Quantum mechanics, electron-transfer

Moser, C.C., Dutton, P.L. Biological electron transfer measurement, mechanism, engineering requirements. In Quantum mechanical simulation methods for studying biological systems, D. Bicout and M. Field, eds. Springer, Berlin (1996) 201-214. 

Despite the fact that Bohr s stopping power theory is useful for heavy charged particles such as fission fragments, Rutherford s collision cross section on which it is based is not accurate unless both the incident particle velocity and that of the ejected electron are much greater than that of the atomic electrons. The quantum mechanical theory of Bethe, with energy and momentum transfers as kinematic variables, is based on the first Born approximation and certain other approximations [1,2]. This theory also requires high incident velocity. At relatively moderate velocities certain modifications, shell corrections, can be made to extend the validity of the approximation. Other corrections for relativistic effects and polarization screening (density effects) are easily made. Nevertheless, the Bethe-Born approximation... 

A photoinduced oxidative addition of Bu"I and Pr I towards [Rh2(dicp)4] (dicp = 1,3-diisocyanopropane) using low-energy irradiation (553 nm) has been described, and proceeds under a nitrogen atmosphere with quantum yields of 25.2 and 22.6, respectively. Based on the kinetics measured in the presence and absence of quenchers, an electron-transfer chain mechanism has been proposed in which alkyl radicals are involved. " The same authors have also described a new methodology for the experimental determination of redox potentials and have applied this to measure the one-electron oxidation potentials of l-benzyl-l,4-dihydronicotinamide and of [Rh2(dicp)4p. ... 

The reader may desire an explanation of the low values of y derived by Barton and coworkers [30, 131, 137-140] from fluorescence quenching data for systems in which the dynamics of electron transfer have not been directly measured. In most cases, the absolute efficiency (quantum yield) of the quenching processes studied in these systems is rather low, and thus they may represent long-range electron transfer by mechanisms other than superexchange, such as to those described by Felts et al. [125], Davis and colleagues [126], and Okada et al. [127]. However, the author considers that it is highly unlikely that such processes occur with rate constants > 10 s . In view of the complex nature of these systems, the author is loath to offer a detailed interpretation, and refers the reader to commentaries by others who have been directly involved in this research [13, 15]. 

Fluorescence imaging is the most powerful technique currently available for continuous observation of the dynamic intracellular processes of living cells. Fluorescein is widely employed as the core of various fluorescence probes used in imaging important biological effectors. Despite the extensive use of fluorescein derivatives and the importance of the applications, the mechanism that controls the quantum yield of fluorescence has not been fully established. I report herein photoinduced electron transfer (PeT) mechanism that can control the fluorescence quantum yields of fluorescein and boron dipyrromethene (BODIPY) derivatives. 

No further chemical input is necessary for substrate oxidation to occur once the second electron is transferred. Quantum mechanical calculations have provided insights into the protonation and 0-0 bond cleavage steps. Density function theory (DFT) calculations on the ferric-peroxo form of P450eryF indicated fast protonation at the distal oxygen by... 

The written version of a lecture has surveyed the applications of the hydrophobic effect as a mechanistic tool. The article is not only a review of the author s earlier work, but also contains the results of new experimental studies and quantum-mechanical calculations. Studies involving the hydrophobic effect have been helpful in distinguishing displacements occurring by single electron transfer (SET) mechanisms and those occurring by direct nucleophilic attack with various geometries. 

The discussion thus far in this chapter has been centred on classical mechanics. However, in many systems, an explicit quantum treatment is required (not to mention the fact that it is the correct law of physics). This statement is particularly true for proton and electron transfer reactions in chemistry, as well as for reactions involving high-frequency vibrations. 

Computer simulations of electron transfer proteins often entail a variety of calculation techniques electronic structure calculations, molecular mechanics, and electrostatic calculations. In this section, general considerations for calculations of metalloproteins are outlined in subsequent sections, details for studying specific redox properties are given. Quantum chemistry electronic structure calculations of the redox site are important in the calculation of the energetics of the redox site and in obtaining parameters and are discussed in Sections III.A and III.B. Both molecular mechanics and electrostatic calculations of the protein are important in understanding the outer shell energetics and are discussed in Section III.C, with a focus on molecular mechanics. 

