Abstract

1. Structural changes in rare-gas cluster cations.Aleš Vítek, FrantišekKarlický,René KalusDepartment of Physics, University of Ostrava, Ostrava, Czech RepublicFinancial support: the Grant Agency of the Czech Republic (grants No. 203/02/1204 and 203/04/2146), Ministry of Education of the Czech Republic (grant No. 1N04125). Prague Ostrava Abstract Methods Potential energy surface 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 the most important three-body polarization interactions of the induced dipole – induced dipole type (DIM+SO+ID-ID) [3] have been used. Diatomic inputs are due to I. Paidarová (J. Heyrovský Institute of Physical Chemistry, Prague) [4]. [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) 3230. [3] M. Amarouche et al., J. Chem. Phys. 88 (1988) 1010. [4] R. Kalus et al., Chem. Phys. 294 (2003) 141. Simulations Constant-energy (MC-NVE) and constant-temperature (MC-NVT) Monte Carlo simulations have been performed. Both the zero angular momentum samplings (MC-NVE-J0, MC-NVT-J0) and the non-zero angular momentum samplings (MC-NVE, MC-NVT) have been employed. Total numbers of samples used to calculate averages: 105 (out of 5.106) outside the coexistence region, 106 (2.5 . 105 for Kr13+) (out of 5.107 or 25.106) within the coexistence region. Constant-energy and constant-temperature Monte Carlo simulations have been performed to localize temperature-dependent structural changes in selected krypton cluster cations, Kr3+, Kr4+, and Kr12-14+. The trimer and tetramer cations are used to analyze possible structural changes in the ionic cores of larger KrN+ clusters, the Kr12-14+ cations are included as representatives of these larger clusters to assess the role of solvation effects and to study the phase changes occurring in neutral solvation shells. The intra-cluster interactions of KrN+ are described by means of previously developed models based on the diatomics-in-molecules approach with the inclusion of the spin-orbit coupling and the most important three-body polarization interactions. This work is a part of a broader project concerning structural changes in rare-gas cluster cations. The main motivation of this project is to obtain a detailed information on thermodynamics of Rgn+ to interpret properly available experimental data on these clusters. Lindemann coefficient The Lindemann coefficient, d, (or the 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 coefficient indicates that a phase change occurs in the system. • Ionic core • The following parameters have been calculated to describe the structural • changes occurring in the ionic core of the clusters: • DQ = 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), • CNEI = average number of atoms exchanged between the ionic core and neutral shell of the cluster (Core – Neutral Exchange Index). Caloric curve Kr3+ Kr3+ Kr3+ Kr4+ Kr4+ Kr13+ Kr4+ • Conclusions • similar results are obtained for all the three interaction models employed (DIM, DIM+SO, and DIM+SO+ID-ID), thus, the spin-orbit coupling is not crucial for the thermodynamic properties of the Krn+ clusters; • non-negligible differences can be seen for different sampling methods used (MC-NVT, MC-NVE wit or without J = 0), in particular in disordered, liquid-like region of cluster internal energies; • there seem to be two successive phase changes in the krypton trimer cation, Kr3+, a low-energy phase change and a high-energy one; the former can only be seen on the Lindemann coefficient curve and consists in permutational exchanges of atoms, preserving at the same time the fairly firm structure of the trimer (linear symmetric), i. e. an ordered, solid-like state; the latter involves, unlike, more substantial structural changes, including switches between the trimer-core and dimer-core isomers of the cluster, and yield a strongly disordered, liquid-like state of the cluster; • for the Kr4+ and Kr13+ clusters, phase changes, clearly seen both on the Lindemann coefficient curve and the curves reflecting the evolution of the ionic cores of these clusters (DQ, ANCA, and CNEI), involve isomerizations between trimer-core and tetramer-core isomers and a transition to a liquid-like state of these clusters even at very low clusters internal energies. Kr13+ Kr13+