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Our recent research has especially focused upon electron transfer (ET) reactions, many of them within charge-localized organic mixed valence (MV) compounds that have two charge-bearing units (M) symmetrically attached to a bridge (B) and are at an oxidation level that is an odd number, so the charges on the M groups might be different. An MV radical cation is usefully considered to be M⁺ B M⁰. Such MV compounds are the most revealing electron transfer systems because as Hush pointed out in 1967, a classical analysis of the optical spectrum assuming the two-state model that Marcus used allows determination of both the reorganization energy (ƛ) and electronic coupling (H_ab), which should be all the information needed to calculated the ET rate constant. Our group was the first to measure ET rate constants within MV compounds using ESR, by using bis(hydrazines), such as the radical cations of 1-4, which have an unusually large and tunable ƛ value, allowing study of

systems with large enough H_ab to have accurately analyzable optical spectra. We demonstrated that Hush’s simple method for extracting the ET parameters, with a couple of minor adjustments to improve the accuracy, produces accurate rate constants.7,11 Because the band maximum is ƛ, which is the sum of solvent and internal vibrational components, and ƛ_s increases with solvent polarity for radical cations, the position of the band maximum for MV compounds provides a simple way of assessing the polarity of ionic liquids.¹

We have also intensively studied intermolecular ET in collaboration with Jack Pladziewicz (UW-Eau Claire), who is an expert at stopped-flow kinetics. This work established that the Marcus classical cross rate theory is accurate enough to experimentally determine intrinsic reactivities (barrier for zero driving force ET reactions) for electrochemically reversible 0,+1 couples, including ferrocenes, tetraalkylhydrazines, and heteroatom-substituted unsaturated compounds. (Despite the fact that if the widely used more modern and sophisticated Bixon-Jortner theory were accurate for such reactions, cross rate theory could not work). Combined with the method for calculation of the internal vibrational component of ƛ that we introduced in 1987, we extracted the first convincing set of H_ab values for intermolecular ET reactions.⁸

We have studied MV radical anions in collaboration with J. P. Telo (Technical University of Lisbon), who is an expert at ESR kinetics.^2,3,17 This work has shown that Hush theory works rather well for dinitroaromatic radical anions that have slow enough ET, but breaks down as expected when the barrier to ET gets low enough that “solvent friction” limits the rate constant. Dinitroaromatic radical anions are especially suitable for low barrier studies because their charge-localized and delocalized spectra are distinct enough to recognize when the energy difference between them is so small that both are present in solution, which is not true for most MV compounds. The radical anions from 5-8 have all been shown to become delocalized in low solvent ƛ solvents and localized in high solvent ƛ ones, so that the rate constants can be measured by ESR in properly chosen solvents, although a faster method of measuring would have to be used in very low barrier cases.

We discovered excited state mixed valence (ESMV) in collaboration with Jeff Zink (UCLA), who is an expert at resonance Raman and electronic spectroscopy. In ESMV, the ground state has a single minimum but the electronically excited state is usefully formulated as having Marcus-Hush-type diagrams, as for the charge-delocalized mixed valence systems 9^•+ and 10^•+.6,12,16ESMV does not require radical ions, however, and the

non-MV oxidation levels of disubstituted aromatics in general including neutral 1-3 exhibit ESMV.¹³ Although 9^•+ and 10^•+ have delocalized relaxed excited states because of large excited state electronic couplings, 1-3 have localized relaxed excited states because their excited state couplings are small. The most important thing to come out of ESMV so far has been the realization that because what people have called the MV transition for delocalized MV compounds is not fundamentally related to the transition for charge-localized ones, the transition energy for delocalized MV compounds cannot be equated with 2H_ab, which has been done for decades by both experimentalists and theoreticians. To extract electronic couplings for delocalized MV compounds, the relative energies of at least four MOs are necessary, and they cannot be extracted from the optical spectrum because at least some of the transitions are strongly forbidden and must be too weak to observed. Zink and I developed the neighboring orbital model to allow estimation of H_ab for delocalized MV compounds,⁹ and have applied it to aromatic diamine radical cations.¹⁰ Implementation of the neighboring orbital model requires accurate knowledge of the energy separation between the singly occupied MO of a radical ion and the doubly occupied or virtual MOs involved. Because orbital occupancy changes the energy of an MO by several electron volts, open shell calculations that could possibly get the geometry correctly cannot be used to obtain the MO energies. Our group developed the Koopmans-based methods that artificially fill the SOMO by calculating the radical ion geometry with a different number of electrons, and shown to the astonishment of theoreticians, that the energy gaps calculated for SOMO to virtual orbitals when used with DFT calculations are obtained with about the accuracy of the filled to SOMO transitions (which are what Koopmans theorem addressed and have been used for decades).^5,14,15 This is a real surprise because the energies of the virtual orbitals, which are empty are not optimized during the geometry optimization process, and nobody apparently expected that their energy separations would be worth looking at.

We have also been collaborating with a Chinese theoretician, Yi Zhao, who uses the Zhu-Nakamura tunneling functions (which date from 1994), which are very different from the ones that Bixon-Jortner theory uses (which date from 1932), and with Zink we have shown that the resonance Raman and optical spectra of 4•+ are indeed consistent with the measured rate constant (the optical spectrum was not consistent with Bixon-Jortner theory).⁴

In unpublished work we have made bis(hydrazines) that are charge-delocalized, by lowering ƛ with aryl substituents, so that very fast ET rate constants may be studied, and are also studying a series of bis(p-phenylenediamine)-based paracyclophanes that show unusual properties for their +1 and +2 oxidation levels.