The entropic contribution to the free energy is notoriously difficult to calculate from molecular dynamics simulations. Here we compare and contrast six methods for obtaining the entropy from a single simulation, using pure water and a pure Lennard-Jones fluid as test systems. Since particle insertion is only applicable for a few small molecule systems, including those studied here, more generally applicable methods are desired. Furthermore, some of these methods were developed before computational resources became powerful enough to adequately evaluate their accuracy and precision. The approaches, which are applicable to systems regardless of the complexity of the constituent molecules, are compared to gold standard values obtained from combining thermodynamic integration and particle insertion. These methods are now re-evaluated using today’s commonly available computational power. The methods investigated here to obtain the entropy include: (1) a cumulant expansion of the energy distribution through fourth order; (2) Berendsen’s Quasi-Gaussian Entropy Theory; (3) an analytic energy distribution function approach; (4) an effective harmonic oscillator approach; (5) a recently suggested single molecule approach; and (6) an entropy expansion in distribution functions through third order. We show that Berendsen’s approach is good to third order. Methods (1), (2), (3), and (5) are difficult to converge due to rare, high-energy configurations. For these methods to work, the complete sampling of highly improbably configurations would be required. We show that this incomplete sampling issue is directly analogous to the known problems with the particle deletion approach. The single molecule approach is problematic for calculating absolute entropies due to a missing cavity term. We argue that the single molecule approach could be useful for calculating the entropy of a solute undergoing conformational changes, but this requires further testing.

Calculating the entropy of fluids from molecular dynamics simulations

2019 Spring National Meeting

The official archive and repository for all ACS Meetings & Expositions abstracts and select posters or presentations.