Development of a local hybrid functional for density functional theory
Scuseria, Gustavo E.
Doctor of Philosophy
Self-interaction error appears because the exchange interaction of a system does not cancel the self-coulomb energy of its electron density, yet this exchange interaction contributes to the non-dynamical correlation interaction of the system. The use of exact Hartree-Fock (HF) exchange can correct the self-interaction error, but does not include any non-dynamical correlation required to correctly model the system. This thesis presents a novel approach for constructing hybrid functionals using variable amounts of regular density functional theory (DFT) exchange and exact HF exchange according to the local properties of each system. The idea behind this local mix is to allow for the inclusion of non-dynamical correlation when required, and the correction of the self-interaction error when needed. In this work, the local mix of HF and DFT exchange is driven by the ratio of the Weizsacker approximation to the kinetic energy density with the exact kinetic energy density. This particular choice of local mix yields 100% of exact exchange in one-electron regions, which reduces the self-interaction error. Exact exchange is introduced in this scheme using the exact exchange energy density derived from the definition of the non-local exchange energy density. Unlike other works that tried to correct self-interaction error, this local hybrid approach is computationally feasible for a wide range of molecules. Dissociation energy curves, binding energies, and equilibrium geometries for two-center, three-electron symmetric radical cations can be modeled accurately using this scheme, something that cannot be done accurately with traditional density functionals. This work also presents examples of reaction energy barriers showing a significantly closer agreement to experimental results than traditional density functionals. Calculations of properties of radicals, charge transfer complexes, and Rydberg excited states interactions could also benefit from the flexibility of our local hybrid scheme.