E. D. Belega

The partition functions and thermodynamic properties of small clusters of rare gas atoms

The partition functions Z(T) for the clusters Arn, Krn, and Xen (n=2, 3, and 4) were calculated with the smoothed density of energy levels ρ(E). The latter was determined in the semiclassical approximation by Monte Carlo integration over the phase space and corrected by the rotational asymptotic for the lowest levels and by the trajectory separation method for the bound states above the dissociation threshold. In the temperature range of 5<T<150 K that is of crucial interest for the cluster formation studies in the supersonic jets, the results have an estimated accuracy of about 5%. The structure of the phase space of tetramer (n=4) clusters and their conformational transition dynamics were studied. The possibility of a link between such transitions and clusters melting is discussed.

A method of calculation of the thermodynamic properties of Ar3

Abstract Calculation of the complete energy spectrum of the quantum system Ar 3 is extremely difficult. The reason is the strong nonlinearity that entangles the modes of internal motion even at the lowest energy levels of the system. One can say that vibrations of the trimer are never small and that its vibrational modes are never normal. For our purposes the exact (pointwise) density of states can be replaced by the smoothed density of states. To decrease the errors, the volume Ω( E ) should be converted into the convolution of two sixfold integrals for energies less than − 1. For energy E >− 1 the conformation can represent a relatively stable trimer or it can eventually turn into a “dimer-monomer at infinity” configuration. To distinguish between these two cases, we studied the evolution of the initial state with time by the three-body trajectories method. The method is applicable to the calculation of thermodynamic properties in the low-temperature region 2 T 〈30 K and to the treatment of chemical equilibrium for trimers of rare gases.

The dynamics of water hexamer isomerization

The dynamics of water hexamer isomerization was analyzed by classic molecular dynamics using TIP4P and TIP5P empirical interaction potentials. Periodic jump transitions between structural isomers occurred as the internal energy of the cluster grew. Structures prevailing over the energy intervals corresponding to the quasi-liquid and quasi-solid cluster phases were determined. The lifetimes of structural isomers were found.

Effective numbers of modes applied to analysis of internal dynamics of weakly bound clusters

The dependence of the volume of the chaotic component in the internal dynamics of triatomic van der Waals clusters on the angular momentum is calculated using the Monte Carlo and molecular dynamics methods. It has been found that this dependence is nonmonotonic and that its functional form varies for different values of the total energy. The effective number of rotational modes was used to clarify why a change in the volume of chaotic component of the phase space happens for certain values of the angular momentum. We conclude that a large fraction of regular trajectories in relation to all trajectories appears only when there is a possibility for the regular motion to perform a rotation different from that for a chaotic motion. When such difference is small, the regular motion disappears. The effective number of rotational modes can be used to estimate the difference in the type of rotation and is a convenient parameter which controls changes in the dynamics of the system.

Melting of the water hexamer

Results are presented for a molecular dynamics simulation of melting of the water hexamer from three-dimensional configurations (the book, cage, and prism isomers). The interactions between water molecules are described using two rigid potentials-TIP4P and TIP5P. The isomer geometry is determined using the connectivity matrix of the H-bond network graph. It is found in a numerical experiment that the Lindemann index, which shows the fluctuations in the length of intermolecular bonds, behaves similarly for all the studied initial isomers of the cluster. The melting of the cluster is found to depend on the interaction potential used in the study. For the cluster’s full energy, regions are identified which can be attributed to the premelting phase, which is dominated by the book isomer for TIP4P and ring isomer for TIP5P. The energy region attributed to the quasi-liquid phase of the cluster is shown to be characterized by isomers with ring and linear structures for both of the potentials.