Search

A method for time series analysis of molecular dynamics simulation of a protein is presented. In this approach, wavelet analysis and principal component analysis are combined to decompose the spatio-temporal protein dynamics into contributions from a hierarchy of different time and space scales. Unlike the conventional Fourier-based approaches, the time-localized wavelet basis captures the vibrational energy transfers among the collective motions of proteins. As an illustrative vehicle, we have applied our method to a coarse-grained minimalist protein model. During the folding and unfolding transitions of the protein, vibrational energy transfers between the fast and slow time scales were observed among the large-amplitude collective coordinates while the other small-amplitude motions are regarded as thermal noise. Analysis employing a Gaussian-based measure revealed that the time scales of the energy redistribution in the subspace spanned by such large-amplitude collective coordinates are slow compared to the other small-amplitude coordinates. Future prospects of the method are discussed in detail. [ABSTRACT FROM AUTHOR]

Sets of finite-time Lyapunov exponents characterize the stability and instability of classically chaotic dynamical trajectories. Here we show that their sample distributions can contain subpopulations identifying different types of dynamics. In small isolated molecules these dynamics correspond to distinct elementary motions, such as isomerizations. Exponents are calculated from constant total energy molecular dynamics simulations of H2O and H3O+, modelled with a classical, reactive, all-atom potential. Over a range of total energy, exponent distributions for these systems reveal that phase space exploration is more chaotic near saddles corresponding to isomerization and less chaotic near potential energy minima. This finding contrasts with previous results for Lennard-Jones clusters, and is explained in terms of the potential energy landscape. [ABSTRACT FROM AUTHOR]

We analyze the configurational excitation of a cluster for both a microcanonical and a canonical ensemble of atoms and apply this analysis to the Lennard-Jones cluster of 13 atoms. Dividing the cluster excitations into configurational and thermal classes, we evaluate the anharmonicity coefficient of atomic vibrations and the entropy jump as a function of temperature on the basis of computer simulations of the Lennard-Jones 13-atom cluster as a canonical and a microcanonical ensemble of atoms. This analysis shows the role of anharmonicity of atomic vibrations and exhibits the importance of the temperature dependence of the entropy jump in the range of phase coexistence for cluster thermodynamics. [ABSTRACT FROM AUTHOR]

A simple model system has been used to develop thermodynamics and kinetics for bulk and surface aggregation processes capable of competing with each other. The processes are the stepwise aggregation of monomers in a fluid medium and on an inpenetrable solid surface bounding the fluid medium, besides the adsorption and desorption of the same species at the solid-fluid interface. Emphasis is on aggregation processes in the high friction limit. The theoretical model is used to compare the kinetics and thermodynamics of the processes and to infer the conditions in which one process dominates another, in the high friction limit, such as in a liquid. The motivation of this study is obtaining insight into competition between aggregation in solution and on an adjoining surface, such as a cell membrane. [ABSTRACT FROM AUTHOR]

We derive the energy fluctuation Δ2E, and the time autocorrelation κ(τ) and its Fourier transformation—the fluctuation spectra S(ω)—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. It is also more suitable for analyzing the underlying dynamic, kinetic behavior near the equilibrium and the behavior of the long-time-scale rare events. We utilize our technique to analyze the solid-liquid phase coexistence of the 13-atom Morse cluster and the fcc-to-icosahedral structure transition of the 38-atom Lennard-Jones cluster. For the processes studied, the fluctuation spectra from the master equation simplify the analysis of the transition matrix, and the important relaxation modes are easily extracted. [ABSTRACT FROM AUTHOR]

Recent studies have identified several motifs for potential energy surfaces corresponding to distinct dynamic and thermodynamic properties. The corresponding disconnectivity graphs were identified as “palm tree,” “willow tree,” and “banyan tree” patterns. In the present contribution we present a quantitative analysis of the relation between the topography and dynamics for each of these motifs. For the palm tree and willow tree forms we find that the arrangement of the stationary points in the monotonic sequences with respect to the global minimum is the most important factor in establishing the kinetic properties. However, the results are somewhat different for motifs involving a rough surface with several deep basins (banyan tree motif), with large barriers relative to the energy differences between minima. Here it is the size of the barrier for escape from the region relative to the barriers at the bottom that is most important. The present results may be helpful in distinguishing between the dynamics of “structure seeking” and “glass forming” systems. © 2005 American Institute of Physics. [ABSTRACT FROM AUTHOR]

