量子化学(第6版)(英文版)

.3 operators 37
3.1 operators, 37
3.2 eigenfunctions and eigenvalues, 41
3.3 operators and quantum mechanics, 42
3.4 the three-dimensional, many-particle schr6dinger equation, 48
3.5 the particle in a three-dimensional box, 51
3.6 degeneracy, 54
3.7 average values, 56
3.8 requirements for an acceptable wave function, 59
3.9 summary, 60
4 the harmonic oscillator 65
4.1 power-series solution of differential equations, 65
4.2 the one-dimensional harmonic oscillator, 68
4.3 vibration of molecules, 77
4.4 numerical solution of the one-dimensional time-independent schrodinger equation, 80
4.5 summary, 91
5 angular momentum 97
5.1 simultaneous specification of several properties, 97
5.2 vectors, 100
5.3 angular momentum of a one-particle system, 105
5.4 the ladder-operator method for angular momentum, 117
5.5 summary, 122
6 the hydrogen atom 116
6.1 the one-particle central-force problem, 126
6.2 noninteracting particles and separation of variables, 128
6.3 reduction of the two-particle problem to two one-particle problems, 130
6.4 the two-particle rigid rotor, 133
6.5 the hydrogen atom, 137
6.6 the bound-state hydrogen-atom wave functions, 144
6.7 hydrogenlike orbitals, 153
6.8 the zeeman effect, 157
6.9 numerical solution of the radial schrodinger equation, 159
6.10 summary, 161
7 theorems of quantum mechanics 166
7.1 introduction, 166
7.2 hermitian operators, 167
7.3 expansion in terms of eigenfunctions, 173
7.4 eigenfunctions of commuting operators, 178
7.5 parity, 181
7.6 measurement and the superposition of states, 184
7.7 position eigenfunctions, 189
7.8 the postulates of quantum mechanics, 192
7.9 measurement and the interpretation of quantum mechanics, 196
7.10 matrices, 200
7.11 summary, 203
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, 220
8.5 linear variation functions, 223
8.6 matrices, eigenvalues, and eigenvectors, 230
8.7 summary, 238
9 perturbation theory 248
9.1 introduction, 248
9.2 nondegenerate perturbation theory, 249
9.3 perturbation treatment of the helium-atom ground state, 255
9.4 variation treatments of the ground state of helium, 258
9.5 perturbation theory for a degenerate energy level, 261
9.6 simplification of the secular equation, 265
9.7 perturbation treatment of the first excited states of helium, 267
9.8 comparison of the variation and perturbation methods, 273
9.9 time-dependent perturbation theory, 274
9.10 interaction of radiation and matter, 276
9.11 summary, 279
10 electron spin and the spin-statistics theorem 283
10.1 electron spin, 283
10.2 spin and the hydrogen atom, 286
10.3 the spin-statistics theorem, 286
10.4 the helium atom, 290
10.5 the pauli exclusion principle, 292
10.6 slater determinants, 296
10.7 perturbation treatment of the lithium ground state, 298
10.8 variation treatments of the lithium ground state, 299
10.9 spin magnetic moment, 299
10.10 ladder operators for electron spin, 303
10.11 summary, 305
11 many-electron atoms 309
11.1 the hartree-fock self-consistent-field method, 309
11.2 orbitals and the periodic table, 316
11.3 electron correlation, 319
11.4 addition of angular momenta, 322
11.5 angular momentum in many-electron atoms, 327
11.6 spin-orbit interaction, 338
11.7 the atomic hamiltonian, 341
11.8 the condon-slater rules, 343
11.9 summary, 346
12 molecular symmetry 351
12.1 symmetry elements and operations, 351
12.2 symmetry point groups, 359
12.3 summary, 365
13 electronic structure of diatomic molecules 369
13.1 the born-oppenheimer approximation, 369
13.2 nuclear motion in diatomic molecules, 373
13.3 atomic units, 378
13.4 the hydrogen molecule ion, 379
13.5 approximate treatments of the h+2 ground electronic state, 383
13.6 molecular orbitals for hi excited states, 392
13.7 mo configurations of homonuclear diatomic molecules, 397
13.8 electronic terms of diatomic molecules, 403
13.9 the hydrogen molecule, 409
13.10 the valence-bond treatment of h2, 412
13.11 comparison of the mo and vb theories, 415
13.12 mo and vb wave functions for homonuclear diatomic molecules, 417
13.13 excited states of he, 420
13.14 scf wave functions for diatomic molecules, 422
13.15 mo treatment of heteronuclear diatomic molecules, 425
13.16 vb treatment of heteronuclear diatomic molecules, 428
13.17 the valence-electron approximation, 429
13.18 summary, 430
14 theorems of molecular quantum mechanics 435
14.1 electron probability density, 435
14.2 dipole moments,438
14.3 the hartree-fock method for molecules, 440
14.4 the virial theorem, 450
14.5 the virial theorem and chemical bonding, 456
14.6 the hellmann-feynman theorem, 460
14.7 the electrostatic theorem, 463
14.8 summary, 468
15 molecular electronicstructure 471
15.1 ab initio, density-functional, semiempirical,
and molecular-mechanics methods, 471
