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Fundamentals of Quantum Chemistry
Molecular Spectroscopy and
Modern Electronic Structure Computations
Molecular Spectroscopy and
Modern Electronic Structure Computations
By Michael Mueller
- Publisher: Springer
- Number Of Pages: 280
- Publication Date: 2001-06-28
- Binding: Hardcover
Product Description
This text is designed as a practical introduction to quantum chemistry. Quantum chemistry is applied to explain and predict molecular spectroscopy and the electronic structure of atoms and molecules. In addition, the text provides a practical guide to using molecular mechanics and electronic structure computations including ab initio, semi-empirical, and density functional methods. The use of electronic structure computations is a timely subject as its applications in both theoretical and experimental chemical research is increasingly prevalent.
This text is written in a format that fosters mastery of the subject both in competency in the mathematics and in obtaining a conceptual understanding of quantum mechanics. The chemistry student's interest is maintained early on in the text where quantum mechanics is developed by applying it to molecular spectroscopy and through conceptual questions labeled as Chemical Connection. Questions throughout the text labeled as Chemical Connection and Points of Further Understanding focus on conceptual understanding and consequences of quantum mechanics. If an Instructor chooses, these questions can be used as a basis for classroom discussion encouraging cooperative learning techniques.
This text provides a solid foundation from which students can readily build further knowledge of quantum chemistry in more advanced courses. In cases where this is a final course in quantum chemistry, this text provides the student not only with an appreciation of the importance of quantum mechanics to chemistry, but also with a practical guide to using electronic structure computations.
This text is written in a format that fosters mastery of the subject both in competency in the mathematics and in obtaining a conceptual understanding of quantum mechanics. The chemistry student's interest is maintained early on in the text where quantum mechanics is developed by applying it to molecular spectroscopy and through conceptual questions labeled as Chemical Connection. Questions throughout the text labeled as Chemical Connection and Points of Further Understanding focus on conceptual understanding and consequences of quantum mechanics. If an Instructor chooses, these questions can be used as a basis for classroom discussion encouraging cooperative learning techniques.
This text provides a solid foundation from which students can readily build further knowledge of quantum chemistry in more advanced courses. In cases where this is a final course in quantum chemistry, this text provides the student not only with an appreciation of the importance of quantum mechanics to chemistry, but also with a practical guide to using electronic structure computations.
Table of Contents
Ch. 1 Classical Mechanics 1
1.1 Newtonian Mechanics 1
1.2 Hamiltonian Mechanics 3
1.3 The Harmonic Oscillator 5
Ch. 2 Fundamentals of Quantum Mechanics 14
2.1 The de Broglie Relationship 14
2.2 Accounting for Wave Character in Mechanical Systems 16
2.3 The Born Interpretation 18 2.4 Particle-in-a-Box 20
2.5 Hermitian Operators 27 2.6 Operators and Expectation Values 27
2.7 The Heisenberg Uncertainty Principle
29 2.8 Particle in a Three-Dimensional Box and Degeneracy 33
Ch. 3 Rotational Motion 37
3.1 Particle-on-a-Ring 37
3.2 Particle-on-a-Sphere 42
Ch. 4 Techniques of Approximation 54
4.1 Variation Theory 54