A molecule undergoing reaction may form a short-lived intermediate. Under certain conditions, the rate at which the reaction proceeds toward the product state via the intermediate may exceed that of a simple, direct path. The competition of two alternative reactive pathways is analyzed here in terms of a stochastic model. The approach allows one to diagnose this competition as a function of the energy of the intermediate relative to the barrier heights of the potential surface and values of the reactive vibrational modes. The result has applications to a variety of problems in chemical physics, ranging from the “lock-and-key” mechanism for the enzymatic activity to control of temporal evolution of complex systems by optimal laser fields. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The glassy state of argon is examined from the standpoint that this state of a system is an ensemble of frozen excited configurations. The basis is experimental data for deposition of an argon stream on a very cold substrate; the measurements provide the dependence of the saturated vapor pressure over this system. The immobile state prepared by such deposition is an amorphous argon, and the activation energy for its transition to the crystalline state is found from a theoretical model. A criterion is established for the minimum cooling rate of liquid rare gases to form the glassy state. An analogous glassy state for clusters is analyzed, and a minimum rate of cooling for its formation is also developed. The glassy state of a bulk system of atoms bound by pair interactions, thermodynamically unstable, relaxes to equilibrium by diffusion of voids to the boundary; the corresponding phase change of a cluster can be thought of at least as easily in terms of diffusion of atoms to sites in its lowest-energy, ordered configuration. A common feature of these small systems is the way their counterparts of the glassy state form from fast cooling of liquid aggregate states to become frozen liquid states. [ABSTRACT FROM AUTHOR]

In this paper, the interbasin motion (IBM) approach is applied to studying dynamics of conformationally constrained peptides, being extended to a nonideal contact of the system with a thermal bath. The coupling of the system with the thermal bath is expressed in terms of a memory function. The aim of the present study is twofold. First, we present a dynamical diagnosis of the three hexapeptide variants with the main focus on the transitions between basins rather than between individual states. Second, the present study is intended to pinpoint a way for extracting useful information about the strength of the system-solvent coupling and how this interaction affects the propensity of relaxation towards the native state. We show that a slight variation of the value of the memory friction parameter may induce a sizable modification of the relaxation time. In addition, the change of the memory friction parameter produces alterations on short time scales among the population distributions. Especially, high energy basins seem affected the most. In the Markovian limit, the basin populations computed within the IBM model are compared to those obtained by using state-to-state transition rates in the full master equation approach. The two methods yield similar results when the separation of time scales between intra- and interbasin dynamics is completely achieved. [ABSTRACT FROM AUTHOR]

We explore the distance fluctuation criterion (“Lindemann criterion”) for melting transitions. Distances from average positions in accord with Lindemann, or interparticle distances, in accord with Jellinek and Berry or Etters and Kaelberer, are examined. The primary goal is to determine which of these offers the more useful criterion. The choice of origin can sometimes effect the significance of the index. We study three systems with two kinds of potentials. They are all composed of 64 particles: (a) and (b), a homopolymer and a cluster that consist of beads interacting pairwise through square-well potentials, and (c) a cluster of particles interacting pairwise through Morse potentials. For each of the noncrystalline structures, in contrast to the crystals originally studied by Lindemann, the fluctuation parameter based on interparticle distances gives a clearer separability of liquid and solid phases than that based on fluctuations from average positions. The solid-like forms of the Morse cluster, the square-well cluster, and the square-well homopolymer have similar behavior, indicating that a broad class of systems can be evaluated with this index. In these systems, relative fluctuation parameters provide a suitable criterion for the melting transition. The critical values for the interparticle distance criterion, which are in the range of 0.03–0.05, are smaller than those for the Lindemann criterion (0.1–0.15). © 2002 American Institute of Physics. [ABSTRACT FROM AUTHOR]