We have seen that 10" M s is about the fastest second-order rate constant that we might expect to measure this corresponds to a lifetime of about 10 " s at unit reactant concentration. Yet there is evidence, discussed by Grunwald, that certain proton transfers have lifetimes of the order 10 s. These ultrafast reactions are believed to take place via quantum mechanical tunneling through the energy barrier. This phenomenon will only be significant for very small particles, such as protons and electrons. 

Quantum mechanical effects in inorganic and bioinorganic electron transfer. T. Guarr and G. McLendon, Coord. Chem. Rev., 1985, 68,1 (227). 

The transfer of electrons in proteins by a quantum mechanical tunnelling mechanism is now firmly established. Electron transfer within proteins... 

Excited state electron transfer also needs electronic interaction between the two partners and obeys the same rules as electron transfer between ground state molecules (Marcus equation and related quantum mechanical elaborations [ 14]), taking into account that the excited state energy can be used, to a first approximation, as an extra free energy contribution for the occurrence of both oxidation and reduction processes [8]. 

Figure 25. Electron-transfer rate the electronic coupling strength at T = 500 K for the asymmetric reaction (AG = —3ffl2, oh = 749 cm ). Solid line-present full dimensional results with use of the ZN formulas. Dotted line-full dimensional results obtained from the Bixon-Jortner formula. Filled dotts-effective ID results of the quantum mechanical flux-flux correlation function. Dashed line-effective ID results with use of the ZN formulas. Taken from Ref. [28].

Tang, J. and Marcus, R. A. (2005) Diffusion-controlled electron transfer processes and power-law statistics of fluorescence intermittency of nanoparticles. Phys. Rev. Lett, 95, 107401-1-107401-4 Tang, J. and Marcus, R. A. (2005) Mechanisms of fluorescence blinking in semiconductor nanocrystal quantum dots./. Chem. Phys., 123,054704-1-054704-12. 

As a rule, high quantum yields for two-electron transfer reactions are expected when the mechanism is one-electron/two-hole or two-electron/one-hole. In the cases of twQ-electron/two-hole or one-electron/one-hole efficient back reactions of the intermediates on the colloidal particles or in solution, respectively, will lead to a low yield of the final products. 

Instead of postulating Zn," as intermediate, as it has a highly negative potential and is possibly unstable in ZnO, one may write the above mechanism with Zn e pairs. The blue-shift in the absorption upon illumination was explained by the decrease in particle size. The Hauffe mechanism was abandoned after it was recognized that an excess electron on a colloidal particle causes a blue-shift of the absorption threshold (see Fig. 19). In fact, in a more recent study it was shown that the blue-shift is also produced in the electron transfer from CH2OH radicals to colloidal ZnO particles When deaerated propanol-2 solutions of colloidal ZnO were irradiated for longer times, a black precipitate of Zn metal was formed. In the presence of 10 M methyl viologen in the alcohol solution, MV was produced with a quantum yield of 80 %... 

In a recent paper. Mo and Gao [5] used a sophisticated computational method [block-localized wave function energy decomposition (BLW-ED)] to decompose the total interaction energy between two prototypical ionic systems, acetate and meth-ylammonium ions, and water into permanent electrostatic (including Pauli exclusion), electronic polarization and charge-transfer contributions. Furthermore, the use of quantum mechanics also enabled them to account for the charge flow between the species involved in the interaction. Their calculations (Table 12.2) demonstrated that the permanent electrostatic interaction energy dominates solute-solvent interactions, as expected in the presence of ion species (76.1 and 84.6% for acetate and methylammonium ions, respectively) and showed the active involvement of solvent molecules in the interaction, even with a small but evident flow of electrons (Eig. 12.3). Evidently, by changing the solvent, different results could be obtained. 

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