4.2 Time-Independent Non-Degenerate Perturbation Theory 60
4.3 Time-Independent Degenerate Perturbation Theory 76
Ch. 5 Particles Encountering a Finite Potential Energy 85
5.1 Harmonic Oscillator 85
5.2 Tunneling, Transmission, and Reflection 96
Ch. 6 Vibrational/Rotational Spectroscopy of Diatomic Molecules 113
6.1 Fundamentals of Spectroscopy 113
6.2 Rigid Rotor Harmonic Oscillator Approximation (RRHO) 115
6.3 Vibrational Anharmonicity 128 6.4 Centrifugal Distortion 132
6.5 Vibration-Rotation Coupling 135 6.6 Spectroscopic Constants from Vibrational Spectra 136
6.7 Time Dependence and Selection Rules 140
Ch. 7 Vibrational and Rotational Spectroscopy of Polyatomic Molecules 150
7.1 Rotational Spectroscopy of Linear Polyatomic Molecules 150
7.2 Rotational Spectroscopy of Non-Linear Polyatomic Molecules 156
7.3 Infrared Spectroscopy of Polyatomic Molecules 168
Ch. 8 Atomic Structure and Spectra 177
8.1 One-Electron Systems 177
8.2 The Helium Atom 191
8.3 Electron Spin 199 8.4 Complex Atoms 200
8.5 Spin-Orbit Interaction 207
8.6 Selection Rules and Atomic Spectra 217
Ch. 9 Methods of Molecular Electronic Structure Computations 222
9.1 The Born-Oppenheimer Approximation 222
9.2 The H[subscript 2][[superscript +] Molecule 224
9.3 Molecular Mechanics Methods 232
9.4 Ab Initio Methods 235
9.5 Semi-Empirical Methods 249
9.6 Density Functional Methods 251
9.7 Computational Strategies 255
1.1 Newtonian Mechanics 1
1.2 Hamiltonian Mechanics 3
1.3 The Harmonic Oscillator 5
Ch. 2 Fundamentals of Quantum Mechanics 14
2.1 The de Broglie Relationship 14
2.2 Accounting for Wave Character in Mechanical Systems 16
2.3 The Born Interpretation 18 2.4 Particle-in-a-Box 20
2.5 Hermitian Operators 27 2.6 Operators and Expectation Values 27
2.7 The Heisenberg Uncertainty Principle
29 2.8 Particle in a Three-Dimensional Box and Degeneracy 33
Ch. 3 Rotational Motion 37
3.1 Particle-on-a-Ring 37
3.2 Particle-on-a-Sphere 42
Ch. 4 Techniques of Approximation 54
4.1 Variation Theory 54
4.2 Time-Independent Non-Degenerate Perturbation Theory 60
4.3 Time-Independent Degenerate Perturbation Theory 76
Ch. 5 Particles Encountering a Finite Potential Energy 85
5.1 Harmonic Oscillator 85
5.2 Tunneling, Transmission, and Reflection 96
Ch. 6 Vibrational/Rotational Spectroscopy of Diatomic Molecules 113
6.1 Fundamentals of Spectroscopy 113
6.2 Rigid Rotor Harmonic Oscillator Approximation (RRHO) 115
6.3 Vibrational Anharmonicity 128 6.4 Centrifugal Distortion 132
6.5 Vibration-Rotation Coupling 135 6.6 Spectroscopic Constants from Vibrational Spectra 136
6.7 Time Dependence and Selection Rules 140
Ch. 7 Vibrational and Rotational Spectroscopy of Polyatomic Molecules 150
7.1 Rotational Spectroscopy of Linear Polyatomic Molecules 150
7.2 Rotational Spectroscopy of Non-Linear Polyatomic Molecules 156
7.3 Infrared Spectroscopy of Polyatomic Molecules 168
Ch. 8 Atomic Structure and Spectra 177
8.1 One-Electron Systems 177
8.2 The Helium Atom 191
8.3 Electron Spin 199 8.4 Complex Atoms 200
8.5 Spin-Orbit Interaction 207
8.6 Selection Rules and Atomic Spectra 217
Ch. 9 Methods of Molecular Electronic Structure Computations 222
9.1 The Born-Oppenheimer Approximation 222
9.2 The H[subscript 2][[superscript +] Molecule 224
9.3 Molecular Mechanics Methods 232
9.4 Ab Initio Methods 235
9.5 Semi-Empirical Methods 249
9.6 Density Functional Methods 251
9.7 Computational Strategies 255
App. I: Table of Physical Constants 259
App. II: Table of Energy Conversion Factors 260
App. III: Table of Common Operators 261 Index 262
App. II: Table of Energy Conversion Factors 260
App. III: Table of Common Operators 261 Index 262
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