DETAILED EXCITON BAND STRUCTURE OF MOLECULAR CRYSTALS.

Abstract

From the experiments on the $^{1}B_{2a}$ state of naphthalene, naphthalene-$d_{8}$, and their dilute mixed crystals, values for $M_{12}$ and $M_{1} (i = a,b,c)$ are deduced where $M_{12}$ represents the interaction between interchange equivalent molecules and the $M_{1}$ represent the interaction between the translationally equivalent molecules along the a,b, and c crystal axes. The quasiresonance shift is found to be $12.3\pm 4 cm^{-1}$ compared to the $147\pm 6 cm^{-1}$ resonance splitting. The translational $(k =0)$ shift is found to be $5\pm 7 cm^{-1}$. Thus, $M_{12}= 18.4 \pm 0.4 cm^{-1}$ and $M_{a}+M_{b}+M_{e} = 2.5\pm 3.5 cm^{-1}$. The site (static) shift is $466\pm 10 cm^{-1}$. The common observation of very narrow lines in the exciton (Davydov) splitting of molecular crystals is not due to the discreteness of exciton levels but is due to the spectroscopic selection rule $(\Delta k = 0)$ and the fact that all molecules are in the ground state $(k = 0)$ at the low temperatures usually employed. By observing transitions between vibrational and electronic exciton states, the complete electronic k band structure is observed. For naphthalene, the observed band agrees with the pure and mixed crystal data reported above. For benzene, it agrees with the location of the forbidden exciton component reported in the 1965 Symposium. Both of the above experiments indicate that $M_{12}\gg M_{1}$. Noting that $M_{12}$ and $M_{1}$ represent interactions between nearly perpendicular and parallel molecules, respectively, this fact may indicate that intramolecular $\sigma-\pi$ mixing should be considered in the calculation of the intermolecular interactions. The quasiresonance data seem to be inconsistent with a recent prediction of the energy of the charge-transfer state in crystalline $naphthalene.