Density functional theory.pptx

Density functional theory

1. Density functional theory By Narayon Rabi das

2. Content History Background of DFT Introduction Many particle problems Hohenberg- kohn theorem Kohn-sham equation

3. History In 1927, Prof. L. Thomas & E. Fermi introduced a statistical method to compute the energy of an atom In 1964, Hohenberg-Kohn published papers that formed the foundation of DFT After the 1970s, DFT widely used in solid state physics In 1998, W. Kohn developed DFT for which he won the Nobel prize

4. Background of DFT To solve many-body problems by Schrodinger’s equation Only up to one electron problem we can solve Schrodinger equation exactly It is very difficult to solve the Schrodinger’s equation for a many-body system We must involve some approximation to solve the problem and a method to obtain an approximate solution to the Schrodinger’s equation of a many body system is DFT

5. Intoduction DFT is a quantum mechanical method to analyze the electronic structure of a system With this theory the properties of many-electron system can be determined by using functionals

6. Many particle problem Find the ground state for a collection of atoms by solving the Schrodinger’s equation If the first thing we do apply Born-Oppenheimer approximation nuclii they are very big and slow but electron are small and fast ie m nuclei >> m e

7. Hohenberg- kohn theorem Based on two theorem Theorem- 1: the external potential for ground state energy E is unique functional of electron density E=E[n(r)] functional is a function of a function Theorem-2 : The electron density that minimizes the energy of the overall functional is the true ground state electron density E[n(r)] ≥ E [n (r)]

8. Kohn-sham equation Solve a set of single depends on wave function that only depend on three spatial variable which is none interacting system The Hamiltonian for single electron system  

9. Thank you