Aqueous solutions of ferrous and ferric iron (Fe(2+/3+)) and of the iron-hexacyano complexes [Fe(CN)(6)](4-/3-) are studied by photoelectron spectroscopy using a liquid microjet in conjunction with synchrotron soft X-rays for ionization. For Fe(2+)(aq) we observe two well-resolved peaks at 7.09 and 9.16 eV electron binding energy (BE) that can be assigned to the iron-hexaaquo complex. For Fe(3+)(aq) we observe only one peak above the highest valence band of liquid water, at 10.08 eV BE. Interpreting the spectra in terms of the one-electron levels of Kohn-Sham density functional theory, we find that the two peaks for Fe(2+)(aq) originate from the energy splitting between the highest occupied β (= minority) spin level (Fe d(t(2g))) and the five highest occupied α (= majority) spin levels (Fe d(t(2g)) and d(e(g))). The peak for Fe(3+)(aq) arises from d-levels that are strongly mixed with the solvent. The spectra of the aqueous hexacyano complexes show a single strong peak at 6.11 and 7.52 eV BE for [Fe(CN)(6)](4-) and [Fe(CN)(6)](3-), respectively, originating from the highest occupied Fe d(t(2g)) levels, and two further peaks at higher BE originating from the cyano ligands. The PE spectra of the reduced aquo and cyano ions are then used to obtain-solely on experimental grounds-values for the reorganization free energy of the oxidized ions. DFT/continuum calculations of this important parameter in the Marcus theory of oxidation reactions are in fairly good agreement with experiment.

In this article, two new approaches are introduced which describe redox reactions through descriptors defined within the field of conceptual density functional theory (DFT). One approach starts with the grand canonical ensemble DFT from which a formula is derived for the chemical potential of the electrode in terms of intrinsic properties of oxidized and reduced states of the electroactive species. Second, starting from a Born-Haber scheme, the redox potential is solely expressed in terms of the vertical electron affinity and ionization potential of oxidized and reduced species, respectively. A large collection of 44 organic and inorganic systems are studied in different solvents including implicit and explicit solvation models. Both strategies seem well capable of reproducing experimental values of redox potentials.

Conceptual DFT aims at describing the properties of molecules in interactions by using chemical reactivity descriptors. Herein, the redox behaviour of a given species, as quantified by the redox potential, is linked to DFT-based descriptors. We made use of a hierarchical decomposition of the corresponding half-reactions into one-electron reduction, protonation, dissociation and water-forming or dissociation reactions. Most of these reactions can be readily described through reactivity descriptors, such as the electrophilicity, nucleofugality and electrofugality, as defined in conceptual DFT. The final expression linking the corresponding free energy changes to the redox potential seems to give correct predictions for the redox potentials of bromo, chloro and nitro oxo acids in the gas phase, as in a polarised continuum model.

Energy-resolved photoemission spectroscopy and density functional molecular dynamics simulations are combined to construct an energy level diagram for the Mn(2+/3+) redox reaction in aqueous solution. Two peaks centered at 8.88 and 10.26 eV electron binding energies can be assigned to the Mn2+ hexa-aquo complex with a peak area ratio of 2:2.83. Using the notation of crystal field theory, the peak at lower energies can be interpreted as arising from ionization from the e(g) levels (highest occupied molecular orbital, HOMO), and the peak at higher energies are from ionization of the t(2g) levels. The difference corresponds to the average crystal field splitting, 1.38 eV. From the position of the HOMO level and the absolute redox potential, an experimental value for the reorganization free energy of the aqueous Mn3+ hexa-aquo complex is estimated to be 2.98 eV. Density functional molecular dynamics simulations can reproduce the experimental vertical ionization energy, redox free energy, and reorganization free energies fairly well, provided that the absolute potential shift in periodic boundary conditions, finite size effects, and inaccuracies of the exchange correlation functional are taken into account. Most strikingly, in the simulations, we observe spontaneous and reversible deprotonation of the aqueous Mn3+ hexa-aquo complex to form MnOH(H2O)5(2+) + H+, in line with the low experimental pKa value of this ion. The interconversion between protonation states leads to interesting redox phenomena for aqueous Mn3+, culminating in a bimodal thermal distribution of the electron affinity.