A quantum chemical approach to the free energy calculations in condensed systems: the QM/MM method combined with the theory of energy representation.

A methodology has been proposed to compute the solvation free energy of a molecule described quantum chemically by means of quantum mechanical/molecular mechanical method combined with the theory of energy representation (QM/MM-ER). The present approximate approach is quite simple to implement and requires much less computational cost as compared with the free energy perturbation or thermodynamic integration. Furthermore, the electron distribution can be treated faithfully as a quantum chemical object, and it is no longer needed to employ the artificial interaction site model, a reduced form of the realistic electron distribution, which is commonly used in the conventional solution theory. The point of the present approach is to employ the QM solute with electron density fixed at its average distribution in order to make the solute-solvent interaction pairwise. Then, the solvation free energy can be computed within the standard framework of the energy representation. The remaining minor contribution originating from the many-body effect inherent in the quantum mechanical description can be evaluated separately within a similar framework if necessary. As a test calculation, the method has been applied to a QM water solute solvated by MM water solvent in ambient and supercritical states. The results of the QM/MM-ER simulations have been in excellent agreement with the experimental values.