---
title: Atomic Cluster Expansion Framework
url: https://www.emergentmind.com/topics/atomic-cluster-expansions
type: topic
---

# Atomic Cluster Expansion Framework

The Atomic Cluster Expansion (ACE) is a hierarchical, systematically improvable framework for constructing invariant, complete, and efficient basis sets for the representation of atomic environments and many-body interactions. ACE has become a central methodology in modern machine-learned interatomic potentials, with widespread adoption in force field development for materials modeling, active learning, electronic structure, and beyond [2308.06462].

## 1. Mathematical Structure and Basis Construction

Atomic Cluster Expansion is founded on a decomposition of the total energy of a system into site energies:
\[
E = \sum_i E_i
\]
Each site energy \(E_i\) is formally expanded as a sum over all body-ordered \(N\)-atom clusters in the neighborhood of atom \(i\):
\[
E_{i} = U_{0}(Z

Source: https://www.emergentmind.com/topics/atomic-cluster-expansions