Estimating configurational entropy and energy of molecular systems from computed spectral density

Abstract

Most methods for estimating configurational entropy from molecular simulation data yield upper limits except for harmonic systems where they are exact. Problems arise at diffusive systems and the presence of conformational transitions. Covariance-based methods, for instance, can considerably overestimate entropy when atomic positions change and cause large, but irrelevant spatial variances. Here we propose a method called Spectrally Resolved Estimation (SRE) for entropy, energy and free energy which is based on the spectral density of vibrations and is inspired by the quasi-harmonic ansatz in solid-state physics. It (a) yields, in contrast with other methods, a lower limit of entropy and an upper limit of free energy, is (b) not corrupted by diffusion, (c) assigns entropic contributions to spectral features and thus reveals the localization and the type of motion underlying these contributions. The spatial extent of conformational transitions has no influence. The method applies to systems of finite volume and is exact for harmonic systems. The exchange of solvent molecules is characteristic of biological macromolecules. Here SRE opens an avenue to the entropy and free energy of partially diffusive systems like proteins. It also enables studying channels, pumps, and enzymes which often contain several internal, functional water molecules that can swap position. The assignment to particular motions can be done by normal modes or local mode analysis including visualization by band-pass filtering. Thus, SRE provides insight into the origin of configurational entropy and is expected to support the rational design of molecules from prodrugs up to engineered proteins. This technical report demonstrates how thermodynamic quantities are gained and analyzed for small molecules by evaluation of spectra computed by quantum mechanical molecular dynamics simulation.