Marcus parabolas

In the Marcus model the important part of the system is donor and acceptor and the process takes place on the potential energy surface of the ground state of the total system, while the first excited state corresponds to the remaining, upper parts of the Marcus parabolas. If eq.(4) is solved, a number of excited states correspond to excitations of the bridge. It is interesting to... 

The exponential term of 4.7 in conjunction with 4.6 contain an important prediction, namely that three distinct kinetic regimes exist, depending on the driving force of the electron transfer process. The three kinetic regimes are also shown schematically in Fig. 4.2 (lower part) in terms of the classical Marcus parabolas ... 

Table 9.4 represents the calculated AG values for the charge separation and charge recombination processes. Hereby, the charge recombination falls into the inverted regime of the Marcus parabola. With these values in hand, it was possible to place the different possible reaction pathways in a state diagram (Fig. 9.25). 

Experimental slope is given first the calculated one (within parentheses) is based on the Marcus parabola, approximated as a straight line in the AG° region involved... 

Figure 9. Free energy dependenee of electron transfer rate (eontinuous line classical treatment, Eq. 14 dotted line quantum treatment, Eq. 10). The three kinetic regimes, normal , activationless , inverted , are shown schematically in terms of classical Marcus parabolae.

The diabatic free-energy profiles of the reactant and product states provide the microscopic equivalent of the Marcus parabolas.26,27 For example, in the case of the (Cl- + CH3-CI —> CICH3 + Cl-) Sn2 reaction, one obtains23 the results shown in Fig. 2. 

This work addressed the issue of enzyme catalysis focusing on the principle of physical organic chemistry and the power of computer simulation approaches. It was shown that when such concepts as reorganization energy and Marcus parabolas are formulated in a consistent microscopic way, they could be used to explore the origin of enzyme catalysis. It was also clarified that phenomenological applications of the Marcus formula or related expressions can lead to problematic conclusions. 

PET reactionscanalsoberepresentedby Marcus parabolas. The R parabola for a PET reaction involving a thermalised excited state of D or A is simply related to that of the... 

The diabatic free energy profiles of the reactant and product states provide the microscopic equivalent of the Marcus parabolas [29, 30]. 

Fig. 31 Schematic drawings of the Marcus parabolas for dimer and monomer...

Fig. 14.27. Electron transfer in the reaction DA -> D+A , as well as the relation of the Marcus parabolas to the concepts of the conical intersection, diabatic and adiabatic states, entrance and exit channels and the reaction barrier. Panel (a) shows two diabatic surfaces as functions of the and 2 variables that describe the deviation from the comical intersection point (within the...

The Marcus parabolas (Fig. 14.27d) represent a special section (along the collective variable) of the hypersurfaces passing through the eonieal intersection (parabolas Vr and Vp). Each parabola represents a diabatie state, so a part of each reactant parabola is on the lower hypersurface, while the other one is on the upper hypersurface. We see that the parabolas are only an approximation to the hypersurface profile. The reaction is of a thermal character, and as a consequence, the parabolas should not pass through the conical intersection, because it corresponds to high energy, instead it passes through one of the saddle points. 

Fig. 14.25. Electron transfer in the reaction DA- -D+A " as well as the relation of the Marcus parabolas to the concepts of the conical intersection, diabatic and adiabatic states, entrance and exit channels and the reaction barrier. Fig. (a) shows two diabatic (and adiabatic) surfaces of the electronic energy as functions of the f and 2 variables that describe the deviation from the conical intersection point (cf. p. 262). Both diabatic surfaces are shown schematically in the form of the two paraboloids one for the reactants (DA), the second for products (D+A ). The region of the conical intersection is also indicated. Fig. (b) also shows the conical intersection, but the surfaces are presented more realistically. The upper and lower parts of Fig. (b) touch at the conical intersection point. On the lower part of the surface we can see two reaction channels each with its reaction barrier (see the text), on the upper part (b) an energy valley is shown that symbolizes a bound state that is separated from the conical intersection by a reaction barrier.

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