(316a) Diffusion Wavelet-Based Decompositions for Coarse-Graining of Polymer Chains

We present an alternative approach to coarse graining, based on the multiresolution diffusion-wavelet approach to operator compression, which does not require explicit preparation of atomistic-to-coarse-grained mappings. Our diffusion-wavelet method takes as input the topology and sparsity of the bonding structure of a molecular system, and returns as output a hierarchical set of degrees of freedom corresponding to system-specific coarse-grained variables. Importantly, the hierarchical compression provides a clear framework for modeling at many model scales (levels), instead of the traditional two-level approach used in most coarse-graining applications.

Our results show that the resulting hierarchy separates localized modes, such as a single C-C vibrational mode, from larger-scale motions, e.g., long-range concerted backbone vibrational modes. Our approach correctly captures small-scale chemical features, such as the ring structures in cellulose, alkane side chains, or CH₂ units, as well as large-scale features of the backbone. In particular, the new method’s finest-scale modes describe degrees of freedom similar to those found in united-atom models and other chemically-defined CG models. Modes at coarser levels describe increasingly large connected portions of the target polymers. For polyethylene and polystyrene, spatial coordinates and their associated forces were compressed by up to two orders of magnitude. The compression in forces is of particular interest as this allows larger timesteps as well as reducing the number of DoFs.