Molecular dynamics at constant temperature and pressure.

approved: enri J.F. Jansen Molecular dynamics is a technique in which the trajectories of a group of particles are calculated as a function of time by integrating the equations of motion. In this thesis we study the use of molecular dynamics for atoms in a crystal. A model is introduced which describes interactions of a physical system with an external heat reservoir in molecular dynamics simulations. This is accomplished by the addition of a "virtual variable" to the Hamiltonian which is used to scale time. Aspects of this model are discussed and examples are presented for a simple system. Similarly, a constant pressure model is introduced in which additional virtual volume variables are added to the Hamiltonian. The volume and shape of the molecular dynamics cell are now free to vary. Simple examples are discussed. Aspects of the computer programs and the algorithms are explained. Particular attention is focused on the methods used to integrate the equations of motion and to calculate Redacted for Privacy the coulomb interactions. Examples of simulations using a zirconium oxide crystal are presented. We study the effects of heat bath and pressure bath simulations, both separately and in combination. Various features of the behavior are investigated with the primary focus on phase changes, numerical errors, and parameters describing the heat and pressure baths. Molecular Dynamics at Constant Temperature and Pressure