Lecturer: Prof. Sheng-Hsien Lin (林聖賢教授)
First present the methods of Newton equations of motion, Lagrange’s equations of motion and Hamiton equations of motion and show how to employ these methods to treat dynamical problems.These will then be compared with quantum mechanical treatments. Particle in a box, harmonic oscillator rigid rotator and hydrogen atom will be solved Approximation methods like perturbation method and variational method will be presented.
Lecturer: Prof. Michitoshi Hayashi (林倫年教授 )
1. Many Electron Systems
-- Hamiltonian
-- Tight-binding systems
-- Nearly free electron systems
-- Born Oppenheimer approximation
-- Molecular Hamiltonian
-- Basis set approach
-- Localized basis set
-- Plain wave
-- Many electron wave functions
-- Slater determinant
-- Exchange correlation of two electrons
-- The Hartree-Fock self-consistent Field Method
-- Exchange energy
2. Ab initio Implementations of Hartree-Fock Molecular Orbital Theory
-- Basis sets
-- Hartree-Fock limit
3. Electron Correlation
-- Dynamical & non-dynamical correlations
-- Configuration interaction
-- Many-body perturbation theory
-- Coupled cluster theory
-- Multi-configuration Self-consistent Field Theory
4. Density Functional Theory
-- The Hohenberg-Kohn theorems
-- Kohn-Sham self-consistent field theory
-- Exchange-correlation functionals
--LDA, LSDA, GGA, Post-GGA
5. Time-dependent density functional theory
-- Runge-Gross theorem
-- Time-dependent Hartree-Fock
-- Linear response theorem
-- Random phase approximation
-- Tamm-Dancoff approximation
6. Applications
Lecture Notes
1. Essence of computational chemistry: theories and models, Second Edition, Christopher J. Cramer, iley
2. Modern Quantum Chemistry, A. Szabo, N. S. Ostlund, Dover
3. Electron correlations in molecules and solids, P. Fulde, Springer
4. A. Dreuw and M. Head-Gordon, Chem. Rev. 2005, 105, 4009-4037
5. M.A.L. Marques and E.K.U. Gross, Annu. Rev. Phys. Chem. 2004. 55:427–55
6. M. E. Casida “Time-dependent density functional response theory for molecules” in Recent Advances in Computational Chemistry Vol.1 Ed. D. P. Chong, page 155 (1995, World Scientific )
