Energetics of Reactions Involving Transition Metal Complexes: Calculation of Relative Electrode Potentials for Cobalt Complexes at Various Ionic Strengths Using Density Functional and Poisson−Boltzmann Methods

Abstract

A combination of nonlocal density functional calculations and the Poisson−Boltzmann method for the evaluation of free energies of hydration has been used to evaluate the electrode potential of [Co(NH3)6]3+ and [Co(en)3]3+ (where en = H2NCH2CH2NH2) using [Co(dien)2]3+ as a reference (where dien = H2NCH2CH2NHCH2CH2NH2). For [Co(en)3]3+, the electrode potential has been calculated to within 61 mV of the experimental value. For [Co(NH3)6]3+, the electrode potential is reproduced to within about 300 mV of experiment. The geometries of the complexes were optimized using the local spin density (LSD) method, with a LSD-optimized double-ζ plus polarization Gaussian basis set. Single-point nonlocal calculations were carried out at the optimized geometry using the Becke and Perdew combination of functionals for exchange and correlation to obtain both the energies and potential-derived charges. The potential-derived charges were used in the Poisson−Boltzmann calculations. The variation of the electrode potential of [Co(en)3]3+ with ionic strength is reproduced well. The suitability of the Poisson−Boltzmann method for treating hydration in these systems is critically assessed in light of the agreement between theory and experiment.