We employ time‐dependent density matrix theory to characterize the concerted double‐hydrogen transfer in benzoic acid dimers—the ‘‘system’’—embedded in their crystalline environment—the ‘‘bath.’’ The Liouville–von Neumann equation for the time evolution of the reduced nuclear density matrix is solved numerically, employing one‐ and two‐dimensional models [R. Meyer and R. R. Ernst, J. Chem. Phys. 93, 5528 (1990)], the state representation for all operators and a matrix propagator based on Newton’s polynomials [M. Berman, R. Kosloff, and H. Tal‐Ezer, J. Phys. A 25, 1283 (1992)]. Dissipative processes such as environment‐induced vibrational energy and phase relaxation, are accounted for within the Lindblad dynamical semigroup approach. The calculation of temperature‐dependent relaxation matrix elements is based on a microscopic, perturbative theory proposed earlier [R. Meyer and R. R. Ernst, J. Chem. Phys. 93, 5528 (1990)]. For the evaluation of the dissipative system dynamics, we compute (i) time‐dependent state populations, (ii) energy and entropy flow between system and bath, (iii) expectation values for the hydrogen transfer coordinate, (iv) characteristic dephasing times and (v) temperature‐dependent infrared spectra, determined with a recently proposed method by Neugebauer etal. Various ‘‘pure’’ and ‘‘thermal’’ nonequilibrium initial states are considered, and their equilibration with the bath followed in time.

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