Download Advances in Chemical Physics, Vol. 74 by Ilya Prigogine, Stuart A. Rice PDF

By Ilya Prigogine, Stuart A. Rice

This precious sequence is dedicated to aiding the reader receive basic information regarding a wide selection of themes in chemical physics, which box the editors interpret very largely. Their purpose is to have specialists current entire analyses of topics of curiosity and to motivate the expression of person issues of view.

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2. The Anthracene Crystal Lattice The first calculations on the anthracene crystal, including the nonanalyticity at K = 0 of the excitonic band, were proposed by Davydov and Sheka in ref. 18. In these calculations, the vibronic aspect was ignored, while the upper electronic levels were included by means of an effective dielectric constant, the term (1/EO)ddbeing replaced by (l/cocr)dd. In 1977, Honma3’ corrected a few points in these calculations. Still in the dipolar approximation, Philpott has since calculated2’ the excitonic energies of the main aromatic crystals, taking into account explicitly many excited electronic states and series of vibronic levels.

We consider here the way coupling to phonons may affect the electronic motion of the crystal states. 18) J,,B;B, nm The terms D , represent the energy stabilization due to van der Waals forces for oneexcitation localized on molecule n and due to neighboring molecules in the ground state. In general, these forces are much larger than the interactions J . which are neglected in a zero-order approximation. The localized electronic excitations are then eigenstates of H; we may investigate the nuclear potential in these electronic states.

We consider the dynamical problem in the above case ha, >> Jk, so that the coupling J2/hR, between various subspaces of constant vibrational quanta can be neglected. a. In the local representation, we denote by Inm) the state with an electronic excitation on site n and one vibrational excitation on site m (the case n = m gives back the vibron v = 1, since the excitations are renormalized). Assuming only bimolecular interactions, for processes on a single particle, with p # m, n and m # n, we obtain the following terms illustrated diagrammatically: and for processes involving two particles m #n, we have the following diagrams: Here D and M denote the exciton energy stabilization and its transfer amplitude respectively; A and p are analogs for the vibration, and D(') and M(') for the vibron.

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