ELECTRA: A Symmetry-breaking Cartesian Network for Charge Density Prediction with Floating Orbitals

We present the Electronic Tensor Reconstruction Algorithm (ELECTRA) - an equivariant model for predicting electronic charge densities using "floating" orbitals. Floating orbitals are a long-standing idea in the quantum chemistry community that promises more compact and accurate representations by placing orbitals freely in space, as opposed to centering all orbitals at the position of atoms. Finding ideal placements of these orbitals requires extensive domain knowledge though, which thus far has prevented widespread adoption. We solve this in a data-driven manner by training a Cartesian tensor network to predict orbital positions along with orbital coefficients. This is made possible through a symmetry-breaking mechanism that is used to learn position displacements with lower symmetry than the input molecule while preserving the rotation equivariance of the charge density itself. Inspired by recent successes of Gaussian Splatting in representing densities in space, we are using Gaussians as our orbitals and predict their weights and covariance matrices. Our method achieves a state-of-the-art balance between computational efficiency and predictive accuracy on established benchmarks.