In this report, we present a general prescription for computing the escape rate of the system from a basin with full consideration of the topographical fingerprint of that basin. The method is based on a solution of the reduced Fokker–Planck equation and built up to allow the separation of the inter-basin dynamics from that of the intra-basin motion. The main result is that when local well populations thermalize within a basin, local minima, especially those of higher energy, enhance the escape rate from the basin. Also, numerical analyses lead to the inference that kinetic traps of “wrong” structures are distinctive topographical patterns which may produce kinetic properties similar to those of the primary basin, i.e., that containing the global minimum, but lie in other basins. © 2001 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Two solid structures, a bcc orientationally disordered phase and a strained monoclinic orientationally ordered phase, may coexist for clusters of octahedral molecules. However, this coexistence is more difficult to observe in computer simulations of SF[sub 6] clusters than of TeF[sub 6] clusters although the SF[sub 6] and TeF[sub 6] molecules have the same symmetry. This study finds why this difference occurs. On the potential surface of the (SF[sub 6])[sub 89] cluster the relative energies of most of the linked minima differ only slightly, and the barriers between them are low. An exception is the global minimum, corresponding to a completely orientationally ordered phase. At relevant temperatures, the fraction of the available phase space of the (SF[sub 6])[sub 89] cluster corresponding to a partially ordered structure is smaller than it is for the (TeF[sub 6])[sub 89] cluster. In simulations, the latter readily exhibits coexistence of the ordered and disordered forms due to better separation of the higher-energy local minima and the larger available phase space volume. © 2001 American Institute of Physics. [ABSTRACT FROM AUTHOR]

We recently developed a new method to extract a many-body phase-space dividing surface, across which the transmission coefficient for the classical reaction path is unity. The example of isomerization of a 6-atom Lennard-Jones cluster showed that the action associated with the reaction coordinate is an approximate invariant of motion through the saddle regions, even at moderately high energies, at which most or all the other modes are chaotic [J. Chem. Phys. 105, 10838 (1999); Phys. Chem. Chem. Phys. 1, 1387 (1999)]. In the present article, we propose a new algorithm to analyze local invariances about the transition state of N-particle Hamiltonian systems. The approximate invariants of motion associated with a reaction coordinate in phase space densely distribute in the sea of chaotic modes in the region of the transition state. Using projections of distributions in only two principal coordinates, one can grasp and visualize the stable and unstable invariant manifolds to and from a hyperbolic point of a many-body nonlinear system, like those of the one-dimensional, integrable pendulum. This, in turn, reveals a new type of phase space bottleneck in the region of a transition state that emerges as the total energy increases, which may trap a reacting system in that region. © 2001 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Studies the robustness of master equations based only on statistical samples of the surface topography. Ability of master equations to predict relaxation on the potential energy surface; Databases used to construct statistical sample sets of transition sequences; Comparison of relaxation predictions with those obtained from the master equations.

Discusses the use of a 46-bead protein model for examining principal coordinate analysis and interpreting topographies of complex potential surfaces. Comparison of the effectiveness of several definitions of the comparison variable for revealing information about topographies and protein folding; Changes in the set of interparticle distances that are used definition of the comparison vector.

Reports that a string-of-beads model used previously to describe folding of a polypeptide into a Beta-barrel is transformed into four-strand model of a self-assembling system which also produces a Beta-barrel. Use of molecular dynamics simulations in the study.

Examines the kinetic results of stochastic master equation modeling of relaxation of complete potential energy surfaces (PES) in (KCl)[sub 5] and Ar[sub 9]. Construction of stochastic master equation; Description of the relaxation profiles of (KCl)[sub 5] and Ar[sub 9]; Analysis of PES basin structure.

Investigates the analog in small clusters of structural phase transitions using clusters of octahedral molecules mimicking TeF[sub 6]. Distributions of molecular orientations; Phaselike forms that occur for solid clusters, closed-shell structures and open-shell structures.

