Non-Equilibrium Dynamics of the Time-Dependent Excitonic Coupling in Fluorescent Protein Dimers

We quantify the excitonic coupling in the homodimer of dimeric Venus fluorescent protein using a quantum-classical hybrid workflow. Employing a transition-density coupling formalism, we calculate $J = 74.38~\mathrm{cm^{-1}}$, which is 5.6 times stronger than the far-field point-dipole estimate of $13.31~\mathrm{cm^{-1}}$. This disparity highlights the critical role of near-field multipolar effects at the 27.6~\r{A} chromophore centroid separation. Furthermore, we argue that a separation of timescales resolves the apparent theoretical tension between robust experimental excitonic couplings and the highly decoherent biological environment. While it has been hypothesised that the fluorescent protein $\beta$-barrel scaffold sustains coupling by attenuating thermal fluctuations, we emphasise that the separation of timescales fundamentally applies irrespective of the exact degree of environmental noise suppression. Collective photoexcitation imprints the Davydov splitting under optical-limit dielectric screening upon absorption, preceding bulk solvent relaxation and sub-picosecond environmental dephasing. To characterise the subsequent post-absorption evolution, we employ stochastic simulations for quantum parts to model the transition from a delocalised exciton superposition to incoherent hopping between localised chromophore states.