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Free energies for photoelectron emission by aqueous solutions of hexaquo cations (V2+, Cr2+, Fe2+), metal complexes [Fe(CN)4−6, Co(NH3)2+6], and inorganic anions (OH−, Cl−, Br−, I−) are calculated from theory and compared with experimental threshold energies. Good agreement is obtained within the estimated error (±0.2 eV) on emission free energies. The free energy for outer-sphere reorganization is calculated from a continuous medium model. The inner-sphere reorganization energy is obtained from a bond-stretching model for hexaquo cations and metal complexes. A new method is developed for the calculation of the inner-sphere reorganization energies of univalent anions from their free energies of hydration. Reorganization free energies for electron transfer reactions [V2+/3+, Cr2+/3+, Mn2+/3, Fe2+/3+, Fe(CN)4−/3−6 ] calculated from experimental threshold energies and computed outer-sphere reorganization free energies yield activation free energies in agreement with the values obtained from kinetic measurements. Improvements are discussed for the determination of threshold energies by extrapolation.

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The energetics of photoionization in condensed phases includes a significant contribution from nonequilibrium processes arising from dielectric dispersion of the solvent at the prevailing photon energy. The solvent is polarized by the varying electric field caused by the change of ionic valence as a result of photoionization. This ionic field varies in a time interval determined by the frequency of incident radiation. The following contributions from nonequilibrium processes to the energetics of photoionization are calculated for transparent and absorbing solvents: electronic polarization, London dispersion, and Born repulsion energies for a discrete model of coordinated solvent molecules in the inner-sphere solvation shell of anions and cations; electronic polarization of the outer-sphere region for a continuous medium model. The losses resulting from the rapid variation of the ionic field for an absorbing solvent are calculated for the inner- and outer-sphere regions, respectively, from a discrete model and a continuous medium. Damping of the ionic field resulting from solvent absorption is negligible. The theory is applied to aqueous solutions in the 7–10.4 eV range of photon energies by using dielectric data from reflectance spectroscopy of liquid water. Experimental dispersion spectra for photoelectron emission have the shape predicted by theory and display all the extrema at the photon energies of the calculated curves. The very pronounced effect of ionic strength on the balance between inner- and outer-sphere contributions predicted by theory (inner–outer sphere splitting) is fully confirmed by experiment. Dispersion spectra of inorganic ions in the range of each of the two absorption bands of liquid water (maxima at ∼8.2 and 10.0 eV) therefore exhibit a double maximum for normal dispersion and a double minimum for anomalous dispersion (12 extrema between 7.2 and 10.4 eV). Specific effect of the nature of anions is evident above 9.0 eV in inner–outer sphere splitting. The present study provides a way of probing the response of liquids and solutions to the rapidly varying intense ionic field resulting from the process of photoionization.

The effect of dielectric dispersion of the solvent on optical electron transfer is interpreted as a shift ΔGd of the free energy level of the ground state in the photoionization process. The shift ΔGd is derived for transparent and absorbing solvents by application of the Marcus theory of nonequilibrium polarization of a continuous medium. Only the inner-sphere solvation shell contributes significantly to the dispersion correction ΔGd. Application is made to photoelectric emission by solutions. The effect of dispersion on the energetics of emission causes deviation from the expected emission law. The resulting dispersion spectra are obtained for photoelectron emission by 17 inorganic anions in aqueous solution in the 7 to 10 eV range of photon energies. The spectra primarily result from dispersion of the solvent and are not strongly affected by the nature of the photoionized anion. Experimental dispersion spectra agree well with the theoretical spectrum predicted from the real and imaginary dielectric constants obtained from reflectance spectroscopy data of liquid water. Dispersion spectroscopy of optical electron transfer developed in this work provides an experimental probe of the inner-sphere solvation shell.