Method for calculating one-exciton absorption spectrum of   space-restricted lattices
  The problem of the one-exciton absorption spectrum is considered for the lattice of two-level interacting atoms whose initial energy splitting depends on the coordinate. It is shown that for some types of interatomic interaction, this problem can be reduced to a differential equation of Schrodinger type, which, in some cases, can be solved in closed form. By way of example, problems on the one dimensional chain having an initial splitting jump and on the spherical cluster are solved. In both cases analitical solutions are obtained, which considerably reduce the time required for calculations of one-dimensional systems and permit the calculation of three-dimensional spherical clusters, whereas the numerical calculation becomes impossible for the clusters with a radius larger than ten lattice constants. The spectra calculated for small systems completely coincide with the spectra obtained by means of numerical diagonalization. The proposed method may appear to be convinient for solving problems related to Frenkel excitons in systems having no translation symmetry (disordered systems). 
G. G. Kozlov