Theoretical studies of the energetics and structures of atomic clusters

Decoding the energy landscape: extracting structure, dynamics and thermodynamics

Describing a potential energy surface in terms of local minima and the transition states that connect them provides a conceptual and computational framework for understanding and predicting observable properties. Visualizing the potential energy landscape using disconnectivity graphs supplies a graphical connection between different structure-seeking systems, which can relax efficiently to a particular morphology. Landscapes involving competing morphologies support multiple potential energy funnels, which may exhibit characteristic heat capacity features and relaxation time scales. These connections between the organization of the potential energy landscape and structure, dynamics and thermodynamics are common to all the examples presented, ranging from atomic and molecular clusters to biomolecules and soft and condensed matter. Further connections between motifs in the energy landscape and the interparticle forces can be developed using symmetry considerations and results from catastrophe theory.

Linearized semiclassical initial value time correlation functions using the thermal Gaussian approximation: Applications to condensed phase systems

The linearized approximation to the semiclassical initial value representation (LSC-IVR) has been used together with the thermal Gaussian approximation (TGA) (TGA/LSC-IVR) [J. Liu and W. H. Miller, J. Chem. Phys. 125, 224104 (2006)] to simulate quantum dynamical effects in realistic models of two condensed phase systems. This represents the first study of dynamical properties of the Ne(13) Lennard-Jones cluster in its liquid-solid phase transition region (temperature from 4 to 14 K). Calculation of the force autocorrelation function shows considerable differences from that given by classical mechanics, namely that the cluster is much more mobile (liquidlike) than in the classical case. Liquid para-hydrogen at two thermodynamic state points (25 and 14 K under nearly zero external pressure) has also been studied. The momentum autocorrelation function obtained from the TGA/LSC-IVR approach shows very good agreement with recent accurate path integral Monte Carlo results at 25 K [A. Nakayama and N. Makri, J. Chem. Phys. 125, 024503 (2006)]. The self-diffusion constants calculated by the TGA/LSC-IVR are in reasonable agreement with those from experiment and from other theoretical calculations. These applications demonstrate the TGA/LSC-IVR to be a practical and versatile method for quantum dynamics simulations of condensed phase systems.

A dynamic lattice searching method with constructed core for optimization of large lennard-jones clusters

A variation of the previous dynamic lattice searching (DLS) method, named as DLS with constructed core (DLSc), was proposed for structural optimization of Lennard-Jones (LJ) clusters. In the new method, the starting random structure is generated with an icosahedron or a decahedron as a core. For a cluster with n shells, the atoms in the inner n - 2 shells are set as a fixed core, and the remaining atoms in the outer 2 shells are optimized by DLS. With applications of DLSc to optimization of LJ100-200 and LJ660-670, it was found that all the putative global minima can be obtained by using the DLSc method, and the method was proved to be high efficient compared with the previous DLS, because the searching space is reduced by the use of the fixed core. However, although DLSc is still an unbiased approach for smaller LJ clusters, it turned out to be biased for large ones. Further works are still needed to make it to be a more general method for cluster optimization problem.

Recent developments in the kinetic theory of nucleation

A review of recent progress in the kinetics of nucleation is presented. In the conventional approach to the kinetic theory of nucleation, it is necessary to know the free energy of formation of a new-phase particle as a function of its independent variables at least for near-critical particles. Thus the conventional kinetic theory of nucleation is based on the thermodynamics of the process. The thermodynamics of nucleation can be examined by using various approaches, such as the capillarity approximation, density functional theory, and molecular simulation, each of which has its own advantages and drawbacks. Relatively recently a new approach to the kinetics of nucleation was proposed [Ruckenstein E, Nowakowski B. J Colloid Interface Sci 1990;137:583; Nowakowski B, Ruckenstein E. J Chem Phys 1991;94:8487], which is based on molecular interactions and does not employ the traditional thermodynamics, thus avoiding such a controversial notion as the surface tension of tiny clusters involved in nucleation. In the new kinetic theory the rate of emission of molecules by a new-phase particle is determined with the help of a mean first passage time analysis. This time is calculated by solving the single-molecule master equation for the probability distribution function of a surface layer molecule moving in a potential field created by the rest of the cluster. The new theory was developed for both liquid-to-solid and vapor-to-liquid phase transitions. In the former case the single-molecule master equation is the Fokker-Planck equation in the phase space which can be reduced to the Smoluchowski equation owing to the hierarchy of characteristic time scales. In the latter case, the starting master equation is a Fokker-Planck equation for the probability distribution function of a surface layer molecule with respect to both its energy and phase coordinates. Unlike the case of liquid-to-solid nucleation, this Fokker-Planck equation cannot be reduced to the Smoluchowski equation, but the hierarchy of time scales does allow one to reduce it to the Fokker-Plank equation in the energy space. The new theory provides an equation for the critical radius of a new-phase particle which in the limit of large clusters (low supersaturations) yields the Kelvin equation and hence an expression for the macroscopic surface tension. The theory was illustrated with numerical calculations for a molecular pair interaction potential combining the dispersive attraction with the hard-sphere repulsion. The results for the liquid-to-solid nucleation clearly show that at given supersaturation the nucleation rate depends on the cluster structure (for three cluster structures considered-amorphous, fcc, and icosahedral). For both the liquid-to-solid and vapor-to-liquid nucleation, the predictions of the theory are consistent with the results of classical nucleation theory (CNT) in the limit of large critical clusters (low supersaturations). For small critical clusters the new theory provides higher nucleation rates than CNT. This can be accounted for by the fact that CNT uses the macroscopic interfacial tension which presumably overpredicts the surface tension of small clusters, and hence underpredicts nucleation rates.

