Coexistence in small inert gas clusters

Origins of phase transitions in small systems

The identification and classification of phases in small systems, e.g., nuclei, social and financial networks, clusters, and biological systems, where the traditional definitions of phase transitions are not applicable, is important to obtain a deeper understanding of the phenomena observed in such systems. Within a simple statistical model, we investigate the validity and applicability of different classification schemes for phase transtions in small systems. We show that the whole complex temperature plane contains necessary information in order to give a distinct classification.

Effect of compression on the global optimization of atomic clusters

Recently, Locatelli and Schoen proposed a transformation of the potential energy that aids the global optimization of Lennard-Jones clusters with nonicosahedral global minima. These cases are particularly difficult to optimize because the potential energy surface has a double funnel topography with the global minimum at the bottom of the narrower funnel. Here we analyze the effect of this type of transformation on the topography of the potential energy surface. The transformation, which physically corresponds to a compression of the cluster, first reduces the number of stationary points on the potential energy surface. Secondly, we show that for a 38-atom cluster with a face-centered-cubic global minimum the transformation causes the potential energy surface to become increasingly dominated by the funnel associated with the global minimum. The transformation has been incorporated in the basin-hopping algorithm using a two-phase approach.

Exact equilibrium statistical mechanics of two particles interacting via Lennard-Jones and Morse potentials

The exact classical statistical phase-space volume is obtained for a finite system consisting of two particles interacting via both Lennard-Jones and Morse potentials and confined in a spherical volume. The case when the center of mass of the system is fixed at the center of the sphere is also considered. It is shown that the microcanonical caloric curve of the system can have properties similar to those of large clusters, and the equation of state of the system can have behavior similar to that of bulk systems. It is also shown that the fixing of the center of mass of the system can appreciably change the properties of the microcanonical caloric curve and the equation of state of the system.

Van der Waals type loop in microcanonical caloric curves of finite systems

The entropy is usually related to the energy density of states. This relation is approximate for the finite systems (clusters) and an exact relation connects the entropy with the phase volume of the system. These relations give the same results only in the thermodynamic limit. We consider the microcanonical caloric curves determined via both the approximate and exact relations. It is proved that if the caloric curve obtained from the exact relation has a van der Waals type loop (or S bend), then the caloric curve obtained from the approximate relation has S-bend, and the reverse statement is not correct. Using properties of the system at low and high energies we have shown that a van der Waals type loop in the caloric curve of the finite system requires a positive value of the second derivative of the logarithm of the canonical total energy distribution function at least at one value of the energy. The latter is the weaker necessary condition for S-bend to occur in the caloric curve than that obtained earlier.

Structural relaxation in atomic clusters: master equation dynamics

The role of the potential energy landscape in determining the relaxation dynamics of model clusters is studied using a master equation. Two types of energy landscape are examined: a single funnel, as exemplified by 13-atom Morse clusters, and the double funnel landscape of the 38-atom Lennard-Jones cluster. Interwell rate constants are calculated using Rice-Ramsperger-Kassel-Marcus theory within the harmonic approximation, but anharmonic model partition functions are also considered. Decreasing the range of the potential in the Morse clusters is shown to hinder relaxation toward the global minimum, and this effect is related to the concomitant changes in the energy landscape. The relaxation modes that emerge from the master equation are interpreted and analyzed to extract interfunnel rate constants for the Lennard-Jones cluster. Since this system is too large for a complete characterization of the energy landscape, the conditions under which the master equation can be applied to a limited database are explored. Connections are made to relaxation processes in proteins and structural glasses.

Largest Lyapunov exponent in molecular systems. II: Quaternion coordinates and application to methane clusters

We present a numerical procedure for extracting Lyapunov characteristic exponents from classical molecular-dynamics simulations of molecular systems. The theoretical frame chosen to describe the orientational degrees of freedom is the quaternions scheme. We apply the method to small methane clusters. Two different model potentials are used to investigate the role of internal molecular motion on the nonlinear dynamics, and several parameters are calculated to study the thermodynamics and chaotic dynamics of these clusters. Evidence is found for a solidlike to plasticlike phase transition occurring with the release of the orientational degrees of freedom, at low temperatures below the melting point. The largest Lyapunov exponent increases significantly during this transition, but it exhibits no particular variation during melting.