Date on Master's Thesis/Doctoral Dissertation


Document Type

Doctoral Dissertation

Degree Name

Ph. D.

Department (Legacy)

Department of Physics

Committee Chair

Wu, Shi-Yu

Author's Keywords

Environment-dependent Hamiltonian; Self-consistency; Charge redistribution


Hamiltonian systems


I will report the development of a semi-empirical self-consistent and environment-dependent model Hamiltonian, which is intended to treat large systems in the order of 10000 atoms. This covers a range of important physical phenomena that are too large to be treated with first-principles calculations. Our model features an aggressive treatment of environment-dependent effects, which are known to limit the accuracy of two-center models which do not include them. Specifically, we account for multi-center integrals, and we use a full iterative treatment of the self-consistency problem, which addressed the important role of charge redistribution. Our results indicate that our treatment is superior to other semi-empirical models that treat environment-dependency in a more phenomenological manner, and either ignore the charge redistribution, or treat it not at equal footing as the environment-dependency. The feasibility of this methodology has been tested for silicon.