Thermodynamics of rare-gas cluster cations. Aleš Vítek, Daniel Hrivňák, René Kalus Department of Physics, University of Ostrava, Ostrava, Czech Republic Financial support: the Grant Agency of the Czech Scientific Foundation (grant No. 203/04/2146), the Grant Agency of the Academy of Sciences (grant No. IAA ), Ministry of Education of the Czech Republic (grant No. 1N04125). Prague Ostrava Abstract The subject of our research has been a theoretical study of thermodynamical properties and phase changes in medium-size krypton cluster cations, Kr 12 +, Kr 13 + and Kr 14 +, by means of Monte Carlo simulations. The simulations have been performed for a broad range of cluster temperatures or internal energies. Singly ionized rare gas clusters are heterogeneous systems. The positive charge is located on a small subunit (ionic core), involving 2–4 atoms, surrounded by a cloud of almost neutral atoms. The Kr 13 + cluster is extremely stable due to its closed–shell configuration. To get a deeper insight into the structural changes in Kr n +, it is interesting to focus on Kr 12 + and Kr 14 + as well, in which one atom is respectively absent from or added to the perfect symmetric configuration of Kr Further, smaller clusters Kr Kr 11 + have been probed. This work is an extension of a previous project concerning structural changes in small clusters Kr 3 + and Kr 4 +. The main goal of this project is to obtain a detailed information on thermodynamics of Rg n + to be subsequently used in a proper interpretation of available experimental data. Methods Simulations Constant-energy (MC-NVE) and constant-temperature (MC-NVT) Monte Carlo simulations with zero angular momentum constraint have been performed. The total number of configurations ranges between ×10 5 with sampling period of 50 configurations (to avoid non-physical correlations). Potential energy surface The intra-cluster interactions have been described by extended diatomics-in- molecules methods (DIM) [1] with the inclusion of the spin-orbit coupling (DIM+SO) through a semi-empirical atoms-in-molecules scheme [2] and with the inclusion of three-body polarization forces acting between two induced dipoles (DIM+SO+ID-ID) [3] as well as three-body dispersion forces (DIM+SO+ID-ID+N3) [4]. Ionic diatomic inputs are due to I. Paidarová (J. Heyrovský Institute of Physical Chemistry, Prague) and F. X. Gadéa (IRSAMC, P. Sabatier University, Toulouse) [5], neutral diatomic potential is taken from semiempirical modelling [6]. [1] F. O. Ellison, J. Am. Chem. Soc. 85 (1963), 3540; P. J. Kuntz, J. Valldorf, Z. Phys. D (1987), 8, 195. [2] J. S. Cohen and B. I. Schneider, J. Chem. Phys. 61 (1974) [3] M. Amarouche et al., J. Chem. Phys. 88 (1988) [4] N. L. Doltsinis, J. P. Knowles, F. Y. Naumkin, Mol. Phys. 96 (1999), 749. [5] R. Kalus et al., Chem. Phys. 294 (2003) 141. [6] A. K. Dham, A. R. Allnatt, W. J. Meath, and R. A. Aziz, Mol. Phys. 67 (1989) Conclusions  Various interaction models for Kr n + have been tested in thermodynamical (Monte Carlo) simulations focusing mainly on phase changes in these species. The inclusion of three-body polarization interactions (DIM+SO+ID-ID) weakens the intra cluster bounds and, at the same time, reduces energy gaps between the most stable and first metastable isomers. As a result (consequently), the three-body polarization interactions lower considerably both the melting and evaporation temperatures. On the other hand, the inclusion of three-body dispersion forces is not crucial for the thermodynamical properties of Kr n +.  A very good agreement has been observed between constant energy (NVE) and constant temperature simulations (NVT).  A single structural change has been detected prior to the evaporation. This phase change, clearly seen both on the Lindemann index curve and on the curves visualize the evolution of the ionic core of these clusters (ΔQ and ANCA), involves isomerizations between trimer-core and tetramer-core structures.  The highest melting temperature and the most clearest maximum on the heat capacity curve has been observed for Kr 13 +, surely due to its symmetry configuration. Melting started at temperatures interval, where mean cluster’s internal energy was much higher than energy of local minima on potentional energy surface. Further, it has been proved that the ionic core melts at higher temperatures than the neutral shell.  Monomer evaporation (Kr n + → Kr n-1 + Kr) starts at temperatures, for which cluster mean energies are much higher than the dissociation. Lower evaporation temperature has been observed for constant temperature simulation (NVT). Parameters Lindemann index δ, (or the relative root-mean-square bond length fluctuation) is defined for a system of n particles as follows: where denotes an ensemble average of quantity X, and Rij is the distance between particles (atoms) i and j. A sharp increase in the Lindemann index indicates that a phase change occurs in the system. δ C = lindemann index of core atoms. δ N = lindemann index of neutral atoms. DIST = the average distance of atoms from their center of mass, DISTC = average distance core atoms from ionic centre of mass, DISTN = average distance neutral atoms from neutral centre of mass, DISTNC = average distance between ionic centre of mass and neutral centre of mass. SAA, SAB, SAC are semi-axes of an ellipsoid, which has the same principal inertia momentum as cluster. ΔQ = Q1-Q2+Q3-Q4, where Q1, Q2, Q3, and Q4 are, respectively, the largest, second largest, third largest, and the fourth largest fragmentary charge localized on a single atom. ANCA = average number of atoms in the ionic core of the cluster (Average Number of Core Atoms). Kr 12 + Kr 13 + Kr 14 + Kr Kr 11 +