Quantum Chemistry

by Levine, Ira N.

• ISBN13: 9780136855125
• ISBN10: 0136855121
• Edition: 5th
• Format: Hardcover
• Copyright: 2009-01-01
• Publisher: Pearson College Div

Summary

"The Sixth Edition of this widely used textbook presents quantum chemistry for beginning graduate students and advanced undergraduates. The subject is carefully explained step-by-step, allowing students to easily follow the presentation. Necessary mathematics is reviewed in detail. Worked examples aid learning. A solutions manual for the problems is available. Extensive discussions of modern abinitio, density functional, semiempirical, and molecular mechanics methods are included."--BOOK JACKET.

Author Biography

Ira N. Levine is Professor of Chemistry at Brooklyn College of the City University of New York.

Table of Contents

PREFACE	ix
1 THE SCHRODINGER EQUATION	1	(20)
1.1 Quantum Chemistry	1	(1)
1.2 Historical Background of Quantum Mechanics	2	(3)
1.3 The Uncertainty Principle	5	(2)
1.4 The Time-Dependent Schrodinger Equation	7	(5)
1.5 The Time-Independent Schrodinger Equation	12	(2)
1.6 Probability	14	(2)
1.7 Complex Numbers	16	(2)
1.8 Units	18	(1)
1.9 Summary	18	(3)
2 THE PARTICLE IN A BOX	21	(14)
2.1 Differential Equations	21	(1)
2.2 Particle in a One-Dimensional Box	22	(6)
2.3 The Free Particle in One Dimension	28	(1)
2.4 Particle in a Rectangular Well	29	(2)
2.5 Tunneling	31	(1)
2.6 Summary	32	(3)
3 OPERATORS	35	(27)
3.1 Operators	35	(4)
3.2 Eigenfunctions and Eigenvalues	39	(1)
3.3 Operators and Quantum Mechanics	40	(6)
3.4 The Three-Dimensional Many-Particle Schrodinger Equation	46	(3)
3.5 The Particle in a Three-Dimensional Box	49	(3)
3.6 Degeneracy	52	(1)
3.7 Average Values	53	(4)
3.8 Requirements for an Acceptable Wave Function	57	(1)
3.9 Summary	58	(4)
4 THE HARMONIC OSCILLATOR	62	(32)
4.1 Power-Series Solution of Differential Equations	62	(3)
4.2 The One-Dimensional Harmonic Oscillator	65	(9)
4.3 Vibration of Molecules	74	(4)
4.4 Numerical Solution of the One-Dimensional Time-Independent Schrodinger Equation	78	(11)
4.5 Summary	89	(5)
5 ANGULAR MOMENTUM	94	(29)
5.1 Simultaneous Specification of Several Properties	94	(3)
5.2 Vectors	97	(5)
5.3 Angular Momentum of a One-Particle System	102	(13)
5.4 The Ladder-Operator Method for Angular Momentum	115	(5)
5.5 Summary	120	(3)
6 THE HYDROGEN ATOM	123	(40)
6.1 The One-Particle Central-Force Problem	123	(2)
6.2 Noninteracting Particles and Separation of Variables	125	(2)
6.3 Reduction of the Two-Particle Problem to Two One-Particle Problems	127	(3)
6.4 The Two-Particle Rigid Rotor	130	(1)
6.5 The Hydrogen Atom	134	(8)
6.6 The Bound-State Hydrogen-Atom Wave Functions	142	(8)
6.7 Hydrogenlike Orbitals	150	(4)
6.8 The Zeeman Effect	154	(3)
6.9 Numerical Solution of the Radial Schrodinger Equation	157	(1)
6.10 Summary	158	(5)
7 THEOREMS OF QUANTUM MECHANICS	163	(45)
7.1 Introduction	163	(1)
