  The ability to perform fast and accurate atomistic simulations is crucial for
advancing the chemical sciences. By learning from high-quality data,
machine-learned interatomic potentials achieve accuracy on par with ab initio
and first-principles methods at a fraction of their computational cost. The
success of machine-learned interatomic potentials arises from integrating
inductive biases such as equivariance to group actions on an atomic system,
e.g., equivariance to rotations and reflections. In particular, the field has
notably advanced with the emergence of equivariant message-passing
architectures. Most of these models represent an atomic system using spherical
tensors, tensor products of which require complicated numerical coefficients
and can be computationally demanding. This work introduces higher-rank
irreducible Cartesian tensors as an alternative to spherical tensors,
addressing the above limitations. We integrate irreducible Cartesian tensor
products into message-passing neural networks and prove the equivariance of the
resulting layers. Through empirical evaluations on various benchmark data sets,
we consistently observe on-par or better performance than that of
state-of-the-art spherical models.
