Adiabatic ET for |GR and imposes the situation of an exclusively extrinsic free of charge energy barrier (i.e., = 0) outside of this variety:G w r (-GR )(6.14a)The same result is obtained within the approach that directly extends the Marcus outer-sphere ET theory, by Diethyl Butanedioate Description expanding E in eq 6.12a to 1st order in the extrinsic asymmetry parameter E for Esufficiently smaller when compared with . Exactly the same outcome as in eq 6.18 is obtained by introducing the following generalization of eq six.17:Ef = bE+ 1 [E11g1(b) + E22g2(1 – b)](6.19)G w r + G+ w p – w r = G+ w p (GR )(six.14b)Therefore, the general treatment of proton and atom transfer reactions of Marcus amounts232 to (a) therapy in the nuclear degrees of freedom 6217-54-5 Data Sheet involved in bond rupture-formation that parallels the one particular leading to eqs six.12a-6.12c and (b) remedy with the remaining nuclear degrees of freedom by a method similar towards the one particular applied to receive eqs 6.7, 6.8a, and six.8b with el 1. Having said that, Marcus also pointed out that the particulars with the treatment in (b) are anticipated to become distinct in the case of weak-overlap ET, exactly where the reaction is expected to happen within a relatively narrow range of the reaction coordinate close to Qt. In fact, in the case of strong-overlap ET or proton/atom transfer, the modifications within the charge distribution are anticipated to happen extra gradually.232 An empirical approach, distinct from eqs six.12a-6.12c, begins using the expression with the AnB (n = 1, 2) bond energy working with the p BEBO method245 as -Vnbnn, exactly where bn will be the bond order, -Vn would be the bond energy when bn = 1, and pn is generally very close to unity. Assuming that the bond order b1 + b2 is unity during the reaction and writing the potential power for formation from 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 particular instances of eq six.19, which can be maintained in a generic type by Marcus. In fact, in ref 232, g1 and g2 are defined as “any function” of b “normalized in order that g(1/2) = 1”. As a specific case, it is noted232 that eq 6.19 yields eq six.12a for g1(b) = g2(b) = 4b(1 – b). Replacing the potential energies in eq six.19 by free energy analogues (an intuitive method that may be corroborated by the truth that forward and reverse price constants satisfy microscopic reversibility232,246) results in the activation free energy for reactions in solutionG(b , w r , …) = w r + bGR + 1 [(G11 – w11)g1(b)(6.20a) + (G2 – w22)g2(1 – b)]The activation barrier is obtained in the worth bt for the degree-of-reaction parameter that offers 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, to get a self-exchange reaction, the activation barrier occurs at b1 = b2 = 1/2 with height Enn = E exchange = Vn(pn – 1) ln two f max (n = 1, two)(six.16)With regards to Enn (n = 1, 2), the energy in the complex formation isEf = b2E= E11b1 ln b1 + E22b2 ln b2 ln(six.17)Right here E= V1 – V2. To compare this strategy together with the one major to eqs six.12a-6.12c, Ef is expressed with regards to the symmetric combination of exchange activation energies appearing in eq 6.13, the ratio E, which measures the extrinsic asymmetry, in addition to a = (E11 – E22)/(E11 + E22), which measures the intrinsic asymmetry. Under conditions of compact intrinsic and extrinsic asymmetry, maximization of Ef with respect to b2, expansion o.