7.2 Hermitian Operators	164	(6)
7.3 Expansion in Terms of Eigenfunctions	170	(5)
7.4 Eigenfunctions of Commuting Operators	175	(3)
7.5 Parity	178	(4)
7.6 Measurement and the Superposition of States	182	(5)
7.7 Position Eigenfunctions	187	(3)
7.8 The Postulates of Quantum Mechanics	190	(4)
7.9 Measurement and the Interpretation of Quantum Mechanics	194	(4)
7.10 Matrices	198	(3)
7.11 Summary	201	(7)
8 THE VARIATION METHOD	208	(37)
8.1 The Variation Theorem	208	(4)
8.2 Extension of the Variation Method	212	(1)
8.3 Determinants	213	(4)
8.4 Simultaneous Linear Equations	217	(3)
8.5 Linear Variation Functions	220	(8)
8.6 Matrices, Eigenvalues, and Eigenvectors	228	(7)
8.7 Summary	235	(10)
9 PERTURBATION THEORY	245	(37)
9.1 Introduction	245	(1)
9.2 Nondegenerate Perturbation Theory	246	(6)
9.3 Perturbation Treatment of the Helium-Atom Ground State	252	(4)
9.4 Variation Treatments of the Ground State of Helium	256	(3)
9.5 Perturbation Theory for a Degenerate Energy Level	259	(4)
9.6 Simplification of the Secular Equation	263	(2)
9.7 Perturbation Treatment of the First Excited States of Helium	265	(7)
9.8 Comparison of the Variation and Perturbation Methods	272	(1)
9.9 Time-Dependent Perturbation Theory	272	(3)
9.10 Interaction of Radiation and Matter	275	(2)
9.11 Summary	277	(5)
10 ELECTRON SPIN AND THE PAULI PRINCIPLE	282	(23)
10.1 Electron Spin	282	(3)
10.2 Spin and the Hydrogen Atom	285	(1)
10.3 The Pauli Principle	285	(3)
10.4 The Helium Atom	288	(2)
10.5 The Pauli Exclusion Principle	290	(5)
10.6 Slater Determinants	295	(2)
10.7 Perturbation Treatment of the Lithium Ground State	297	(1)
10.8 Variation Treatments of the Lithium Ground State	298	(1)
10.9 Spin Magnetic Moment	299	(1)
10.10 Ladder Operators for Electron Spin	300	(2)
10.11 Summary	302	(3)
11 MANY-ELECTRON ATOMS	305	(42)
11.1 The Hartree-Fock Self-Consistent-Field Method	305	(7)
11.2 Orbitals and the Periodic Table	312	(3)
11.3 Electron Correlation	315	(3)
11.4 Addition of Angular Momenta	318	(5)
11.5 Angular Momentum in Many-Electron Atoms	323	(12)
11.6 Spin-Orbit Interaction	335	(2)
11.7 The Atomic Hamiltonian	337	(2)
11.8 The Condon-Slater Rules	339	(3)
11.9 Summary	342	(5)
12 MOLECULAR SYMMETRY	347	(19)
12.1 Symmetry Elements and Operations	347	(8)
12.2 Symmetry Point Groups	355	(7)
12.3 Summary	362	(4)
13 ELECTRONIC STRUCTURE OF DIATOMIC MOLECULES	366	(93)
13.1 The Born-Oppenheimer Approximation	366	(4)
13.2 Nuclear Motion in Diatomic Molecules	370	(5)
13.3 Atomic Units	375	(1)
13.4 The Hydrogen Molecule Ion	376	(5)
13.5 Approximate Treatments of the H^(+)(2) Ground Electronic State	381	(9)
13.6 Molecular Orbitals for H^(+)(2) Excited States	390	(6)
13.7 MO Configurations of Homonuclear Diatomic Molecules	396	(6)
13.8 Electronic Terms of Diatomic Molecules	402	(5)
13.9 The Hydrogen Molecule	407	(3)
13.10 The Valence-Bond Treatment of H(2)	410	(4)
