Thermodynamic Properties of Liquid Water: An Application of a Nonparametric Approach to Computing the Entropy of a Neat Fluid

Because of its fundamental importance to molecular biology, great interest has continued to persist in developing novel techniques to efficiently characterize the thermodynamic and structural features of liquid water. A particularly fruitful approach, first applied to liquid water by Lazaridis and Karplus, is to use molecular dynamics or Monte Carlo simulations to collect the required statistics to integrate the inhomogeneous solvation theory equations for the solvation enthalpy and entropy. We here suggest several technical improvements to this approach, which may facilitate faster convergence and greater accuracy. In particular, we devise a nonparametric kth nearest-neighbors (NN)-based approach to estimate the water-water correlation entropy, and we suggest an alternative factorization of the water-water correlation function that appears to more robustly describe the correlation entropy of the neat fluid. It appears that the NN method offers several advantages over the more common histogram-based approaches, including much faster convergence for a given amount of simulation data; an intuitive error bound that may be readily formulated without resorting to block averaging or bootstrapping; and the absence of empirically tuned parameters, which may bias the results in an uncontrolled fashion.