CliffordIP: Clifford algebra equivariant interatomic potentials for heterogeneous catalysis

Abstract

Decarbonizing the global economy requires efficient catalysts for key electrochemical transformations, including CO2 reduction, nitrogen reduction, and C–C coupling. Yet systematic catalyst discovery is limited by the cost of density functional theory calculations needed to evaluate adsorbate–surface energetics across chemically diverse surfaces. Machine-learning interatomic potentials (MLIPs) can accelerate this workflow, but many leading equivariant architectures rely on spherical harmonics and Clebsch–Gordan tensor products, increasing computational complexity and implementation overhead. Here we introduce CliffordIP, a message-passing interatomic potential built on the Clifford algebra Cl(3, 0), representing atomic environments as 8-dimensional multivectors (scalars, vectors, bivectors, and pseudoscalars) coupled through the geometric product. This naturally captures bond directions, reaction planes, and local chirality relevant to catalytic intermediates, while enforcing full O(3) equivariance, including reflections, via the Pin(3) group. On catalysis-focused adsorbate subsets, CliffordIP reduces energy MAE by 20–24% relative to the next-best baseline on CO2RR, N2RR, and C2 formation, and achieves the strongest in-distribution energy performance among the compared baselines on OC20 and OC22 under a unified, compute-constrained protocol, while remaining competitive in force magnitude. These results establish Clifford algebra as a promising foundation for energy-focused MLIPs in computational catalysis.