The role of bonded energy terms in free energy simulations - Insights from analytical results

A statistical mechanical analysis of the role of bond stretching and angle bending terms, as well as of dummy atoms, in alchemical free energy simulations is presented. It allows one to resolve several ambiguities concerning their treatment from first principles. The relative importance of vibrational, Jacobian factor and potential-of-mean-force-like contributions from bonded energy terms to single and dual free energy differences is compared. Additional conclusions can be drawn for dummy atoms. In particular, it is shown that double free energy differences obtained in thermodynamic cycle calculations can always be made independent of the treatment of dummy atoms. Further, the equivalence of single and dual topology calculations in such applications is demonstrated. The theoretical considerations are accompanied and illustrated by simulation results for the free energy difference of solvation between iso-butane and propane.