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Fundamentals of Quantum Chemistry: Molecular Spectroscopy and Modern Electronic Structure Computations

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& 8220;Description:

This textbook for undergraduate chemistry majors introduces the principles and formulations of quantum mechanics in chemistry, and their application to vibrational and rotational spectroscopy of diatomic and polyatomic molecules. The last chapter presents three methods for performing electronic structure computations of molecules: ab initio, semi-empirical, and density functional.

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& 091;subscript 2& 093;& 091;& 091;superscript +& 093; 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& 8221;

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