Fractional Charge Methods for Correcting Approximate Kohn-Sham Potentials

The Kohn-Sham density functional theory relies on approximating the exchange-correlation energy functional or the corresponding potential. The behavior of the exchange-correlation potential as a function of position in a system can be used to detect and correct deficiencies of the parent functional. The too-fast decay of the potentials derived from common density functionals is a major problem, because it causes inaccurate Rydberg excitation energies and erroneous fractional charges in dissociating molecules. An efficient method to correct the shape of the exchange-correlation potential was proposed by Gaiduk et al. [A. P. Gaiduk, D. S. Firaha, and V. N. Staroverov, Phys. Rev. Lett. 108, 253005 (2012)]. In that method, the potential of an auxiliary system with a fractionally occupied frontier orbital is used to model a potential for the neutral system of interest. In this thesis, we investigate a method to eliminate unphysical partial charges in dissociating polar molecules via the use of the fractional occupation technique. The method proves successful not only for enforcing correct integer charges in the dissociation limit, but also for predicting how atomic charges change at intermediate separations. We also test the hypothesis that a system with an integral number of electrons but fractional nuclear charge may be used to correct Rydberg excitation energies. Our findings show that, although this approach gives rise to some improvements, the optimal charge to be added depends on the system. In contrast, the advantage of the fractional occupation technique is that the parameter required to correct excitation energies is system-independent