# Range separation: The divide between local structures and field theories

## TL;DR

This paper compares the development of electron and liquid structure theories, highlighting their shared controversies between short-range atomistic models and long-range continuum approaches, to guide integrated density functional and atomistic simulations.

## Contribution

It provides a historical and conceptual comparison of two modern condensed matter theories, emphasizing their common philosophical tensions and offering insights for combining density functional and atomistic methods.

## Key findings

- Identification of parallel historical developments
- Analysis of the controversy between short-range and long-range models
- Guidelines for integrating density functional theories with atomistic simulations

## Abstract

This work presents parallel histories of the development of two modern theories of condensed matter: the theory of electron structure in quantum mechanics, and the theory of liquid structure in statistical mechanics. Comparison shows that key revelations in both are not only remarkably similar, but even follow along a common thread of controversy that marks progress from antiquity through to the present. This theme appears as a creative tension between two competing philosophies, that of short range structure (atomistic models) on the one hand, and long range structure (continuum or density functional models) on the other. The timeline and technical content are designed to build up a set of key relations as guideposts for using density functional theories together with atomistic simulation.