Electronic coupling matrix element for electronic excitation energy transfer: S1+S1→S2+S excited state annihilation

For the singlet–singlet annihilation process S1+S1→S2+S0, an expression is derived for the electronic coupling matrix element involved in electronic excitation energy transfer (EET) between two equivalent chromophores. Allowance is made for vibronic coupling to occur between the S1 and S2 states of the chromophores, for each of which the S1←S0 and S2←S0 excitations are, respectively, electric-dipole forbidden and allowed. Attention is also given to aspects of the theory for singlet–singlet (πDπ*D)(nAnA)→(πDπD)(nAπ*A) EET with vibronic coupling. The theory for S1+S1→S2+S0 is illustrated via the results of some model calculations for two C=S chromophores. For each chromophore, the calculations treat explicitly the valence-shell pπ atomic orbitals and a sulphur lone-pair atomic orbital. The results of the calculations highlight the nature of the primary contributors to the vibronic coupling component of the electronic EET matrix element, namely Coulombic-type terms. The theory also shows that a Coulombic term is the primary contributor to the vibronic coupling component for singlet–singlet (πDπ*D)(nAnA)→(πDπD)(nAπ*A) EET.