The polarized reflection spectra of 9-cyanoanthracene crystal at 2°K taken at near normal angles of incidence are reported for a wavelength range corresponding to the first singlet electronic transition. The dielectric funtion is calculated by means of the Kramers-Kronig transformation and the positions and oscillator strengths of the main exciton transitions are located. The factor group splitting in reflection is nearly 80 cm-1, but in the derived absorption spectrum ε2(ω) the splitting is much larger, being approximately 200 cm-1. One component of the dielectric function is negative in the region of the 0-0 transition and the calculation of the theoretical attenuated total reflection spectrum suggests that at 2°K the (100) crystal surface should support an exciton surface polariton. The structure of the exciton band has been calculated for three orthogonal directions in the first Brillouin zone using the point dipole approximation. All four branches show strong negative dispersion in the kc direction, implying that the bottom of the exciton band is not a k = 0 level. This is one reason why the crystal shows no "monomer" fluorescence. The qualitative validity of the point dipole model has been established by calculating the nondipolar part of the exciton transfer interaction for near neighbors. It is found that the nondipolar parts are 25% or less of the individual intermolecular exciton transfer interactions. © 1979 American Institute of Physics.