Dipole Davydov Splittings in Crystalline Anthracene, Tetracene, Naphthalene, and Phenanthrene

The contribution of dipole–dipole interactions to the Davydov splitting (i.e., the dipole Davydov splitting) of the moderately intense ${}^1{A}_g{\mathrm{\hspace{0.17em}\to \hspace{0.17em}}}^1{L}_a$ transitions of anthracene, tetracene, naphthalene, and phenanthrene has been investigated. Unlike most previous calculations, the Bose character of molecular excitons has been taken fully into account by using the classical theory of exciton states. In the dipole approximation this treatment is equivalent to the second quantized formulation of Agranovitch. Formulas are also derived for coupling of Born–Oppenheimer separable states through the full interaction potential. Dipole sums are calculated for infinite crystals by Ewald's method. High‐energy $\mathrm{\pi –\pi *}$ transitions are shown to make sizeable contributions to the Davydov splittings and are responsible for increasing polarization ratios of the 0–0 transition. For anthracene these high‐energy states push the splittings of the 3800‐Å system beyond the accepted values, implying that the residual intermolecular interactions due to higher multipole and exchange effects act in the opposite direction, thereby reducing the total splitting. In tetracene the dipole splittings, after including higher states, are in excellent agreement with experiment, thereby relegating multipoles, etc., to a minor role. The ${}^1{L}_a$ states of naphthalene and phenanthrene are subject to a pinching effect, due to the proximity of levels above and below, which inhibits the development of a large dipole splitting.