R proton localizations inside the reactant and product electronic states bring about their smaller overlap and correspondingly compact vibronic coupling. In other words, V12Sp 1a,2b can even be drastically smaller sized than the thermal power because of the little worth of Sp . That is, PCET occurs inside the vibronically 1a,2b nonadiabatic regime. For extremely substantial reaction totally free energies among 1a and 1b and between 2a and 2b, PESs I and II lessen to parabolas that describe EPT or HAT. Conversely, ifEarly applications and extensions of Marcus theory to proton and atom transfer reactions have been described by Sutin230,231 and by Marcus.232 In truth, Marcus’ Palmitoylcarnitine Metabolic Enzyme/Protease analysis starts with the ET cross-relation inside the weak-coupling limit. Consider the self-exchange weak-overlap ET reactionsOx n + Red n Red n + Ox n (n = 1, 2)(6.1)and also the cross-reactionOx1 + Red two Red1 + Ox(six.2)By assuming the following approximation for the reorganization energy related with all the cross-reaction:232,= 12 = 21 = 11 + 22(six.3)the rate constants knn (n = 1, two) and k12 for eqs six.1 and 6.two are related byk12 (k11k 22K12f12 )1/(six.four)whereK12 = k12 k(six.five)is definitely the equilibrium continuous for the ET cross-reaction. f12 is generally close to unity,7 andln f12 = – (GR two (ln K12)2 = 2kBT four ln(k11k 22/n two)(six.six)Equations six.four and 6.six hold for el 1 and neglect the function terms related with forming the precursor and successor complexes, except that their distinction is often included in thedx.doi.org/10.1021/cr4006654 | Chem. Rev. 2014, 114, 3381-Chemical Testimonials reaction absolutely free energy GR(see ref 7). Indeed, the price constants of your bimolecular reactions in resolution have to be inserted into eq 6.4 for comparison to experiments. These price constants include the function terms wr and wp that are necessary to bring the reactants and solutions to the imply charge donor- acceptor distance inside the activated complicated. In this perspective, the ET cross-reaction rate is7,122,233-G k12 = elZ exp – kBTReview(6.7)In eq 6.7, the energy ratio 244-63-3 web within the exponent is written on a per molecule basis, Z can be a bimolecular collision frequency, plus the activation no cost energy isG = w r + GR 1 +(6.8a)withGR = G+ w p – w r(six.8b)In eq 6.8b, Gis the “standard” absolutely free energy of reaction7,122,236 for separated reactants and items.237,238 Assuming that Z is approximated well by the geometric mean on the homologous frequencies for the self-exchange reactions, Z11 and Z22, and that eq six.three holds, eqs 6.4 and 6.6 are replaced by239 (see also the Supporting Info)k11k 22K12f 1/2 12 k12 el W12 (el)11(el)(six.9a)withwr + wp – w – w 11 22 W12 = exp – kBT(six.9b)andln f12 = – (G+ w p – w r)two 2kBT=1 four ln k11k 22 + Z2(el)11(el)(ln K+wr – wp kBT)applicable to “strong-overlap” reactions such as atom and proton transfers and to strong-overlap ET.232 Extending the Marcus theory for ET amongst weakly interacting redox partners to proton and atom transfer reactions232 requires reconsideration of the assumptions leading to the free of charge energy element within the Marcus rate expression. Mainly Coulombic function is performed to bring reactants together,233 but the principal contribution towards the totally free energy barrier for ET is offered by readjusting bond lengths and angles inside the reactants (i.e., inner-sphere contributions) and by the reorientation of solvent molecules (outer-sphere contribution). The vibrational motion from the ligands along with the dielectric relaxation of your solvent polarization through quite a few degrees of freedom, in the linear response regime, cause the parabolic PFESs.