一、 內容

1. Introduction and Background to Quantum Mechanics

1.1 Aim of Theoretical Chemistry

1.2 Key Concepts from Classical Physics

1.3 Classical Mechanics

1.4 Classical Wave Theory

1.5 Early History of Quantum Mechanics

1.6 Particle Nature of Light

1.7 Wave Nature of Particles

1.8 Uncertainty Principle

1.9 Discovery of Quantum Mechanics

1.10 Concepts in Quantum Mechanics

2. Quantum Theory

2.1 Postulates of Quantum Mechanics

2.2 Definition of Ψ and ︳Ψ︳2

2.3 Operators

2.4 Time-Dependent and Time-Independent Schrödinger Equations

2.5 Eigenvalues

2.6 Expectation Values

2.7 Properties of the Time-Independent Schrödinger Eigenfunctions

3. Particle-in-Box Models

3.1 Particle in a One-Dimensional Box

3.2 Particle in a Two-Dimensional Box

3.3 Particle in a Three-Dimensional Box

3.4 Free-Electron Molecular Orbital Model

4. Rigid-Rotor Models and Angular-Momentum Eigenstates

4.1 Motions of a Diatomic Molecule: Separation of the Center of Mass

4.2 Rigid-Rotor Model in Two Dimensions

4.3 Three-Dimensional Rigid Rotor

4.4 Spherical Harmonics

4.5 Rotational Spectra

4.6 Angular Momentum

4.7 Dirac Notation

4.8 Raising and Lowering Angular-Momentum Operators

5. Molecular Vibrations and Time-Independent Perturbation Theory

5.1 Diatomic Molecule Vibrations

5.2 Raising and Lowering Operators for the Harmonic Oscillator

5.3 Polyatomic Molecule Vibrations

5.4 Time-Independent Perturbation Theory

5.5 Examples

6. The Hydrogen Atom

6.1 The Schrödinger Equation

6.2 Radial Solutions and Eigenvalues

6.3 Energy Eigenvalues; Spectroscopy of the H Atom

6.4 Properties of Hydrogen and Hydrogenlike Wavefunctions

6.5 Atomic Units

7. The Helium Atom

7.1 Schrödinger Equation

7.2 Independent-Particle Model

7.3 The Variation Method

7.4 Better Wavefunctions

8. Electron Spin and the Pauli Principle

8.1 Electron Spin

8.2 The Pauli Principle

8.3 He-Atom Wavefunctions, Including Spin

8.4 Excited State of He

8.5 Energies of He(1s2s) States

8.6 Interaction of Electron Spin with Magnetic Fields

8.7 EPR and NMR

9. Many-Electron Atoms

9.1 Many-Electron Hamiltonian and Schrödinger Equation

9.2 Slater Determinants

9.3 Hartree Method

9.4 Hartree-Fock Method

9.5 Koopmans’ Theorem

9.6 Electron Correlation

9.7 Constants of the Motion

9.8 Angular-Momentum Operators for Many-Electron Atoms

9.9 Relativistic Effects

10. Homonuclear Diatomic Molecules

10.1 Hydrogen Molecular Ion: Born-Oppenheimer Approximation

10.2 LCAO-MO Treatment of H2+

10.3 Other H2+ States

10.4 Electronic Structure of Homonuclear Diatomics

10.5 Electronic structure of H-2: Molecular Orbital and Valence Bond   

      Wavefunctions

10.6 Improvements to MO and VB Results for H2

11. Ab Initio and Density functional Methods

11.1 LCAO-MO-SCF Theory for Molecules

11.2 Atomic Orbitals

11.3 Hartree-Fock Calculations

11.4 Beyond Hartree-Fock

11.5 Density Functional Theory Methods

12. Semiempirical Methods

12.1 Huckel Model

12.2 Extended Huckel Method

12.3 PPP Method

12.4 NDO Methods

13. Applications of Group Theory

13.1 Group Theory for Point Groups

13.2 Applications of Group Theory to Molecular Quantum Mehanics

13.3 Symmetry Properties of Many-Electron Wavefunctions

13.4 Symmetry Properties of Molecular Vibrations

14. Applications of Electronic Structure Theory

14.1 Potential-Energy Functions

14.2 Optimized Geometries and Frequencies

14.3 IR Spectra

14.4 Barriers to Reaction

14.5 Excited States

14.6 Molecular Clusters

14.7 Remarks on Other Methods

15. Time Dependence and Spectroscopy

15.1 Transition Probabilities and the Golden Rule

15.2 Electronic Spectroscopy of Molecules

15.3 Vibrations (Infrared) Spectroscopy

二、 教科書: “Introduction to Quantum Mechanics in Chemistry”

by M. A. Ratner and G. C. Schatz (Prentice Hall)

三、 成績評量: 總成績由期中考(1~2次)、期末考、及平常作業成績評量。