atomic Units in Electronic Structure Calculations

155

(2)

The Schrodinger Equation for Many-Electron Atoms: The Mass-Polarization Effect

157

(3)

Examples of Variational Calculations

160

(10)

Basis Functions for Electronic Calculations

170

(1)

Scaling and the Virial Theorem

171

(3)

Perturbation Theory for Nondegenerate States

174

(5)

Perturbation Theory for Degenerate States

179

(4)

Examples of Perturbation Calculations

183

(8)

Electron Spin and Many-Electron Systems

191

(24)

The Antisymmetry Principle

191

(2)

Spin Angular Momenta and Their Operators

193

(4)

The Orbital Approximation

197

(6)

Two-Electron Wavefunctions

203

(7)

The Helium Atom Revisited

210

(5)

The Quantum States of Atoms

215

(30)

Orbital Angular Momenta in Many-Electron Atoms

215

(5)

Spin-Orbit Coupling in Many-Electron Atoms

220

(5)

Atomic Term Symbols

225

(9)

Energy-Level Diagrams for Atoms

234

(1)

Selection Rules in Many-Electron Atoms

235

(2)

The Zeeman Effect in Many-Electron Atoms

237

(8)

The Algebra of Many-Electron Calculations

245

(24)

Construction of Determinantal Eigenfunctions of S2

245

(5)

Manipulation of Determinants in Many-Electron Calculations

250

(5)

The Ground-State Energy of the Lithium Atom

255

(4)

The Method of Configuration Interaction

259

(5)

The Wavefunctions of the 1s22s22p2 Configuration of the Carbon Atom

264

(5)

The Hartree-Fock Self-Consistent Field Method

269

(39)

The Generation of Optimized Orbitals

270

(8)

Koopmans' Theorem: The Physical Significance of Orbital Energies

278

(3)

Theoretical Basis of the Aufbau Principle

281

(3)

The Electron Correlation Energy

284

(4)

Introduction to Density Matrices

288

(7)

Density Matrix Analysis of the Hartree-Fock Approximation

295

(5)

Natural Orbitals

300

(3)

Roothaan's Equations: The Matrix Solution of the Hartree-Fock Equations

303

(3)

Open-Shell Hartree-Fock Calculations

306

(2)

Introduction to Molecular Structure

308

(23)

The Born-Oppenheimer Approximation

309

(5)

Solution of the Nuclear Equation

314

(8)

Selection Rules for Molecular Electronic Transitions

322

(4)

Molecular Hartree-Fock Calculations

326

(5)

The Electronic Structure of Linear Molecules

331

(72)

Electronic Transitions in Molecules

332

(4)

Summary of the MO-LCAO Approximation

336

(4)

The Hydrogen Molecule Ion, H+2

340

(10)

Scaling and the Virial Theorem for Diatomic Molecules

350

(6)

The Hydrogen Molecule (Dihydrogen)

356

(8)

The Aufbau Principle for Homonuclear Diatomic Molecules

364

(11)

Heteronuclear Diatomic Molecules

375

(6)

Linear Polyatomic Molecules

381

(7)

Molecular Configuration-Interaction Calculations

388

(6)

The Valence Bond Method

394

(3)

Natural Orbital Analysis of Molecular Wavefunctions

397

(3)

Molecular Perturbation Calculations

400

(3)

The Electronic Structure of Nonlinear Molecules

403

(51)

The AHn molecules: Methane, Ammonia, and Water

404

(12)

Localized Molecular Orbitals

416

(7)

Hybrid Orbitals

423

(4)

The Ethylene and Benzene Molecules

427

(10)

Pseudo-potential Methods in MO Calculations on Large Molecules

437

(7)

Calculations on Transient and Experimentally Unobserved Species

444

(10)

Semiempirical Molecular Orbital Methods I: Pi Electron Systems

454

(37)

Partial Electron-Shell Wavefunctions

454

(1)

The Huckel Approximation for Conjugated Hydrocarbons

455

(7)

HMO Calculations on Ethene and 1,3-Butadiene

462

(5)

HMO Treatment of Benzene

467

(4)

HMO Treatment of Heteronuclear Conjugated Systems

471

(4)

The Pariser-Parr-Pople Method

475

(5)

PPP Treatments of Ethene and Butadiene

480

(5)

Orthogonalized Basis Functions

485

(6)

Semiempirical Molecular Orbital Methods II: All Valence-Electron Systems

491

(20)

The Extended Huckel Method

491

(4)

The CNDO Method

495

(4)

Between CNDO and Ab Initio

499

(3)

Qualitative Applications of MO Theory

502

(9)

Appendix 1 Values of Physical Constants

511

(1)

Appendix 2 Electrostatic and Electromagnetic Units

512

(2)

Appendix 3 Evaluation of Some Simple Helium Atom Integrals

514

(5)

Appendix 4 Vector and Operator Algebra

519

(7)

1. Vector Algebra

519

(3)

2. Operator Algebra

522

(4)

Appendix 5 Elements of Matrix Algebra

526

(27)

1. Elementary Properties of Matrices

526

(3)

2. Matrices as Transformation Operators

529

(1)

3. Determinants

530

(4)

4. Some Special Matrices and Their Properties

534

(3)

5. Linear Vector Spaces

537

(3)

6. Matrix Representation of Operators

540

(4)

7. Similarity Transformations

544

(3)

8. Projection Operators

547

(6)

Appendix 6 Molecular Symmetry

553

(28)

1. The Symmetry Elements of Molecules

554

(1)

2. The Concept of Groups

555

(3)

3. Irreducible and Reducible Representations of Point Groups

558

(9)

4. General Properties of Irreducible Representations

567

(2)

5. The Direct-Product Representation

569

(4)

6. Symmetry Projection-Operators

573

(3)

7. Symmetry and Molecular Spectra

576

(5)

Appendix 7 Character Tables for Some Common Molecular Point Groups

581

(10)

INDEXES

Name Index

585

(6)

Subject Index

591

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Elementary Quantum Chemistry, Second Edition

9780486414645

0486414647

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