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Organic light-emitting diodes (OLEDs) devices in the archetype small moleculefluorescent guest-host system tris(8-hydroxyquinolinato) aluminum (Alq$_{3}$)doped with 4-(dicyanomethylene)-2-methyl-6-julolidyl-9-enyl-4H-pyran (DCM2)displays a redshift in light-emission frequency which is extremely sensitive tothe dopant concentration. This effect can be used to tune the emissionfrequency in this particular class of OLEDs. In this work, a model is proposedto describe this effect using a combination of density functional theory (DFT)quantum-chemical calculations and stochastic simulations of exciton diffusionvia a F\"orster mechanism. The results show that the permanent dipole momentsof the Alq$_{3}$ molecules generate random electric fields that are largeenough to cause a non-linear Stark shift in the band gap of neighboring DCM2molecules. As a consequence of these non-linear shifts, a non-Gaussianprobability distribution of highest-occupied molecular orbital tolowest-unoccupied molecular orbital (HOMO-LUMO) gaps for the DCM2 molecules inthe Alq$_{3}$ matrix is observed, with long exponential tails to the low-energyside. Surprisingly, this probability distribution of DCM2 HOMO-LUMO gaps isvirtually independent of DCM2 concentration into Alq$_{3}$ matrix, at least upto a fraction of 10%. This study shows that this distribution of gaps, combinedwith out-of-equilibrium exciton diffusion among DCM2 molecules, are sufficientto explain the experimentally observed emission redshift.

Emission Redshift in DCM2-Doped Alq$_{3}$ Caused by Non-Linear Stark Shifts and F\"orster-Mediated Exciton Diffusion