Site shift surface excitons SSSE in anthracene

1 Site shift surface excitons (SSSE) in anthracene 

In this subsection we go back to more detail than in Section 9.1 discussion of excitations in first monolayers of organic crystals of anthracene family (naphthalene, tetracene and so on). As we explained the spectrum of this states depends on the distance to surface of crystal. For this reason these excitons are called site shift surface excitons (SSSE) what is reflected in title of this subsection. 

In anthracene crystal as it follows from data collected in Table 3.1 the distance between a, b plane is large in comparison with distance between nearest molecules in this plane. As the result, as we already mentioned in Section 9.1, the interactions between molecules in different planes is smaller than interaction between molecules inside the same plane. This means that anthracene crystal the same as other crystals of the its family have layered structure which we explicitly take into account in microscopical theory of surface states. We will use the same Hamiltonian (2.2) as we used in consideration of bulk states in simplest Heitler-London approximation. However, now we have to take into account that translational symmetry exists only along the surface of crystal which we assume parallel to a, b plane. In an infinite crystal the diagonalization of Hamiltonian leads to two exciton bands Eit2(k), so that the general pattern of levels is the one shown schematically in Fig. 12.4b. 

In the given case and in Heitler-London approximation the diagonalization of Hamiltonian (2.2) can be carried out by means of (2.8) with functions uaa taken in the form  

The molecular and exciton levels in a crystal with (a) one molecule and (b) two molecules in a crystal unit cell. 

---