Effect of the Orientation of Donor and Acceptor on the Probability of Energy Transfer Involving Electronic Transitions of Mixed Polarization

The probability of transfer of electronic excitation energy between chromophores by the Forster mechanism depends, among other factors, on the orientation in space of the donor and acceptor chromophores. The orientational dependence of the transfer efficiency has been previously evaluated for the case in which the donor and acceptor electronic transitions are characterized by a single electric transition dipole moment at the range of spectral overlap between donor fluorescence and acceptor absorption. Polarization data for the chromophores involved show that this is often not the case and that the electronic transitions have mixed polarizations and are characterized by two or three transition dipole moments. In this paper we evaluate the orientational dependence of energy transfer when the chromophores have mixed polarizations. First, we relate the magnitude of the transition dipoles of a chromophore to its fluorescence polarization. Then, we evaluate the dependence of the probability of energy transfer on orientation in terms of the one, two, or three transition dipole moments associated with the electronic transitions of each of the chromophores participating in the energy transfer. Finally, we calculate the probability for obtaining a given value for the orientational factor in an ensemble of donor-acceptor pairs the chromophores of which have random orientations but are fixed in space. The results obtained are applied to the evaluation of the distribution of end-to-end distances in a series of oligopeptides studied previously in viscous solutions by energy transfer between chromophores attached to the molecular ends. The donor and acceptor used in that study were naphthalene and dansyl, which have effective polarizations of 0.07 and 0.33, respectively, at the spectral range of interest. It is shown that in this case the orientational dependence of the probability of energy transfer affects the calculated end-to-end distribution function of the oligopeptides to a negligible extent. Calculated estimates are presented for the range of error that can occur in the evaluation of distances between chromophores by energy transfer when the orientations of the chromophores are fixed but unknown. The smaller the fluorescence polarization of the donor and acceptor, the smaller the error, which is not likely to exceed ±10% for polarizations smaller than 0.3.