Potential energy surface to kinetics and thermodynamics of atomic clusters

We address in this thesis several questions of potential energy surface and its relationship to the kinetics and thermodynamics of atomic clusters.; We have developed the algorithm to explore the minima and transition states exhaustively, as well as the state-to-state reaction pathways. The full PES picture has been constructed for the visualization by disconnectivity graph and is utilized in subsequent master equation study.; We developed the time auto-correlation function analysis for the master equation. We derive the energy fluctuation Delta2 E, the time autocorrelation kappa(&tgr;) and its Fourier transformation - the fluctuation spectra S(o) of the master equation transition matrix. The contribution from each eigenmode of the transition matrix to these fluctuation quantities reveals the relevant importance of the individual mode in the relaxation processes. The time scales associated with these relaxation processes are determined by the corresponding eigenvalues. Unlike traditional time evolution analysis, the autocorrelation function and fluctuation spectra analysis does not involve an arbitrary initial population. We utilize our technique to analyze the solid-liquid phase coexistence of the 13-atom Morse cluster and the structure transition of the 38-atom Lennard-Jones cluster.; Study of the microcanonical heat capacities provides quantitative insights into the solid-liquid phase transition of atomic clusters. Several temperatures derived from the momentum and configuration space information are discussed. We investigated the temperature difference between T O, the temperature derived from density of states O and TG, the temperature derived from cumulative phase volume G, where TO--TG = 0 is a quantitative criterion of the onset of negative heat capacities. We also investigated the temperature differences between the configurational temperature and kinetic temperature derived from the total phase volume which have simpler mathematical forms. Study of the rotation effects on the temperature behavior revealed that for a cluster with non-zero angular momentum kinetic temperatures are moderately higher than the configurational temperatures, and the discrepancy between them can be explained by incorporating rotational energy.