Distance and orientation dependence of excitation transfer rates in conjugated systems: Beyond the Forster theory

The distance (R-DA) and orientation dependence of the rate for electronic excitation transfer (EET) from a segment of polyfluorene (PF6) to tetraphenylporphyrin (TPP) is studied using semiempirical quantum chemical methods. The fundamental issue concerns the applicability of the traditional Forster theory, which uses a point-dipole approximation, in describing the transfer rate in such systems involving large chromophores that may approach each other closely. In our theoretical calculation of the resonance-Coulomb rate, explicit account is taken of the extended transition dipole moment densities that are spread along the donor and acceptor molecules. Although we recover the Forster rate at large separations, the present study reveals several results not anticipated in the conventional theory: (a) The actual rate shows a much weaker short-range distance dependence (closer to R-DA(-2) than to the Forster R-DA(-6) value). The Forster expression overestimates the energy transfer rate by more than 2 orders of magnitude at short separation (R-DA < 1 nm). (b) The distance at which the Forster rate is recovered is observed to be rather large (similar to10 nm). Thus, the Forster expression seems to be inappropriate for condensed-phase systems where donors and acceptors can be closely packed, as, for example, in thin films. (c) Significant excitation transfer can occur via states that are optically dark (that is, carry very small oscillator strength). Forster theory excludes these potentially important pathways. (d) Irrespective of the interchromophore separation, the calculated orientation dependence of the resonance-Coulomb rates generally follows the Forster expression, with dependence on the cosine of the angle between the donor and acceptor transition dipole moment vectors. At close distances, however, the orientation dependence can make the rates differ by a factor of similar to2.