Rajesh Dhakal

Date of Award

January 2017

Document Type


Degree Name

Doctor of Philosophy (PhD)


Physics & Astrophysics

First Advisor

William Schwalm


In the work described here, semi-empirical, theoretical tools have been developed to address one-electron properties of substrate/adsorbate systems. The tools are adaptations of the simple, Hückel π-electron theory and of the fast accurate-kinetic

energy theory of F. Harris et al. (FAKE) to systems involving an infinite, mostly periodic substrate via a Green-function formalism. These tools are applied here to study graphene with vacancies and adsorbates, but can be generalized. In π theory, only a small subset of substrate basis states having odd reflection symmetry through the graphene layer are used to treat electrons near the Fermi level, to a very crude level of approximation. The substrate model Hamiltonian has been extended to contain second third and fourth nearest neighbor interactions. In the FAKE method, a semi-empirical tight-binding, charge self-consistent Hamiltonian is developed in which

kinetic energy integrals are evaluated exactly and potential energy terms are extrapolated via a Müllikan formula using the overlaps. The methods are applied to anisolated atomic hydrogen adsorbate, and to vacancy and edge states on the graphene substrates. By comparing to experiments including scanning tunneling microscopy and to theoretical work including augmented plane wave (APW) and first principles density functional and other theoretic work, the theoretical tools developed here are seen to give good results and can in principle provide an efficient, potentially faster

way of handling very large adsorbed molecules.