Excited Singlet Energy Transfer and Migration

Strong coupling case Coulombic interactions between electrons induce the conversion of an excited molecule to its ground state with simultaneous excitation of another molecule from its ground state to the excited state. This phenomenon, the molecular exciton, takes place with a relaxation time of less than 10 14 sec by transfer or migration of energy from a molecule to an adjacent molecule. 

Intermediate coupling case Excitation energy transfer (migration) occurs within the same time range as a vibrational relaxation. This phenomenon corresponds to the case where the exciton migration can be compared to a lattice deformation. 

Weak coupling case Energy transfer or migration proceeds with a hopping mechanism. This phenomenon occurs within the time range of an electronic excitation, i.e., the excitation energy is localized in each molecule. 

As a rule, the weak coupling case is observed in solution, the intermediate coupling case in crystalline solids and oriented membranes, and the strong coupling case within conjugated macromolecules. In order to quantify the energy transfer, we will consider a molecular complex composed of two molecules a and b. The Hamiltonian of this system is given by 

The ground-state wave function, and the energy eigenvalue, g, of this system are expressed by Eq. (1.149) in a way analogous to the valence bond method described for the hydrogen molecule, where k is the force constant of the nucleus motion. 

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