15.2 electronic terms of polyatomic molecules, 472
15.3 the scf mo treatment of polyatomic molecules, 476
15.4 basis functions, 477
15.5 the scf mo treatment of h20, 485
15.6 population analysis and bond orders, 493
15.7 the molecular electrostatic potential, molecular surfaces,
and atomic charges, 496
15.8 localized mos, 501
15.9 the scf mo treatment of methane, ethane, and ethylene, 508
15.10 molecular geometry, 518
15.11 conformational searching, 529
15.12 molecular vibrational frequencies, 535
15.13 thermodynamic properties, 538
15.14 ab initio quantum chemistry programs, 541
15.15 performing ab initio calculations, 542
15.16 speeding up hartree-fock calculations, 547
15.17 solvent effects, 552
16 electron-correlation methods 566
16.1 configuration interaction, 566
16.2 m011er-plesset (mp) perturbation theory, 578
16.3 the coupled-cluster method, 585
16.4 density-functional theory, 591
16.5 composite methods for energy calculations, 613
16.6 the diffusion quantum monte carlo method, 615
16.7 relativistic effects, 616
16.8 valence-bond treatment of polyatomic molecules, 618
16.9 the gvb, vbscf, and bovb methods, 626
16.10 chemical reactions, 628
17 semiempirical and molecular-mechanics treatments of molecules 636
17.1 semiempirical mo treatments of planar conjugated molecules, 636
17.2 the hiickel mo method, 637
17.3 the pariser-parr-pople method, 657
17.4 general semiempirical mo and dft methods, 659
17.5 the molecular-mechanics method, 672
17.6 empirical and semiempirical treatments of solvent effects, 688
17.7 chemical reactions, 692
18 comparisons of methods 700
18.1 molecular geometry, 700
18.2 energy changes, 703
18.3 other properties, 711
18.4 hydrogen bonding, 713
18.5 conclusion, 716
18.6 the future of quantum chemistry, 717
appendix 719
bibliography 722
answers to selected problems 725
index 731

.　　· The PM5, PM6, RMI, PDDG/PM3, and SCC-DFTB methods (Section 17.4)
　　A solutions manual for the problems in the book is available.
　　The expanding role of quantum chemistry makes it highly desirable for students in all areas of chemistry to understand modern methods of electronic structure calcula-tion, and this book has been written with this goal in mind.
　　I have tried to make explanations clear and complete, without glossing over diffi-cult or subtle points. Derivations are given with enough detail to make them easy to fol-low, and I avoid resorting to the frustrating phrase "it can be shown that" wherever possible. The aim is to give students a solid understanding of the physical and mathe-matical aspects of quantum mechanics and molecular electronic structure. The book is designed to be useful to students in all branches of chemistry, not just future quantum chemists. However, the presentation is such that those who do go on in quantum chem-istry will have a good foundation and will not be hampered by misconceptions.
　　An obstacle faced by many chemistry students in learning quantum mechanics is their unfamiliarity with much of the required mathematics. In this text I have included detailed treatments of operators, differential equations, simultaneous linear equations,and other needed topics. Rather than putting all the mathematics in an introductory chapter or a series of appendices, I have integrated the mathematics with the physics and chemistry. Immediate application of the mathematics to solving a quantum-mechanical problem will make the mathematics more meaningful to students than would separate study of the mathematics. I have also kept in mind the limited physics background of many chemistry students by reviewing topics in physics.
　　This book has benefited from the reviews and suggestions of Leland Allen,N. Colin Baird, Steven Bernasek, James Bolton, W. David Chandler, Donald Chesnut,R. James Cross, David Farrelly, Melvyn Feinberg, Gordon A. Gallup, David Goldberg,Tracy Hamilton, John Head, Warren Hehre, Hans Jaff& Miklos Kertesz, Nell Kestner,Harry King, Peter Kollman, Mel Levy, Errol Lewars, Joel Liebman, Frank Meeks,Robert Metzger, Pedro Muifio, William Palke, Sharon Palmer, Gary Pfeiffer, Russell Pitzer, Kenneth Sando, Harrison Shull, James J. P. Stewart, Richard Stratt, Arieh Warshel, John S. Winn, and Michael Zerner. The following people provided reviews for the sixth edition: Gary DeBoer, Douglas Doren, Daniel Gerrity, Robert Griffin, Sharon Hammes-Schiffer, James Harrison, Robert Hinde, Anna Krylov, Tien-Sung Tom Lin,Ryan McLaughlin, Charles Millner, John H. Moore, Kirk Peterson, Oleg Prezhdo,Frank Rioux, Fu-Ming Tao, Ronald Terry, Alexander Van Hook, and Peter Weber. I wish to thank these people and several anonymous reviewers.
　　I would appreciate receiving any suggestions that readers may have for improving the book.
　　Ira N. Levine
　　INLevine@brooklyn.cuny. edu