Accelerating SCF Convergence Through Equivariant Density‐Matrix Learning and Analytic Refinement

ABSTRACT We present dm‐PhiSNet , a physically constrained PhiSNet ‐based equivariant model that predicts one‐electron reduced density matrices (1‐RDMs) directly from molecular geometries in an atomic‐orbital (AO) basis to accelerate self‐consistent‐field (SCF) convergence. Training follows a two‐stage schedule with progressively introduced physically motivated objectives, and the resulting predictions are refined by a lightweight analytic block. This block enforces electron‐number conservation, drives the 1‐RDM toward generalized idempotency with respect to the AO overlap matrix , and regularizes the occupation spectrum of the density matrix in an orthogonalized AO representation. Across six closed‐shell systems—, , , HF, ethanol, and —the refined 1‐RDMs provide SCF initial guesses that substantially reduce iteration steps by 49%–81% relative to standard initializations. Beyond SCF acceleration, the learned 1‐RDMs yield accurate one‐shot total energies and Hellmann–Feynman atomic forces without force supervision, indicating that the model captures chemically meaningful electronic structure. These results demonstrate that combining equivariant learning with analytic constraint enforcement provides a simple, general route to solver‐ready density‐matrix initializations and accelerated SCF calculations.