Lowest singlet-exciton energies

Figure 2-8. Convergence of the excitation energy to the lowest-lying singlet exciton computed by CIS and TDDFT using the Slater-Vosko-Wilk-Nusair functional with the STO-3G basis set as a function of the number of wave vector sampling points (K) [50]. The error is defined as the absolute difference from the K = 100 results. The converged (K = 100) result with TDDFT is very close to the fundamental energy gap...

For lowest energy singlet excitons in anthracene (22) r 10 9s, 7 5x xl0 9cm3/s, so that only for N < 1016cm 3 can the bimolecular quenching be not very significant. 

However, if a singlet exciton has a large oscillator strength, Bose-Einstein condensation is nevertheless possible for excitons but only if the minimum energy in the lowest excitonic band does not correspond to the center of the Brillouin zone. In the opposite case we have to take into account that the retardation drastically modifies the spectrum of excitons, transforming excitons into polari-tons. In such 3D crystals the condensation of excitons is impossible because the spectrum of polaritons in the region of small k (see Ch. 4) coincides with the spectrum of photons with energy E(k) —> 0 at k —> 0. However, for polaritons in a microcavity Bose-Einstein condensation is possible because in a microcavity there exists a so-called cut-of frequency (see Ch. 10)... 

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