Quantum chemistry:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boston u.a.
Acad. Press
1993
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| Ausgabe: | 2. ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XX, 711 S. graph. Darst. |
| ISBN: | 0124575552 |
Internformat
MARC
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Datensatz im Suchindex
| _version_ | 1804122758853951488 |
|---|---|
| adam_text | QUANTUM CHEMISTRY
Second Edition
John P Lowe
DEPARTMENT OF CHEMISTRY
THE PENNSYLVANIA STATE UNIVERSITY
UNIVERSITY PARK, PENNSYLVANIA
ACADEMIC PRESS, INC
Harcourt Brace amp; Company, Publishers
Boston San Diego New York
London Sydney Tokyo Toronto
CONTENTS
PREFACE TO THE SECOND EDITION xvii
PREFACE TO THE FIRST EDITION xix
Chapter 1 Classical Waves and the Time-Independent
Schrodinger Wave Equation
1-1 Introduction 1
1-2 Waves 1
1-3 The Classical Wave Equation 3
1-4 Standing Waves in a Clamped String 7
1-5 Light as an Electromagnetic Wave 9
1-6 The Photoelectric Effect 11
1-7 The Wave Nature of Matter 15
1-8 A Diffraction Experiment with Electrons 16
1-9 Schrodinger s Time-Independent Wave Equation 19
1-10 Conditions on ji 21
1-11 Some Insight into the Schrodinger Equation 23
1-12 Summary 23
Problems 24
Reference 26
Chapter 2 Quantum Mechanics of Some Simple Systems
2-1 The Particle in a One-Dimensional Box 27
2-2 Detailed Examination of Particle-in-a-Box Solutions 30
2-3 The Particle in a One-Dimensional Box with One Finite Wall 38
2-4 The Particle in an Infinite Box with a Finite Central Barrier 44
2-5 The Free Particle in One Dimension 48
2-6 The Particle in a Ring of Constant Potential 51
2-7 The Particle in a Three-Dimensional Box: Separation of Variables 53
2-8 The Scattering of Particles in One Dimension 57
2-9 Summary 61
Problems 62
References 66
Chapter 3 The One-Dimensional Harmonic Oscillator
3-1 Introduction 67
3-2 Some Characteristics of the Classical One-Dimensional Harmonic Oscillator 67
ix
X CONTENTS
3-3 The Quantum-Mechanical Harmonic Oscillator 70
3-4 Solution of the Harmonic Oscillator Schrodinger Equation 72
3-5 Quantum-Mechanical Average Value of the Potential Energy 81
3-6 Vibrations of Diatomic Molecules 82
3-7 Summary 8 2
Problems 83
Chapter 4 The Hydrogenlike Ion, Angular Momentum,
and the Rigid Rotor
4-1 The Schrodinger Equation and the Nature of Its Solutions 86
4-2 Separation of Variables 102
4-3 Solution of the R, amp;, and D Equations 104
4-4 Atomic Units 106
4-5 Angular Momentum and Spherical Harmonics 108
4-6 Angular Momentum and Magnetic Moment 113
4-7 Angular Momentum in Molecular Rotations—The Rigid Rotor 114
4-8 Summary 116
Problems 118
References 121
Chapter 5 Many-Electron Atoms
5-1 The Independent Electron Approximation 122
5-2 Simple Products and Electron Exchange Symmetry 124
5-3 Electron Spin and the Exclusion Principle 127
5-4 Slater Determinants and the Pauli Principle 132
5-5 Singlet and Triplet States for the Is2s Configuration of Helium 134
5-6 The Self-Consistent Field, Slater-Type Orbitals, and the Aufbau Principle 140
5-7 Electron Angular Momentum in Atoms 145
5-8 Overview 157
Problems 157
References 160
Chapter 6 Postulates and Theorems of Quantum Mechanics
6-1 Introduction 161
6-2 The Wavefunction Postulate 161
6-3 The Postulate for Constructing Operators 162
6-4 The Time-Dependent Schrodinger Equation Postulate 163
6-5 The Postulate Relating Measured Values to Eigenvalues 164
6-6 The Postulate for Average Values 166
6-7 Hermitian Operators 167
6-8 Proof That Eigenvalues of Hermitian Operators Are Real 168
6-9 Proof That Eigenfunctions of an Hermitian Operator Form an Orthogonal Set 168
CONTENTS XI
6-10 Demonstration That Eigenfunctions of an Hermitian Operator May Be
Expressed as an Orthonormal Set 169
6-11 Proof That Commuting Operators Have Simultaneous Eigenfunctions 170
6-12 Completeness of Eigenfunctions of an Hermitian Operator 171
6-13 The Variation Principle 172
6-14 The Pauli Exclusion Principle 173
6-15 Measurement, Commutators, and Uncertainty 173
6-16 Time-Dependent States 174
6-17 Summary 181
