The influence of nonbilinear system-bath coupling on quantum-mechanical activated rate processes

The dependence of quantum-mechanical activated rate processes on the system-bath coupling strength was investigated in the case of a double-well nonbilinearly coupled to a harmonic bath, where the system-bath coupling is linear in the bath coordinates and nonlinear in the reaction coordinate. Such nonbilinear coupling is known to give rise to a classical friction kernel which is explicitly dependent on the reaction coordinate. We show that it can also lead to quantum-mechanical barrier-crossing rates, whose dependence on the system-bath coupling strength is qualitatively different from that observed in the quantum-mechanical bilinear case and classical nonbilinear case. More specifically, it is shown that the quantum-mechanical barrier-crossing rate may monotonically increase as a function of the system-bath coupling strength, in cases where the classical barrier-crossing rate goes through a turnover, and that the rate of quantum-mechanical barrier-crossing can be lower than that of classical barrier-crossing. We show that those purely quantum-mechanical effects are of a thermodynamical, rather than dynamical, nature, and that they originate from the difference in friction between the barrier top and the reactant and product wells. Our conclusions are supported by results obtained via the CMD method, which were also found to be in very good agreement with numerically exact calculations based on the QUAPI method.