We propose a new effective Monte Carlo (MC) procedure for direct calculation of the free energy in a single MC run. The partition function of the expanded ensemble is introduced including a sum of canonical partition functions with a set of temperatures and additive factors (modification). Random walk in the space of both particle coordinates and temperatures provides calculation of free energy in a wide range of T. The method was applied to a primitive model of electrolyte including the region of low temperatures. In similar way other variants of expanded ensembles are constructed (e.g., over the number of particles N or volume V). Its facilities in quantum statistics (path integral Monte Carlo) and some other applications are also discussed.

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In this work, we have considered the crystallisation behaviour of supercooled water in the presence of surface defects of varying size (surface fraction, α from 1 to 0.5). Ice nucleation on Ag exposed β-AgI (0001 plane) surface is investigated by molecular dynamics simulation at a temperature of 240 K. For systems with α > 0.67, the surface layers crystallise within 150 ns. In the system with defects, we observe two distinct stacking patterns in the layers near the surface and find that systems with AA stacking cause a monotonic decrease in the early nucleation dynamics with an increase in defect size.Where AB stacking (α = 0.833) is observed, the effect of the defect is diminished and the dynamics are similar to the plain AgI surface. This is supported by the variation in the orientational dynamics, hydrogen bond network stability, and tetrahedrality with respect to the defects. We quantify results in terms of the network topology using double-diamond cages (DDCs) and hexagonal cages (HCs). The configurations of the initially formed layers of ice strongly affect the subsequent growth even at long timescales. We assert that the retarded ice growth due to defects can be explained by the relative increase in DDCs with respect to HCs.

The structural properties of the hydrated hydroxide ion are studied in terms of a many-body potential energy function that has been parameterized according to the experimentally determined ͓Arshadi et al., J. Phys. Chem. 74, 1475, 1483 ͑1970͔͒ enthalpy and entropy changes for the first five association reactions of the ion with H 2 O. Clusters in the nϭ1 -15 size range are examined through a canonical Monte Carlo simulation at Tϭ297 K. The resultant structures, irrespective of the cluster size, are predominantly linear of the dendrite type, with the first shell consisting of two water molecules. Minimum energy structures at Tϭ0 K for nϭ2 and 3 compare well with ab initio conformations.

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