Charge-constrained atomic cluster expansion

The atomic cluster expansion (ACE) efficiently parametrizes complex energy surfaces of pure elements and alloys. Due to the local nature of the many-body basis, ACE is inherently local or semilocal for graph ACE. Here, we employ descriptor-constrained density-functional theory (DFT) for parametrizing ACE with charge or other degrees of freedom, thereby transfering the variational property of the density functional to ACE. The descriptors can be of scalar, vectorial, or tensorial nature. From the simplest case of scalar atomic descriptors we directly obtain charge-dependent ACE with long-range electrostatic interactions between variable charges. We observe that the variational properties of the charges greatly help in training, avoiding the need for charge-constrained DFT calculations.