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DENSITY
FUNCTIONAL
THEORY
By
Narayon Rabi das
Content
 History
 Background of DFT
 Introduction
 Many particle problems
 Hohenberg-kohn theorem
 Kohn-sham equation
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
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
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
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
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)]
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
Thank you

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Density functional theory.pptx

  • 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