On the Singlet-Exciton States of Crystalline Anthracene

In this paper we present a detailed analysis of the lower excited states of crystalline anthracene. Starting with zero‐order product wavefunctions, the treatment differs from standard formulations in that interactions between molecules are computed directly by the use of π‐electron theory, by the inclusion of the effects of extensive configuration mixing, and by the inclusion of long‐range interactions out to the convergence limit. It is found that: (1) The computation of interaction energies cannot be reduced to dipole—dipole terms alone. By the use of π‐electron theory it is shown that short‐range high‐order multipole (greater than dipole) interactions make important contributions to both the diagonal and off‐diagonal elements of the energy matrix. (2) Long‐range interactions of the dipole—dipole type are of importance for distances of the order of the wavelength of light. By application of momentum‐conservation conditions, it is shown that the long‐range dipole—dipole interactions, including the effects of retardation of the potential, are absolutely convergent. Major contributions to the Davydov splitting arise from molecular separations ranging from 50 Å to the convergence limit. (3) For the case of allowed singlet—singlet transitions, electron‐exchange interactions are small relative to other contributions to the interaction energy. (4) Under the experimental conditions used to date, the Davydov splitting should be independent of crystal thickness. (5) In anthracene, crystal‐field mixing of the p and β molecular states has a large effect on the Davydov splitting. Inclusion of mixing with higher excited π states has little effect on the Davydov splitting, but is required in the calculation of the polarization ratios in the vibronic components of the p band. (6) Charge‐transfer exciton states play only a minor role in altering the properties of singlet exciton states arising from allowed transitions. (7) The detailed calculations reported herein yield good agreement with the observed Davydov splitting (ΔE) and polarization (P) ratios in anthracene, e.g., for the ¹A_1g→¹B_2u band: $$\begin{array}{ccccc}\mathrm{Vibronic\; band}& \mathrm{\Delta E(}\mathrm{calc}\mathrm{.)(}{\mathrm{cm}}^{\text{−1}})& \mathrm{\Delta E(}\mathrm{obs}\mathrm{.)(}{\mathrm{cm}}^{\text{−1}})& \mathrm{P(}\mathrm{calc}\mathrm{.)}& \mathrm{P(}\mathrm{obs}\mathrm{.)}\\ & & & & \\ \text{0–0}& 207& 230& \text{3.5}& 5\\ \text{0–1}& 102& 145& \text{2.5}& \text{4.5}\\ \text{0–2}& 54& 80& \text{1.9}& 3\end{array}$$