Ligand Entropy in Gas-Phase, Upon Solvation and Protein Complexation. Fast Estimation with Quasi-Newton Hessian

A method of rapid entropy estimation for small molecules in vacuum, solution, and inside a protein receptor is proposed. We show that the Hessian matrix of second derivatives built by a quasi-Newton optimizer during geometry optimization of a molecule with a classical molecular potential in these three environments can be used to predict vibrational entropies. We also show that a simple analytical solvation model allows for no less accurate entropy estimation of molecules in solution than a physically rigorous but computationally more expensive model based on Poisson's equation. Our work also suggests that scaled particle theory more precisely estimates the hydrophobic part of solvation entropy than the using a simple surface area term.