Free-energy differences of OPC-water and SPC/HW-heavy-water models using the Bennett acceptance ratio

Surface tension, vapor density of OPC-water and SPC/HW-heavy-water models have been estimated at low temperatures using the scaled model. The free-energy difference, - $$ , of n-molecules and (n-1)-molecules plus a free probe has been calculated using the Bennett acceptance ratio with the aid of Monte-Carlo simulations. Our results show that the relation between the free-energy difference divided by $$ and the number of molecules to the power minus one-third is linear for $$ . Consequently, the surface tension can be extracted from the straight line slope, whereas the vapor density can be extracted from the intercept, which is proportional to the logarithmic ratio of liquid density to that of vapor density. By scaling the free-energy differences, for at least three different temperatures, to $$ we estimated the critical temperature and hence the surface tension and the vapor density at a wide range of temperatures. The free-energy differences have been calculated at 240K, 260K, and 280K for OPC-water, and at 260K, 280K, and 300K for the SPC/HW-heavy water model.