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

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.