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Lipophilic dyes such as laurdan and prodan are widely used in membrane biology due to a strong bathochromic shift in emission that reports the structural parameters of the membrane such as area per molecule. Disentangling of the factors which control the spectral shift is complicated by the stabilization of a charge-transfer-like excitation of the dye in polar environments. Predicting the emission therefore requires modeling both the relaxation of the environment and the corresponding evolution of the excited state. Here, an approach is presented in which (i) the local environment is sampled by a classical molecular dynamics (MD) simulation of the dye and solvent, (ii) the electronically excited state of prodan upon light absorption is predicted by numerical quantum mechanics (QM), (iii) the iterative relaxation of the environment around the excited dye by MD coupled with the evolution of the excited state is performed, and (iv) the emission properties are predicted by QM. The QM steps are computed using the many-body Green's function in the GW approximation and the Bethe-Salpeter equation with the environment modeled as fixed point charges, sampled in the MD simulation steps. The comparison to ultrafast time-resolved transient absorption measurements demonstrates that the iterative molecular mechanics (MM)/QM approach agrees quantitatively with both the polarity-dependent shift in emission and the time scale over which the charge transfer state is stabilized. Together the simulations and experimental measurements suggest that the evolution into the charge transfer state is slower in amphiphilic solvents.

Ultrafast Formation of the Charge Transfer State of Prodan Reveals Unique Aspects of the Chromophore Environment