Mixed quantum–classical Liouville simulation of vibrational energy transfer in a model α-helix at 300 K

We apply several mixed quantum–classical Liouville-based methods and Ehrenfest (mean-field) dynamics to the simulation of vibrational energy flow between amide I modes in a one-dimensional model of a hydrogen-bonded polypeptide. Three solutions of the mixed quantum–classical Liouville (MQCL) equation are implemented: a surface-hopping solution, an adiabatic solution, and a mean-field-like method known as the Poisson Bracket Mapping Equation (PBME) solution. The energy transport is investigated by calculating the time-dependent populations of the subsystem states localized on the different amide I modes following excitation at one end of the chain. In the cases of surface-hopping and adiabatic dynamics, the excitation delocalizes on a timescale of a few hundred femtoseconds, while for PBME and Ehrenfest dynamics it delocalizes on a timescale of picoseconds. When hydrogen bond distortions are introduced at each end of the chain, surface-hopping and adiabatic dynamics predict energy hopping between these distal sites, while no transfer occurs if PBME and Ehrenfest dynamics are used. Given the more accurate nature of the surface-hopping solution, these results demonstrate that the mean-field dynamics generated by the PBME and Ehrenfest approaches fail for modelling this energy transfer process, as they yield a very different picture of the quantum dynamics. The insights gained from this study set the stage for simulations of vibrational energy flow in more realistic models of peptides via the surface-hopping and adiabatic dynamics solutions of the MQCL equation.