Wavepacket diffusion

To deal with ET in organic semiconductors, one has to incorporate the coherent motion of electron in the multi-states. The single two-state rate model developed for the donor-acceptor system may not be used straightforwardly. Here, we display a time-dependent wavepacket diffusion (TDWPD) approach for the charge carrier dynamics. In the approach, the nuclear vibrational motions are dealt with the semi-classical fluctuations on the electronic energies of molecules. In this way, we can apply the approach to the nanoscale organic crystals. 

Electron Mobilities of N-type Organic Semicondnctors from Time-Dependent Wavepacket Diffusion Method Pentacenequinone Derivatives... 

The transition from direct to indirect photodissociation proceeds continuously (see Figure 7.21) and therefore there are examples which simultaneously show characteristics of direct as well as indirect processes the main part of the wavepacket (or the majority of trajectories, if we think in terms of classical mechanics) dissociates rapidly while only a minor portion returns to its origin. The autocorrelation function exhibits the main peak at t = 0 and, in addition, one or two recurrences with comparatively small amplitudes. The corresponding absorption spectrum consists of a broad background with superimposed undulations, so-called diffuse structures. The broad background indicates direct dissociation whereas the structures reflect some kind of short-time trapping. 

This is inherently impossible in the time-independent approach because the wavefunction contains the entire history of the wavepacket. The real understanding, however, is provided by classical mechanics. Plotting individual trajectories easily shows the type of internal motion leading to the recurrences which subsequently cause the diffuse structures in the energy domain. The next obvious step, finding the underlying periodic orbits, is rather straightforward. 

Although the diffuse structures for H2O and for H2S look rather alike, they reflect quite different dynamical situations. In both cases, they are caused by symmetric stretch motion. However, in the case of H2O the wavepacket performs symmetric stretching motion on the rim of the dissociative PES between the two fragment channels, whereas in the case of H2S the wavepacket oscillates in the well of the binding PES. In the first case, the instability of the trajectory on top of the saddle [see Figure 8.6(a)] damps the oscillatory motion while in the second case the damping is caused by coupling to a dissociative state. The net result is... 

Suter, H.U., Huber, J.R., von Dirke, M. Untch, A., and Schinke, R. (1992). A quantum mechanical, time-dependent wavepacket interpretation of the diffuse structures in the... 

The motion of the exciton wavepacket causes the transport of energy. In order to find the appropriate energy diffusion coefficient we must estimate the mean free path and the mean free time of the wavepackets. This situation is quite similar to that of phonon heat conductivity (see, for example, (12)). 

PES for a long time, i.e. which does not dissociate either on the upper or on the lower PES. As discussed by Weide et the short-time dynamics of the wavepacket which does not quickly dissociate is governed by a periodic classical orbit that basically performs bending motion in the deep potential well. For a more detailed discussion of diffuse structures and periodic classical orbits, see Ref. 1. Thus, in contrast to H2S and the excitation of ozone in the Chappuis band, the diffuse structures are due to bending excitation rather than due to excitation of the symmetric stretch mode. Because the equilibrium angles in the two electronic states are so drastically different, the progression is long. 

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