J. Li et al., CALCULATION OF REDOX POTENTIALS AND PK(A) VALUES OF HYDRATED TRANSITION-METAL CATIONS BY A COMBINED DENSITY-FUNCTIONAL AND CONTINUUM DIELECTRIC THEORY, Inorganic chemistry, 35(16), 1996, pp. 4694-4702
Density functional and continuum dielectric theories have been combine
d to calculate molecular properties such as hydration enthalpies, redo
x 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 react
ion 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 enthalp
ies are 409, 1073, 431, and 1046 kcal/mol for Mn2+, Mn3+, Fe2+, and Fe
3+, respectively, comparing fairly well to the experimental measuremen
ts of 440, 1087, 465, and 1060 kcal/mol. The calculated redox potentia
ls for the Mn2+/Mn3+ and Fe2+/Fe3+ pairs are 1.59 and 1.06 V, respecti
vely, 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 M
n2+, Mn3+, Fe2+, and Fe3+, respectively, deviate significantly from th
e 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 calculate
d redox potentials and pK(a) values appear to converge toward the expe
rimental data with increasing size of the cluster models. For such hig
hly charged cations, the second hydration shell in the cluster model i
s indispensable, since this buffer shell retains strong hydrogen bonds
and electron transfer between the inner and outer shells as well as t
he solute-solvent dispersion interaction.