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This is the eBook of the printed book and may not include any media, website access codes, or print supplements that may come packaged with the bound book. Known for its solid presentation of mathematics, this bestseller is a rigorous but accessible introduction to both quantum chemistry and the math needed to master it. Quantum Chemistry, Seventh Edition covers quantum mechanics, atomic structure, and molecular electronic structure, and provides a thorough, unintimidating treatment of operators, differential equations, simultaneous linear equations, and other areas of required math. Practical for readers in all branches of chemistry, the new edition reflects the latest quantum chemistry research and methods of computational chemistry, and clearly demonstrates the usefulness and limitations of current quantum-mechanical methods for the calculation of molecular properties. Cover 1 Title Page 3 Copyright Page 4 Contents 6 Preface 12 Chapter 1 The Schrödinger Equation 15 1.1 Quantum Chemistry 15 1.2 Historical Background of Quantum Mechanics 16 1.3 The Uncertainty Principle 20 1.4 The Time-Dependent Schrödinger Equation 21 1.5 The Time-Independent Schrödinger Equation 25 1.6 Probability 28 1.7 Complex Numbers 30 1.8 Units 31 1.9 Calculus 32 Summary 32 Problems 33 Chapter 2 The Particle in a Box 35 2.1 Differential Equations 35 2.2 Particle in a One-Dimensional Box 36 2.3 The Free Particle in One Dimension 42 2.4 Particle in a Rectangular Well 42 2.5 Tunneling 44 Summary 45 Problems 45 Chapter 3 Operators 48 3.1 Operators 48 3.2 Eigenfunctions and Eigenvalues 52 3.3 Operators and Quantum Mechanics 53 3.4 The Three-Dimensional, Many-Particle Schrödinger Equation 58 3.5 The Particle in a Three-Dimensional Box 61 3.6 Degeneracy 64 3.7 Average Values 65 3.8 Requirements for an Acceptable Wave Function 68 Summary 69 Problems 70 Chapter 4 The Harmonic Oscillator 74 4.1 Power-Series Solution of Differential Equations 74 4.2 The One-Dimensional Harmonic Oscillator 76 4.3 Vibration of Diatomic Molecules 85 4.4 Numerical Solution of the One-Dimensional Time-Independent Schrödinger Equation 88 Summary 98 Problems 98 Chapter 5 Angular Momentum 104 5.1 Simultaneous Specification of Several Properties 104 5.2 Vectors 108 5.3 Angular Momentum of a One-Particle System 113 5.4 The Ladder-Operator Method for Angular Momentum 124 Summary 128 Problems 129 Chapter 6 The Hydrogen Atom 132 6.1 The One-Particle Central-Force Problem 132 6.2 Noninteracting Particles and Separation of Variables 134 6.3 Reduction of the Two-Particle Problem to Two One-Particle Problems 135 6.4 The Two-Particle Rigid Rotor 138 6.5 The Hydrogen Atom 142 6.6 The Bound-State Hydrogen-Atom Wave Functions 149 6.7 Hydrogenlike Orbitals 157 6.8 The Zeeman Effect 161 6.9 Numerical Solution of the Radial Schrödinger Equation 163 Summary 164 Problems 165 Chapter 7 Theorems of Quantum Mechanics 169 7.1 Notation 169 7.2 Hermitian Operators 170 7.3 Expansion in Terms of Eigenfunctions 175 7.4 Eigenfunctions of Commuting Operators 181 7.5 Parity 184 7.6 Measurement and the Superposition of States 186 7.7 Position Eigenfunctions 191 7.8 The Postulates of Quantum Mechanics 194 7.9 Measurement and the Interpretation of Quantum Mechanics 198 7.10 Matrices 201 Summary 205 Problems 205 Chapter 8 The Variation Method 211 8.1 The Variation Theorem 211 8.2 Extension of the Variation Method 215 8.3 Determinants 216 8.4 Simultaneous Linear Equations 219 8.5 Linear Variation Functions 223 8.6 Matrices, Eigenvalues, and Eigenvectors 229 Summary 237 Problems 237 Chapter 9 Perturbation Theory 246 9.1 Perturbation Theory 246 9.2 Nondegenerate Perturbation Theory 247 9.3 Perturbation Treatment of the Helium-Atom Ground State 252 9.4 Variation Treatments of the Ground State of Helium 256 9.5 Perturbation Theory for a Degenerate Energy Level 259 9.6 Simplification of the Secular Equation 262 9.7 Perturbation Treatment of the First Excited States of Helium 264 9.8 Time-Dependent Perturbation Theory 270 9.9 Interaction of Radiation and Matter 272 Summary 274 Problems 275 Chapter 10 Electron Spin and the Spin–Statistics Theorem 279 10.1 Electron Spin 279 10.2 Spin and the Hydrogen Atom 282 10.3 The Spin–Statistics Theorem 282 10.4 The Helium Atom 285 10.5 The Pauli exclusion Principle 287 10.6 Slater Determinants 291 10.7 Perturbation Treatment of the Lithium Ground State 292 10.8 Variation Treatments of the Lithium Ground State 293 10.9 Spin Magnetic Moment 294 10.10 Ladder Operators for Electron Spin 297 Summary 299 Problems 299 Chapter 