Expected for traditional ET. The topology with the class of PCET reaction systems motivating this model is illustrated in Figure 38.Figure 38. Representative molecular structure for application of your model in eq 11.1 (cf. Figure 1 in ref 187). A dicarboxylic acid dimer forms the PT interface. Substituents act as the photoexcited electron donor (De ) and electron acceptor (Ae).(ten.20)The model Hamiltonian of Cukier incorporates a normal spinboson representation of ET reactions, and its matrix is expressed, with regards to mass-weighted nuclear coordinates and the Pauli matrices x and z (the identity matrix is implicitly assumed for the diagonal terms), as187,= VIF(R )x + Hp(R ) – 1 + 2 GzThis rate expression was obtained by Borgis and Hynes as a limiting case of a theoretical therapy encompassing the PT vibrationally nonadiabatic and adiabatic regimes. Equation ten.20 also holds for EPT below the identical circumstances.186 As in eq 5.29, S is an efficient frequency for solvent motion, plus the activation free of charge energy barrier Gact is offered by the distinction among the values in the ground vibronic level at its maximum and minimum with respect for the solvent collective coordinate (or set of solvent coordinates) S. For kBT, the prefactor is a lot more complicated and is dependent upon 228 inside a manner consistent with many-body transition-state theory inside the frictionless limit.379-385 This theory might be employed, normally, to receive the prices of transition among the minima corresponding towards the four diabatic states of Figure 20,116,214 and one more special case is represented by eq 5.29 for adiabatic ET.two g P 2 + two Q – j j z j j j 2 j(11.1)11. CUKIER THEORY OF PCET In the extended Marcus theory described in section six, a proton or atom transfer reaction amounts to a bond rupture and formation along 56390-09-1 Autophagy internal coordinates (bond distances) that define inner-sphere solute modes of reorganization as within the framework of pure ET. This viewpoint was adopted in Cukier’s therapy of PCET reactions,187 which also involves a description with the proton-solvent interaction that is equivalent to the description of electron-solvent interaction.116,188 Cukier’s first description of PCET187,386 reactions was based on the breakdown from the Condon approximation for the electronic coupling with respect towards the motion with the transferring protons. The model was motivated by experiments on photoinduced intramolecular ET at nearly fixed distance (in a range common of nonadiabatic ET) mediated by a hydrogenbonded interface and characterized by a distinct isotope effect upon deuteration of your proton interface.387 The first proposed model assumed that the ET matrix element, VIF(R), depended around the proton configuration in the interface, as measured by a coordinate, or perhaps a set of coordinates, R. Fermi’s golden rule gives a PCET rate that is certainly proportional to |VIF(R)|two inside the electronically nonadiabatic regime. As a result, the failure of theIn eq 11.1, VIF(R) = V0 exp(-|R|) is definitely the ET matrix element, characterized by a decay continuous as well as a maximum worth of V0 for the symmetric (transition-state) configuration from the proton(s) described by R = 0.388 Hp(R) = T p(R) + Vp(R) may be the Hamiltonian related together with the proton, which incorporates its kinetic power along with the efficient proton possible Vp(R). The latter is actually a double-well potential that corresponds to a hydrogenbonded proton localized on a single or the other side with the PT interface. Qj, Pj, j, and gj are the mass-weighted coordinate, the corresponding.
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