F Ef about b2 – 1/2 = 0, and truncation to initially order lead toE = Ef max 1 + E4(6.18)The following conclusions are drawn in the Marcus formulation of electron, proton, and atom transfer reactions: (i) When the reaction no cost energy is small adequate in comparison to the reorganization power, eqs six.7, 6.8 apply to each ET and atom transfer, right after inclusion from the relevant degrees of freedom and evaluation of your suitable free of charge energy quantities. (ii) As a consequence of point i, the cross-relation (eqs 6.4-6.six or eqs six.9-6.10) remains intact (in addition, it might also be improved to account for steric and statistical effects232), assisting with all the interpretation of experimental data. Failure with the cross-relation has also been observed and connected towards the Alclometasone manufacturer presence of significant contributions to the activation barrier that happen to be independent from the degree-of-reaction parameter.232 (iii) Marcus’ treatment permits interpretion and quantification of the Br sted slope241 as a measure on the proximity with the activated complicated for the solutions from the reaction,247 which assists with interpreting atom transfer and PCET reaction information. (iv) The cross-relation along with the Br sted coefficient inside the extended Marcus theory allow the investigation of intrinsic reactions barriers and isotopic effects of wide experimental relevance. These 4 points guide the productive application with the extended Marcus theory, which has broad relevance to interpretation of charge transfer data, which Octadecanal supplier includes multiple-site concerted electron-proton transfer reaction information.six.two. Implications from the Extended Marcus Theory: Br sted Slope, Kinetic Isotope Effect, and Cross-RelationFor a homologous set of reactions with roughly equal reorganization energies and function terms,230 the Br sted241 (or the Leffler247) slopedx.doi.org/10.1021/cr4006654 | Chem. Rev. 2014, 114, 3381-Chemical Reviews= G/G= G/GR (6.21)Reviewcorrelates the reaction rate with equilibrium properties of the systems,249 because of the connection involving Gand the equilibrium continual (see section 3 in the Supporting Details). Equation 6.21 is often rewritten in terms of the alterations in G and Ginduced by structural variation:G = G(six.22)which shows how reflects the fraction of alter in the reaction absolutely free energy that’s observable as a modify inside the activation barrier.247,250 Equations 6.20a and 6.20b imply that= bt(6.23)which hyperlinks the Br sted coefficient towards the degree-of-reaction parameter b at Qt, and as a result for the productlike character in the activated complex. In specific, is the order from the bond getting formed according to the BEBO model. In weak-overlap reactions in remedy, will be the contribution on the items to the possible power function that determines the distribution of activated complicated coordinates. In addition, includes a similar which means in strong-overlap ET, proton, and HAT reactions (see ref 232 plus the discussion under). If eq five.29 may be utilized, one particular obtains= GR 1 1 +(six.24)result from very simple application of eq six.24. For example, eq six.24 is inappropriate to describe the deprotonation of substituted nitroalkanes260 or hydride transfer reactions.250 The activation cost-free energies obtained in ref 250 in the extended Marcus theory agree effectively with ab initio values obtained in the MP2261,262 amount of theory. In general, eqs 6.24 and 6.25 are applicable to reaction mechanisms where the totally free energy landscape close to the activated complicated and along a single (or far more) appropriate reaction coordinate(s) could be decomposed int.