Potential energy landscape based theory and simulations of dynamics and thermodynamics

The dynamics and thermodynamics of a model Lennard-Jones system are studied in terms of the underlying many-body potential energy landscape (PEL) and molecular dynamics (MD) simulations. The PEL is described primarily with the Inherent Structure (IS) formalism, which partitions the landscape into the basins of attraction of the local minima (the IS). Any liquid configuration is then mapped to an IS via steepest descent minimization of the potential energy. With information about the distribution in energy of the IS, the intrabasin vibrational free energy, and their density dependence, any thermodynamic quantity can be calculated. Dynamics are described in terms of IS transitions and the barriers involved therein. A second PEL based approach, that of Instantaneous Normal Modes (INM), associates the unstable normal modes of the liquid with reaction coordinates for diffusion. The diffusion constant is related to the fraction of unstable modes.; It is demonstrated that for supercooled liquids, diffusion can be described as a Markov process; the diffusion constant can be calculated from the rate of IS transitions, and the mean distance between successive IS involved in a transition, up to the mode coupling temperature, Tc. Since IS transitions involve barrier crossing, the microscopic barriers are characterized and their relation to macroscopic diffusion is explored, leading to the identification of entropic transport as the dominant mechanism for diffusion at low temperatures. Conjugate gradient filtering is proposed as a method for obtaining the fraction of unstable modes relevant for diffusion, and the relation of those modes to the diffusion constant is verified.; Thermodynamics in the IS formalism are tested for the first time in a system with complete information on the distribution of IS energies. A new procedure for obtaining the vibrational free energy is proposed and the predictions of the IS formalism are compared to simulations. The equation of state is rewritten in terms of the PEL and modifications to the van der Waals equation are proposed, with expressions for the parameters in terms of PEL properties.; The results presented give new insights into the relevance of the topology of the PEL to dynamics and thermodynamics.