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Density functional and continuum dielectric theories have been combined to calculate molecular properties such as hydration enthalpies, redox potentials, and absolute pK a values of transition metal cations in solution. The discrete cluster model, which is treated explicitly by density functional theory, includes six waters in the first hydration shell and another twelve waters in the second shell. The solvent reaction field is obtained from a finite-difference solution to the Poisson−Boltzmann equation and is coupled to the nonlocal density functional calculation in a self-consistent way. The calculated hydration enthalpies are 409, 1073, 431, and 1046 kcal/mol for Mn2+, Mn3+, Fe2+, and Fe3+, respectively, comparing fairly well to the experimental measurements of 440, 1087, 465, and 1060 kcal/mol. The calculated redox potentials for the Mn2+/Mn3+ and Fe2+/Fe3+ pairs are 1.59 and 1.06 V, respectively, in good agreement with the experimental values of 1.56 and 0.77 V. The computed absolute pK a values, 14.0, −6.5, 9.0, and −4.0 for Mn2+, Mn3+, Fe2+, and Fe3+, respectively, deviate significantly from the experimental results of 10.6, 0.1, 9.5, and 2.2 but show the proper behavior with changes in oxidation state and metal type. The calculated redox potentials and pK a values appear to converge toward the experimental data with increasing size of the cluster models. For such highly charged cations, the second hydration shell in the cluster model is indispensable, since this buffer shell retains strong hydrogen bonds and electron transfer between the inner and outer shells as well as the solute−solvent dispersion interaction.

An improved approach to the calculation of molecular electronic structures, solvation energies, and pK, values in condensed phases is described. The electronic structure of the solute is described by density functional quantum mechanics, and electrostatic features of environmental effects are modeled through external charge distributions and continuum dielectrics. The reaction potential produced by atom-centered point-charge and dipole fits to the molecular charge distribution is computed via finite-difference solutions to the PoissonBoltzmann equation. The coupling of the reaction potential into the molecular Hamiltonian is achieved through numerical integration, and the entire system is iterated to self-consistency. Sample calculations of solvation energies, solvated dipole moments, and absolute pK, values are provided for a variety of small organic molecules to illustrate applications of the method. This approach should be readily extensible to more complex systems such as proteins because it is straightforward to include counterion effects and multiple dielectric regions in the formulation.

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