Polynomial path for the calculation of liquid state free energies from computer simulations tested on liquid water

as well as its range of appli- cability in conjunction with Monte Carlo computer simulations using thermodynamic integration based on Gaussian quadratures. The technique employed is compared with the slow growth method (an other vari- ant of thermodynamic integration), with the perturbation method and with the use of the grand-canonical ensemble. INTRODUCTION AND BACKGROUND The calculation of the free energy, long recognized as a computationally exacting task, is of special importance due to the role of the free energy in determininig chemical equilibria. As reviewed recently, 1 4 free energy simulation techniques are characterized by the path selected that connects the two systems in the configuration space (e.g. the choice of the coupling parameter, vide infra) and by the quantity chosen whose Boltzmann average is related to the free energy — with the exception of calculations in the grand-canonical ensemble where the chemical potential is fixed at the outset. The various choices of the coupling parameter, described in detail in ref. 2, fall into two distinct classes