| This dissertation is composed of two parts. Part I presents a rigorous, systematic study on developing the non-Hamiltonian statistical phase space principles. Using the classical statistical mechanical theory of non-Hamiltonian systems, it is shown that the invariant phase space measure and the complete set of conservation laws of the dynamical system can be combined with a rigorously correct version of the generalized Liouville equation to produce a well defined expression for the phase space distribution. In particular, the development of a new continuous dynamical approach for generating the canonical ensemble, the Generalized Gaussian Moment Thermostatting (GGMT) method, is discussed.; In part II, principles of ab initio molecular dynamics with Density functional (DFT) based “state-of-art” electronic structure calculations are elaborated. Its implementation using the plane wave expansion of the electronic orbitals is applied to the study of the protonic defects in liquid ammonia. It is shown that satisfactory results for the solvation structure and dynamical properties of the system are obtained. Finally, a simple and well defined real space basis approach, the Discrete Variable Representation (DVR) method is devised in order to enhance the computational efficiency and reduce the overall scaling of electronic structure calculations in comparison to the plane-wave approach. |
