  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.