Xenon melting curve to 80 GPa and 5p-d hybridization

Measurements made in a laser heated diamond-anvil cell are reported that extend the melting curve of Xe to 80 GPa and 3350 K. The steep lowering of the melting slope (dT/dP) that occurs near 17 GPa and 2750 K results from the hybridization of the 5p-like valence and 5p-like conduction states with the formation of clusters in the liquid having icosahedral short-range order (ISRO).

Simulating the photoelectron spectra of rare-gas clusters

Motivated by the recent experiments of the Swedish group [M. Tchaplyguine, R. R. Marinho, M. Gisselbrecht et al., J. Chem. Phys. 120, 345 (2004)], we simulate the photoelectron spectra of pure xenon and argon clusters. The clusters are modeled using molecular dynamics with Hartree-Fock-dispersion type pair potentials while the spectrum is calculated as the sum of final state energy shifts of the atoms ionized within the cluster relative to the isolated gas phase ion. A self-consistent polarization formalism is used. Since signal electrons must travel through the cluster to reach the detector, we have accounted for the attenuation of the signal intensity by integrating an exponentially decaying scattering expression over the geometry of the cluster. Several different approaches to determining the required electron mean free paths (as a function of electron kinetic energy) are considered. Our simulated spectra are compared to the experimental results.

Entropic effects on the size dependence of cluster structure

We show that the vibrational entropy can play a crucial role in determining the equilibrium structure of clusters by constructing structural phase diagrams showing how the structure depends upon both size and temperature. These phase diagrams are obtained for example rare gas and metal clusters.

Icosahedron-fcc transition size by molecular dynamics simulation of Lennard-Jones clusters at a finite temperature

We studied finite-temperature ensembles of solid clusters produced by cooling liquid droplets either by evaporation or by a thermostat through a molecular dynamics calculation using the Lennard-Jones potential. The ensembles consist of either single or binary component clusters with 25% of the atoms 8% smaller in diameter than the other 75%. These clusters (380 clusters in total) exhibit various structures in the size range of n=160-2200, where n is the number of atoms in a cluster. For increasing size, the clusters show a gradual transition from icosahedral to a variety of structures: decahedral, face centered cubic, a small amount of hexagonal, and some icosahedral structures. They are asymmetrical or faulted. Electron diffraction patterns calculated with average structure factors of clusters after grouping them into several size regions are very similar to those experimentally observed. The size transition is around n=450 for single component clusters whatever the cooling process, evaporation or thermostat. This size is smaller than the experimental transition size estimated for argon clusters formed in a supersonic expansion. The transition size for binary component clusters is around n=600 for evaporative cooling, and larger for thermostatic cooling. The larger transition size found for the binary component clusters is consistent with the large icosahedral Au-Fe and Au-Cu alloy clusters observed experimentally.

COMPUTATIONAL STUDIES OF CLUSTERS:Methods and Results

▪ Abstract  The experimental and computational study of clusters has been an active field of research for over a decade. This review provides an overview of some of the methods that have been developed to study clusters and some of the results that have been obtained. Included are computational approaches to explore the potential energy surface for clusters, methods to extract thermodynamic properties from the potential surface information and approaches to insure simulation studies are performed in an ergodic fashion. The methods have proved to be useful in studying the structural transition from clusters to bulk phases, phase changes in small clusters and the importance of quantum effects. The review ends with a discussion of problems in cluster chemistry and physics that are of interest for future investigations.