Seminal insights provided by the iconic R. S. Mulliken and his "charge-transfer" theory, H. Taube and his "outer/inner-sphere" mechanisms, R. A. Marcus and his "two-state non-adiabatic" theory, and N. S. Hush and his "intervalence" theory are each separately woven into the rich panoramic tapestry constituting chemical research into electron-transfer dynamics, and its mechanistic dominance for the past half century and more. In this Account, we illustrate how the simultaneous melding of all four key concepts allows sharp focus on the charge-transfer character of the critical encounter complex to evoke the latent facet of traditional electron-transfer mechanisms. To this end, we exploit the intervalence (electronic) transition that invariably accompanies the diffusive encounter of electron-rich organic donors (D) with electron-poor acceptors (A) as the experimental harbinger of the collision complex, which is then actually isolated and X-ray crystallographically established as loosely bound pi-stacked pairs of various aromatic and olefinic donor/acceptor dyads with uniform interplanar separations of r(DA) = 3.1 +/- 0.2 A. These X-ray structures, together with the spectral measurements of their intervalence transitions, lead to the pair of important electron-transfer parameters, H(DA) (electronic coupling element) versus lambdaT (reorganization energy), the ratio of which generally defines the odd-electron mobility within such an encounter complex in terms of the resonance stabilization of the donor/acceptor assembly [D, A] as opposed to the reorganization-energy penalty required for its interconversion to the electron-transfer state [D(+*), A(-*)]. We recognize the resonance-stabilization energy relative to the intrinsic activation barrier as the mechanistic binding factor, Q = 2H(DA)/lambdaT, to represent the quantitative measure of the highly variable continuum of inner-sphere/outer-sphere interactions that are possible within various types of precursor complexes. First, Q << 1 identifies one extreme mechanism owing to slow electron-transfer rates that result from the dominance of the intrinsic activation barrier (lambdaT) between the encounter and successor complexes. At the other extreme of Q > or = 1, the overwhelming dominance of the resonance stabilization (H(DA)) predicts the odd-electron mobility between the donor and acceptor to occur without an activation barrier such that bimolecular electron transfer is coincident with their diffusional encounter. In between lies a potentially infinite set of states, 0 < Q < 1 with opposing attractive and destabilizing forces that determine the location of the bound transition states along the reaction coordinate. Three prototypical potential-energy surfaces evolve as a result of progressively increasing the donor/acceptor bindings (H(DA)) extant in the precursor complex (at constant lambdaT). In these cases, the "outer-sphere" mechanism is limited by the weak donor/acceptor coupling that characterizes the now classical Marcus outer-sphere mechanism. Next, the "inner-s...

The high symmetry and stability of phenalenyl systems, both as the planar pi-radical (P*) and as the pi-cation (P+), are desirable characteristics of prototypical aromatic donor/acceptor pairs that encourage their use as (binary) models for the study of intermolecular interactions extant in stacked molecular arrays. Thus, quantitative ESR spectroscopy of the paramagnetic P* identifies its spontaneous self-association to the diamagnetic P2, previously characterized as the stacked pi-dimer by X-ray crystallography. Likewise, the rapid cross-association of P* with the closed-shell P+ leads to the stacked pi-dimer cation P2*+ with the "doubled" ESR spectrum diagnostic of complete (odd) electron delocalization. These pi-associations are confirmed by UV-vis studies that reveal diagnostic near-IR bands of both P2 and P2*+-strongly reminiscent of intermolecular charge-transfer absorptions in related aromatic (donor/acceptor) pi-associations. Ab initio molecular-orbital calculations for the pi-dimer P2 predict a binding energy of DeltaED = -11 kcal mol(-1), which is in accord with the experimental enthalpy change of DeltaHD = -9.5 kcal mol(-1) in dichloromethane solution. Most importantly, the calculations reproduce the intermonomer spacings and reveal the delicate interplay of attractive covalent and dispersion forces, balanced against the repulsions between filled orbitals. For comparison, the binding energy in the structurally related cationic pi-pimer P2*+ is calculated to be significantly larger with DeltaEP approximately -20 kcal mol(-1) (gas phase), owing to favorable electrostatic interactions not present in the neutral pi-dimer (which outweigh the partial loss of covalent interactions). As a result, our theoretical formulation can correctly account for the experimental enthalpy change in solution of DeltaHP = -6.5 kcal mol(-1) by the inclusion of differential ionic solvation in the formation of the pi-pimer.

Intense colorations and new charge‐transfer absorption bands are observed upon addition of a halide (Cl−, Br−, I−) to neutral organic π acceptors with electron‐deficient olefinic and aromatic centers. These phenomena results from noncovalent anion–π interactions (shown schematically), which were confirmed by X‐ray crystallography.

