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

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.