On the interpretation of the observed linear free energy relationship in phosphate hydrolysis: a thorough computational study of phosphate diester hydrolysis in solution

The hydrolysis of phosphate esters is crucially important to biological systems, being involved in, among other things, signaling, energy transduction, biosynthesis, and the regulation of protein function. Despite this, there are many questions that remain unanswered in this important field, particularly with regard to the preferred mechanism of hydrolysis of phosphate esters, which can proceed through any of multiple pathways that are either associative or dissociative in nature. Previous comparisons of calculated and observed linear free energy relationships (LFERs) for phosphate monoester dianions with different leaving groups showed that the TS character gradually changes from associative to dissociative with the increasing acidity of the leaving group, while reproducing the experimental LFER. Here, we have generated ab initio potential energy surfaces for the hydrolysis of phosphate diesters in solution, with a variety of leaving groups. Once again, the reaction changes from a compact concerted pathway to one that is more expansive in character when the acidity of the leaving group increases. When such systems are examined in solution, it is essential to take into consideration the contribution of solute to the overall activation entropy, which remains a major computational challenge. The popular method of calculating the entropy using a quasi-harmonic approximation appears to markedly overestimate the configurational entropy for systems with multiple occupied energy wells. We introduce an improved restraint release approach for evaluating configurational entropies and apply this approach to our systems. We demonstrate that when this factor is taken into account, it is possible to reproduce the experimental LFER for this system with reasonable accuracy.