Path relaxation

Figure Bl.15.8. (A) Left side energy levels for an electron spin coupled to one nuclear spin in a magnetic field, S= I =, gj >0, a<0, and a l 2h)<(a. Right side schematic representation of the four energy levels with )= Mg= , Mj= ). +-)=1, ++)=2, -)=3 and -+)=4. The possible relaxation paths are characterized by the respective relaxation rates W. The energy levels are separated horizontally to distinguish between the two electron spin transitions. Bottom ENDOR spectra shown when a /(21j)< ca (B) and when co < a /(2fj) (C).

Phenomenologically, the FNDOR experiment can be described as the creation of alternative relaxation paths for the electron spins, which are excited with microwaves. In the four-level diagram of the system... 

Simultaneous application of an RF field at a frequency corresponding to the ++)<- +-) (i.e. 2<- l) transition then opens a relaxation path via T, and Pj or, more directly, via W p The extent to which these relaxation... 

A different example of non-adiabatic effects is found in the absorption spectrum of pyrazine [171,172]. In this spectrum, the, Si state is a weak structured band, whereas the S2 state is an intense broad, fairly featureless band. Importantly, the fluorescence lifetime is seen fo dramatically decrease in fhe energy region of the 82 band. There is thus an efficient nonradiative relaxation path from this state, which results in the broad spectrum. Again, this is due to vibronic coupling between the two states [109,173,174]. 

According to these equations, the effect of selectively perturbing the spin states of spins i and j is to isolate the cross-relaxation paths common to these two spins. Combining Eqs. 15 and 19, the individual cross-relaxation terms are readily determined from single-selective and double-selective relaxation-rate measurements, that is. 

In chemisorbed systems, the molecular orbitals of the adsorbate are mixed with the electronic states of the substrate, producing strong adsorption bonds, i.e. the frequency of the adsorbate mode is well above the highest phonon frequency of the substrate. The relaxation of these vibrational excited states via emission of substrate phonons has only a low probability, because many phonons have to be enoitted during the decay. Non-radiative damping by electron-hole pair excitation appears to be the dominant relaxation path in these systems. 

Figure 16.3. The two lowest states during the dissociation of cyclopropane along the C2H4 relaxed path. The dashed lines, indicating the diabatic energies, were not computed but have been added merely to guide the eye.

The Photoactive Yellow Protein (PYP) is the blue-light photoreceptor that presumably mediates negative phototaxis of the purple bacterium Halorhodospira halophila [1]. Its chromophore is the deprotonated trans-p-coumaric acid covalently linked, via a thioester bond, to the unique cystein residue of the protein. Like for rhodopsins, the trans to cis isomerization of the chromophore was shown to be the first overall step of the PYP photocycle, but the reaction path that leads to the formation of the cis isomer is not clear yet (for review see [2]). From time-resolved spectroscopy measurements on native PYP in solution, it came out that the excited-state deactivation involves a series of fast events on the subpicosecond and picosecond timescales correlated to the chromophore reconfiguration [3-7]. On the other hand, chromophore H-bonding to the nearest amino acids was shown to play a key role in the trans excited state decay kinetics [3,8]. In an attempt to evaluate further the role of the mesoscopic environment in the photophysics of PYP, we made a comparative study of the native and denatured PYP. The excited-state relaxation path and kinetics were monitored by subpicosecond time-resolved absorption and gain spectroscopy. 

Experimentally measured ph for the system (17) for two qualitatively different situations are shown in Figs. 7 and 8. It is immediately evident (1) that the prehistory distributions are sharp and have well-defined ridges (2) that the ridges follow very closely the theoretical trajectories obtained by solving numerically the equations of motion for the optimal paths, shown by the full curves on the top planes. It is important to compare the fluctuational path bringing the system to (qf, stable state in thermal equilibrium, Fig. 7, and away from it, Fig. 8. Figure 7 plots the distribution for the system (17) in thermal equilibrium, namely A = 0. The... 

Figure 14 Illustration of the general procedure used to locate the initial relaxation direction (IRD) toward the possible decay products, (a) General photochemical relaxation path leading (via conical intersection decay) to three different final structures, (b) Potential energy surface for a model elliptic conical intersection plotted in the branching plane, (c) Corresponding energy profile (as a function of the angle a) along a circular cross section centered on the conical intersection point and with radius d.

Figure 17 Computed relaxation paths from the conical intersection of Figure 15. Although two similar valleys develop close to the crossing point, the third one (initially a ridge) starts far and is energetically unfavored.

Px, whereas the direction leading to P2 (the more unstable diradical intermediate) is a ridge. The valley to P2 develops only at a larger distance from the apex of the cone (see Figure 17). Thus calculations show36 82 and experiments confirm4 5 83-87 that there are two almost equivalent relaxation paths, which will be populated after decay from the conical intersection one leading to cyclohexadiene (R) and the other to hexatriene (Px), with very similar quantum yields (i.e., product ratio). We shall return to discuss this problem in a little more detail in the next section. 

Competitive Ground State Relaxation Paths from Conical Intersection... 

M. Garavelli, P, Celani, M. Fato, M. Olivucci, and M.A. Robb,/. Phys. Chem. A, 101,2023 (1997). Relaxation Paths from a Conical Intersection The Mechanism of Product-Formation in Cyclohexadiene/Hexatriene Photochemical Interconversion. 

As a simple example a three-level system with slow reorientation is considered. States (0) and (1) are directly coupled to the excitation pulse, while the intermediate level (2) is populated in the relaxation path of the excess population Ni of the upper level on its way back to the ground state. The temporal evolution of the population numbers and the pump intensity Ipu is given by ... 

Figure 1 Relaxation path, determined from MD simulation, for the vibrational relaxation of the OH stretch for HOD dissolved in D2O. The levels are labeled according to the standard ordering (OD stretch, bend, OH stretch).

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