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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