Marcus inversion region

In most cases, when the driving force is lower than the reorganization energy, the electron transfer rate increases when the driving force AG0 is increased. There is, however, the so-called Marcus inversion region (—AG0>A), such that the larger the driving force, the lower the electron transfer rate. 

Because of the quadratic dependence, the variation of ln(fcET) versus AG° is expected to be a parabol whose maximum corresponds to AG° = 0 (Figure 4.5). Beyond the maximum (AG° > 0), fcET decreases when AG° increases (normal region), whereas below the maximum (AG° < 0), the inverse behavior is expected (Marcus inverse region). 

The most interesting feature of Expression 2.3 is the quadratic expression for the free energy, which in a Morse potential energy curve for a given reaction leads to the Marcus inversion region. In this case, the quadratic potential energy variation of the initial and final states is responsible for the equation since the Morse curves really approach parabolas. Two quadratic dependencies with the reaction coordinates are then introduced into the Arrhenius expression between the activation energy and the rate constant. 

Confirming the Marcus Inversion Region for Electron Transfer... 

Coriolis coupling (p. 906 and 912) critical points (p. 888) cross section (p. 901) curvature coupling (p. 906 and 914) cycloaddition reaction (p. 944) democratic coordinates (p. 898) diabatic and adiabatic states (p. 949) donating mode (p. 914) early and late reaction barriers (p. 895) electrophilic attack (p. 938) entrance and exit channels (p. 895) exo- and endothermic reactions (p. 909) femtosecond spectroscopy (p. 889) Franck-Condon factors (p. 962) intrinsic reaction coordinate (IRC) (p. 902) inverse Marcus region (p. 954) mass-weighted coordinates (p. 903)... 

MO and AD pictures (p. 805) reaction stages (p. 806) role of states DA, D+A , D+A (p. 811) HOMO-LUMO crossing (p. 815) nucleophilic attack (p. 816) electrophilic attack (p. 818) cycloaddition reaction (p. 823) Woodward-Hoffmann rules (p. 825) Diels-Alder reaction (p. 825) diabatic and adiabatic potentials (p. 828) inverse Marcus region (p. 833) collective coordinate (p. 836) mean force potential (p. 836) Franck-Condon factors (p. 840) reorganization energy (p. 841)... 

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