Title: A Cartesian-3j Framework for Machine Learning Interatomic Potentials

Abstract:

While machine learning interatomic potentials (MLIPs) have significantly enhanced extrapolation capabilities in computational chemistry, the field has predominantly relied on spherical tensors (STs) for equivariant models. In contrast, Cartesian tensor formulations, despite their inherent compatibility with atomic coordinates and tensorial targets, have seen less development. To address this gap, we present a framework for irreducible Cartesian tensors (ICTs) that introduces the \texttt{Cartesian-3j} symbol and Cartesian Generalized Clebsch-Gordan Coefficients. These components act as direct equivalents to the \texttt{Wigner-3j} symbol and Generalized Clebsch-Gordan coefficients used in ST coupling.

We have extended the \texttt{e3nn} library to accommodate ICT products and utilized this infrastructure to construct Cartesian versions of the \texttt{MACE}, \texttt{NequIP}, and \texttt{Allegro} models. This approach enables the first controlled comparison where model architectures remain constant, isolating the impact of changing only the tensor basis. Our results indicate that while irreducible Cartesian models can match the accuracy of their spherical counterparts, naive Cartesianization leads to inefficient scaling in terms of memory and computation. This finding underscores the necessity for specialized Cartesian architectural designs. By applying ICTs within our proposed framework, we introduce \texttt{TACE-v1-OAM-M}, which demonstrates performance on the Matbench Discovery benchmark that is competitive with current state-of-the-art ST models.

Source: arXiv Generated at: 2026-06-03 00:00:00 UTC