We explicitly compute the non-equilibrium molecular dynamics of protons in the solid acid CsH2PO4 on the micrometer length scale via a multiscale Markov model: The molecular dynamics/matrix propagation (MDM) method. Within the MDM approach, the proton dynamics information of an entire molecular dynamics simulation can be condensed into a single M × M matrix (M is the number of oxygen atoms in the simulated system). Due to this drastic reduction in the complexity, we demonstrate how to increase the length and time scales in order to enable the simulation of inhomogeneities of CsH2PO4 systems at the nanometer scale. We incorporate explicit correlation of protonation dynamics with the protonation state of the neighboring proton sites and illustrate that this modification conserves the Markov character of the MDM method. We show that atomistic features such as the mean square displacement and the diffusion coefficient of the protons can be computed quantitatively from the matrix representation. Furthermore, we demonstrate the application potential of the scheme by computing the explicit dynamics of a non-equilibrium process in an 8 μm CsH2PO4 system during 5 ms.
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