Determination of transition moment directions in molecules of low symmetry using polarized fluorescence. I. Theory

Abstract

A theoretical description of angle-resolved fluorescence depolarization experiments of dye molecules in stretched polymer films is presented. It is shown how the technique can be used for the determination of transition moment directions in organic molecules of low symmetry. The application of these angle-resolved measurements to the determination of the direction of the transition moments in a number of dye molecules is discussed in the following paper. The theoretical treatment implicitly assumes that the motions of the fluorescent molecules are slow on the time scale of their excited state lifetime (in the order of ns) so that their orientation is identical at the times of absorption and emission. Furthermore the molecules are taken to be uniaxially distributed around the stretch direction of the polymer film and it is shown how this can be checked experimentally. The macroscopic orientational distribution is assumed to be invariant for a rotation of 180° of the molecules around a ‘‘mechanical’’ symmetry axis chosen in the molecular frame as well as to a reflection in the molecular plane (C2v D2h symmetry). The treatment presented makes use of the Wigner rotation matrix formalism in the description of the fluorescence intensities in terms of molecular orientational properties (order parameters and angles between transition moments and the mechanical symmetry axis). The advantge of this formalism is the ease with which rotational transformations are carried out between molecular and laboratory frames and further that the symmetry properties of both the molecules and the system are treated in a simple and general way.