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Charge and structural relaxation of electronically excited states in embedded systems are strongly affected by the environment. It is known that the largest part of environment effects comes from electrostatics. However, polarization can also play a role by tuning the electronic and geometrical properties of the states, finally modifying the fluorescence. Here we present the formulation of analytical excited-state gradients within a polarizable QM/MM approach and their implementation within the ONIOM framework. A time-dependent DFT level of theory is used in combination with an induced dipole formulation of the polarizable embedding. The formation and relaxation of the bright excited state of an organic dye (DAPI) intercalated in a DNA pocket is used to quantify the role played by the mutual polarization between the QM subsystem and the embedding and also to investigate the onset of overpolarization, which is a known limit of the model with potentially detrimental effects. On the one hand, the results indicate the robustness of the QM-classical interface and, on the other hand, show the non-negligible effect of polarization between DAPI and a DNA pocket in determining the fluorescence properties of the embedded dye.

Excited-State Gradients in Polarizable QM/MM Models: An Induced Dipole Formulation