CT excitons

Photoexcitation of the complex is accompanied by charge transfer from the donor TBPDA molecule to the acceptor C6o one and CT-exciton is formed. Depending on mutual orientation of spins of components (electrons and holes), CT-exciton can be either a singlet or a triplet one. Free charge carriers are formed in molecular crystals mainly due to thermal or impurity dissociation of triplet CT-excitons [6],... 

The appearance of one or more CT-excitons below the conduction band of the conjugated chain may not appear to be of major importance for the properties of the material. In fact the consequences of the occurrence of excitons are significant. Slater and Shockley (1936) demonstrated that the descriptions of the system by Bloch functions, i.e. the band model, and by localised excitations, i.e. excitons, were related to one another by a unitary transformation. They were also the first to consider the impact of the... 

It should be noted that the above classification of the electroabsorption spectrum is valid only approximately, because first of all eqn (11.11) is correct only in the case of weak absorption and, second, the Frenkel and CT exciton states usually mix. We finally mention that the change of the refractive index Sn is of the same order as 5k new experimental techniques are required to measure this change, however. Good candidates for such methods have been proposed by War-man and coworkers (18). The success of such measurements could be the basis of electrorefraction spectroscopy, complementary to the existing electroabsorption spectroscopy. 

To numerically simulate the time evolution of CTEs distributed over a two-dimensional donor-acceptor interface the D-A sites were arranged in a square lattice. It was assumed that the D-A interface is uniformly irradiated with a time independent source of intensity I. Only one CTE can be generated at any site, so every D-A site can be either occupied or not. The CT exciton generated at a given lattice site will stay there and it cannot move to another D-A site because of self-trapping. 

Once generated, there are two mechanisms for the CTE to disappear. First, recombination occurs because of the finite lifetime r of the CTE. The second mechanism is via dissociation. The CT exciton dissociates when, due to the dipole-dipole interaction, the energy of the particular exciton exceeds some threshold. If there are n CTEs occupying the D-A interface, the electrostatic energy of the ith exciton in the electric field of the other excitons surrounding this site is ... 

We start the simulations when there are no CTEs at the interface. Under the influence of the pumping the excitons begin to appear. After the time r, the number of CT excitons occupying the lattice reaches the steady state value. In our current work we take a time interval of 5 r to ensure that the steady state is reached. From this time on the necessary statistical information is collected. 

Next, during the same time step, we calculate the energy of every CTE in the electrostatic field produced by the dipole moments of all other excitons. The energy of the ith CT exciton can be found using eqn (11.21). If this energy is greater than the dissociation threshold, B, the CT exciton dissociates. Finally, we recalculate the energies of all CT excitons that remain at the D-A interface. 

FlG. 11.5. Position of the energy distribution peak as a function of the number of CT excitons, m. The position of the energy peak obtained from the numerical simulation appears to be proportional to nl B. Reprinted with permission from Kiselev et al. (20). Copyright Elsevier (1998). 

In the analysis of the lowest electronic excitations in quasi-one-dimensional crystals, it is natural to take into account not only Frenkel excitons, but also one-dimensional charge-transfer (CT) excitons. We will show below that the spectrum of excited states in the molecular chain is strongly sensistive to the mixing of Frenkel and CT states. 

However, even in perfect ID structures, the mixing of Frenkel and CT excitons destroys this simple picture. Below, following (43), we show that this mixing is responsible for the appearance of new excitonic states, which are localized at the ends of a one-dimensional crystal chain and which are analogous to Tamm surface states of electrons. Their energy can be blue- or red-shifted in comparison with the bulk states. In the case of red-shift, these states can determine the fluorescence spectrum of a molecular chain. They can also play an important role in quantum confinement of the states in the molecular chain. For the description... 

The wavefunction of the crystal in the state with one mixed F CT exciton is... 

We can assume that ee and are real. That means that a > 0 and a >p. In the case that the interaction between Frenkel and CT excitons is absent and therefore a = (3 = 0, we obtain from eqn (12.47) the solutions... 

On the other hand, if a coupling between Frenkel and CT excitons (a ... 

Fig. 6.13 Excitons with different radii diagram of a Frenkel exciton, a Wannier exciton, and a charge-transfer (CT) exciton.

The energy of a CT exciton, Fct, in which the electron and the hole are located on neighbouring molecules, is given by... 

In crystals which are composed of two different partner molecules, CT excitations and with them CT excitons are frequently the predominant lowest excitation states and are thus responsible for the lowest-energy transitions in the singlet system. We will illustrate this using the example of the weak donor-acceptor complex anthracene/pyromellitic acid dianhydride, (A/PMDA) (Fig. 6.14). The ground state is neutral and nonpolar, with only a small charge-transfer fraction. The lowest optical excitation starts from the ground state of the donor D, anthracene, (from its highest occupied orbital or HOMO) and leads to the lowest unoccupied orbital (LUMO) of the acceptors A, PMDA, within the mixed stack DADADA. A polar ex-... 

Fig. 6.16 Detection of a CT exciton in anthracene-PMDA by means of the Stark effect. The sharp zero-phonon line at the absorption edge (dashed line, without an electric field) splits in the presence of an electric field (ofca. 4 lO Vcm" ) into two components (solid line). From [38].

Moreover, CT excitons are thought to be formed by intermolecular interaction in certain polymeric systems containing small molecules. A typical example is poly(N-vinyl carbazole) doped with trinitrofluorenone (TNF), a system which played a major role in early photoconductive studies on polymeric systems (see Chart 2.1). 

---