On the theory of two-photon induced fluorescence anisotropy with application to indoles

Useful relationships are derived from the general work by McClain [J. Chem. Phys. 57, 2264 (1972)] to connect the traditional two-photon polarization ratio of absorptivities using circularly and linearly polarized light (Ω) in fluid media with the expected anisotropy of fluorescence induced by two-photon excitation in viscous media or shortly after pulsed excitation. Emphasis is on ππ* transitions of planar systems with small out-of-plane two-photon tensor elements. Large ranges of anisotropy are found for most of the tensor space. The maximum and minimum anisotropies for ππ* excitations and emissions appear to be 0.6123 and −0.3277, somewhat larger than the previously supposed values of 4/7 (0.5714) and −2/7 (−0.2857). Application is made to indole and three-substituted indoles for which two-photon tensor shapes and orientations are deduced. Some predictions from semiempirical molecular orbital theory—including simulated aqueous solvent effects—are presented which agree qualitatively with experimental two-photon anisotropies reported in the literature.