Bath-to-System Timescale Dependence of Bloch−Redfield−HEOM Corrections in a DASA Photoswitch

Solvent effects on donor−acceptor Stenhouse adducts (DASAs) involve both changes in electronic structure and changes in the timescale of environmental response. Here, solvent-dependent vertical excitations are characterized using linear-response and state-specific TD-DFT continuum-solvation calculations while the early photodynamics are examined separately with an independently specified reduced two-state open-quantum-system model. The two analyses share the same solvent set, but the calculated excitation energies do not determine the effective coupling, energetic bias, or bath reorganization parameter used in the dynamical model. Across the five solvents, the LR and nonequilibrium state-specific descriptions differ by approximately 38−43 nm for the S1 transition, whereas the solvent-to-solvent variation within the state-specific results spans only about 9.35 nm. Solvent-derived longitudinal relaxation rates are then used to define the bath timescale of a Drude−Lorentz environment, and matched Bloch−Redfield and hierarchical equations of motion (HEOM) dynamics are compared under otherwise controlled conditions. The principal diagnostic is the maximum absolute difference in the effective reactive-state population over the 0−15 ps propagation window. Across the converged scan points, the BR−HEOM discrepancy shows an overall decrease from slow- to fast-bath conditions, superimposed on a nonmonotonic broad crossover when bath and system rates become comparable. Varying the effective energy bias changes the discrepancy magnitude but preserves the slow-crossover-fast ordering over the tested biases and bath rates. These results distinguish static solvent-response effects from dynamical solvent-relaxation timescales and identify bath-to-system rate competition as a useful organizing coordinate within the tested reduced-model parameter range and stated numerical-convergence criteria.