Extraction of configurational entropy from molecular simulations via an expansion approximation

Abstract

A method is presented for extracting the configurational entropy of solute molecules from molecular dynamics simulations, in which the entropy is computed as an expansion of multidimensional mutual information terms, which account for correlated motions among the various internal degrees of freedom of the molecule. The mutual information expansion is demonstrated to be equivalent to estimating the full-dimensional configurational probability density function (PDF) using the generalized Kirkwood superposition approximation (GKSA). While the mutual information expansion is derived to the full dimensionality of the molecule, the current application uses a truncated form of the expansion in which all fourth- and higher-order mutual information terms are neglected. Truncation of the mutual information expansion at the $n\text{th}$ order is shown to be equivalent to approximating the full-dimensional PDF using joint PDFs with dimensionality of $n$ or smaller by successive application of the GKSA. The expansion method is used to compute the absolute (classical) configurational entropy in a basis of bond-angle-torsion internal coordinates for several small molecules as well as the change in entropy upon binding for a small host-guest system. Convergence properties of the computed entropy values as a function of simulation time are investigated and comparisons are made with entropy values from the second generation Mining Minima software. These comparisons demonstrate a deviation in $-TS$ of no more than about $2\mathrm{kcal}∕\mathrm{mol}$ for all cases in which convergence has been obtained.