In the present work, we have performed quantum chemical calculations to determine preferable species among the ionic complexes that are present in ambient water due to the autodissociation of water molecule. First, we have formulated the relative population of the hydrated complexes with respect to the bare ion (H(3)O(+) or OH(-)) in terms of the solvation free energies of the relevant molecules. The solvation free energies for various ionic species (H(3)O(+), H(5)O(2) (+), H(7)O(3) (+), H(9)O(4) (+) or OH(-), H(3)O(2) (-), H(5)O(3) (-), H(7)O(4) (-), H(9)O(5) (-)), categorized as proton or hydroxide ion in solution, have been computed by employing the QM/MM-ER method recently developed by combining the quantum mechanical/molecular mechanical (QM/MM) approach with the theory of energy representation (ER). Then, the computed solvation free energies have been used to evaluate the ratio of the populations of the ionic complexes to that of the bare ion (H(3)O(+) or OH(-)). Our results suggest that the Zundel form, i.e., H(5)O(2) (+), is the most preferable in the solution among the cationic species listed above though the Eigen form (H(9)O(4) (+)) is very close to the Zundel complex in the free energy, while the anionic fragment from water molecules mostly takes the form of OH(-). It has also been found that the loss of the translational entropy of water molecules associated with the formation of the complex plays a role in determining the preferable size of the cluster.

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The isoalloxazine ring (flavin ring) is a part of the coenzyme flavin adenine dinucleotide and acts as an active site in the oxidation of a substrate. We have computed the free energy change Deltamicro(red) associated with one-electron reduction of the flavin ring immersed in water by utilizing the quantum mechanical/molecular mechanical method combined with the theory of energy representation (QM/MM-ER method) recently developed. As a novel treatment in implementing the QM/MM-ER method, we have identified the excess charge to be attached on the flavin ring as a solute while the remaining molecules, i.e., flavin ring and surrounding water molecules, are treated as solvent species. Then, the reduction free energy can be decomposed into the contribution Deltamicro(red)(QM) due to the oxidant described quantum chemically and the free energy Deltamicro(red)(MM) due to the water molecules represented by a classical model. By the sum of these contributions, the total reduction free energy Deltamicro(red) has been given as -80.1 kcal/mol. To examine the accuracy and efficiency of this approach, we have also conducted the Deltamicro(red) calculation using the conventional scheme that Deltamicro(red) is constructed from the solvation free energies of the flavin rings at the oxidized and reduced states. The conventional scheme has been implemented with the QM/MM-ER method and the calculated Deltamicro(red) has been estimated as -81.0 kcal/mol, showing excellent agreement with the value given by the new approach. The present approach is efficient, in particular, to compute free energy change for the reaction occurring in a protein since it enables ones to circumvent the numerical problem brought about by subtracting the huge solvation free energies of the proteins in two states before and after the reduction.

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