Canonically consistent quantum master equation for proton-transfer reactions

Abstract

The canonically consistent quantum master equation (CCQME) method to treat system–bath dynamics is used to describe intramolecular proton transfer in the thioacetylacetone molecule (TAA, C5H8OS), modeled as an N-level quantum system coupled to a solvent. The solvent is represented as a harmonic bath (a continuum of oscillators) characterized by Ohmic–Drude spectral density. We benchmark the secularized population dynamics and steady-state populations predicted by CCQME against numerically exact hierarchical equations of motion (HEOM) theory and compare it to the corresponding secularized Redfield results. Our results reveal that Redfield dynamics deviates increasingly from the HEOM reference as the system–bath coupling strength grows. In contrast, for not too strong couplings, the secularized CCQME population dynamics remains consistent with HEOM over an extended system–bath coupling range and approaches the second-order mean force Gibbs state. A complementary non-secular calculation shows that retaining population–coherence coupling reveals limitations of the second-order treatment for coherence-sensitive observables.