PHY 5085
DENSITY FUNCTIONAL THEORY-I
Three hours lecture, Three credit hours.
(Güz Yarıyılı)
I. PREREQUISITES
: None
II. TEXTBOOK
: C. Filhais, F. Nogueria, M. Marques (Eds.), A Primer in
Density Functioanl Theory, Springer, Nevyork, 2002.
REFERENCE BOOKS
:
1) D. Josbent (Edit.), Denisty Functioanls: Theory and
Applications, Springer, NewYork, 1998
2) H. Eschiring, The Fundamentals of Density Functioanl
Theory, Leipzig, 1996.
3) E.K.U. Gross and R.M. Dreizler (Edits.) Density Functioanl
Theory, Plemum Press, NewYork, 1995.
III. COURSE OBJECTIVES
:
Density functional theory for electrons in atoms molecules and solids has a sucessful
history during the past decades, application of DFT has become the most effective method for
the calculation of ground-state structural and electronic properties of molecules and solids.
In this course, the DFT for atoms, molecules and solids, starting from the electronic
structure of atoms will be dicussed.
Since the applications of DFT span all kind of many particle problems the course divided
in two semesters.
In the first semester the DFT will be introduced and application for atoms and molecules
disscussed. In the second semester mostly application for solids will be discussed.
IV. COURSE OUTLINE
WEEK 1. Quantum Mechanics in brief
1.1. Postulates of QM
1.2. Some Approximations in QM
1.3. Variation Principle
WEEK 2. Three particle systems
2.1. The He Atom
2.1.1. The J integral
2.1.2. The K Integral
WEEK 3.
3.1. Hartree-Fock Appoximation
WEEK 4. Introductin to DFT
WEEK 5. Fundamentals of DFT
5.1. Introduction
5.2. Basic DFT
WEEK 6. Density Functionals for Non-Relativistic Coulomb Systems
6.1. QM Many-Electron Problem
6.2. Wavefunction Theory
WEEK 7. Density Functionals for Non-Relavistic Coulomb Systems
7.1. Hellmann-Feynman Theory
7.2. Virial Theorem
7.3. Definitions of Density Functionals
WEEK 8. Density Functionals for Non-Relavistic Coulomb Systems
8.3.1. Density Variotional Principle
8.3.2. Kohn-Sham Non-Intracting System
8.3.3. Exchange Energy and Correlation Energy
8.3.4. Coupling Constant Integration
WEEK 9. Formal Properties of Functionals
9.1. Uniform Coordinate Scaling
9.2. Local Lower Bounds
WEEK 10. Formal Properties of Functionals
10.1. Spin sealing Relations
10.2. Size Consisteney
10.3. Derivative Discontinuity
WEEK 11. An Example: Uniform Electron Cas
11.1. Kinetic Energy
11.2. Exchange Energy
11.3. Correlation Energy
WEEK 12. Local, Semi Local and on-Local Approximations
12.1. Local Spin Density Approximations
12.2. Gradient Expansions
12.3. Gereralized Gradient Approximations
WEEK 13. Local, Semi Local and on-Local Approximations
13.1. Construction of GGA
13.2. GGA Nonlocality
13.3. Hybrid Functionals
WEEK 14. Jacob’s Ladder of Density Functional Approximations
WEEK 15. Discussion and Summary
V. GRADING
A mid-term exam (preferably a take-home exam) and 2 assignments are given, also each
student must give a presentation in the semester. The final grade will be constructed upon
50% of the assignments, 25% of the presentation and 25% of the mid-term