a Monte Carlo Simulation of Water Clusters.

A Bennett NVT (constant number, N, volume, V, and temperature, T) Metropolis Monte Carlo method and the Stillinger-Rahman revised central force potentials (RSL2) are used to calculate Helmholtz free energy differences for small n and n-1 rigid molecule clusters at T = 263 K. From the slope and intercept (at n = infty ) of the free energy differences for n = 2, 3, 4, 5, 6, 13, 18, 24, 40, and 60 (plotted versus n ^{2over 3} - (n-1)^{2over 3}) an effective surface tension for the small water clusters and an equilibrium vapor pressure, P_{ rm o}, are extracted. Assuming simple scaled forms for the reduced vapor pressure (ln (P _{rm c}/P_ {rm o}) ~ W_{rm o} (T _{rm c}/T-1)) and for the effective surface tension /kT per surface molecule ( sigma/ (kT_rho_ {rm b}^{2over 3} ) ~ Omega (T_{rm c}/T -1), rho_{rm b} is bulk liquid density) this data gives T_ {rm c} = 650 +/- 10 K and an effective excess surface entropy per surface molecule, Omega ~ 1.7 +/- 0.1. The latter quantity (a fundamental parameter in the scaled formalism for homogeneous and heterogeneous water nucleation) is 13% larger than the experimental bulk liquid value of 1.5. Small cluster density profiles, dipole moment distributions, heat capacity and root mean squared displacements of oxygen atoms are also presented. The small water clusters are shown to be liquid-like at T/T_{rm c} ~ 0.4 and to have "surface" water molecules with average dipole moments oriented parallel to a surface of constant radius. It is suggested that the latter effect increases the excess surface entropy for these potentials and produces the comparatively large value of Omega.