Entropy Calculations of Single Molecules by Combining the Rigid-Rotor and Harmonic-Oscillator Approximations with Conformational Entropy Estimations from Molecular Dynamics Simulations

As shown by previous theoretical and computational work, absolute entropies of small molecules that populate different conformers can be predicted accurately on the basis of the partitioning of the intramolecular entropy into vibrational and conformational contributions. Herein, we further elaborate on this idea and propose a protocol for entropy calculations of single molecules that combines the rigid rotor harmonic oscillator (RRHO) entropies with the direct sampling of the molecular conformational space by means of classical molecular dynamics simulations. In this approach, the conformational states are characterized by discretizing the time evolution of internal rotations about single bonds, and subsequently, the mutual information expansion (Mm) is used to approach the full conformational entropy from the converged probability density functions of the individual torsion angles, pairs of torsions, triads, and so on. This RRHO&MIE protocol could have broad applicability, as suggested by our test calculations on systems ranging from hydrocarbon molecules in the gas phase to a polypeptide molecule in aqueous solution. For the hydrocarbon molecules, the ability of the RRHO&MIE protocol to predict absolute entropies is assessed by carefully comparing theoretical and experimental values in the gas phase. For the rest of the test systems, we analyze the advantages and limitations of the RRHO&MIE approach in order to capture high order correlation effects and yield converged conformational entropies within a reasonable simulation time. Altogether, our results suggest that the RRHO&MIE strategy could be useful for estimating absolute and/or relative entropies of single molecules either in the gas phase or in solution.