Towards Accurate Ab Initio QM/MM Calculations of Free-Energy Profiles of Enzymatic Reactions

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Reliable studies of enzymatic reactions by combined quantum mechanical/molecular mechanics (QM/MM) approaches, with an ab initio description of the quantum region, presents a major challenge to computational chemists. The main problem is the need for a large amount of computer time to evaluate the QM energy, which in turn makes it extremely challenging to perform proper configurational sampling. This work presents major progress toward the evaluation of ab initio QM/MM free-energy surfaces and activation free energies of reactions in enzymes and in solutions. This is done by exploiting our previous idea of using the empirical valence bond (EVB) method as a reference potential and then using the linear response approximation (LRA) approach to evaluate the free energies of transfer from the EVB to the QM/MM surfaces in the reactant and product state. However, the new crucial step involves the use of a constraint at the transition state that fixes the system at a given value of the reaction coordinate and allows us to use the LRA at the transition state. The advance offered by the present approach is particularly significant because it evaluates the free energy associated with both the substrate and the solvent motions. This evaluation appeared to be a relatively simple task once one uses a classical reference potential. The main problem has been using the reference potential for the evaluation of the free-energy contributions associated with the solute motions where the difference between the reference EVB potential and the QM/MM potential can be large. The present refinement finally allows us to overcome the problems with the solute fluctuations and therefore to obtain, for the first time, a free-energy barrier that reflects the solute entropy properly. Thus, we present a way to evaluate the complete QM/MM activation free energy with an equal footing treatment of the solute and the solvent. This provides a general consistent and effective strategy for evaluating the QM/MM activation free energies in proteins and in solution. Our advance allows one to explore consistently various mechanistic and catalytic proposals while using ab initio (ai) QM/MM approaches.