Ballistic wavepacket motion

As discussed above, a similar delay of the emission rise of about 50 fs is found for all investigated molecules. The wavelength dependence of the emission amplitude follows the cw emission spectrum [33] which is attributed to the keto-form, the product of the ESIPT. The transmission increase is therefore identified as the delayed rise of the emission from the keto-form. This assignment is also in agreement with recent fluorescent up-conversion experiments which measure the time 

A second important observation is that the temporal shape of the emission rise follo vs a step function. This is demonstrated in Fig. 11.8. It sho vs the results of fitting an exponential increase convoluted with the crosscorrelation (a), a delayed step like rise convoluted with the crosscorrelation (b) and the complete model function (c) to an experimental trace of HBT at a probe wavelength of 564 nm where the oscillatory contributions are quite weak. The exponential increase and the delayed step function give almost the same ESIPT time [33]. However, the exponential increase deviates significantly from the data at short delay times whereas the step function matches quite accurately the essential shape of the trace. 

A ballistic wavepacket motion is incompatible with a tunneling process of the proton from the enol to the keto site. The transition probability of a single attempt is much smaller than 1 and many tunnel events are necessary for an efficient population transfer leading to a gradual population rise in the product state. However, if the proton itself would move from the enol to the keto site via a barrierless path, the ESIPT would take less than 10 fs because of the small proton mass [18]. This is a first indication that slower motions of the molecular skeleton are the speed determining factors and that the proton mode is not the relevant reaction coordinate [27]. 

The delay of the emission rise is in the order of 50 fs for many investigated molecules (see above), and the wavelength dependence of the amphtude matches the fluorescence of the keto form. The emission rise reflects therefore the time for which the molecule adopts the keto form and represents the duration of the ESIPT. This assignment is also in agreement with recent fluorescence upconversion 

An exponential signal rise is expected if the dynamics can be described as a rate-governed population transfer between two states. This seems to be an inadequate model for the ESIPT. The step function, on the other hand, points to an almost classical ballistic motion along the PES [31]. The wavepacket produced by the optical excitation seems to move completely to the product state without pronounced spreading or splitting. The population appears delayed but within a very short time interval in the product state. A ballistic wavepacket motion is incompatible with a tunneling process of the proton from the enol to the keto site. 

If the proton itself would move from the enol to the keto site via a barrier-less path, the ESIPT would take less than 10 fs because of the small proton mass [34]. 

This is a first indication that slower motions of the molecular skeleton are the speed-determining factors [30]. 

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