Statistical thermodynamics and homogenous nucleation of atomic microclusters

A systematic investigation is carried out of the multiplicity of potential energy minima for up to 13 atoms interacting under central two-body potentials of Lennard-Jones and Morse type. The sets of minima discovered by various growth algorithms are believed to be virtually exhaustive of all possible N-atom isomers for the potentials used, with N 14. These are classified according to the presence of crystallographic or non-crystallograpnic (5-fold) symmetry, and their energy distributions are statistically analyzed. It is shown that non-crystallographic configurations predominate in structures of both greatest and least binding energy. A striking result is the extreme sensitivity of the number of possible stable minima tovariations in the range and softness of the pair potential. Thus, of no fewer than 988 energetically distinct minima for 13 Lennard-Jones (6-12) atoms, only some 36 are supported by the Morse (a = 3) potential. A vibrational analysis is performed for each configuration and the resulting vibrational frequencies are used to construct an approximation to the multi-configuration partition function (MCPF). This partition function is compared with the corresponding single-configuration partition function derived from the most stable cluster (SCPF) . Tnermodynamic properties for monatomic systems of rare gases, based on a rigid rotor/harmonic oscillator (RRHO) approach, are obtained via both single- and multi-configuration partition functions. It is seen that the validity of the single-configuration approximation depends strongly upon the distribution of isomer energies and less strongly upon the number of these isomers. From the computed partition functions equilibrium constants and relative concentrations are estimated, asis the size of the critical nucleus at various pressures. The first five reduced virial coefficients are calculated and a correspondence between the equilibrium constants and Mayer's Cluster Integrals presented. The use of graph theory in the enumeration of geometrically distinct isomers in 3 and higher dimensional spaces is noted, and adjacency matrices for some specific isomers constructed. Inspection of these matrices enables one to determine how compact the corresponding structures are.