Calculation of the excitation transfer matrix elements between the <i>S</i>2 or <i>S</i>1 state of carotenoid and the <i>S</i>2 or <i>S</i>1 state of bacteriochlorophyll

Abstract

Formalism of the excitation transfer matrix element applicable for any multiconfigurational wave functions is made. On the basis of the resultant formulas, the excitation transfer matrix elements between the S2 or S1 state of a carotenoid, neurosporene, and the S2 or S1 state of bacteriochlorophyll a are calculated at various stacked configurations of the two molecules. The results show that the excitation transfer from the carotenoid S1 state to the bacteriochlorophyll S1 state via the Coulomb mechanism including multipole–multipole interactions takes place very efficiently in a speed more rapid than that via the electron-exchange mechanism. The results also show that the excitation transfer from carotenoid to bacteriochlorophyll occurs directly from the carotenoid S2 state, as well as from the carotenoid S1 state. Furthermore, it is shown that the excitation transfer matrix element due to the electron-exchange interaction has an oscillatory dependence on the displacement of one molecule from the other when the distance between the planes of the π systems is kept constant. Based on these results, a possible mechanism of the excitation transfer from carotenoid to bacteriochlorophyll in vivo is discussed.