Electron densities skip the self-consistency loop: one Kohn-Sham step reproduces the self-consistent structure

A neural network can supply the electron density directly instead of running the iteration to self-consistency. The usual route iterates the electron density until it is self-consistent, and that loop carries the cost. On QM9, SwinUNETR-V2 and NeXtUNETR reach normalized mean absolute density errors of 0.075% and 0.046%, respectively, described as state-of-the-art accuracy.

The predicted density is good enough to carry the downstream electronic-structure calculation through a single Kohn-Sham step. That single step stands in for the repeated self-consistent iteration. For NeXtUNETR, the median errors after that step are 0.036 meV in total energy, 0.65 meV/angstrom in forces and 1.8 meV in the HOMO-LUMO gap.

Forces derived from the predicted density can be used for geometry optimization and ab initio molecular dynamics. The forces recover the self-consistent minima in geometry optimization and also drive ab initio molecular dynamics. This use is shown for the forces reported for NeXtUNETR, at 0.65 meV/angstrom error.

Both networks transfer beyond QM9 after fine-tuning on small datasets. QM9 covers only the elements and molecule sizes it contains. After fine-tuning, both networks transfer accurately to systems containing elements absent from QM9 or larger than its molecules.

The demonstrated scope is density accuracy on QM9, the energy, force and gap errors after a single Kohn-Sham step for NeXtUNETR, and force behavior in geometry optimization and ab initio molecular dynamics; transfer is reported after fine-tuning on small datasets, for systems containing elements absent from QM9 or larger than its molecules.

Density errors are reported as normalized mean absolute errors on QM9, while energy, force and gap errors are medians for NeXtUNETR; the transfer results rely on fine-tuning on small datasets rather than direct zero-shot use.