Quantum Corrections to the Free Energy Difference between Peptides and Proteins Conformers

The calculation of the free energy of conformation is key in understanding the function of biomolecules and has attracted significant interest in recent years. Most current computational approaches evaluate the difference in conformational free energy in the classical limit based on the common "dogma" that only the lowest-frequency modes make a significant contribution to it, i.e. they assume that quantum mechanical corrections are negligible. Here, I show for three biomolecular systems described in the rigid-rotor, harmonic-oscillator approximation that the zero-point energy contribution, although small, is not negligible even at room temperature. I find that a quantum correction arises from the intermediate-frequency vibrational modes and that its magnitude is strongly correlated with the number of atoms in the system. A straightforward, though approximate, way to account for this quantum correction in the calculation of conformational free-energy differences by classical molecular dynamics is presented. The relevance of the quantum correction analyzed in this paper is discussed in the context of conventional force fields for proteins.