Classically forbidden electronic transitions

The breakdown of the SH scheme in the case of classically forbidden electronic transitions should not come as a surprise, but is a consequence of the rather simplifying assumptions [i.e., Eqs. (37) and (43)] underlying the SH model. On a semiclassical level, classically forbidden transitions may approximately be described within an initial-value representation (see Section VIII) or by introducing complex-valued trajectories [55]. On the quasi-classical... 

As discussed above, this discrepancy may be caused by classically forbidden electronic transitions—that is, cases in which a proposed hopping process is rejected due to a lack of nuclear kinetic energy. Figure 11c supports this idea by showing the absolute numbers of successful (thick fine) and rejected (thin line) surface hops. In accordance with the initial decay of the adiabatic population, the number of successful surface hops is largest during the first 20 fs. For larger times, the number of rejected hops exceeds the number of successful surface hops. This behavior clearly coincides with the onset of the deviations between the two classically evaluated curves Nk t) and P t). We therefore conclude that the observed breakdown of the consistency relation (42) is indeed caused by classically forbidden electronic transitions. 

As discussed above, this discrepancy may be caused by classically forbidden electronic transitions, i.e. cases in which a proposed hopping process is rejected due to a lack of nuclear kinetic energy. Figure 4(c) supports this... 

Jasper, A. W., Stechmann, S. N., Truhlar, D. G. (2002). Fewest-switches with time uncertainty A modified trajectory surface-hopping algorithm with better accuracy for classically forbidden electronic transitions. Journal of Chemical Physics, 116(13), 5424-5431. 

To summarize, it has been found that the SH method is able to at least qualitatively describe the complex photoinduced electronic and vibrational relaxation dynamics exhibited by the model problems under consideration. The overall quality of SH calculations is typically somewhat better than the quality of the mean-field trajectory results. In particular, this holds in the case of several curve crossings (see Fig. 2) as well as when the dynamics and the observables of interest are essentially of adiabatic nature— for example, for the calculation of the adiabatic population dynamics associated with a conical intersection (see Figs. 3 and 12). Furthermore, we have briefly discussed various consistency problems of a simple quasi-classical SH description. It has been shown that binned electronic population probabilities and no momentum adjustment for classically forbidden transitions help us to improve this matter. There have been numerous suggestions to further improve the hopping algorithm [70-74] however, the performance of all these variants seems to depend largely on the problem under consideration. 

Vibrational Contributions Contribution of vibrational modes has been described for TPA [5-9, 11-17, 19, 22, 23, 31, 37, 61, 235, 309, 343-345] and for other nonlinear optical processes [346]. One classical example is the 1A j -1 B2u TP transition of benzene, the so-called green band. This electronic transition is allowed due to a vibronic coupling mechanism [346]. Semiempirical [60, 61] as well as ab initio response theory calculations using the Herzberg-Teller expansion [344] demonstrate the role of vibronic coupling. Such contributions can either enhance an allowed transition or intensify a symmetry-forbidden transition. 

The vibrational analysis of the highly structured 2600 A absorption system is of course one of the classic tales of spectroscopy, and it is told with superb clarity in two reviews. Suffice it to say that the initial analysis of Sponer, Nordheim, Sklar, and Teller, the further extensive work of Ingold and co-workers, and most recently the rotational analysis of the electronic spectrum by Callomon, Dunn, and Mills link this transition firmly with the state. The last-mentioned work now provides the most precise value of the forbidden electronic origin (the 0,0 band) of the transition. The origins are at 38,086.1 cm for C Hs vapor and 38,289 cm- for CeDg vapor. 

When spectral bands are weak there is a reason. Often it means that they are bands which are forbidden but—obviously—not totally forbidden. The weak bands with which we are concerned are of this type. Electronic transitions which correspond to strong bands are electric dipole in type. Classically, the electric vector associated with the incident light beam behaves like a pair of alternating -I- and — charges across the molecule. These oscillating charges induce an oscillating dipole in the molecule when the... 

Fig. 12.2 Left The ground (X, solid line), excited (6, dashed line) and dissociative [a1g(3II), dotted line] electronic state potentials of the iodine molecule. The arrow indicates the electronic excitation. The initial excited wave packet is located in the Franck-Condon region near to the inner classical turning point of the B state. The transition from the B to the a state is forbidden by symmetry in the isolated molecule but becomes allowed when the molecule is placed in a solvent.

The classic cases of the HT mechanism concern coupling between two electronic states of different symmetry or between the different components of two degenerate states of the same symmetry. An important example of the first case occurs when electric dipole transitions to one of the two states are forbidden (e.g. the Laporte-forbidden d—d and f-f transitions). In this case, the forbidden transition may acquire absorption intensity by HT mixing with an allowed transition via a non-totally symmetric mode of appropriate symmetry (the irreducible representation of the active mode must be contained in the direct product of the irreducible representations for the two states coupled by the HT mechanism). 

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