The fragment spin difference scheme for triplet-triplet energy transfer coupling.

To calculate the electronic couplings in both inter- and intramolecular triplet energy transfer (TET), we have developed the "fragment spin difference" (FSD) scheme. The FSD was a generalization from the "fragment charge difference" (FCD) method of Voityuk et al. [J. Chem. Phys. 117, 5607 (2002)] for electron transfer (ET) coupling. In FSD, the spin population difference was used in place of the charge difference in FCD. FSD is derived from the eigenstate energies and populations, and therefore the FSD couplings contain all contributions in the Hamiltonian as well as the potential overlap effect. In the present work, two series of molecules, all-trans-polyene oligomers and polycyclic aromatic hydrocarbons, were tested for intermolecular TET study. The TET coupling results are largely similar to those from the previously developed direct coupling scheme, with FSD being easier and more flexible in use. On the other hand, the Dexter's exchange integral value, a quantity that is often used as an approximate for the TET coupling, varies in a large range as compared to the corresponding TET coupling. To test the FSD for intramolecular TET, we have calculated the TET couplings between zinc(II)-porphyrin and free-base porphyrin separated by different numbers of p-phenyleneethynylene bridge units. Our estimated rate constants are consistent with experimentally measured TET rates. The FSD method can be used for both intermolecular and intramolecular TET, regardless of their symmetry. This general applicability is an improvement over most existing methodologies.