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Example text
The background is always in its electronic ground state (b ¼ 0). Thus we have F. Mu¨h and T. Renger 26 À Á À Á À Á À Á ΔUm ð0Þ À ΔU vac 0 ¼ U m, 1 ð0Þ À U m, 0 0 À U vac, 1 0 þ U vac, 0 0 ð1Þ ð1Þ ¼ W 10 À W 00 À ðU vac, 1 ð0Þ À U vac, 0 ð0ÞÞ ¼ X qðmÞ ð1; 1Þ qðbgÞ ð0; 0Þ I J ðmÞ R À RJ I I, J À X qðmÞ ð0; 0Þ qðbgÞ ð0; 0Þ I J À ΔUvac ð0Þ ðmÞ I, J RI À RJ ð1:53Þ that is, ðmÞ ðmÞ ðbgÞ X qI ð1; 1Þ À qI ð0; 0Þ qJ ð0; 0Þ ΔU m ð0Þ ¼ ðmÞ I, J RI À RJ ðmÞ ð1:54Þ ðmÞ Here, we have used the atomic partial charges qI (1, 1) and qI (0, 0) that represent the charge distribution of the pigment in the first excited and the ground state, respectively, and the charge distribution of the environment in its ground state ðbgÞ is represented by the charges qJ (0, 0).
The resulting vector is the transition dipole or transition dipole moment μ01 that can be calculated from the first moment of the transition density: ð X ðmÞ ðmÞ ðmÞ ðmÞ RI qI ð0; 1Þ ð1:62Þ μ01 ¼ dx x ρ01 ðxÞ ¼ I Within this point-dipole approximation, the excitonic coupling is given as V mn % ðmÞ μ01 ðnÞ μ01 Á R3mn À3 ðmÞ ðnÞ μ01 Á Rmn μ01 Á Rmn R5mn ð1:63Þ where Rmn is a vector joining the centers of the two pigments and Rmn is the corresponding center-to-center distance. 63) is quite popular.
61. Mennucci B, Curutchet C. The role of the environment in electronic energy transfer: a molecular modeling perspective. Phys Chem Chem Phys. 2011;13:11538–50. 62. Hauska G, Schoedl T, Remigy H, Tsiotis G.