Exciton transfer integral

In this section we derive an expression for the transfer integral for the resonant exciton transfer depicted in Fig. 9.1. Consider a system consisting of two molecules, m and n. The total Hamiltonian for the sj tem is the sum of the intramolecular Hamiltonians, Hm and Hn, and the intermolecular Hamiltonian, Hmn- The eigenstates of Hm and Hn are M)m and iV) , respectively. 

Suppose that initially molecule m is in an excited state, EX)m, and molecule n is in its the groimd state, GS) . In the absence of intermolecular interactions the initial state, i), is a direct product of these molecular states  

The transfer of energy results in a final state, F), defined by  

This transfer of energy is mediated by the Coulomb interactions between the pair of molecules. Thus, the transfer integral, Wmn is defined as  

Expressing the intermolecular direct Coulomb Hamiltonian in second quantization (as described in Section 2.6), namely, 

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The exciton transfer is coherent when the transfer time is fast compared to dissipative relaxation times, where the dissipative relaxation is usually inter or intramolecular vibrational relaxation and the transfer time is proportional to the inverse of the exciton transfer integral (described in the next section). In this limit the exciton is described by a wavefunction, whose time d3mamics are controlled... 

To conclude this section we note that the triplet exciton transfer integral is... 

Fig. 9.2. CoUinear (a) and parallel (b) arrangement of a pair of molecules in a dimer. The exciton transfer integral, J, is negative for the coUinear arrangement and positive for the parallel arrangement.

Dimers We discuss dimers for two particular geometrical arrangements, namely coUinear and parallel, as shown in Fig. 9.2. In the coUinear arrangement the exciton transfer integral, J = —2J (R), whereas in the parallel arrangement, J = where is defined in eqn (9.12). In both cases there are bonding,... 

Comparison of the thermal energy required to excite an exciton with the activation energy for electronic conductivity allows determination of U and t], the on-site electron-electron repulsion and the intra-dimer one-electron transfer integral. We find U % 1,3 and 1,1 eV tj 0,4 and 0,35 eV for the Rb+ and TMB+ salt, respectively. ... 

The local or extended nature of molecular-ion (or exciton) states in molecular solids is determined by a competition between fluctuations in the local site energies of these states (which tend to localize them) and the hopping integrals for inter-site excitation transfer (which tend to delocalize them). In order to define this fluctuation-induced localization concept more precisely, consider the model defined by the one-electron Hamiltonian... 

In these relations the operator B (Bn) describes the creation (annihilation) of a molecular excitation at lattice site n. We assume below that n 1,2,. ..,Ar, where N is the number of molecules in the chain and we consider one electronically excited molecular state. Then E-p is the on-site energy of a Frenkel exciton and Mnni is the hopping integral for molecular excitation transfer from molecule n to molecule n. In the summation in HF the terms with n = n are omitted. The Hamiltonian HF describes the Frenkel excitons in the Heitler-London approximation. 

Whereas under photoexcitation the exciplex is excited indirectly via energy transfer from the excitons, it is the primary neutral excitation in electroluminescence. This is shown in Fig. 2.24, parts (a) and (b), where the EL emission for both TFB and PFB blends is dominated by the exciplexes. This becomes particularly clear when comparing the EL spectra with the delayed emission spectra in Fig. 2.23, parts (c) and (d). In contrast, the time-integrated PL from similarly prepared blend films (also plotted in Fig. 2.24) is primarily due to bulk excitons. We note that exciplex EL emission has been observed previously, which suggests that these exciplexes may also be formed by the mechanism of direct electron-hole capture at the interface [37, 41, 42]. 

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