Tetrathiafulvalene (TTF) as the prototypical electron donor for solid-state (electronics) applications is converted to the unusual cation-radical salt, TTF+* CB- (where CB- is the non-coordinating closo-dodecamethylcarboranate), for crystallographic and spectral analyses. Near-IR studies establish the spontaneous self-association of TTF+* to form the diamagnetic [TTF+,TTF+] dication and to also undergo the equally rapid cross-association with its parent donor to form the mixed-valence [TTF+*,TTF] cation-radical. The latter, most importantly, represents the first (dyad) member of a series of p-doped tetrathiafulvalene (stacked) arrays, and the thorough scrutiny of its electronic structure with the aid of Mulliken-Hush (two-state) analysis of the diagnostic (intervalence) NIR band reveals Robin-Day Class II behavior. The theoretical consequences of the unique structure of the mixed-valence [TTF+*,TTF] dyad on (a) the electron-transfer mechanism for self-exchange, (b) the molecular-orbital analysis of the Marcus reorganization energy, and (c) the ab initio computation of the coupling element or transfer integral in p-doped (solid-state) arrays are discussed.

Unusual dimers with wide interplanar separations, that is, very long bonds with d(D) approximately 3.05 A, are common to the spontaneous self-association of various organic pi-radicals in solution and in the crystalline solid state, independent of whether they are derived from negatively charged anion radicals of planar electron acceptors (TCNE-*, TCNQ-*, DDQ-*, CA-*), positively charged biphenylene cation-radical (OMB+*), or neutral phenalene radical (PHEN*). All dimeric species are characterized by intense absorption bands in the near-IR region that are diagnostic of the charge-transfer transitions previously identified with intermolecular associations of various electron-donor/acceptor dyads. The extensive delocalizations of a pair of pi-electrons accord with the sizable values of (i) the enthalpies (-Delta H(D)) and entropies (-Delta S(D)) of pi-dimerization measured by quantitative UV-vis/EPR spectroscopies and (ii) the electronic coupling element H(ab) evaluated from the strongly allowed optical transitions, irrespective of whether the diamagnetic dimeric species bear a double-negative charge as in (TCNE)(2)(2-), (TCNQ)(2)(2-), (DDQ)(2)(2-), (CA)(2)(2-) or a double-positive charge as in (OMB)(2)(2+) or are uncharged as in (PHEN)(2). These long-bonded dimers persist in solution as well as in the solid state and suffer only minor perturbations with Delta d(D) < 10% from extra-dimer forces that may be imposed by counterion electrostatics, crystal packing, and so forth. The characteristic optical transitions in such diamagnetic two-electron dimers are shown to be related to those in the corresponding paramagnetic one-electron pimers of the same pi-radicals with their parent acceptor, both in general accord with Mulliken theory.

Intermolecular electron transfer (ET) between the free phenothiazine donor (PH) and its cation radical (PH*+) proceeds via the [1:1] precursor complex (PH)(2)*+ which is transiently observed for the first time by its diagnostic (charge-resonance) absorption band in the near-IR region. Similar intervalence (optical) transitions are also observed in mixed-valence cation radicals with the generic representation: P(br)P*+, in which two phenothiazine redox centers are interlinked by p-phenylene, o-xylylene, and o-phenylene (br) bridges. Mulliken-Hush analysis of the intervalence (charge-resonance) bands afford reliable values of the electronic coupling element H(IV) based on the separation parameters for (P/P*+) centers estimated from some X-ray structures of the intermolecular (PH)(2)*+ and the intramolecular P(br)P*+ systems. The values of H(IV), together with the reorganization energies lambda derived from the intervalence transitions, yield activation barriers DeltaG(ET)() and first-order rate constants k(ET) for electron-transfer based on the Marcus-Hush (two-state) formalism. Such theoretically based values of the intrinsic barrier and ET rate constants agree with the experimental activation barrier (E(a)) and the self-exchange rate constant (k(SE)) independently determined by ESR line broadening measurements. This convergence validates the use of the two-state model to adequately evaluate the critical electronic coupling elements between (P/P*+) redox centers in both (a) intermolecular ET via the precursor complex and (b) intramolecular ET within bridged mixed-valence cation radicals. Important to intermolecular ET mechanism is the intervention of the strongly coupled precursor complex since it leads to electron-transfer rates of self-exchange that are 2 orders of magnitude faster (and activation barrier that is substantially lower) than otherwise predicted solely on the basis of Marcus reorganization energy.

The nature of halogen bonding is examined via experimental and computational characterizations of a series of associates between electrophilic bromocarbons R-Br (R-Br=CBr3F, CBr3NO2, CBr3COCBr3, CBr3CONH2, CBr3CN, etc.) and bromide anions. The [R-Br, Br(-)] complexes show intense absorption bands in the 200-350 nm range which follow the same Mulliken correlation as those observed for the charge-transfer associates of bromide anions with common organic π-acceptors. For a wide range of the associates, intermolecular R-Br···Br(-) separations decrease and intramolecular C-Br bond lengths increase proportionally to the Br(-)→R-Br charge transfer; and the energies of R-Br···Br(-) bonds are correlated with the linear combination of orbital (charge-transfer) and electrostatic interactions. On the whole, spectral, structural and thermodynamic characteristics of the [R-Br, Br(-)] complexes indicate that besides electrostatics, the orbital (charge-transfer) interactions play a vital role in the R-Br···Br(-) halogen bonding. This indicates that in addition to controlling the geometries of supramolecular assemblies, halogen bonding leads to electronic coupling between interacting species, and thus affects reactivity of halogenated molecules, as well as conducting and magnetic properties of their solid-state materials.

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