Orbital-free QM/MM simulation combined with a theory of solutions

In a recent study, we developed a kinetic-energy density functional that can be utilized in orbital-free quantum mechanical/molecular mechanical (OF-QM/MM) simulations. The functional includes the nonlocal term constructed from the response function of the reference system of the QM solute. The present work provides a method to combine the OF-QM/MM with a theory of solutions based on the energy representation to compute the solvation free energy of the QM solute in solution. The method is applied to the calculation of the solvation free energy Δμ of a QM water solute in an MM water solvent. It is demonstrated that Δμ is computed as -7.7 kcal/mol, in good agreement with an experimental value of -6.3 kcal/mol. We also develop a theory to map the free energy δμ due to electron density polarization onto the coordinate space of electrons. The free energy density obtained by the free-energy mapping for the QM water clarifies that each hydrogen atom makes a positive contribution (+34.7 kcal/mol) to δμ, and the oxygen atom gives the negative free energy (-71.7 kcal/mol). It is shown that the small polarization free energy -2.4 kcal/mol is generated as a result of the cancellation of these counteracting energies. These analyses are made possible by the OF-QM/MM approach combined with a statistical theory of solutions.