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, C$_4$H$_6$OS), 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 an Ohmic-Drude spectral density. We benchmark CCQME against numerically exact hierarchical equations of motion (HEOM) theory and compare to Redfield theory. Our results reveal that Redfield dynamics deviates increasingly from the HEOM reference as the system-bath coupling strength grows. In contrast, the recently proposed CCQME remains consistent with HEOM at intermediate coupling.

Figures (9)

• Figure 1: Enol (left) and enethiol (right) tautomers of TAA and corresponding PES along transfer coordinate $q$. The first five eigenstates are indicated. Note that the lowest state is localized in the left, and the first excited state is localized in the right well.
• Figure 2: Population dynamics of the three lowest eigenstates of the TAA proton-transfer coordinate at $T=300~\mathrm{K}$ for different system--bath couplings $\gamma$ up to $2.5~\mathrm{ps}$ compared with HEOM (black symbols), CCQME (blue solid), and Redfield (red dashed). Horizontal lines indicate the Gibbs (green) and second-order mean-force Gibbs (orange) stationary populations. The system was initially in the ground state.
• Figure 3: Time-averaged ground-state population error $\Delta$ (in %) as a function of the system--bath coupling strength $\gamma$, comparing the CCQME and Redfield predictions with the numerically exact HEOM benchmark. The blue solid curve shows $\Delta$ (CCQME--HEOM), the red dashed curve shows $\Delta$ (Redfield--HEOM), and the purple dash--dotted curve shows $\Delta$ (Redfield--CCQME). The errors are averaged over the propagation time window $0$--$2.5$ ps corresponding to the dynamics in Fig. \ref{['FIG1']}.
• Figure 4: (a) Population dynamics of the three lowest eigenstates and expectation value of transfer coordinate $q$ for a Gaussian wavepacket as initial state, with coupling strength $\gamma=0.5$. (b) Corresponding coordinate expectation values $\expval{q}(t)$.
• Figure 5: Convergence of HEOM for increasing (a) hierarchy depth and (b) number of bath expansion terms, in case of the ground-state population dynamics for $\gamma=1.0$.