Factorization of the classical or quantum evolution operator yields an efficient algorithm for simulating large systems as suggested by a perturbation theoretical framework. The dynamics of many-atom systems simultaneously express particle-like and collective variables. A method that explicitly takes this multiscale aspect of the dynamics into account is shown to yield a practical computational algorithm for molecular dynamics. The efficiency is predicated on the choice of collective variables and an efficient algorithm for reconstructing an ensemble of atom-resolved states consistent with the time-advanced coarse-grained state. This is achieved by the evolution of the collective variables, which enables larger time steps to be taken relative to those for classical molecular dynamics. The algorithm can be adapted to a variety of methods in computational particle mechanics driven by an inter-particle potential. Ambiguities in using coarse-grained force fields are avoided because the approach is truly multiscale, i.e. it provides both the atom-resolved and the coarse-grained dynamics. Completeness of the coarse-grained description is addressed via introduction of a flexible definition of the collective variables. Generalizations and developments, including the semi microscopic theory of granular media and the mix quantum – classical dynamics of an <i>N</i>-atom system are suggested. The method is implemented using the MolSSI molecular mechanics interoperable components (MMIC) framework. This enables simulation of a wide range of large systems in biological, pharmaceutical, and materials sciences.

A multiscale simulation of many-atom systems

ACS Fall 2021

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