The Effective Potential in Kohn-Sham Theory

Abstract

Density functional theory (DFT)} is a widely used technique for electronic structure calculations. It allows a first principles solution of the many-electron Schrödinger equation by relating the electron density of the systems ground state to that of a fictitious non-interacting system. The success of DFT methods comes from the use of approximations to the exact total energy functional that, with an appropriate functional, accurately determine the ground state properties of a system.
The work presented in this thesis uses properties of the Kohn-Sham effective potential to correct errors in DFT approximations, particularly those associated with self-interactions. Applying a constraint to the effective potential enforcing the correct, self-interaction free asymptotic behaviour significantly improves the calculation of ionisation energies for the LDA, PBE, and B3LYP functionals. For LDA this error is reduced from 4.08 eV to 1.61 eV, with a similar reduction in error found for PBE and B3LYP. Additional methods to improve this self-interaction correction are presented and expanded upon, including a self-interaction free hybrid scheme for the constrained minimisation method. This hybrid further improves ionisation energies over the constrained method. Average errors of PBE ionisation energies are reduced from 4.41 eV to 0.34 eV. These improvements are also found to extend to the ionisation energies of all occupied orbitals and electron affinities.
A post-scf correction that corrects ionisation energies from the Kohn-Sham eigenvalue to those from a calculation is also developed. Ionisation energies for the LDA approximation are improved from an average error of 3.99 eV to 0.93 eV, with similar improvements seen for lower lying ionisation energies and electron affinities. The final work of this thesis shows that, unlike conventional band theory, spin-DFT (SDFT) can predict insulating behaviours in periodic systems from a unit cell containing an odd number of electrons. Additionally, this result is shown for a novel method for implementing DFT; combining SDFT XC energy functionals with a spin-independent effective potential, through the use of the optimised effective potential method.
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