Calculations of activation entropies of chemical reactions in solution

The elucidation of the role of entropic effects in enzyme catalysis is a problem of practical and fundamental interest. In order to address this problem it is essential to develop simulation methods capable of evaluating the entropic contribution, (Delta S-double dagger)', of the reacting fragments to the total activation entropy, Delta S-double dagger. In fact, the general ability to evaluate activation entropies of chemical reactions in solution has long been a challenge to computational chemists. The present work develops and examines a method for evaluation of (Delta S-double dagger)' and Delta S-double dagger. This method introduces a thermodynamic cycle that considers the transformation between the reactants state (RS) and the transition state (TS) in two paths. In the first path the reacting fragments are constrained to move along a single reaction coordinate while in the second path they are allowed to move also in the subspace perpendicular to the reaction coordinate. The difference between the activation barriers that correspond to the two paths provides the desired -T(Delta S-double dagger)'. The cycle also involves two steps where a Cartesian restraint that fixes the reacting fragments in the RS and TS is released. The free energies, Delta G''s, associated with these restraint release steps are used to complete the thermodynamic cycle and to provide the actual estimate of (Delta S-double dagger)'. This estimate is optimized by using different initial conditions and by selecting the smallest value of \Delta G'\. The solvent contributions to the activation entropy are evaluated using a newly developed version of the Langevin dipole model. The potential surfaces used in the present work are obtained by the empirical valence bond (EVB) method. This method provides analytical yet reliable potential surfaces that reflect properly the motions of the reacting fragments and the coupling between these motions and the solvent polarization. The analytical representation of the EVE surfaces allows us to perform the extensive sampling necessary in order to obtain converging results. Our method is examined by evaluating the activation entropy for the hydrolysis of formamide in water. It is found that the calculated activation entropies reach convergence in a reasonable computer time and that the agreement between the calculated and observed results is reasonable. This method can be easily implemented in studies of enzymatic reactions and helps in assessing the importance of entropic effects in enzyme catalysis.