# Electron Density Prediction

The electron density is the central variable of density functional theory, and obtaining it normally means iterating to self-consistency. Two Transformer-inspired networks, SwinUNETR-V2 and its attention-free counterpart NeXtUNETR, predict the density directly, reaching normalized mean absolute density errors of 0.075% and 0.046% on QM9. For NeXtUNETR, a single Kohn-Sham step on the predicted density reproduces the self-consistent electronic structure, with median errors of 0.036 meV in total energy, 0.65 meV/angstrom in forces and 1.8 meV in the HOMO-LUMO gap.

The electron density is the central variable of density functional theory, and obtaining it normally means iterating to self-consistency. Two Transformer-inspired networks, SwinUNETR-V2 and its attention-free counterpart NeXtUNETR, predict the density directly, reaching normalized mean absolute density errors of 0.075% and 0.046% on QM9. For NeXtUNETR, a single Kohn-Sham step on the predicted density reproduces the self-consistent electronic structure, with median errors of 0.036 meV in total energy, 0.65 meV/angstrom in forces and 1.8 meV in the HOMO-LUMO gap.

Treating density query points as virtual atoms that share one encoder with real atoms lets electron-density supervision shape interatomic-potential representations: density error on MP falls below ChargE3Net, and joint training cuts zero-shot force error on larger molecules.

Treating density query points as virtual atoms that share one encoder with real atoms lets electron-density supervision shape interatomic-potential representations: density error on MP falls below ChargE3Net, and joint training cuts zero-shot force error on larger molecules.

The authors introduce OrbFlow, an SE(3)-equivariant generative model that learns a probability path over the full GTO coefficient space via flow matching and is trained with a two-phase trajectory curriculum that mitigates discretization drift during numerical integration; it reduces density error on QM9 by 13.6% relative to the previous best model, reduces error by 51% to 63% on every molecule of the MD benchmark relative to the strongest prior method sharing its basis, cuts SCF iterations by up to 68%, transfers zero-shot to unseen exchange-correlation functionals, and recovers dipole and quadrupole moments to within a few percent of DFT references without any SCF calculation.

The authors introduce OrbFlow, an SE(3)-equivariant generative model that learns a probability path over the full GTO coefficient space via flow matching and is trained with a two-phase trajectory curriculum that mitigates discretization drift during numerical integration; it reduces density error on QM9 by 13.6% relative to the previous best model, reduces error by 51% to 63% on every molecule of the MD benchmark relative to the strongest prior method sharing its basis, cuts SCF iterations by up to 68%, transfers zero-shot to unseen exchange-correlation functionals, and recovers dipole and quadrupole moments to within a few percent of DFT references without any SCF calculation.