Density matrix model for hydrogen transfer in the benzoic acid dimer

The double hydrogen transfer in benzoic acid dimers (‘the system’) embedded in a crystal (‘the bath’) is studied with time-dependent density matrix theory. The Liouville-von Neumann equation is solved for a two-dimensional model, using a state representation for the operators, and a polynomial expansion to treat the time evolution of the reduced nuclear density matrix. The bath-induced vibrational relaxation and dephasing processes are treated within the Lindblad formalism, with interlevel transition probabilities obtained from a microscopic perturbative theory due to Meyer and Ernst. The approach of various initial non-equilibrium states towards thermal equilibrium, is monitored with the help of: (i) state populations, (ii) system-bath energy exchange, (iii) the von Neumann and relative entropies and (iv) the decay of ‘coherences’. Simulations are carried out at low and at high bath temperatures.