Approximation of Symmetric Functions with Polynomials and Spherical Harmonics
Author ACEsuit
18 Stars
Updated Last
2 Years Ago
Started In
November 2019



This is currently a development branch of ACE. For the latest stable version see DEV-v0.8.x

Preliminary Documentation

This package implements approximation schemes for permutation and isometry invariant functions, with focus on modelling atomic interactions. It provides constructions of symmetric polynomial bases, imposing permutation and isometry invariance. Heavy use is made of trigonometric polynomials and spherical harmonics to obtain rotation invariance. There are also implementations of pure permutation invariant bases and of bases with only cylindrical symmetries for bond energies. Documentation is a work in progress; if you wish to use the code please contact the author.


When using this software, please cite the following references

  • Drautz, R.: Atomic cluster expansion for accurate and transferable interatomic potentials. Phys. Rev. B Condens. Matter. 99, 014104 (2019). doi:10.1103/PhysRevB.99.014104

  • M. Bachmayr, G. Csanyi, G. Dusson, S. Etter, C. van der Oord, and C. Ortner. Approximation of potential energy surfaces with spherical harmonics. arXiv:1911.03550v2; http PDF


ACE.jl is © 2019, Christoph Ortner

ACE.jl is published and distributed under the Academic Software License v1.0 (ASL).

ACE.jl is distributed in the hope that it will be useful for non-commercial academic research, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ASL for more details.

You should have received a copy of the ASL along with this program; if not, write to Christoph Ortner, It is also published at

You may contact the original licensor at