13.11 Comparison of the MO and VB Theories	414	(2)
13.12 MO and VB Wave Functions for Homonuclear Diatomic Molecules	416	(3)
13.13 Excited States of H(2)	419	(2)
13.14 Electron Probability Density	421	(2)
13.15 Dipole Moments	423	(3)
13.16 The Hartree-Fock Method for Molecules	426	(10)
13.17 SCF Wave Functions for Diatomic Molecules	436	(3)
13.18 MO Treatment of Heteronuclear Diatomic Molecules	439	(3)
13.19 VB Treatment of Heteronuclear Diatomic Molecules	442	(1)
13.20 The Valence-Electron Approximation	443	(1)
13.21 CI Wave Functions	444	(7)
13.22 Summary	451	(8)
14 THE VIRIAL THEOREM AND THE HELLMANN-FEYNMAN THEOREM	459	(21)
14.1 The Virial Theorem	459	(7)
14.2 The Virial Theorem and Chemical Bonding	466	(3)
14.3 The Hellmann-Feynman Theorem	469	(3)
14.4 The Electrostatic Theorem	472	(6)
14.5 Summary	478	(2)
15 AB INITIO AND DENSITY-FUNCTIONAL TREATMENTS OF MOLECULES	480	(146)
15.1 Ab Initio, Density-Functional, Semiempirical, and Molecular-Mechanics Methods	480	(1)
15.2 Electronic Terms of Polyatomic Molecules	481	(4)
15.3 The SCF MO Treatment of Polyatomic Molecules	485	(1)
15.4 Basis Functions	486	(8)
15.5 Speeding Up Hartree-Fock Calculations	494	(4)
15.6 The SCF MO Treatment of H(2)O	498	(7)
15.7 Population Analysis	505	(3)
15.8 The Molecular Electrostatic Potential and Atomic Charges	508	(3)
15.9 Localized MOs	511	(6)
15.10 The SCF MO Treatment of Methane, Ethane, and Ethylene	517	(11)
15.11 Molecular Geometry	528	(11)
15.12 Conformational Searching	539	(6)
15.13 Molecular Vibrational Frequencies	545	(3)
15.14 Thermodynamic Properties	548	(2)
15.15 Ab Initio Quantum Chemistry Programs	550	(1)
15.16 Performing Ab Initio Calculations	551	(6)
15.17 Configuration Interaction	557	(6)
15.18 Moller-Plesset (MP) Perturbation Theory	563	(5)
15.19 The Coupled-Cluster Method	568	(5)
15.20 Density-Functional Theory	573	(19)
15.21 Composite Methods for Energy Calculations	592	(1)
15.22 Solvent Effects	593	(9)
15.23 Relativistic Effects	602	(2)
15.24 Valence-Bond Treatment of Polyatomic Molecules	604	(8)
15.25 The Generalized Valence-Bond Method	612	(1)
15.26 Chemical Reactions	613	(13)
16 SEMIEMPIRICAL AND MOLECULAR-MECHANICS TREATMENTS OF MOLECULES	626	(67)
16.1 Semiempirical MO Treatments of Planar Conjugated Molecules	626	(1)
16.2 The Free-Electron MO Method	627	(2)
16.3 The Huckel MO Method	629	(21)
16.4 The Pariser-Parr-Pople Method	650	(2)
16.5 General Semiempirical MO Methods	652	(12)
16.6 The Molecular-Mechanics Method	664	(16)
16.7 Empirical and Semiempirical Treatments of Solvent Effects	680	(4)
16.8 Chemical Reactions	684	(9)
17 COMPARISONS OF METHODS	693	(17)
17.1 Molecular Geometry	693	(3)
17.2 Energy Changes	696	(7)
17.3 Other Properties	703	(2)
17.4 Hydrogen Bonding	705	(2)
17.5 Conclusion	707	(1)
17.6 The Future of Quantum Chemistry	708	(2)
APPENDIX	710	(2)
BIBLIOGRAPHY	712	(3)
ANSWERS TO SELECTED PROBLEMS	715	(6)
INDEX	721