A statistically based method of characterizing the topography of a multidimensional potential surface classifies not only local minima and saddles but entire basins containing many minima, and divides separating basins and monotonic sequences of local minima within each basin. The data, so classified, fold readily into the formalisms of chemical kinetic isomerization theory and master equations to provide a connection between that topography and the dynamics on the surface. This analysis, in particular, permits an interpretation of the glass-forming or ‘‘focusing’’ character of the surface. The method is illustrated with a model system derived, with simplifications, from the 19-atom Lennard-Jones cluster. The method also leads naturally to control problems including the determination of optimum conditions for forming glasses or selected structures, such as particular crystal structures or folded protein structures. © 1995 American Institute of Physics. [ABSTRACT FROM AUTHOR]

We have investigated the effect of potential energy saddles on the evolution of chaos in small (three- to seven-atom) inert gas clusters by comparing the local Kolmogorov entropy (K entropy) accumulated near a saddle with that accumulated in a potential well. We find that saddles which are relatively flat along the isomerization coordinate are most effective at reducing the local K entropy in the saddle region, indicating that these saddles tend to regularize the dynamics close to the saddle point. In three- and four-atom clusters, we also find that flat saddles decouple some or all of the cluster’s vibrational modes from one another; this leads to approximately quasiperiodic behavior in some degrees of freedom near the saddle regions of these clusters. [ABSTRACT FROM AUTHOR]

Binary clusters, notably salt clusters with their combination of attractive and repulsive long-range forces, exhibit structural and dynamical behavior different from that of homogeneous clusters. The melting and freezing, nonwetting, and the complexity of the potential surface of (KCl)32 are used to make the comparison. A new method to estimate the density of configurational states is described and applied to the evaluation of thermodynamic properties of (KCl)32. In particular, with this new method we compute for several temperatures the fraction or probability, P([lowercase_phi_synonym],β), of clusters vibrating around a configuration with minimum energy [lowercase_phi_synonym]. The behavior of P([lowercase_phi_synonym],β) with temperature T is indicative of a coexistence of solidlike and liquidlike forms of (KCl)32 for a range of temperatures. The input data required by this new method can be obtained from constant temperature molecular dynamics simulations. [ABSTRACT FROM AUTHOR]

The alkali halide cluster (KCl)32 is demonstrated to be large enough to exhibit ordered and highly disordered structures. The disordered high-energy stable packings of (KCl)32 are identified as amorphous structures. We term the large collection of amorphous (KCl)32 structures the ‘‘microamorphous’’ state, on the basis that they are as disordered as the bulk glass phase. Liquid (KCl)32 was quenched to investigate how fast the cooling rate must be to trap (KCl)32 in one of the high-energy amorphous structures. Even at unrealistically fast cooling rates, (KCl)32 was able to locate its microcrystal structure. A shielded Coulomb interaction potential was used to test whether reducing the range of the pairwise potential would make it possible to prepare amorphous binary clusters. Several different values of the shielding range were tested. These results are discussed in terms of the structure of the underlying potential energy surface. A short study was conducted of the temperature dependence of the time it takes, on average, for supercooled (KCl)32 to relax into the crystalline regions of its potential energy surface. Lastly, we rationalize, in terms of the potential energy surface, the qualitative temperature dependence of the heat capacity for both the first-order and glass transitions. [ABSTRACT FROM AUTHOR]

We have calculated the Kolmogorov entropy for three- and seven-particle clusters bound by Lennard-Jones potentials and for three-particle clusters bound by Morse potentials of various ranges. We have used two quite different methods, one of which is new, which give consistent results. We find that all of these systems are classically chaotic over a wide range of energies surrounding the estimated quantum-mechanical zero point energies. Furthermore, for the three-particle clusters, we can rationalize the variation in the degree of chaos with total energy in terms of the local structure of the clusters’ potential energy surface. [ABSTRACT FROM AUTHOR]

