The surface tension of water: A Monte Carlo calculation using an umbrella sampling algorithm

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Abstract
In this paper we describe a Monte Carlo calculation of the surface tension of water at 25 °C. The procedure used involves computing the free energy required to create a surface in a system of 256 water molecules with periodic boundary conditions imposed. In order to optimize computing time we have used a modified version of an umbrella sampling algorithm suggested by Torrie and Valleau. The excess surface free energy is computed in a series of steps, the most important of which consist of incremental calculations in which the interface is gradually created. Our final result is γ=97±6 dynes/cm, larger than the experimental value of 72 dyn/cm. Reasons for the rather large difference are discussed. Our result can be used as a basis for comparison of the surface tension of water/air interfaces with the surface tension of other aqueous interfaces calculated using the same technique.