Planewise summation of point dipole-dipole interactions for some aromatic hydrocarbon crystals

Abstract

Lattice sums of point dipole‐dipole interactions have been evaluated by the method of planewise summation for wave vectors perpendicular to the (001) plane of aromatic hydrocarbon crystals. The interaction between a plane of dipoles and a single dipole located at the origin is called a plane sum. It is found that the magnitude of plane sums falls off very rapidly with perpendicular distance of the plane from the origin. The contribution from all plane sums not containing the origin is less than 10% of the total lattice sum for naphthalene, approximately 1% for anthracene and phenanthrene, and negligible in the cases of tetracene and pentacene. Some results for L axis dipoles on translationally inequivalent molecules are given below (units cm⁻¹/Ų). I_1L,2L(0) is the plane sum for the plane containing the origin, I_1L,2L(1) is the nearest neighbor plane sum, and Ewald sum is the infinite crystal lattice sum. $$\begin{array}{cccc}\mathrm{Crystal}& I_{\text{1L,2L}}\text{(0)}& I_{\text{1L, 2L}}\text{(1)}& \mathrm{Ewald\; sum}\\ \mathrm{Naphthalene}& 3333& \text{−57}& 3219\\ \mathrm{Anthracene}& 2701& \text{−20}& 2661\\ \mathrm{Tetracene}& 4577& \text{−1}& 4575\\ \mathrm{Pentacene}& 4631& 0& 4631\\ \mathrm{Phenanthrene}& 4246& 5& 4255\end{array}$$ It is suggested that the existence of weakly coupled crystal planes simplifies the theoretical treatment of several exciton processes. A brief discussion is given for absorption and reflection spectra, exciton band structure and exciton‐phonon coupling.