Histogram methods for entropy estimation suffer from two fundamental and related problems. The first problem is that the widths of the histogram bins must be sufficient to capture the underlying probability density function (PDF). Bins that are too large are unable to describe sharply peaked PDFs and will underestimate the entropy. Conversely, bins that are too small require vast amounts of sampling to reach convergence and will otherwise overestimate the entropy. One alternative to this histogram method is to estimate the entropy using the k-nearest neighbors (KNN) algorithm. KNN provides an asymptotically unbiased estimate of the entropy and can deal effectively with sharply peaked PDFs.[1] We are interested in thermodynamic entropy estimation using inhomogeneous fluid solvation theory (IFST), a statistical mechanical method for calculating solvation free energies by quantifying the effect of a solute acting as a perturbation to bulk solvent.[2] The solvation entropy is calculated in terms of translational and orientational ordering of solvent molecules in the solute reference frame (solute-water terms) and translational and orientational ordering of solvent molecules relative to one another (water-water terms). In IFST, the solute-water orientational entropy has generally been estimated by integrating correlation functions using a histogram method and recent work has highlighted the problems with this approach.[3] Here we incorporate a KNN approach to compute solvation free energies for 15 small molecules and nine singly charge ions. To enable this, we study a number of distance metrics for molecular orientations and identify quaternion metrics as superior to those based on the Euler angles. Importantly, it is demonstrated that samples from molecular dynamics simulation must be independent for effective use of the KNN algorithm. This finding impacts any application of the KNN algorithm to time series data. References [1] Hnizdo, V., J. Tan, B.J. Killian, and M.K. Gilson, J. Comput. Chem., 2008. 29 (10): p. 1605-1614.[2] Lazaridis, T., J. Phys. Chem. B, 1998. 102 (18): p. 3531-3541.[3] Huggins, D.J. and M.C. Payne, J. Phys. Chem. B, 2013. 117 (27): p. 8232�8244.

Improved estimations of hydration entropies using the k-nearest neighbours algorithm

248th National Meeting (2014)

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