Dynamics caging

This is no longer the case when (iii) motion along the reaction patir occurs on a time scale comparable to other relaxation times of the solute or the solvent, i.e. the system is partially non-relaxed. In this situation dynamic effects have to be taken into account explicitly, such as solvent-assisted intramolecular vibrational energy redistribution (IVR) in the solute, solvent-induced electronic surface hopping, dephasing, solute-solvent energy transfer, dynamic caging, rotational relaxation, or solvent dielectric and momentum relaxation. 

Thus, F(oj) has a complicated codependence. The latter will be mirrored in the photoionization cross section of the encaged atom. Correspondingly, the photoionization cross section of the encaged atom in the dynamical-cage approximation might differ greatly from that in the frozen-core approximation, both quantitatively and qualitatively. 

In summary, despite the assumption of a zero thickness A of the fullerene cage [38,39] being an obvious drawback of the quantum mechanical model, this model seems to be more realistic than the discussed classical models of the C cage [43,44], Correspondingly, in the present paper, the screening factor F(co) from [38,39] is used whenever the dynamical-cage approximation is deemed to be appropriate for the calculation of the photoionization of the atom encaged in Cm-... 

Figure 19 RPAE 5s photoionization cross section of encaged Xe, as marked, (a) a A [33], the A-potential model at the frozen-cage approximation level (b) "5 A [64], the A-potential model at the dynamical-cage approximation level (c) o rs [35], the 5-potential model at the frozen-cage approximation level (d) [38], the 5-potential model at the dynamical-cage approximation level (e)...

The quintessence of the reversed electron correlation effect is illustrated in Figure 20 by nonrelativistic HF and RPAE calculated data of the 4s photoionization cross section of free Ca and encaged Ca, Ca C60 near threshold, both at the frozen-cage approximation level, afs A, [20] and dynamical-cage approximation level, afsA [64]. 

At the dynamical-cage approximation level (see the lower main panel in Figure 20), the role of the dynamical screening of the incoming radiation by the C60 cage is tremendous [64], resulting in the impressively enhanced 4s photoionization cross section afsA compared to that calculated at the frozen-cage approximation level. 

Note, as in the discussed case of the ns photoionization cross sections of Mg, Ca, Sr and Ba, the presented pfsAa and pfsAb parameters for Hg must be corrected by accounting for the dynamical-cage effect, since the... 

Gorman, P.D., English, N.J., MacElroy, J.M.D. Dynamical cage behaviour and hydrogen migration in hydrogen and hydrogen-tetrahydrofuran clathrate hydrates. J. Chem. Phys. 136, 044506 (2012)... 

The SRLS mechanism has been invoked to explain the segmental rotational dynamics of spin-labeled polystyrene in toluene solution. This study provides an example of a system in which the dynamic cage is defined by constrained diffusion of the spin label attached to a polymer. The SRLS model is appropriate to analyze these spectra, since the local ordering environment is coupled to the global tumbling modes of the polymer. Moreover, the high (250-GHz) frequency ESR spectra of this... 

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