Marcus-like model

The study of proton transfer in solution with coupling to a rate promoting vibration in the sense we discussed above, was pioneered by Borgis and Hanes. They used a Marcus-like model with the important addition that the tunneling matrix element between the reactant and product states is written as... 

This treatment is confined to tunneling correction to TST and is not valid for any Marcus-like model (e.g., environmentally coupled tuimeling). Thus, an Arrhenius plot of KIEs can distinguish between data that might be fitted by a tunneling correction model (e.g., A]/Ah > 1 with A a 0) and data that can only be fitted by a Marcus-like model (e.g., Aj/Ah > 1 with large AEa)-... 

Figure 12.7. Illustration of Marcus-like models energy surface of environmentally coupled hydrogen tunneling. Two orthogonal coordinates are presented p, the environmental energy parabolas for the reactant state (R) and the product state (P) and q, the H-transfer potential surface at each p configuration. The gray shapes represent the populated states (e.g., the location of the...

As mentioned in Section 13.1, the temperature dependent behavior of KIEs (that is temperature dependent versus temperature independent) is a key experimental result when considering the nature of the tunneling. Based on the phenomenological model provided by the Marcus-like framework for H-tunneling [14, 30, 31], the... 

An important aspect of the Gao-Marcus model is that it provides a theoretical structure for the understanding of quantum state density isotope effects in general, and is not specifically confined to the formation of ozone itself. This feature is important because as discussed above we are now aware that MIF s occur widely in nature. The theory aids in prediction of where MIF s will be likely found, and once found, in rationalizing how they were chemically produced. 

The forbidden retro-[ls -I- 2s]-cycloaddition can now be treated using a simple curve-crossing model analagous to the Marcus-Hush theory of electron-transfer [11]. The ground state at the quadricyclane-like geometry is the... 

J. Troe Professor Marcus, you were mentioning the 2D Sumi-Marcus model with two coordinates, an intra- and an intermolecu-lar coordinate, which can provide saddle-point avoidance. I would like to mention that we have proposed multidimensional intramolecular Kramers-Smoluchowski approaches that operate with highly nonparabolic saddles of potential-energy surface [Ch. Gehrke, J. Schroeder, D. Schwarzer, J. Troe, and F. Voss, J. Chem. Phys. 92, 4805 (1990)] these models also produce saddle-point avoidances, but of an intramolecular nature the consequence of this behavior is strongly non-Arrhenius temperature dependences of isomerization rates such as we have observed in the photoisomerization of diphenyl butadiene. 

Excited State Charge Transfer. Our goal here is to discuss aspects of ET theory that are most relevant to the charge transfer processes of excited molecules. One important point is that often the solvent relaxation is not well modeled with a single t, but rather a distribution of times apply. This subject has been treated by Hynes [63], Nadler and Marcus [65], Rips and Jortner [66], Mukamel [67], Newton and Friedman [68], Zusman [62], Warshel [71], and Fonseca [139], We also would like to study ET in the strongly adiabatic regime since experimental results on BA indicate this is the correct limit. Finally, we would like to treat the special case of three-well ET, which is the case for BA. 

Most systematic studies on gas-phase SN2 reactions have been carried out with methyl halides, substrates which are free of complications due to competing elimination. Application of the Marcus rate-equilibrium formalism to the double-minimum potential energy surface led to the development of a model for intrinsic nucleophilicity in S 2 reactions233. The key quantities in this model are the central energy barriers, Eq, to degenerate reactions, like the one of equation 22, which are free of a thermodynamic driving force. 

Stine and Marcus.63 These results are in excellent agreement (as few %) with the accurate quantum mechanical values obtained by Secrest and Johnson24 even for extremely weak transitions with a probability as small as 10" n. It is thus encouraging that the semiclassical model is able to describe such quantum-like phenomena for which ordinary (i.e. real-valued) classical trajectory methods would clearly be inapplicable. 

---