Which can be described in Marcus’ ET theory along with the associated dependence from the activation barrier G for ET around the reorganization (no cost) energy and around the driving force (GRor G. is the intrinsic (inner-sphere plus outer-sphere) activation barrier; namely, it’s the kinetic barrier in the absence of a driving force. 229 G R or G represents the thermodynamic, or extrinsic,232 contribution for the reaction barrier, which can be separated in the impact utilizing the cross-relation of eq 6.four or eq 6.9 as well as the concept on the Br sted slope232,241 (see under). Proton and atom transfer reactions involve bond breaking and creating, and therefore degrees of freedom that essentially contribute to the intrinsic activation barrier. If the majority of the reorganization energy for these reactions arises from nuclear modes not involved in bond rupture or formation, eqs 6.6-6.8 are expected also to describe these reactions.232 In this case, the nuclear degrees of freedom involved in bond rupture- formation give negligible contributions towards the reaction coordinate (as defined, e.g., in refs 168 and 169) along which PFESs are plotted in Marcus theory. Even so, inside the numerous instances where the bond rupture and formation contribute appreciably towards the reaction coordinate,232 the potential (no cost) power landscape on the reaction differs significantly from the standard one particular within the Marcus theory of charge transfer. A major difference between the two cases is effortlessly understood for gasphase atom transfer reactions:A1B + A two ( A1 2) A1 + BA(6.11)w11 + w22 kBT(six.10)In eq 6.10, wnn = wr = wp (n = 1, 2) are the work terms for the nn nn exchange reactions. If (i) these terms are sufficiently modest, or 18550-98-6 Purity cancel, or are incorporated into the respective price constants and (ii) when the electronic transmission coefficients are roughly unity, eqs 6.4 and 6.5 are recovered. The cross-relation in eq 6.four or eq 6.9 was 566203-88-1 Protocol conceived for outer-sphere ET reactions. Nevertheless, following Sutin,230 (i) eq six.four could be applied to adiabatic reactions exactly where the electronic coupling is sufficiently compact to neglect the splitting among the adiabatic absolutely free energy surfaces in computing the activation no cost energy (in this regime, a given redox couple might be expected to behave inside a comparable manner for all ET reactions in which it can be involved230) and (ii) eq 6.four is often applied to match kinetic data for inner-sphere ET reactions with atom transfer.230,231 These conclusions, taken together with encouraging predictions of Br sted slopes for atom and proton transfer reactions,240 and cues from a bond energy-bond order (BEBO) model applied to calculate the activation energies of gas-phase atom transfer reactions, led Marcus to create extensions of eq five.Stretching 1 bond and compressing another results in a prospective energy that, as a function on the reaction coordinate, is initially a continual, experiences a maximum (similar to an Eckart potential242), and ultimately reaches a plateau.232 This considerable difference from the possible landscape of two parabolic wells may also arise for reactions in answer, thus leading for the absence of an inverted free of charge energy effect.243 In these reactions, the Marcus expression for the adiabatic chargetransfer rate demands extension prior to application to proton and atom transfer reactions. For atom transfer reactions in option having a reaction coordinate dominated by bond rupture and formation, the analogue of eqs six.12a-6.12c assumes the validity on the Marcus price expression as employed to describe.