Atomic cluster expansion as a platform for constructing atomic scale models

Classical and machine learning interatomic potentials alike incorporate design choices that reflect the intuition of their authors and that are justified only a-posterioi by the performance of the model. Design choices comprise, for example, the form of the embedding function of an embedded atom potential or a specific angular dependence of a descriptor in a machine learning potential.

The atomic cluster expansion (ACE) [1-3] takes a different route. Based on the broad assumption of locality, it establishes a complete and orthonormal basis for the space of local atomic configurations. The ACE basis functions immediately comply with the basic symmetry requirements of atomic scale physics, they are invariant under translation, rotation, inversion and permutation of atoms. This enables the systematic expansion and convergence of atomic scale properties in analogy to quantum mechanics, where one is used to converging basis functions for the accurate representation of energies and forces. And the completeness enables ACE to represent common machine learning descriptors and potentials.

It is straightforward to include other properties than atomic energies in ACE, for example magnetic moments or charge transfer. By lifting the constraint of rotational invariance, vectorial or tensorial properties can be represented with a rotationally equivariant ACE. Furthermore, extensions to self-consistent models and non-local or semi-local interactions are possible and provide links to message passing networks. Finally, ACE is not limited to atoms but when applied to electrons recovers many-electron wavefunction representations.

 

[1] R. Drautz, Phys. Rev.  B99, 014104 (2019).

[2]  G. Dusson, M. Bachmayr, G. Csanyi, R. Drautz, S. Etter, C. van der Oord, and C. Ortner, (2020), arXiv:1911.03550v3.

[3] R. Drautz, Phys. Rev. B102, 024104 (2020).