R proton localizations inside the reactant and product electronic states cause their tiny overlap and correspondingly small vibronic coupling. In other words, V12Sp 1a,2b can even be considerably smaller than the thermal energy due to the compact value of Sp . That’s, PCET occurs within the vibronically 1a,2b nonadiabatic regime. For pretty significant reaction free of charge energies among 1a and 1b and between 2a and 2b, PESs I and II decrease to parabolas that describe EPT or HAT. Conversely, ifEarly applications and extensions of Marcus theory to proton and atom transfer reactions had been described by Sutin230,231 and by Marcus.232 In truth, Marcus’ evaluation begins with the ET cross-relation in the weak-coupling limit. Consider the self-exchange weak-overlap ET reactionsOx n + Red n Red n + Ox n (n = 1, 2)(six.1)plus the cross-reactionOx1 + Red 2 Red1 + Ox(6.two)By assuming the following approximation for the reorganization power associated with the cross-reaction:232,= 12 = 21 = 11 + 22(6.three)the rate constants knn (n = 1, two) and k12 for eqs six.1 and six.2 are connected byk12 (k11k 1622848-92-3 web 22K12f12 )1/(6.4)whereK12 = k12 k(six.5)may be the equilibrium constant for the ET cross-reaction. f12 is often close to unity,7 andln f12 = – (GR two (ln K12)two = 2kBT 4 ln(k11k 22/n two)(six.6)Equations six.4 and six.6 hold for el 1 and neglect the 1231929-97-7 In Vitro function terms associated with forming the precursor and successor complexes, except that their difference is usually included in thedx.doi.org/10.1021/cr4006654 | Chem. Rev. 2014, 114, 3381-Chemical Critiques reaction absolutely free energy GR(see ref 7). Certainly, the price constants on the bimolecular reactions in option need to be inserted into eq 6.four for comparison to experiments. These price constants include things like the function terms wr and wp that happen to be necessary to bring the reactants and merchandise towards the imply charge donor- acceptor distance inside the activated complex. Within this viewpoint, the ET cross-reaction rate is7,122,233-G k12 = elZ exp – kBTReview(6.7)In eq 6.7, the energy ratio in the exponent is written on a per molecule basis, Z is a bimolecular collision frequency, and the activation absolutely free energy isG = w r + GR 1 +(six.8a)withGR = G+ w p – w r(6.8b)In eq 6.8b, Gis the “standard” free of charge energy of reaction7,122,236 for separated reactants and merchandise.237,238 Assuming that Z is approximated nicely by the geometric imply on the homologous frequencies for the self-exchange reactions, Z11 and Z22, and that eq 6.3 holds, eqs six.4 and 6.six are replaced by239 (see also the Supporting Facts)k11k 22K12f 1/2 12 k12 el W12 (el)11(el)(6.9a)withwr + wp – w – w 11 22 W12 = exp – kBT(6.9b)andln f12 = – (G+ w p – w r)2 2kBT=1 four ln k11k 22 + Z2(el)11(el)(ln K+wr – wp kBT)applicable to “strong-overlap” reactions including atom and proton transfers and to strong-overlap ET.232 Extending the Marcus theory for ET involving weakly interacting redox partners to proton and atom transfer reactions232 requires reconsideration in the assumptions leading towards the free energy element within the Marcus rate expression. Mainly Coulombic perform is performed to bring reactants with each other,233 but the principal contribution for the free power barrier for ET is provided by readjusting bond lengths and angles in the reactants (i.e., inner-sphere contributions) and by the reorientation of solvent molecules (outer-sphere contribution). The vibrational motion on the ligands plus the dielectric relaxation of your solvent polarization through numerous degrees of freedom, in the linear response regime, cause the parabolic PFESs.