Multi-replica biased sampling for photoswitchable π-conjugated polymers

In recent years, π-conjugated polymers are attracting considerable interest in view of their light-dependent torsional reorganization around the π-conjugated backbone, which determines peculiar light-emitting properties. Motivated by the interest in designing conjugated polymers with tunable photoswitchable pathways, we devised a computational framework to enhance the sampling of the torsional conformational space and, at the same time, estimate ground-to excited-state free-energy differences. This scheme is based on a combination of Hamiltonian Replica Exchange Method (REM), parallel bias metadynamics, and free-energy perturbation theory. In our scheme, each REM samples an intermediate unphysical state between the ground and the first two excited states, which are characterized by time-dependent density functional theory simulations at the B3LYP/6-31G level of theory. We applied the method to a 5-mer of 9,9-dioctylfluorene and found that upon irradiation, this system can undergo a dihedral inversion from-155° to 155°, crossing a barrier that decreases from 0.1 eV in the ground state (S0) to 0.05 eV and 0.04 eV in the first (S1) and second (S2) excited states. Furthermore, S1 and even more S2 were predicted to stabilize coplanar dihedrals, with a local free-energy minimum located at ±44°. The presence of a free-energy barrier of 0.08 eV for the S1 state and 0.12 eV for the S2 state can trap this conformation in a basin far from the global free-energy minimum located at 155°. The simulation results were compared with the experimental emission spectrum, showing a quantitative agreement with the predictions provided by our framework.