Problems 182
References 184
Chapter 7 The Variation Method
7-1 The Spirit of the Method 185
7-2 Nonlinear Variation: The Hydrogen Atom 186
7-3 Nonlinear Variation: The Helium Atom 190
7-4 Linear Variation: The Polarizability of the Hydrogen Atom 192
7-5 Linear Combination of Atomic Orbitals: The H2+ Molecule-Ion 202
7-6 Molecular Orbitals of Homonuclear Diatomic Molecules 217
7-7 Basis Set Choice and the Variational Wavefunction 229
7-8 Beyond the Orbital Approximation 231
Problems 234
References 239
Chapter 8 The Simple Hiickel Method and Applications
8-1 The Importance of Symmetry 240
8-2 The Assumption of a-n Separability 240
8-3 The Independent ^-Electron Assumption 242
8-4 Setting up the Huckel Determinant 243
8-5 Solving the HMO Determinantal Equation for Orbital Energies 247
8-6 Solving for the Molecular Orbitals 248
8-7 The Cyclopropenyl System: Handling Degeneracies 250
8-8 Charge Distributions from HMOs 252
8-9 Some Simplifying Generalizations 256
8-10 HMO Calculations on Some Simple Molecules 260
8-11 Summary: The Simple HMO Method for Hydrocarbons 265
8-12 Relation between Bond Order and Bond Length 266
8-13 n-Electron Densities and Electron Spin Resonance Hyperfine Splitting Constants 269
8-14 Orbital Energies and Oxidation-Reduction Potentials 273
8-15 Orbital Energies and Ionization Potentials 276
8-16 jt-Electron Energy and Aromaticity 277
8-17 Extension to Heteroatomic Molecules 284
8-18 Self-Consistent Variations of a and 0 287
8-19 HMO Reaction Indices 288
8-20 Conclusions 296
Problems 297
References 306
Xii CONTENTS
Chapter 9 Matrix Formulation of the Linear Variation Method
9-1 Introduction 308
9-2 Matrices and Vectors 308
9-3 Matrix Formulation of the Linear Variation Method 316
9-4 Solving the Matrix Equation 318
9-5 Summary 321
Problems 321
References 323
Chapter 10 The Extended Hiickel Method
10-1 The Extended Huckel Method 324
10-2 Mulliken Populations 336
10-3 Extended Huckel Energies and Mulliken Populations 339
10-4 Extended Huckel Energies and Experimental Energies 342
Problems 345
References 349
Chapter 11 The SCF-LCAO-MO Method and Extensions
11-1 Ab Initio Calculations 350
11-2 The Molecular Hamiltonian 351
11-3 The Form of the Wavefunction 351
11-4 The Nature of the Basis Set 352
11-5 The LCAO-MO-SCF Equation 352
11-6 Interpretation of the LCAO-MO-SCF Eigenvalues 354
11-7 The SCF Total Electronic Energy 355
11-8 Basis Sets 356
11-9 The Hartree-Fock Limit 359
11-10 Correlation Energy 360
11-11 Koopmans Theorem 361
11-12 Configuration Interaction 363
11-13 Size Consistency and the Moller-Plesset Treatment of Correlation 369
11-14 Examples of Ab Initio Calculations 371
11-15 Approximate SCF-MO Methods 385
11-16 Notes on Other Methods 387
Problems 388
References 390
Chapter 12 Time-Independent Rayleigh-Schrodinger
Perturbation Theory
12-1 An Introductory Example 392
12-2 Formal Development of the Theory for Nondegenerate States 392
12-3 A Uniform Electrostatic Perturbation of an Electron in a Wire 397
CONTENTS Xlll
12-4 The Ground-State Energy to First Order of Heliumlike Systems 404
12-5 Perturbation at an Atom in the Simple Huckel MO Method 407
12-6 Perturbation Theory for a Degenerate State 409
12-7 Polarizability of the Hydrogen Atom in the n=2 States 411
12-8 Degenerate-Level Perturbation Theory by Inspection 413
12-9 Interaction between Two Orbitals: An Important Chemical Model 416
12-10 Connection between Time-Independent Perturbation Theory and Spectroscopic
Selection Rules 417
Problems 421
References 428
Chapter 13 Group Theory
13-1 Introduction 429
13-2 An Elementary Example 429
13-3 Symmetry Point Groups 431
13-4 The Concept of Class 434
13-5 Symmetry Elements and Their Notation 437
13-6 Identifying the Point Group of a Molecule 443
13-7 Representations for Groups 444
13-8 Generating Representations from Basis Functions 447
13-9 Labels for Representations 453
13-10 Some Connections between the Representation Table and Molecular Orbitals 454
13-11 Representations for Cyclic and Related Groups 456
13-12 Orthogonality in Irreducible Inequivalent Representations 459