An investigation of melting, freezing, and coexistence phenomena in binary clusters is presented with the salt clusters (KCl)4 and (KCl)5 as specific examples. The results of molecular dynamics simulations are combined with analyses of the potential surfaces, notably the energies and geometries at the minima and saddle points. On the basis of this knowledge, the molecular dynamics results are interpreted in terms of melting, freezing, and phase coexistence, and the ways a nonrigid system may explore its potential surface. A comparison is made of isomerization rates derived from molecular dynamics and Rice–Ramsberger–Kassel–Marcus (RRKM) theory. [ABSTRACT FROM AUTHOR]

By using the pairwise Morse potential as the principle vehicle we have explored the influence of the range of the pair potential on the structure of multidimensional potential-energy surfaces. A scaling relation and a set of reduced units are presented for the homoatomic pairwise-additive Morse potential. The reduced potential has one free parameter, βr0 or ρ0, regulating the range of interaction. Based on several diatomic species, the chemically important range of ρ0 is approximately 2≤ρ0≤7. The number of geometrically distinct minima and transition states depends on ρ0; the larger is ρ0, the narrower is the potential and the greater is the number of geometrically different minima. To illustrate this we found all minima and important low-energy transition states for the Morse six-and seven-particle clusters as functions of ρ0 in its chemically interesting range. From these the dominant mechanisms of isomerization of six- and seven-particle clusters are inferred and compared with experimental and theoretical results for main-group and transition-metal clusters. A nomenclature for saddle points and isomerizations is introduced. The saddle regions of the potentials reveal the dominance of diamond–square–diamond and edge-bridging mechanisms. Knowledge of the stationary points and rearrangement mechanisms allows us to determine the proper molecular symmetry groups and the topologies of the potential-energy surfaces at any arbitrary energy. [ABSTRACT FROM AUTHOR]

An investigation of melting, freezing, and coexistence phenomena is presented for small clusters using Ar7, Ar8, Ar13, and Ar14 as specific representative examples. Combining the results of molecular dynamics simulations, especially short-time kinetic energy averages and quenching, with accurate calculations of the local minima and transition states illuminates the relationship between the potential energy surface and dynamical processes. The results are consistent with a recent general defect theory of melting. [ABSTRACT FROM AUTHOR]

A simple theory for melting, freezing, and phase coexistence is presented with emphasis on the relation between small clusters and spinodal behavior. This theory, coupled with the results of computer simulations, suggests a reinterpretation of spinodals and first-order phase changes. We find sufficient conditions for a system of mutually attracting quasiparticles to exhibit the characteristic ‘‘S-bend’’ found, e.g., for subcritical isotherms of a van der Waals fluid, and discuss how the theory may be extended explicitly to finite clusters. [ABSTRACT FROM AUTHOR]

The successive diagonalization–truncation method is applied to the calculation of the vibrational eigenvalues of the Ar trimer bound by pairwise Lennard-Jones potentials. The statistics of the eigenvalues reveal strongly chaotic behavior of the cluster, consistent with the classical dynamics studies. Moreover, the zero-point energy is higher than the highest energy at which regular dynamics were found classically, indicating that for all energies physically accessible to the cluster, the dynamics are chaotic. [ABSTRACT FROM AUTHOR]

Extensive classical simulations of the melting–freezing transition of small clusters (N=7–33) of rare gas atoms have been performed in which quenching by steepest descent has been coupled to isoergic molecular dynamics. A mechanistic description of the phase change is given in terms of the local potential minima accessed in the transition region and the isomerization pathways for and the frequencies of interwell passages. All of the small clusters, at energies low in the transition range of energy, exhibit some separation (by factors of approximately 5 to 60) of the short time scale for motions about the various potential minima and the longer time scale separating interwell passages. The onset of diffusion is marked by passages over saddles linking the minima. Fully liquid-like behavior is observed for all the clusters when the time scale separation for the motions no longer exists. The coexistence and magic number phenomena observed in previous simulations are explained in terms of the kinds of potential minima on the surface and the accessibility of one from another. The existence of a potential energy minimum very low relative to the nearest accessible, high-lying minima as well as time scale separation are necessary conditions for the observation of the kind of coexistence of liquid-like and solid-like forms over a well-defined energy or temperature range predicted by a quantum statistical model and observed, e.g., in isoergic and isothermal simulations of the Ar13 cluster. Such conditions are met in some but not all clusters. Structures with underlying pentagonal, and especially icosahedral, symmetry are important for clusters in the size range N=7–33, not only in previously recognized cases; defective icosahedral structures occur among the lower-energy minima even for some clusters for which they had not been considered. [ABSTRACT FROM AUTHOR]

