Crossing probability

In solution when iodine is excited to the bound B excited state, dissociation and recombination processes occur. The dissociation is the result of solvent-induced curve crossing to the dissociative a state, the recombination a result of momentum reversals arising from collisions with the surrounding solvent molecules. Eigenstates of the B state will decay in a continuous manner, whereas wavepackets—if the curve-crossing probability is less than unity—decay in a stepwise manner, giving rise to successive pulses of product. The B and a curves cross near the center of the B state, whereas the B state wavepacket is initially created near the left turning point thus there... 

The treatment of intersystem crossing, that is, of the k c and kbisc paths in equation (22), is in principle similar to that for knr.There is an added spin-orbit coupling term in the evaluation of the electronic factor in the treatment of the crossing probability. Although theory has provided a useful framework for discussing nonradiative processes, it has not so far been of much diagnostic or predictive value in the case of coordination compounds. 

The first experimental confirmation of the above proposal was made from the studies involving the detection of the state of spin alignment (20,85) from the optical decay at very low temperatures. The results showed that the strong radiative level is populated fastest by the intersystem crossing process. From a knowledge of the symmetry of the spin radiative level, it was easily concluded that in quinoxaline, the most favored intersystem crossing process is Sn - -> T. The first quantitative measurements of the relative intersystem crossing probability to the different zf levels, and thus the relative importance of the different mechanisms,... 

The process of passing through two separate bottlenecks can reduce the reactive flux below that predicted by the minimum of the two minima. Assuming that the crossing probabilities are given correctly by TST for each encounter of the bottleneck, and that the dynamics is chaotic between the two bottlenecks, implies that the effective transition state flux is given by [19]... 

Because the intersystem crossing probability is low, the triplet reaction can in general be initiated only by sensitization. The difference between singlet and triplet reactions can be utilized synthetically, as indicated in Scheme 47 (Baggiolini et al., 1970 Sadler et al., 1984) ... 

Meanwhile new criteria to distinguish between thermal activation and nuclear tunnelling mechanisms in the photochemistry of ketones was proposed [74]. This criteria is based on the influence of spin-orbit coupling on the crossing probability, P, at the crossing w. The experimental test of this criteria showed nuclear tunnelling is the dominant mechanism in H abstractions [75]. TET was then applied to Norrish type I reactions [76]. 

This is satisfactory in that eq. 4.48 is identical with the semiclassical Landau-Zener expression for the crossing probability between R and P surfaces of the same curvature in the weak-coupling limit (Newton, 1991). 

The next step was the calculation of the MECP from a singlet, open-shell biradical intermediate INTI (Figure 6.42) to the triplet state. It was then followed by the calculation of the singlet triplet crossing probability. The exact procedure has been described in Section 6.1.1. The final situation is such that both pathways— the singlet and the triplet— participate in the process since a considerable part of the species still remains in the singlet state and proceeds on the singlet surface. 

Once the magnitude of the coupling between the two surfaces is determined, one can calculate the probability of crossing from one spin state to another at a given geometry. There are several well-established approximation methods for obtaining the crossing probability. Once obtained, it can then be incorporated into a statistical theory of rate such as the nonadiabatic version of RRKM theory to obtain rate constants for spin-forbidden processes. ... 

Published theoretical descriptions of the Ca(5 Pi) - Ca(5 Pj) alignment system have considered the formal Landau Zener curve crossing probability [29] and have used foil quantum mechanical descriptions [30]. Unfortunately, all the theoretical descriptions are limited by the lack of accurate potential surfaces for the van der Waals states of the electronic levels. However, in the future, accurate information may become available from recent experiments to investigate metal atom + rare gas van der Waals potentials using supersonic jet spectroscopy [31-34]. Thus there is an excellent chance that it will also be possible to obtain more accurate theoretical descriptions, which will elucidate important subtleties of alignment effects in energy transfer and reactions. 

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