Adiabatic ET for |GR and imposes the situation of an exclusively extrinsic no cost power barrier (i.e., = 0) outside of this range:G w r (-GR )(6.14a)The same result is obtained inside the strategy that straight extends the Marcus outer-sphere ET theory, by expanding E in eq six.12a to first order inside the extrinsic asymmetry parameter E for Esufficiently small compared to . Exactly the same result as in eq six.18 is obtained by introducing the following generalization of eq 6.17:Ef = bE+ 1 [E11g1(b) + E22g2(1 – b)](six.19)G w r + G+ w p – w r = G+ w p (GR )(6.14b)Therefore, the general therapy of proton and atom transfer reactions of Marcus amounts232 to (a) treatment of the nuclear degrees of freedom involved in bond rupture-formation that parallels the 1 top to eqs 6.12a-6.12c and (b) treatment of the remaining nuclear degrees of freedom by a system comparable for the one particular utilized to receive eqs 6.7, six.8a, and 6.8b with el 1. Even so, Marcus also pointed out that the particulars from the treatment in (b) are expected to be distinctive from the case of weak-overlap ET, exactly where the reaction is anticipated to take place within a relatively narrow selection of the reaction coordinate close to Qt. In truth, inside the case of strong-overlap ET or proton/atom transfer, the changes in the charge distribution are anticipated to take place much more progressively.232 An empirical approach, distinct from eqs six.12a-6.12c, starts using the expression on the AnB (n = 1, two) bond energy employing the p BEBO method245 as -Vnbnn, where bn will be the bond order, -Vn will be the bond power when bn = 1, and pn is generally quite close to unity. Assuming that the bond order b1 + b2 is unity throughout the reaction and writing the possible power for formation in the complicated from the initial configuration asEf = -V1b1 1 – V2b2 2 + Vp pHere b is often a degree-of-reaction parameter that ranges from zero to unity along the reaction path. The above two models could be derived as unique situations of eq 6.19, that is maintained within a generic kind by Marcus. Actually, in ref 232, g1 and g2 are defined as “any function” of b “normalized to ensure that g(1/2) = 1”. As a unique case, it is noted232 that eq six.19 yields eq 6.12a for g1(b) = g2(b) = 4b(1 – b). Replacing the potential energies in eq six.19 by totally free power analogues (an intuitive approach that’s corroborated by the truth that forward and reverse rate constants satisfy microscopic reversibility232,246) results in the activation free of charge power for reactions in solutionG(b , w r , …) = w r + bGR + 1 [(G11 – w11)g1(b)(six.20a) + (G2 – w22)g2(1 – b)]The activation barrier is obtained at the worth bt for the degree-of-reaction parameter that gives the transition state, defined byG b =b = bt(six.20b)(six.15)the activation energy for atom transfer is obtained as the maximum worth of Ef along the reaction path by setting dEf/db2 = 0. Thus, for any self-exchange reaction, the activation barrier occurs at b1 = b2 = 1/2 with height Enn = E exchange = Vn(pn – 1) ln 2 f max (n = 1, 2)(six.16)With 706782-28-7 Autophagy regards to Enn (n = 1, two), the power of the complex formation isEf = b2E= E11b1 ln b1 + E22b2 ln b2 ln(6.17)Right here E= V1 – V2. To examine this strategy together with the one particular top to eqs 6.12a-6.12c, Ef is expressed when it comes to the symmetric combination of exchange activation energies appearing in eq 6.13, the ratio E, which measures the extrinsic asymmetry, as well as a = (E11 – E22)/(E11 + E22), which measures the intrinsic asymmetry. Beneath situations of compact intrinsic and extrinsic asymmetry, maximization of Ef with respect to b2, expansion o.