We have carried out a molecular dynamics (MD) simulation study of melting of Ar7. By periodically quenching trajectories, we are also able to follow the path of the cluster through configuration space. This procedure yields information about isomerization rates, isomerization dynamics, and the connectivity of the phase space as a function of energy. New criteria for melting and the coexistence of phases in small clusters are compared with the traditional T(E) curves and rms bond fluctuations available from time averages in MD simulations. [ABSTRACT FROM AUTHOR]

Examines the temperature dependence of the coexistence ratios of phaselike forms of atomic clusters of two kinds, a homogeneous cluster bound by pairwise Lennard-Jones forces that simulates argon and a binary, ionic cluster simulating. Isothermal molecular dynamics; Analytical model based on highly simplified densities of states; Phase behavior of alkali halide cluster.

Reports on the power and efficiency limits for internal combustion engines via methods of finite-time thermodynamics. Description of analytical expressions for the upper bounds of power and efficiency of an internal combustion engine; Ways of improving internal combustion engines; Balances of energy and entropy for the engine.

Variational wave functions are constructed for the ground and several low-lying excited states of the alkaline earth atoms Be, Mg, Ca, Sr, and Ba. Effective core potentials are employed to treat these atoms as pseudo-two-electron systems. Conditional probability distributions ρ(r2,θ12|r1=ζ), representing the probability of finding one electron at a distance r2 from the nucleus with interelectronic angle θ12, given that the other electron is at a distance r1 from the nucleus, are plotted for several states of the alkaline earths at various values of ζ. We find that the molecular model which so successfully classifies and describes the collective rotational and vibrational states of doubly excited He carries over well to these ground and low-lying states of the lighter alkaline earths. For the heavier atoms, though the angular correlation remains strong, the application of the molecular model becomes less clear. Some states exhibit behavior intermediate between independent particle-like and collective, and ‘‘interloper states’’ appear which have no immediate interpretation in terms of a single vibrator-rotator model or relationship to the states of doubly-excited helium. [ABSTRACT FROM AUTHOR]

We investigate the structures of clusters bound by the Morse potential by mapping the structure of the global minimum as a function of both cluster size and the range of the pair potential. We consider values of the range parameter appropriate to a loosely bound diatomic molecule (longest), two C60 molecules (shortest), and at regular intervals between these two limits. We have studied all cluster sizes with 25 atoms or less and a selection of sizes containing between 35 and 80 atoms. The effect of decreasing the range of the potential is to destabilize strained structures. For the larger clusters the structure of the global minimum changes from icosahedral to decahedral to face-centered cubic as the range is decreased. We have also investigated the effects of temperature on the equilibrium structure by performing a model calculation for a 75-atom cluster. © 1995 American Institute of Physics. [ABSTRACT FROM AUTHOR]

We present rovibrational energies and transition intensities for H2O calculated at several levels of approximation, beginning with the adiabatic approximation (separating slow bending and rotation from fast stretching modes), then coupling the slow modes with the symmetric stretch, and culminating with the inclusion of all the couplings in the Hamiltonian. Evaluation of each approximation is made by comparing the results of the ab initio spectra to experiment. A space-fixed rovibrational basis set is used for the variational calculations. [ABSTRACT FROM AUTHOR]

