Excitons coherent motion

After the photon absorption, the exciton moves coherently till time 0.1-1 ps. The contribution of this regime to the quantum yield of the excitation transfer to the reaction center (RC) charge transfer state is less than a few per cent. From this point of view, the role of the coherent motion is insignificant. Due to averaging over different configurations of the photosynthetic unit and other experimental conditions, however, the coherent effects are not observable for t>0.1 ps. The intermediate regime,... 

In this section we discuss the coherent motion of excitons through an assembly or aggregate of N molecules. This is applicable when h/ J is much smaller than the dissipative relaxation times. 

Suppose that the operator creates an exciton on the mth molecule. Thus, it corresponds to exciting the molecule from its ground state to the state EX)to with an excitation energy A. The Hamiltonian that describes the coherent motion of the exciton through the aggregate is... 

In a perfectly ordered solid or a perfectly ordered macromolecule excitons move according to quantum-mechanical kinetics, i.e., like wave packets. Because this requires strict phase relationships in space and time, this mode of motion, addressed in the literature as coherent motion of excitons, is perturbed by all deviations from regularity. Chains of conjugated polymers always include various defects such as kinks and torsions. These break the conjugation. Typically, regular sequences extend only over five to ten repeat units. The results of measurements for a series of oligomers like the ones displayed in Fig. 7.4 can be used for the estimate. The red shift of the exciton frequency to with increasing monomer number, n, can be described by the equation... 

The description of excitation motion outlined in the previous sections assumes completely incoherent nearest neighbor hopping. This was treated in detail because it is the case of widest applicability especially with the materials of interest discussed in the final section. However, it should be noted that in some cases excitons can move coherently over several lattice spacings before being scattered i). For this case the diffusion coefficient is expressed in terms of the group velocity of the exciton v and the time between scattering events r. 

Dynamics. Cluster dynamics constitutes a rich held, which focused on nuclear dynamics on the time scale of nuclear motion—for example, dissociahon dynamics [181], transihon state spectroscopy [177, 181, 182], and vibrahonal energy redistribuhon [182]. Recent developments pertained to cluster electron dynamics [183], which involved electron-hole coherence of Wannier excitons and exciton wavepacket dynamics in semiconductor clusters and quantum dots [183], ultrafast electron-surface scattering in metallic clusters [184], and the dissipahon of plasmons into compression nuclear modes in metal clusters [185]. Another interesting facet of electron dynamics focused on nanoplasma formation and response in extremely highly ionized molecular clusters coupled to an... 

Reineker, P. (1982). Exciton Dynamics in Molecular Crystals and Aggregates. Stochastic Liouville Equation Approach Coupled Coherent and Incoherent Motion, Optical Lineshapes, Magnetic Resonance Phenomena. Springer Tracts in Modern Physics, Vol. 94, Springer, Berlin, Heidelberg. 

Assuming coherent exciton motion during the coherence time r, the mean free path L can also be estimated I = rv (v is the velocity of the excitons). The velocity V can be obtained from the relation mv = kT, with the effective exciton mass m. 

At r< 16 K, the triplet exciton motion within the one-dimensional stacks is coherent and is determined by the exchange integral Iaa = Ibb = 7 cm". This corresponds to an exchange frequency of coaa = 2 lAA/h = 2.7 10 s . For T> 16 K, the exciton motion within the stacks becomes increasingly incoherent. 

A considerable amount of theoretical work has been done on the lineshape of the EPR absorption under the influence of exciton motion. Haken and Strobl (1967, 1973) developed a stochastic model for the description of energy transfer by excitons that includes both the coherent and incoherent... 

The bottom row of color plots in Figure 12 displays the electronic modes of M7. Mode (a3) is localized at the P3 linear segment of M7 and is virtually identical to mode P3 (a). Similarly, M7(a2) and M7(al) resemble P2(a) and PI (a), respectively. The absence of coherence across mefa substitutions shown in this figure is remarkable the optical excitations are clearly confined to the various segments, meta conjugation makes a dear barrier for excitonic motion whereas para-conjugation is transparent to electronic coherences. This difference does not show up in the ground state, which is very similar for P7 and M7. 

In general the exciton dynamics exhibits both coherent and incoherent behaviour, where the incoherence arises from the couphng of the system to a dissipative environment. This is conveniently modelled by an equation of motion for the reduced density operator, p, defined by... 

From (1.32) it is obvious that in the presence of diffusion an effective broadening of the nuclear resonant line via rd(q) takes place leading to an accelerated decay of the nuclear exciton. The intuitive picture is that due to the diffusive motions of resonant atoms the spatial coherence between the scattered wave trains is partially destroyed, leading to increasing destructive interferences at latter times after the excitation. 

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