Magnetic and Electric Field Spectra of Organic Crystals: Optical Measurements of Zero-Field Splittings

Abstract

The theory of the Zeeman and Stark effects in molecular crystal exciton bands is presented. The development emphasizes the role of the intermolecular potential in determining the spin alignments in the crystal, and it is shown that the interactions $V$ , and the projections of spins from one molecule onto those of another ${\mathrm{〈T}}_{\alpha }{\mathrm{\hspace{0.17em}|\hspace{0.17em}T}}_{\beta }〉$ , determine the crystal spin quantization in the absence of external fields through matrix elements of the type ${\mathrm{V\; 〈T}}_{\alpha }{\mathrm{\hspace{0.17em}|\hspace{0.17em}T}}_{\beta }〉$ . A complete anisotropic Zeeman study in weak and strong fields is presented for the benzophenone crystal. It is shown that relatively low‐resolution optical studies can be used to determine zero‐field splitting parameters to about 5% accuracy. The higher resolution studies have led to the assignments, and relative ordering of the twelve k = 0 exciton components of the ${}^3\mathrm{n\pi *}$ state of benzophenone crystals. These results are confirmed by Stark and Stark–Zeeman experiments which demonstrate the applicability of the theory outlined. The final best set of molecular spin‐splitting parameters, and intermolecular matrix elements are $$\begin{array}{ccc}\text{X\hspace{0.17em}=\hspace{0.17em}−\hspace{0.17em}0.03,}& \text{Y\hspace{0.17em}=\hspace{0.17em}−\hspace{0.17em}0.09,}& \text{Z\hspace{0.17em}=\hspace{0.17em}+\hspace{0.17em}0.12}{\mathrm{cm}}^{\text{−1}}\\ V_{12}\text{\hspace{0.17em}=\hspace{0.17em}−\hspace{0.17em}0.23,}& V_{13}\text{\hspace{0.17em}=\hspace{0.17em}+\hspace{0.17em}0.03,}& V_{14}\text{\hspace{0.17em}=\hspace{0.17em}+\hspace{0.17em}0.07}{\mathrm{cm}}^{\text{−1}}.\end{array}$$ . The benzophenone crystal triplet exciton states, at k = 0, are close to those expected for strong spin coupling, but the similarity of magnitude of the $V$ terms and the spin splittings causes the pure excitonlike spin states to be slightly mixed at zero field.