Means are presented for using stationary points in two ways. One, for well-understood potentials, elucidates relations between the form of the surface and the dynamics that it supports, including the determination of the effective molecular symmetry group. The other, for potentials of uncertain quality, provides a test for unphysical characteristics and suggests how the surface might be improved if it is found to be unsatisfactory in some respect. Our approach involves comparison of transition state calculations using the slowest slide and Cerjan–Miller algorithms for two example systems: the Lennard-Jones Ar7 cluster and the Handy–Carter many-body-expansion potential for the ground state of formaldehyde. [ABSTRACT FROM AUTHOR]

The Grassberger–Procaccia method has been employed to study the transitions which occur as a classical Ar3 cluster, modeled by pairwise Lennard-Jones potentials, passes from a rigid, solid-like form to a nonrigid, liquid-like form with increasing energy. Power spectra and lower bounds on the fractal dimensions and K entropies are presented at several energies along the caloric curve for the Ar3 cluster. In addition, the full spectrum of Liapunov exponents has been computed at these same energies to get an accurate value of the K entropy. Chaotic behavior, though relatively small, is observed even at low energies where the power spectrum displays largely normal-mode structure. The degree of chaotic behavior increases with energy at energies where some degree of regularity is observed in the spectrum. However, at energies that just allow the system to pass into and across saddle regions separating local potential minima, the phase space appears to be separable into a region within the equilateral triangle potential well where the behavior is highly chaotic, and a region of lower dimensions and less chaos around the saddle of the linear configuration. Dimensions from approximately three to eight are observed. A clear separability of time scales for establishment of different extents of ergodicity permits the determination of fractal dimensions of the manifold on which the phase points moves, for time scales of physical, i.e., observable significance. We believe this to be the first evaluation of the dimensionality of the space on which the phase point moves, for a Hamiltonian system displaying this range of dimensions. [ABSTRACT FROM AUTHOR]

Simulations by constant energy molecular dynamics have been performed for numerous clusters in the size range N=7–33. Detailed investigations have been conducted on the portions of the caloric curves in which the transition between rigid and nonrigid behavior occurs, to study the N dependence of the solid–liquid phase change. Clusters of several sizes display a coexistence of forms, each with a characteristic mean temperature, over a well-defined energy range in the transition region, as had been observed for the Ar13 cluster. Within the coexistence region, the high temperature form is solid-like and the low temperature form behaves in a liquid-like fashion. The caloric curves of state for these clusters take on two-valued forms when averages are calculated for each of the two ‘‘phases’’ separately; the two branches are smooth extensions of the curves from the single phase regions. Clusters of other sizes do not display this clear coexistence of phases, but appear to pass through a ‘‘slush-like’’ state during the melting transition. The coexistence behavior is not a smooth function of N. The clusters Ar13 and Ar19, and to a certain extent Ar7, display high stability properties indicative of magic number behavior. [ABSTRACT FROM AUTHOR]

Microcanonical simulations have shown that Ar13 clusters have sharp but unequal melting and freezing energies. Between these energies, a hot solid-like form and a cooler, liquid-like form coexist in dynamic equilibrium. Monte Carlo and isothermal molecular dynamics simulations confirm that this coexistence behavior persists under canonical conditions as well. Many properties demonstrate the solid and liquid character of the two coexisting ‘‘phases.’’ One previous result seemed to contradict this: Quirke and Sheng evaluated nearest neighbor angular distribution function P(θ); its nonzero value for θ=π/2 at 33 K was interpreted as that of a hot solid in a ‘‘premelting expansion.’’ Actually, that result is the average of a bimodal distribution, one mode for the solid and the other for the liquid. The average shifts smoothly with T, and each form’s P(θ) changes slightly with temperature. The solid has tiny nonzero probability for π/2. The liquid has a minimum probability there, but far above zero. Mean-square displacements and power spectra calculated at 33 K from the Nosé constant temperature molecular dynamics method exhibit properties which are clearly distinguishable and identifiable with two distinct phases, as they are under isoergic conditions. Hence our results can be added to the evidence supporting the picture for finite systems of two phases coexisting over a finite temperature and energy range. [ABSTRACT FROM AUTHOR]