Atomic cluster expansion and wave function representations

The atomic cluster expansion (ACE) has been highly successful for the parameterisation of symmetric (invariant or equivariant) properties of many-particle systems. Here, we generalize its derivation to anti-symmetric functions. We show how numerous well-known linear representations of wave functions naturally arise within this framework and we explore how recent successful nonlinear parameterisations can be further enhanced by employing ACE methodology. From this analysis we propose a wide design space of promising wave function representations.