Date of Award

2011

Degree Type

Thesis

Degree Name

Master of Science

Program

Chemistry

Supervisor

Dr. Viktor N. Staroverov

Abstract

In the Kohn-Sham density-functional theory, one has to approximate (“model”) either the exchange-correlation density functional or the ,corresponding exchange- correlation potential. If one chooses to approximate the potential, then one needs to use the van Leeuwen-Baerends line integral to assign an energy to the density coming from a given approximate potential. The problem with this approach is that when a model potential does not have a parent functional, the line integral is path- dependent and so the energy is ambiguously defined. For such potentials, existing paths are far from optimal. In this work, we introduce two new density parametriza- tions for the line-integral formula and obtain the corresponding energy expressions. We then use these expressions to explore several existing model exchange potentials. The first energy expression corresponds to a path in which the electron density is constructed by gradually filling frozen Kohn-Sham orbitals in accordance with the aufbau principle, either orbital-by-orbital or subshell-by-subshell. The second en­ ergy expression uses the Janak theorem and requires knowing the dependence of the highest-occupied molecular orbital (HOMO) energy on the HOMO’s occupation num­ ber. We also propose a new derivation of Janak’s theorem that reveals its connection to the van Leeuwen-Baerends line integral. In addition, we revisit Slater’s transition- state method and show that in the intervals between N and N —1 electrons, the total energy calculated from a typical density-functional approximation deviates from lin­ earity quadratically. We also find that the HOMO energy calculated for an (TV—1/2)- electron system becomes almost exact, which indicates that the (N —l/2)-electron potential is more accurate than the potential of the iV-electron system. This sug­ gests that the accuracy of molecular properties calculated with existing approximate exchange-correlation functionals may be improved if the corresponding Kohn-Sham potentials are constructed from electron-deficient densities.

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