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
mnuclei>> me

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)]≥ E0[n0(r)]

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

9. Thank you