Line Shapes of Triplet ESR Spectra: The Effects of Intermolecular Exciton Transfer

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Abstract
The system considered is a molecule like triptycene where triplet excitation can jump between several equivalent sites whose Hamiltonians do not commute. The line shapes are calculated from the Bloch equations for the density matrix, and the result involves inverting a certain matrix with complex elements which depend on the jumping rate. The method is similar to Sack's method for sites whose Hamiltonians do commute. The complete line‐shape function is found in zero magnetic field and when the field is along the triad axis. General perturbation formulas are derived for finding the broadenings and frequency shifts which occur in the limits of very fast and very slow jumping. The direct calculation of the line shapes for tribenzotriptycene in a glassy matrix has not been attempted, but the results obtained for the oriented triplet agree quite well with the observed ESRspectra of the glass. The method is also applied to the problem of a spin ½ which jumps between two sites with different gtensors.