A core strength of the Theoretical Chemical and Quantum Physics Group

## Outline

Density Functional Theory (DFT) is presently the most successful (and also the most promising) approach to modelling the electronic structure of matter. It can predict a variety of molecular properties: vibrational frequencies, atomisation energies, ionisation energies, electric and magnetic properties, molecular structures *etc*. The original theory has also been generalised and extended to deal with phenomenon like spin polarisation and superconductivity, as well as the introduction of time and temperature dependencies.

DFT is a **ground state** (GS) theory, which describes an interacting system of fermions via its density rather than its many-body wavefunction. The GS properties of a system, including the energy E, can be expressed as functionals of the GS electron density. Practical applications of DFT are based on approximations of the so-called exchange-correlation potential. The exchange-correlation potential describes the effects of the Pauli principle and the Coulomb potential beyond a pure electrostatic interaction of the electrons. Possessing the exact exchange-correlation potential means that the many-body problem could be solved exactly, which is clearly not feasible in solids.

The most common approximation is the local density approximation (LDA), which locally substitutes the exchange-correlation energy density of an inhomogeneous system by that of an electron gas evaluated at the local density. While many ground state properties (lattice constants, bulk moduli, etc.) are well described in the LDA, the dielectric constant is overestimated by 10-40% compared to experiment. This overestimation stems from the neglect of a polarisation-dependent exchange correlation field. This, and other limitations have forced the invention of other exchange-correlation functionals such as the Generalised Gradient Approximation (GGA). The TCQP Group employ a number of different potentials in their work and are selected on a per system basis.

## Recent Publications

N.C. Wilson and S.P. Russo, *Hybrid density functional theory study of the high-pressure polymorphs of α-Fe _{2}O_{3} hematite*, Phys. Rev. B

**79**, 094113 (2009)

S.P. Russo, I.E. Grey, and N.C. Wilson, *Nitrogen/Hydrogen Codoping of Anatase: A DFT Study*, J. Phys. Chem. C 112(20) (2008)

For more information about this project, please contact Salvy Russo