Energy transfer, nonadiabatic transition

The nonadiabatic transition state theory given in the Section II.C, namely, Eq. (17), can be applied to the electron-transfer problem [28]. Since the electron transfer theory should be formulated in the free energy space, we introduce the... 

In order to switch the system into the upper target state 5) merely the sine-phase 0 has to be varied by half an optical cycle, that is, by A(p = n. In this case, the main pulse is phase-shifted by Af = -l- r/2 with respect to the pre-pulse and couples in antiphase to the induced charge oscillation. Hence, the interaction energy is maximized and the upper dressed state u) is populated selectively. Due to the energy increase, the system rapidly approaches the upper target state 5). The ensuing nonadiabatic transitions between the dressed states u) and 1 5) result in a complete population transfer from the resonant subsystem to the upper target state, which is selectively excited by the end of the pulse. 

Changes in the energy gap, AE, and the nonadiabatic transition probability, P10, in the aqueous solution simulations are dominated in the initial stages by the coupled proton-electron transfer event and the subsequent relaxation of the system into the excited CT state. Similar to the gas phase, variations in AE and P10 at longer time-scales were found to depend strongly on the out-of-plane motions of the system (for instance the dihedral angles 0 and ). However, the presence of... 

Nonadiabatic coupling mixes all terms. However, if Ae is sufficiently high, the location of - and 11-11 nonadiabatic coupling due to radial motion will be different from that of a -11 coupling due to rotational motion. This argument, and also the fact that the probability of nonresonant transition is small, permit depolarization and transition with energy transfer to be treated separately. Let us discuss now the latter. According to the theory of nearly adiabatic perturbations (Section II),... 

In contrast, this single-surface model does not apply to Ca-HCl, and a two-surface calculation was performed where the H-atom departure is induced by the electron jump from the van der Waals potential to the electron transfer potential. The quantal nature of this nonadiabatic transition allows one to reproduce all the features of the spectrum. This includes the small linewidth of some transitions and, more important, the inverse energy dependence observed in the spectrum, where the broadest bands are those of lowest energy [244], in figure 13. 

In the simplest case, the R mode is characterized by a low frequency and is not dynamically coupled to the fluctuations of the solvent. The system is assumed to maintain an equilibrium distribution along the R coordinate. In this case, ve can exclude the R mode from the dynamical description and consider an equilibrium ensemble of PCET systems with fixed proton donor-acceptor distances. The electrons and transferring proton are assumed to be adiabatic with respect to the R coordinate and solvent coordinates within the reactant and product states. Thus, the reaction is described in terms of nonadiabatic transitions between two sets of intersecting free energy surfaces ( R, and ej, Zp, corresponding to... 

The energy-conserving delta function is actually where the protein seems to play its major role. Because the transfer of charge in this model is sudden, the electron transition is between states of constant atomic position (a nonadiabatic transition). The atoms from which this transfer occurs are bound harmonically to the lattice and when in thermal equilibrium have a Gaussian distribution around the center of the potential ... 

Certain features of the results are quite interesting. The cross sections show a strong dependence on the vibrational quantum number for both reactant electronic states. If the Franck-Condon principle were valid for the nonadiabatic transitions which occur in this system, then the charge transfer cross section would be independent of the reactant vibrational level [19]. It is well known that the Franck-Condon principle breaks down badly at low collision energies for most charge transfer systems. The most remarkable result seen in Fig. 4 is the very small cross section for N2+ (X v = 0) + Ar at all three collision energies its maximum value is 1.6 A2 at 20 eV. (By comparison the cross sections for other N2+ (X v) -I- Ar states are at least 14 A2.) This occurs even though there is a product state, Ar+(2P3/2) + N2(v = 0), which is only 0.18 eV away thus, this. In addition, the Franck-Condon factor for the transition N2 (X v = 0) - N2 (v = 0) is 0.92 ... 

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