Efficient Computational Research Protocol to Survey Free Energy Surface for Solution Chemical Reaction in the QM/MM Framework: The FEG-ER Methodology and Its Application to Isomerization Reaction of Glycine in Aqueous Solution.

In solution chemical reaction, we often need to consider a multidimensional free energy (FE) surface (FES) which is analogous to a Born-Oppenheimer potential energy surface. To survey the FES, an efficient computational research protocol is proposed within the QM/MM framework; (i) we first obtain some stable states (or transition states) involved by optimizing their structures on the FES, in a stepwise fashion, finally using the free energy gradient (FEG) method, and then (ii) we directly obtain the FE differences among any arbitrary states on the FES, efficiently by employing the QM/MM method with energy representation (ER), i.e., the QM/MM-ER method. To validate the calculation accuracy and efficiency, we applied the above FEG-ER methodology to a typical isomerization reaction of glycine in aqueous solution, and reproduced quite satisfactorily the experimental value of the reaction FE. Further, it was found that the structural relaxation of the solute in the QM/MM force field is not negligible to estimate correctly the FES. We believe that the present research protocol should become prevailing as one computational strategy and will play promising and important roles in solution chemistry toward solution reaction ergodography.