Multi-scale coarse-graining of non-conservative interactions in molecular liquids

A new bottom-up procedure for constructing non-conservative (dissipative and stochastic) interactions for dissipative particle dynamics (DPD) models is described and applied to perform hierarchical coarse-graining of a polar molecular liquid (nitromethane). The distant-dependent radial and shear frictions in functional-free form are derived consistently with a chosen form for conservative interactions by matching two-body force-velocity and three-body velocity-velocity correlations along the microscopic trajectories of the centroids of Voronoi cells (clusters), which represent the dissipative particles within the DPD description. The Voronoi tessellation is achieved by application of the K-means clustering algorithm at regular time intervals. Consistently with a notion of many-body DPD, the conservative interactions are determined through the multi-scale coarse-graining (MS-CG) method, which naturally implements a pairwise decomposition of the microscopic free energy. A hierarchy of MS-CG/DPD models starting with one molecule per Voronoi cell and up to 64 molecules per cell is derived. The radial contribution to the friction appears to be dominant for all models. As the Voronoi cell sizes increase, the dissipative forces rapidly become confined to the first coordination shell. For Voronoi cells of two and more molecules the time dependence of the velocity autocorrelation function becomes monotonic and well reproduced by the respective MS-CG/DPD models. A comparative analysis of force and velocity correlations in the atomistic and CG ensembles indicates Markovian behavior with as low as two molecules per dissipative particle. The models with one and two molecules per Voronoi cell yield transport properties (diffusion and shear viscosity) that are in good agreement with the atomistic data. The coarser models produce slower dynamics that can be appreciably attributed to unaccounted dissipation introduced by regular Voronoi re-partitioning as well as by larger numerical errors in mapping out the dissipative forces. The framework presented herein can be used to develop computational models of real liquids which are capable of bridging the atomistic and mesoscopic scales.