Multi-scale approach for the prediction of atomic scale properties

TL;DR

This paper introduces a multi-scale modeling framework that combines local and non-local information to improve the prediction of atomic-scale properties, addressing limitations of existing machine learning methods.

Contribution

The authors develop a novel multi-scale approach that integrates local and long-range effects, formalized through a multipole expansion, enhancing the modeling of collective and delocalized phenomena.

Findings

Successfully models electrostatics, polarization, and dispersion effects.

Demonstrates applicability across molecular physics, surface science, and biophysics.

Outperforms traditional local-only models in capturing long-range interactions.

Abstract

Electronic nearsightedness is one of the fundamental principles governing the behavior of condensed matter and supporting its description in terms of local entities such as chemical bonds. Locality also underlies the tremendous success of machine-learning schemes that predict quantum mechanical observables -- such as the cohesive energy, the electron density, or a variety of response properties -- as a sum of atom-centred contributions, based on a short-range representation of atomic environments. One of the main shortcomings of these approaches is their inability to capture physical effects, ranging from electrostatic interactions to quantum delocalization, which have a long-range nature. Here we show how to build a multi-scale scheme that combines in the same framework local and non-local information, overcoming such limitations. We show that the simplest version of such features can be put in formal correspondence with a multipole expansion of permanent electrostatics. The data-driven nature of the model construction, however, makes this simple form suitable to tackle also different types of delocalized and collective effects. We present several examples that range from molecular physics, to surface science and biophysics, demonstrating the ability of this multi-scale approach to model interactions driven by electrostatics, polarization and dispersion, as well as the cooperative behavior of dielectric response functions.