F. Calvo

Quantum partition functions from classical distributions: Application to rare-gas clusters

We investigate the thermodynamic behavior of quantum many-body systems using several methods based on classical calculations. These approaches are compared for the melting of Lennard-Jones (LJ) clusters, where path-integral Monte Carlo (PIMC) results are also available. First, we examine two quasiclassical approaches where the classical potential is replaced by effective potentials accounting for quantum corrections of low order in ℏ. Of the Wigner–Kirkwood and Feynman–Hibbs effective potentials, only the latter is found to be in quantitative agreement with quantum simulations. However, both potentials fail to describe even qualitatively the low-temperature regime, where quantum effects are strong. Our second approach is based on the harmonic superposition approximation, but with explicit quantum oscillators. In its basic form, this approach is in good qualitative agreement with PIMC results, and becomes more accurate at low temperatures. By including anharmonic corrections in the form of temperature-depe...

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.

Entropic effects on the structure of Lennard-Jones clusters

We examine in detail the causes of the structural transitions that occur for those small Lennard-Jones clusters that have a nonicosahedral global minima. Based on the principles learned from these examples, we develop a method to construct structural phase diagrams that show in a coarse-grained manner how the equilibrium structure of large clusters depends on both size and temperature. The method can be augmented to account for anharmonicity and quantum effects. Our results illustrate that the vibrational entropy can play a crucial role in determining the equilibrium structure of a cluster.

Formation and destruction of polycyclic aromatic hydrocarbon clusters in the interstellar medium

Aims. The competition between the formation and destruction of coronene clusters under interstellar conditions is investigated theoretically. Methods. The unimolecular nucleation of neutra! clusters is simulated with an atomic model combining an explicit classical force field and a quantum tight-binding approach. Evaporation rates are calculated in the framework of the phase space theory and are inserted in an infrared emission model and compared with the growth rate constants. Results. It is found that, in interstellar conditions, most collisions lead to cluster growth. The time evolution of small clusters (containing up to 312 carbon atoms) was specifically investigated under the physical conditions of the northern photodissociation region of NGC 7023. These clusters are found to be thermally photoevaporated much faster than they are reformed, thus providing an interpretation for the lowest limit of the interstellar cluster size distribution inferred from observations. The effects of ionizing the clusters and density heterogeneities are also considered. Based on our results, the possibility that PAH clusters could be formed in PDRs is critically discussed.

Quantum anharmonic densities of states using the Wang–Landau method

The Wang-Landau sampling method is adapted to the calculation of quantum densities of states for fully coupled anharmonic systems. The accuracy of the method is illustrated against exact counting for two molecules with separable oscillators, namely, the Zundel complex H(5)O(2) (+) and the Na(11) cluster. Application to the fully coupled naphthalene molecule (C(10)H(8)) reveals significant deviations in the finite temperature thermodynamical properties that are not captured by simple perturbation theory. There are no limitations in the size of the molecules that can be treated with this method.

Sampling along reaction coordinates with the Wang-Landau method

The multiple range random walk algorithm recently proposed by Wang and Landau [2001, Phys. Rev. Lett., 86, 2050] is adapted to the computation of free energy profiles for molecular systems along reaction coordinates. More generally, we show how to extract partial averages in various statistical ensembles without invoking simulations with constraints, biasing potentials or unknown parameters. The method is illustrated on a model 10-dimensional potential energy surface, for which analytical results are obtained. It is then applied to the potential of mean force associated with the dihedral angle of the butane molecule in the gas phase and in carbon tetrachloride solvent. Finally, isomerization in a small rocksalt cluster, (NaF)4, is investigated in the microcanonical ensemble, and the results are compared to those of parallel tempering Monte Carlo.

From molecular clusters to bulk matter. I. Structure and thermodynamics of small CO2, N2, and SF6 clusters

The thermodynamics and structural properties of small molecular XN clusters (X=N2, CO2, and SF6) are investigated using molecular dynamics simulations. In this paper we compare the behavior of carbon dioxide, nitrogen, and sulfur hexafluoride for a given cluster size of N=13. Evidence is provided for “dynamical coexistence” between solidlike and liquidlike forms of the cluster, in a finite energy range, in the case of (CO2)13 and (N2)13 but not (SF6)13. In addition (N2)13 exibits a solid–solid phase transition characterized by the release of the molecular orientational degree of freedom. A systematic use of the dynamic quenching method enables us to interpret these different behaviors in terms of the energy distribution of minima in the potential energy surface of the systems. A comparison of the strain energies of these clusters, using a model recently proposed by Wales and co-workers, enables us to understand why different molecular clusters exhibit different crossover points from icosahedral to bulk pr...

All-exchanges parallel tempering

An alternative exchange strategy for parallel tempering simulations is introduced. Instead of attempting to swap configurations between two randomly chosen but adjacent replicas, the acceptance probabilities of all possible swap moves are calculated a priori. One specific swap move is then selected according to its probability and enforced. The efficiency of the method is illustrated first on the case of two Lennard-Jones (LJ) clusters containing 13 and 31 atoms, respectively. The convergence of the caloric curve is seen to be at least twice as fast as in conventional parallel tempering simulations, especially for the difficult case of LJ31. Further evidence for an improved efficiency is reported on the ergodic measure introduced by Mountain and Thirumalai [J. Phys. Chem. 93, 6975 (1989)], calculated here for LJ13 close to the melting point. Finally, tests on two simple spin systems indicate that the method should be particularly useful when a limited number of replicas are available.

Characterization of anharmonicities on complex potential energy surfaces: Perturbation theory and simulation

We have systematically investigated the effect of anharmonicity on the equilibrium properties of systems with a complex potential energy surface. Anharmonicities are modeled by the temperature dependence of the harmonic frequencies {νi} near a stationary point of the PES. The low-temperature behavior is described by a simple thermal expansion ν(i)(β)=ν0(i)[1−α1(i)/β+α2(i)/2β2+⋯], where the coefficients {αj(i)} are obtained from perturbation theory. Using a simple diagrammatic representation, we give the complete expressions for the first two coefficients α1 and α2 in terms of derivatives of the potential. This approach is illustrated for the example of a bulk Lennard-Jones system of 32 particles, in both the solid and the liquid states. We also determine the anharmonic frequencies from reversible-scaling Monte Carlo simulations, which appear particularly well suited to this problem. As an example, we have studied a model biopolymer that exhibits significant first and second order anharmonicities. To show ...

Configurational density of states from molecular dynamics simulations

Abstract The multiple histogram method has been adapted to treat distributions of potential energies taken from classical molecular dynamics simulations carried out at different total energies. For clusters with a Lennard-Jones pairwise interaction, it is compared to the results of the original method, which was developed for constant temperature Monte Carlo simulations. The same caloric curves are found in both cases. Since the Monte Carlo algorithm is always cheaper, this makes it a method of choice for studying clusters at thermodynamic equilibrium.