# Electronic coarse graining: Predictive atomistic modeling of condensed matter

## Abstract

Atoms and molecules adapt to their environment through a rich hierarchy of electronic responses. These include dipolar many-body polarization contributions arising in the classical limit, many-body polarization beyond dipole order, as well as pair and many-body dispersion interactions and cross interactions at all orders arising from multipolar quantum fluctuations. Such fundamental phenomena give rise to emergent behavior across the physical and life sciences. However, their incorporation in simulations of large complex systems faces significant challenges as these are intrinsically many-body phenomena. Here the impetus for and development of a new class of molecular model employing embedded quantum Drude oscillators (QDO) as a coarse-grained but complete representation of electronic responses at long range within Gaussian statistics is given. The resulting level of completeness in physical description enables isolated molecule properties to define model parameters, thereby eliminating fitting to condensed phase data. This provides a physical and intuitive basis for predictive, next-generation simulation wherein all long-range diagrams emerge naturally from the model permitting the study of complex systems in novel environments. The model is derived from a many-body Hamiltonian and would afford no advantage without an O(N) scaling, strong coupling solution to avoid artificial truncation from perturbation theory and associated multipolar expansions which is possible due to the model's Gaussian structure. A scalar field theory and path integral form of the QDO Hamiltonian cast in such a way as to generate a strong coupling solution to the coarse-grained electronic structure are presented. Forces can be generated "on the fly" using modern adiabatic molecular dynamics methods with linear compuational complexity. Thus, the approach is applicable to large condensed phase systems at finite temperature and pressure. Example applications and future perspectives are presented for key physical systems such as the phase diagram of water from ice to the supercritical regime.