Introduction to Quantum Mechanics in Chemistry (Ratner, Mark A.; Schatz, George C.)

Abstract

1. Introduction and Background to Quantum Mechanics. Aim of Theoretical Chemistry. Key Concepts from Classical Physics. Classical Mechanics. Classical Wave Theory. Early History of Quantum Mechanics. Particle Nature of Light. Wave Nature of Particles. Uncertainty Principle. Discovery of Quantum Mechanics. Concepts in Quantum Mechanics. 2. Quantum Theory. Postulates of Quantum Mechanics. Definitions of ...Y and ...|Y|2. Operators. Time-Dependent and Time-Independent Schrodinger Equations. Eigenvalues. Expectation Values. Properties of the Time-Independent Schrodinger Eigenfunctions. 3. Particle-in-Box Models. Particle in a One-Dimensional Box. Particle in a Two-Dimensional Box. Particle in a Three-Dimensional Box. Free-Electron Molecular Orbital Model. 4. Rigid-Rotor Models and Angular Momentum Eigenstates. Motions of a Diatomic Molecule: Separation of the Center of Mass. Rigid-Rotor Model in Two Dimensions. Three-Dimensional Rigid Rotor. Spherical Harmonics. Rotational Spectra. Angular Momentum. Dirac Notation. Raising and Lowering Angular-Momentum Operators. 5. Molecular Vibrations and Time-Independent Perturbation Theory. Diatomic Molecule Vibrations. Raising and Lowering Operators for the Harmonic Oscillator. Polyatomic Molecule Vibrations. Time-Independent Perturbation Theory. Examples. 6. The Hydrogen Atom. The Schrodinger Equation. Radial Solutions and Eigenvalues. Energy Eigenvalues Spectroscopy of the H Atom. Properties of Hydrogen and Hydrogenlike Wavefunctions. Atomic Units. 7. The Helium Atom. Schrodinger Equation. Independent-Particle Model. The Variational Method. Better Wavefunctions. 8. Electron Spin and the Pauli Principle. Electron Spin. The Pauli Principle. He-Atom Wavefunctions, Including Spin. Excited State of He. Energies of He(1s2s) States. Interaction of Electron Spin with Magnetic Fields. EPR and NMR. 9. Many-Electron Atoms. Many-Electron Hamiltonian and Schrodinger Equation. Slater Determinants. Hartree Method. Hartree-Fock Method. Koopmans' Theorem. Electron Correlation. Constants of the Motion. Angular-Momentum Operators for Many-Electron Atoms. Relativistic Effects. 10. Homonuclear Diatomic Molecules. Hydrogen Molecular Ion: Born-Oppenheimer Approximation. LCAO-MO Treatment of H2 +. Other H2 + States. Electronic Structure of Homonuclear Diatomics. Electronic Structure of H2: Molecular Orbital and Valence Bond Wavefunctions. Improvements to MO and VB Results for H2. 11. Ab Initio and Density Functional Methods. LCAO-MO-SCF Theory for Molecules. Atomic Orbitals. Hartree-Fock Calculations. Beyond Hartree-Fock. Density Functional Theory Methods. 12. Semiempirical Methods. Huckel Model. Extended Huckel Method. PPP Method. NDO Methods. 13. Applications of Group Theory. Group Theory for Point Groups. Applications of Group Theory to Molecular Quantum Mechanics. Symmetry Properties of Many-Electron Wavefunctions. Symmetry Properties of Molecular Vibrations. 14. Applications of Electronic Structure Theory. Potential-Energy Functions. Optimized Geometries and Frequencies. IR Spectra. Barriers to Reaction. Excited States. Molecular Clusters. Remarks on Other Methods. 15. Time Dependence and Spectroscopy. Transition Probabilities and the Golden Rule. Electronic Spectroscopy of Molecules. Vibration (Infrared) Spectroscopy. Appendices. Mathematical Background. Two-Electron Repulsion Integral. Character Tables. Atomic Units, Energy Conversion Factors, and Physical Constants. Solutions to Odd-Numbered Problems. Index.