By Ben-nun M., Martinez T.J.
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J. martı´nez Because the concept of minimum energy path is not well-defined when multiple electronic states are involved, the initial data set is simply taken as the union of points which one considers important on each of the electronic states—for example, local minima on each electronic state. The weights of each data point, wi in Eq. 34), were taken to be the same on all electronic states because they only depend on the location of the data points. Hence, the difference between I electronic states (VShepard ðRÞ) is manifested only in the parameters of each of the Taylor expansions: I VShepard ðRÞ ¼ X wi ðZÞTiI ðZÞ ð2:37Þ i Because the Shepard interpolation method is global, it is affected by cusped regions in the PES.
After $ 50 fs the molecule is typically twisted, but excited-state quenching does not even begin until 50 fs. Therefore torsion is not the sole coordinate responsible for the return to the ground electronic state. Significant quenching to the ground electronic state requires pyramidalization of one of the methylene units. Attempts at hydrogen migration are also observed, but only rarely have we seen the molecule decay to the ground electronic state via a hydrogenmigration conical intersection. The corresponding electronic dynamics involves three electronic states: N, V, and Z in Mulliken notation.
Because ethylene is the shortest unsaturated hydrocarbon, its photochemistry is special in some respects. Simple particle-in-a-box considerations suggest (and theory and experiment confirm) that ethylene will have the largest excitation energy (as compared to longer conjugated systems). At the same time, ethylene also has a small number of internal modes. Consequently, photoexcitation of ethylene leads to fragmentation in addition to the isomerization that is the hallmark of longer polyenes [149–151].