# Simulation of many-electron systems that exchange matter with the environment

## TL;DR

This paper reviews computational methods for simulating many-electron systems that exchange matter with their environment, highlighting current approaches, challenges, and future directions in materials science and chemical physics.

## Contribution

It provides an overview of existing quantum and classical techniques for modeling open-boundary electronic systems, emphasizing their differences and potential for advancing the field.

## Key findings

- Diverse computational approaches with varying efficiency and accuracy
- Identification of conceptual and pragmatic strengths in current methods
- Potential for combining approaches to push simulation frontiers

## Abstract

The computational treatment of many-electron systems capable of exchanging {electrons and nuclei} with the environment represents one of the outermost frontiers in simulation methodology. The exchanging process occurs in a large variety of natural and artificially induced phenomena which are of major relevance to several leading fields of academic research and modern technology. In this progress report I will present an overview of problems in current materials science and chemical physics where the corresponding computational approaches require the concept of an electronic system with open boundaries. Quantum and Quantum/Classical computational techniques treat the exchange of electrons with the environment at different computational efficiency, conceptual rigorousness and numerical accuracy. The overall emerging picture shows a rich availability of interesting ideas, some with a higher weight on the pragmatic side, others with higher weight on the conceptual side; possible combinations, in perspective, may push the field much beyond its current frontiers.