The role of bonded terms in free energy simulations. 2. Calculation of their influence on free energy differences of solvation

Calculations of the free energy difference of solvation are used to study the contributions arising from alchemical changes of bond stretching and angle bending energy terms in the force field. The results illustrate the theoretical analysis of such terms given in the companion paper (Boresch, S.; Karplus, M. The Role of Bonded Terms in Free Energy Simulations: 1. Theoretical Analysis. J. Phys. Chem. A 1998, 103, 103(10)). Three model systems are investigated: (a) two one-dimensional harmonic oscillators interacting with a third particle that represents the solvent, (b) the aqueous solvation of two diatomic molecules, and (c) the aqueous solvation of ethane and methanol. In each case, the computations are carried out with both a single topology and a dual topology methodology. A comparison of free energy components of the single and double free energy differences obtained in the calculations makes it possible to identify the three contributions that the theoretical analysis showed were involved, i.e., vibrational pmf-type, and Jacobian factor terms. The verification of the theoretical analysis by illustrative examples provides the basis for addressing the question of whether the so-called self-terms can make significant contributions to double free energy differences. This is accomplished by identifying the effect of coupling of the three contributions from bonded energy terms on a double free energy difference. For the model systems studied, coupling and, hence, self-terms are found to be of little importance. The analysis resolves the ambiguities concerning this issue in the literature.