Calculations of singlet exciton states of the molecular crystals naphthalene and anthracene have been performed by Craig and Walsh,1Craig and Hobbins,2and more recently by Silbey, Jortner, Vala and Rice3and Silbey, Jortner and Rice.4Theoretical treatments follow the orignial work of Davydov for the interaction of a molecule and the weak crystal field. Since intermolecular overlap in a molecular crystal is small, the interaction between molecules may be represented as a multipole expansion. For an intense transition (f> 1.0) the Craig method retains only dipole terms in the expansion. These dipole sums are evaluated by the Ewald Kornfeld procedure or by direct summation over a sphere of 20–30 Å. Silbeyet al., however, compute the intermolecular interactions to 55 Å using π-electron wavefunctions or dipole summation, and beyond 55 Å using dipole sums. The main differences in the results of the treatments are due to the contributions of these long range interactions.