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Most methods for estimating configurational entropy from molecular simulationdata yield upper limits except for harmonic systems where they are exact.Problems arise at diffusive systems and the presence of conformationaltransitions. Covariance-based methods, for instance, can considerablyoverestimate entropy when atomic positions change and cause large, butirrelevant spatial variances. Here we propose a method called SpectrallyResolved Estimation (SRE) for entropy, energy and free energy which is based onthe spectral density of vibrations and is inspired by the quasi-harmonic ansatzin solid-state physics. It (a) yields, in contrast with other methods, a lowerlimit of entropy and an upper limit of free energy, is (b) not corrupted bydiffusion, (c) assigns entropic contributions to spectral features and thusreveals the localization and the type of motion underlying these contributions.The spatial extent of conformational transitions has no influence. The methodapplies to systems of finite volume and is exact for harmonic systems. Theexchange of solvent molecules is characteristic of biological macromolecules.Here SRE opens an avenue to the entropy and free energy of partially diffusivesystems like proteins. It also enables studying channels, pumps, and enzymeswhich often contain several internal, functional water molecules that can swapposition. The assignment to particular motions can be done by normal modes orlocal mode analysis including visualization by band-pass filtering. Thus, SREprovides insight into the origin of configurational entropy and is expected tosupport the rational design of molecules from prodrugs up to engineeredproteins. This technical report demonstrates how thermodynamic quantities aregained and analyzed for small molecules by evaluation of spectra computed byquantum mechanical molecular dynamics simulation.

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