Building Physics into Electronic Structure Models for Coarse-Grained Molecular Representations

There is the potential to dramatically improve the scalability of electronic characterizations in disordered soft materials if the costs of multiscale simulation workflows, backmapping, and ad nauseam quantum chemistry can be bypassed. One tenable solution to this challenge is to predict ab initio-quality electronic structure of soft materials directly from a coarse-grained molecular representation, in which electronic properties of molecules are parameterized by sets of collective degrees of freedom of the molecule instead of all atomistic coordinates. While such an approach is conceptually straightforward (and implicitly rife throughout theories of quantum dynamics and phenomenological electronic structure models), applications of this philosophy to fully-detailed atomistic systems with ab initio accuracy are lacking from the literature. Here, I will discuss our machine learning-driven approach to this problem, denoted electronic coarse-graining, in which the electronic structure of a molecule is directly regressed from a reduced (coarse-grained) representation. I will focus on emerging approaches that attempt to build physics into electronic coarse-graining models by leveraging series expansions of the Hamiltonian matrix and pre-defined coarse-grained "basis sets" using invariant graph neural network driven projections.