11 Many-Electron Atoms 303 11.1 The Hartree–Fock Self-Consistent-Field Method 303 11.2 Orbitals and the Periodic Table 309 11.3 Electron Correlation 312 11.4 Addition of Angular Momenta 314 11.5 Angular Momentum in Many-Electron Atoms 319 11.6 Spin–Orbit Interaction 330 11.7 The Atomic Hamiltonian 332 11.8 The Condon–Slater Rules 334 Summary 337 Problems 338 Chapter 12 Molecular Symmetry 342 12.1 Symmetry Elements and Operations 342 12.2 Symmetry Point Groups 349 Summary 355 Problems 356 Chapter 13 Electronic Structure of Diatomic Molecules 358 13.1 The Born–Oppenheimer Approximation 358 13.2 Nuclear Motion in Diatomic Molecules 361 13.3 Atomic Units 366 13.4 The Hydrogen Molecule Ion 367 13.5 Approximate Treatments of the H+[2(Sub)] Ground Electronic State 371 13.6 Molecular Orbitals for H+[2(Sub)] Excited States 379 13.7 MO Configurations of Homonuclear Diatomic Molecules 383 13.8 Electronic Terms of Diatomic Molecules 389 13.9 The Hydrogen Molecule 393 13.10 The Valence-Bond Treatment of H[2(Sub)] 396 13.11 Comparison of the MO and VB Theories 398 13.12 MO and VB Wave Functions for Homonuclear Diatomic Molecules 400 13.13 Excited States of H[2(Sub)] 403 13.14 SCF Wave Functions for Diatomic Molecules 404 13.15 MO Treatment of Heteronuclear Diatomic Molecules 407 13.16 VB Treatment of Heteronuclear Diatomic Molecules 410 13.17 The Valence-Electron Approximation 410 Summary 411 Problems 412 Chapter 14 Theorems of Molecular Quantum Mechanics 416 14.1 Electron Probability Density 416 14.2 Dipole Moments 418 14.3 The Hartree–Fock Method for Molecules 421 14.4 The Virial Theorem 430 14.5 The Virial Theorem and Chemical Bonding 436 14.6 The Hellmann–Feynman Theorem 440 14.7 The Electrostatic Theorem 443 Summary 446 Problems 447 Chapter 15 Molecular Electronic Structure 450 15.1 Ab Initio, Density-Functional, Semiempirical, and Molecular-Mechanics Methods 450 15.2 Electronic Terms of Polyatomic Molecules 451 15.3 The SCF MO Treatment of Polyatomic Molecules 454 15.4 Basis Functions 456 15.5 The SCF MO Treatment of H[2(Sub)]O 463 15.6 Population Analysis and Bond Orders 470 15.7 The Molecular Electrostatic Potential, Molecular Surfaces, and Atomic Charges 474 15.8 Localized MOs 478 15.9 The SCF MO Treatment of Methane, Ethane, and Ethylene 484 15.10 Molecular Geometry 494 15.11 Conformational Searching 504 15.12 Molecular Vibrational Frequencies 510 15.13 Thermodynamic Properties 512 15.14 Ab Initio Quantum Chemistry Programs 514 15.15 Performing Ab Initio Calculations 515 15.16 Speeding Up Hartree–Fock Calculations 521 15.17 Solvent Effects 524 Problems 532 Chapter 16 Electron-Correlation Methods 539 16.1 Correlation Energy 539 16.2 Configuration Interaction 542 16.3 Møller–Plesset (MP) Perturbation Theory 553 16.4 The Coupled-Cluster Method 560 16.5 Density-Functional Theory 566 16.6 Composite Methods for Energy Calculations 586 16.7 The Diffusion Quantum Monte Carlo Method 589 16.8 Noncovalent Interactions 590 16.9 NMR Shielding Constants 592 16.10 Fragmentation Methods 594 16.11 Relativistic Effects 595 16.12 Valence-Bond Treatment of Polyatomic Molecules 596 16.13 The GVB, VBSCF, and BovB Methods 603 16.14 Chemical Reactions 605 Problems 609 Chapter 17 Semiempirical and Molecular-Mechanics Treatments 614 17.1 Semiempirical MO Treatments of Planar Conjugated Molecules 614 17.2 The Hückel MO Method 615 17.3 The Pariser–Parr–Pople Method 633 17.4 General Semiempirical MO and DFT Methods 635 17.5 The Molecular-Mechanics Method 648 17.6 Empirical and Semiempirical Treatments of Solvent Effects 662 17.7 Chemical Reactions 666 17.8 The Future of Quantum Chemistry 669 Problems 670 Appendix 675 Bibliography 679 Answers to Selected Problems 681 Index 693 A 693 B 694 C 695 D 697 E 698 F 700 G 700 H 701 I 702 J 703 K 703 L 703 M 704 N 706 O 706 P 708 Q 709 R 709 S 710 T 712 U 712 V 713 W 714 X 714 Z 714

Known for its solid presentation of mathematics, this bestseller is a rigorous but accessible introduction to both quantum chemistry and the math needed to master it. Quantum Chemistry, Seventh Edition covers quantum mechanics, atomic structure, and molecular electronic structure, and provides a thorough, unintimidating treatment of operators, differential equations, simultaneous linear equations, and other areas of required math. Practical for readers in all branches of chemistry, the new edition reflects the latest quantum chemistry research and methods of computational chemistry, and clearly demonstrates the usefulness and limitations of current quantum-mechanical methods for the calculation of molecular properties.