13-13 Characters and Character Tables 461
13-14 Using Characters to Resolve Reducible Representations 465
13-15 Identifying Molecular Orbital Symmetries 466
13-16 Determining in Which Molecular Orbital an Atomic Orbital Will Appear 469
13-17 Generating Symmetry Orbitals 470
13-18 Hybrid Orbitals and Localized Orbitals 473
13-19 Symmetry and Integration 476
Problems 479
References 484
Chapter 14 Qualitative Molecular Orbital Theory
14-1 The Need for a Qualitative Theory 485
14-2 Hierarchy in Molecular Structure and in Molecular Orbitals 485
14-3 H2+ Revisited 486
14-4 H2: Comparisons with H2+ 489
14-5 Rules for Qualitative Molecular Orbital Theory 491
14-6 Application of QMOT Rules to Homonuclear Diatomic Molecules 492
14-7 Shapes of Polyatomic Molecules: Walsh Diagrams 495
14-8 Frontier Orbitals 509
14-9 Qualitative Molecular Orbital Theory of Reactions 512
Problems 526
References 529
XIV CONTENTS
Chapter 15 Molecular Orbital Theory of Periodic Systems
15-1 Introduction S30
15-2 The Free Particle in One Dimension 530
15-3 The Particle in a Ring 533
15-4 Benzene 534
15-5 General Form of One-Electron Orbitals in Periodic Potentials—Bloch s
Theorem 538
15-6 A Retrospective Pause 542
15-7 An Example: Polyacetylene with Uniform Bond Lengths 543
15-8 Electrical Conductivity 552
15-9 Polyacetylene with Alternating Bond Lengths—Peierls Distortion 553
15-10 Electronic Structure of All-Trans Polyacetylene 558
15-11 Comparison of EHMO and SCF Results on Polyacetylene 558
15-12 Effects of Chemical Substitution on the Pi Bands 561
15-13 Poly-Paraphenylene—A Ring Polymer 563
15-14 Energy Calculations 571
15-15 Two-Dimensional Periodicity and Vectors in Reciprocal Space 572
15-16 Periodicity in Three Dimensions—Graphite 574
15-17 Summary 589
Problems 590
References 592
Appendix 1 Useful Integrals 593
Appendix 2 Determinants 595
Appendix 3 Evaluation of the Coulomb Repulsion Integral
over Is AOs 598
Appendix 4 Angular Momentum Rules 603
Appendix 5 The Pairing Theorem 614
Appendix 6 Huckel Molecular Orbital Energies, Coefficients,
Electron Densities, and Bond Orders for Some
Simple Molecules 618
Appendix 7 Derivation of the Hartree-Fock Equation 627
CONTENTS XV
Appendix 8 The Virial Theorem for Atoms and Diatomic
Molecules 638
Appendix 9 Bra-Ket Notation 643
Appendix 10 Values of Some Useful Constants and Conversion
Factors 645
Appendix 11 Group Theoretical Charts and Tables 649
Appendix 12 Hints for Solving Selected Problems 663
Appendix 13 Answers to Problems 666
INDEX 701
|
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| indexdate | 2024-07-09T17:18:58Z |
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| language | English |
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| spelling | Lowe, John P. Verfasser aut Quantum chemistry John P. Lowe 2. ed. Boston u.a. Acad. Press 1993 XX, 711 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Chimie quantique Quantum chemistry Quantenchemie (DE-588)4047979-1 gnd rswk-swf Quantenmechanik (DE-588)4047989-4 gnd rswk-swf Quantenchemie (DE-588)4047979-1 s DE-604 Quantenmechanik (DE-588)4047989-4 s 1\p DE-604 HEBIS Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005526557&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Lowe, John P. Quantum chemistry Chimie quantique Quantum chemistry Quantenchemie (DE-588)4047979-1 gnd Quantenmechanik (DE-588)4047989-4 gnd |
| subject_GND | (DE-588)4047979-1 (DE-588)4047989-4 |
| title | Quantum chemistry |
| title_auth | Quantum chemistry |
| title_exact_search | Quantum chemistry |
| title_full | Quantum chemistry John P. Lowe |
| title_fullStr | Quantum chemistry John P. Lowe |
| title_full_unstemmed | Quantum chemistry John P. Lowe |
| title_short | Quantum chemistry |
| title_sort | quantum chemistry |
| topic | Chimie quantique Quantum chemistry Quantenchemie (DE-588)4047979-1 gnd Quantenmechanik (DE-588)4047989-4 gnd |
| topic_facet | Chimie quantique Quantum chemistry Quantenchemie Quantenmechanik |
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