Revisiting Hydrogen Bond Thermodynamics in Molecular Simulations

In processes involving aqueous solutions and in almost every biomolecular interaction, hydrogen bonds play important roles. Though weak compared to the covalent bond, hydrogen bonds modify the stability and conformation of numerous small and large molecules and modulate their intermolecular interactions. We propose a simple methodology for extracting hydrogen bond strength from atomistic level simulations. The free energy associated with hydrogen bond formation is conveniently calculated as the reversible work required to reshape a completely random pair probability distribution reference state into the one found in simulations where hydrogen bonds are formed. Requiring only the probability density distribution of donor-acceptor pairs in the first solvation shell of an electronegative atom, the method uniquely defines the free energy, entropy, and enthalpy of the hydrogen bond. The method can be easily extended to molecules other than water and to multiple component mixtures. We demonstrate and apply this methodology to hydrogen bonds that form in molecular dynamics simulations between water molecules in pure water, as well as to bonds formed between different molecules in a binary mixture of a sugar (trehalose) and water. Finally, we comment on how the method should be useful in assessing the role of hydrogen bonds in different molecular mechanisms.