Condensed phase QM/MM simulations utilizing the exchange core functions to describe exchange repulsions at the QM boundary region

In a recent work, we developed a method [H. Takahashi et al., J. Chem. Phys. 143, 084104 (2015)] referred to as exchange-core function (ECF) approach, to compute exchange repulsion E_ex between solute and solvent in the framework of the quantum mechanical (QM)/molecular mechanical (MM) method. The ECF, represented with a Slater function, plays an essential role in determining E_ex on the basis of the overlap model. In the work of Takahashi et al. [J. Chem. Phys. 143, 084104 (2015)], it was demonstrated that our approach is successful in computing the hydrogen bond energies of minimal QM/MM systems including a cationic QM solute. We provide in this paper the extension of the ECF approach to the free energy calculation in condensed phase QM/MM systems by combining the ECF and the QM/MM-ER approach [H. Takahashi et al., J. Chem. Phys. 121, 3989 (2004)]. By virtue of the theory of solutions in energy representation, the free energy contribution δμ_ex from the exchange repulsion was naturally formulated. We found that the ECF approach in combination with QM/MM-ER gives a substantial improvement on the calculation of the hydration free energy of a hydronium ion. This can be attributed to the fact that the ECF reasonably realizes the contraction of the electron density of the cation due to the deficit of an electron.