Marcus theory theoretical calculations

EXPERIMENT 5.6 MARCUS THEORY THEORETICAL CALCULATION OF THE OUTER-SPHERE RATE CONSTANT, kos, FOR THE REACTION BETWEEN [Co(ox)2(EN)] AND [Co(en)3]2+11... 

The next two chapters are devoted to ultrafast radiationless transitions. In Chapter 5, the generalized linear response theory is used to treat the non-equilibrium dynamics of molecular systems. This method, based on the density matrix method, can also be used to calculate the transient spectroscopic signals that are often monitored experimentally. As an application of the method, the authors present the study of the interfadal photo-induced electron transfer in dye-sensitized solar cell as observed by transient absorption spectroscopy. Chapter 6 uses the density matrix method to discuss important processes that occur in the bacterial photosynthetic reaction center, which has congested electronic structure within 200-1500cm 1 and weak interactions between these electronic states. Therefore, this biological system is an ideal system to examine theoretical models (memory effect, coherence effect, vibrational relaxation, etc.) and techniques (generalized linear response theory, Forster-Dexter theory, Marcus theory, internal conversion theory, etc.) for treating ultrafast radiationless transition phenomena. 

This confusion initiated a lot of experimental inspections and theoretical revisions of the FEG law. There is no need to review all of them here because the most reliable explanation of the effect was given by Marcus and Siders [108]. In view of the fact that all transient effects are ignored in the Markovian theory, where k(t) = k, it follows from Eq. (3.13) that the Markovian Ko coincides with k but not with ko. Therefore, Marcus and Siders calculated k by means of DET and concluded that the fastest transfer (at the top of the FEG... 

Aj may be evaluated from x-ray and infrared (IR) data or from theoretical calculations. However, for organic outer sphere electron transfers, this contribution is usually much smaller than Ao. In our opinion one of the greatest merits of the Marcus [43] and Levich-Dogonadze [44] theories is that they allow rather correct predictions of Aq through simple equations. Thus for most outer sphere electron transfers, reasonably accurate values of the rate constants can be predicted. 

Finally, theoretical studies, particularly by Wolfe et al. (26) and more recently by Evleth and co-workers (27), provided some additional justification for our analysis. Quantum calculations of barriers for cross-reactions are in agreement with values that would have been derived from a Marcus theory analysis of other calculated barriers. Jorgensen and co-workers (28, 29) carried this analysis further using statistical mechanics simulations that show that the gas phase potential surface indeed translates into the solution surface in the way that we predicted. (For a dicussion of an alternative way to apply Marcus theory to double-minimum surfaces, as well as a note on Cl + CH3C1, see reference 29a.)... 

The agreement between the two sets of data is reasonably satisfactory. The ability of the Marcus theory to predict values of k and k has also been tested, and Table 3.2 presents a comparison made by Hale [25] of the experimental and theoretical values of the free energy of activation for electrode processes (the experimental values of have been calculated from k using Equations... 

This chapter is organized as follows. Section 18.2 describes the theoretical foundation of Marcus theory, formulated in a molecular rather than dielectric continuum solvent framework. Its non-Gaussian extension is presented in section 18.3 and its implications for rate calculations are discussed in section 18.4. The theory is then confronted to various molecular simulation results in section 18.5 and a conclusion is proposed in section 18.6. 

A theoretical study of the hydrolysis of arenediazonium ions, combining Marcus theory with density functional theory (DPT) calculations, indicates the possibility of reaction by an 5 2 pathway, with the transition state (1), rather than an 5 1 pathway There has been a survey of the use of arenediazonium ions in synthetic reactions including their use as aryl radical precursors, aryl cation precursors, and super-electrophiles in transition-metal-catalysed reactions ... 

Electron transfer (ET) reactions are important processes in chemistry and biology. Theoretical studies of processes are challenging because of the quanmm nature of the processes and the complicated roles of the solvent. An ab initio QM/MM approach for electron transfer reactions based on DFT calculations with the fi actional number of electrons approach (FNE) was reported by Zeng et al. [696]. With this method the oxidation free energies and the diabatic FES for the electron transfer process of Ru and Fe complexes in aqueous solution could be computed. The accurate oxidation free energies and the FES obtained from the calculation indicate that the FNE is an efficient order parameter that can be used to describe the redox reaction process and sample the solvent conformations along the reaction [696], The method is related to the EVB method proposed by Warshel and Aqvist [169] or the ansatz of the Marcus theory. 

From a kinetic viewpoint, electron transfer processes involving excited states, as well as those involving ground state molecules, can be dealt with in the frame of the Marcus theory [4] and of the successive, more sophisticated theoretical models [5]-The only difference between electron transfer processes involving excited state instead of ground state molecules is that in the first case, in the calculation of the free energy change, the redox potential of the excited state couple has to be used (2.6 and 2.7). 

Let us now consider the results of theoretical calculation of the reorganization energy. Marcus formulas (3.14) and (3.16) represent the simplest version of the theory. For a reaction involving two ions of the same radius a, which are in direct contact (R = 2a), as well as for the electrode reaction of an ion which approaches the electrode until they are in direct contact (R = a), these formulas can be simplified and lead to the following relations ... 

Rabinovitch et al. (85) studied the reaction of H atoms with trans-ethylene-d2 as a function of ethylene pressure in the temperature range — 78 to 160°C. They were able to account for all secondary reactions of the hot ethyl radicals and to determine the rates of their decomposition (relative to stablization). Simultaneously they calculated the theoretical rates on the basis of the Rice-Ramsperger-Kassel theory of uni-molecular reactions, using expressions derived by Marcus (71), and found a reasonable agreement with the experimental values. Similar satisfactory agreements had been found previously by Rabinovitch and Die-sen (84) for hot sec-butyl radicals. Extensive studies of hot radicals produced by H or D atom additions to various olefins have been carried... 

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