Abstract
In order to provide a general background for the following discussions on the localizability and motion of electronic excitation, we attempt to review some of the basic concepts related to excitons in molecular crystals [1–7]. One of our purposes is to define rigorously, in the limit of a weak matter-radiation interaction, the light absorbing entities and the subsequent processes of electronic excitation energy transformation. We know that individual molecules can only be taken as the light absorbing entities under very special conditions, which must be discussed in each case.
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References
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These modes may be seen in the following way: a molecular excitation to level lnn> may be represented by an electronic oscillator μon exp [i(En-En)t/h], where μon is a matrix element of an electronic dipole operator. The resonant electronic oscillators, associated with each site, couple weakly and form modes of electronic oscillations: μok exp [i(E k -E o )t/h].
These situations may be illustrated as follows [10, 11] (noting by ΔE ss the Stokes shift): in the weak coupling case the excitation relaxes in the molecular potential (ΔE ss > U) and vibrates many times before transfer to the neighbours occurs (ΔE> U), i.e. the nuclei of the molecule feel mainly the electronic potential of a free excited molecule [12]. In the strong coupling case by contrast, the excitation transfers to the neighbours before relaxing (U> ΔE) and before any vibation takes place (U>ΔE), i.e. the nuclei of each molecule vibrate in the same potential of a de-localized electronic state. These `pictures’ involving relaxation and transfer between identical molecules can be invoked only when an external perturbation of strength γ o> U destroys the excitonic coherence between the identical molecules (see conclusion of the present paper).
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These transitions are better described by the non-adiabatic operator, i.e. the energy term neglected in the adiabatic approximation separating the intramolecular motions from the lower energy lattice motions [25].
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Abragam, A.: The Principles of Nuclear Magnetism, Oxford (1961) Chap. 10.
Note however that this crossed relaxation term disappears by symmetry for the dimers. (Cl. Aslangul, private communication).
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Voltz, R., Kottis, P. (1976). Excitons and Electronic Collective Excitations in Molecular Organic Solids. In: Chalvet, O., Daudel, R., Diner, S., Malrieu, J.P. (eds) Localization and Delocalization in Quantum Chemistry. Localization and Delocalization in Quantum Chemistry, vol 2. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-1456-4_11
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