ABSTRACT During the past decades, the calculation of accurate free-energy differences from molecular simulations has become feasible in practice. In contrast, the reliable estimation of absolute entropies and entropy differences from these simulations is a notoriously difficult problem. This article investigates critically the method to estimate configurational entropies from molecular dynamics simulations based on the quasi-harmonic approximation. The theory, assumptions, and approximations underlying this method are presented, as well as its connection with essential-mode and normal-mode analyses. In particular, the following points are considered: (i) the relationship between quasi-harmonic and essential modes; (ii) the requirement of mass-weighting (or metric-tensor-weighting) in quasi-harmonic analysis; (iii) the effect of anharmonicities in the individual modes on the estimated entropy; (iv) the effect of pairwise (supralinear) correlations among the different modes on the estimated entropy. The analyses are carried out in the context of long (hundreds of nanoseconds) molecular dynamics simulations involving the reversible folding of β-peptides, considering individually the specific properties of the folded and unfolded ensembles. The anharmonicity correction to the quasi-harmonic entropy is small. In contrast, the pairwise (supralinear) correlation correction is large and affects to a larger extent the entropy of the folded state than that of the unfolded state. The proposed procedure to evaluate corrections for anharmonicity and correlation effects allows for an improved calculation of absolute entropies, as well as of entropy differences for molecular systems which undergo conformational transitions.
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