Fluorescence quenching by excimer formation: quenching constant approximations for excimer formation-dissociation by classical potential models

Fluorescence quenching by excimer formation is studied on the assumption that the excimer formation and dissociation can be modeled as overdamped motion in an attractive potential (classical potential models). An approach to the zeroth-order, concentration-independent quenching constants is proposed which starts from a mean reaction-time ansatz and reduces the calculation essentially to the solution of the eigenvalue problem for the Smoluchowski operator which describes the excimer equilibration. For a square-well potential model it is shown that a quenching constant expansion in terms of relaxation modes, truncated at the kinetic level, gives a satisfactory approximation of the recently obtained exact zeroth-order result under defined conditions. It is demonstrated how this two-mode approach can be applied for a quenching constant estimation if the excimer formation and dissociation are modeled by more realistic interaction potentials, as for instance, Morse- or Gaussian-type ones.