## Density functional theory & practiceSpezialvorlesung, Universität Stuttgart, WS 2003/04, Do 14:00-15:30, V 57.05E. Koch, MPI-FKF
In 1929, P.A.M. Dirac noted that with the advent of quantum mechanics
"The fundamental laws necessary for the mathematical treatment of large
parts of physics and the whole of chemistry are thus fully known, and the
difficulty lies only in the fact that application of these laws leads to
equations that are too complex to be solved."
Mainly because the many-body wavefunction for n( in the ground state. With the density as a basic
variable one only has to find a function of r)3 variables, independently
of the number of electrons in the system. Unfortunately the equations for
determining the density are not known so that one has to work with approximate
equations. The success of density functional theory is based on the fact that
very good approximations have been found — and on the availability of
computers of ever increasing speed. This allows practical calculations of
numerous physical properties for vast classes of molecules and solids.
These achievements were recognized with the 1998 Nobel Prize in Chemistry to
Walter Kohn.
In the lecture we will explain the basic concepts of density functional theory and discuss practical aspects. The main goal is to give a feeling of what can be done with these methods (which are by now implemented in standard codes that are sometimes even freely available) and where such calculations can be trusted. As practical applications we will discuss how to calculate and interpret band structures, how to do Car-Parrinello molecular dynamics, and we will address approaches for calculating excited states. ## Contents of Lectures**Introduction & perspective:**slides- electronic structure methods
W.Kohn: An essay on condensed matter physics in the twentieth century Review of Modern Physics**71**S59-S77 (1999) J.Hafner: Atomic-scale computational materials science Acta Materialia**48**71-92 (2000) P.Coleman: Many-body physics: Unfinished revolution
`cond-mat/0307004` - Born-Oppenheimer approximation
Potential energy surfaces - atomic units
The NIST reference on Constants, Units, and Uncertainty
- electronic structure methods
**Theorems:**slides- density matrices; exchange-correlation hole
- coupling-constant integration
- Hohenberg-Kohn: The density as the basic variable
- Kohn-Sham: mapping to single-electron problem
**Practice:**slides- Solving the one-dimensional Schrödinger equation
- Run your own DFT for atoms
- practical density functionals (LDA, GGA)
more degrees of freedom: LSD, SIC, orbital functionals
- self-consistency
- basis sets
- large systems: O(N)
**Applications:**- ground state: energy, structure, elastic constants
- forces: molecular dynamics
- excited states?
- parameters for correlated systems
- No.3: Ground State of the Electron Gas by a Stochastic Method (D.M. Ceperley and B.J. Alder)
- No.5: Unified Approach for Molecular Dynamics and Density Functional Theory (R. Car and M. Parrinello)
Some DFT conferences: - XII-th International
Workshop on Computational Physics and Materials Science
8-10 Jan. 2004, Gif sur Yvette - 16th Annual Workshop on Recent Developments
in Electronic Structure Methods
27-30 May 2004, Rutgers University, NJ
## ReferencesErik Koch |