Extended strong-coupling limit

W. Barford, Excitons in the strong coupling limit of the one-dimensional extended Hubbard model, Phys. Rev. B 65 (2002) 205118. 

There are many studies of the transfer of electrons from enzymes to substrates, across biological membranes, to (or from) electrodes from (or to) substrates, between adsorbed molecular dyes and semiconductor particles, within synthetic films and nano-scale arrays, within molecular wires , and so on. Only a few, general comments will be offered on these topics here. The basic physics of molecular electron transfer does not change with the scale of the system, as long as identifiable molecular moieties are present with at least partly localized electronic configurations. The nature of the properties observed, the experimental probes available, and the level of theoretical treatment that is useful may be very different. Different approaches, different limiting models are used for extended arrays (or lattices) of very strongly coupled moieties. 

Investigation of reaction surfaces and reaction hypersurfaces If the translational motion of the reaction complex couples with other LAMs of the complex, the RP can be sharply curved in the regions with strong coupling. The actual trajectory of the reaction complex deviates far from the RP and a correct dynamic description can only be achieved if the reaction valley is extended to a minimum energy reaction surface or hypersurface, which embeds all LAMs. Calculations needed to describe the reaction (hyper) surface can become rather expensive and, therefore, this approach is limited to... 

When the limiting conditions of the friction approximation are not valid, e.g., there is strong non-adiabatic coupling or rapid temporal variation of the coupling, there is at present no well-defined first principles method to calculate the breakdown in the BOA. The fundamental problem is that DFT cannot calculate excited states of adsorbates and quantum chemistry techniques, that can in principle calculate excited states, are not possible for extended systems. 

A scheme as described here is indispensable for a quantum dynamical treatment of strongly delocalized systems, such as solid hydrogen (van Kranendonk, 1983) or the plastic phases of other molecular crystals. We have shown, however (Jansen et al., 1984), that it is also very suitable to treat the anharmonic librations in ordered phases. Moreover, the RPA method yields the exact result in the limit of a harmonic crystal Hamiltonian, which makes it appropriate to describe the weakly anharmonic translational vibrations, too. We have extended the theory (Briels et al., 1984) in order to include these translational motions, as well as the coupled rotational-translational lattice vibrations. In this section, we outline the general theory and present the relevant formulas for the coupled... 

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