Frozen-mode small polaron quantum master equation with variational bound for excitation energy transfer in molecular...

The small polaron quantum master equation (SPQME) is a powerful method for describing quantum dynamics in molecular systems. However, in the slow-bath regime where low-frequency vibrational modes dominate the dynamics, the fully dressed small polaron coordinates lead to errors in the SPQME theory. Furthermore, low-frequency modes also cause infrared divergence in the SPQME method, making the theory applicable only to systems described by spectral densities of the super-Ohmic form. In this study, we propose to treat these low-frequency vibrations as dynamically arrested "frozen" modes in a semiclassical representation and apply the small polaron representation only to the high-frequency vibrations. Furthermore, we show that a variational polaron approach can be utilized to determine the frequency upper bound of the frozen modes, allowing dynamical simulations free of manually tuned parameters. This frozen-mode SPQME is applied to models describing excitation energy transfer (EET) in molecular aggregates and comprehensively compared with the quasiadiabatic path integral method a well as the Redfield theory to demonstrate the applicability of this new method. We show that errors due to slow baths in the original SPQME theory are significantly reduced by the frozen-mode approximation. More significantly, we show that the new approach successfully extends the SPQME theory to be applicable to systems with the Drude-Lorentz spectral density, resulting in a great expansion of the applicability of the SPQME theory for EET problems. In summary, we demonstrate a "frozen-mode" SPQME that provides efficient and accurate simulations of EET dynamics of molecular systems in a broad parameter regime.