Hybrid methods: Combining density functional and wavefunction theory

Abstract

Hybrid methods of density-functional and wavefunction theory have proven to be powerful tools in electronic structure theory. The Kohn-Sham scheme is already a hybrid scheme, since part of the kinetic energy of the system is calculated from the Kohn-Sham wavefunction. In the empirical hybrid methods a fraction of exact exchange, also calculated from the Kohn-Sham wavefunction, is mixed with density functional approximations to exchange and correlation. These methods give a significant improvement in accuracy over local- and gradient-corrected approximations to the exchange-correlation energy. We show how insight into the nature of exchange and correlation in molecules and atoms can be used to construct nonempirical hybrid schemes. We review density-functional perturbation theory and incorporate second-order density-functional perturbation theory into the nonempirical hybrid scheme. The relation between the nonempirical- and the empirical hybrid methods is analyzed.