Towards Accelerated SCF Workflows with Equivariant Density-Matrix Learning and Analytic Refinement

TL;DR

This paper introduces a physically constrained equivariant model that predicts density matrices directly from molecular geometries, significantly accelerating SCF calculations and accurately capturing electronic structure without force supervision.

Contribution

The work presents m-PhiSNet, a novel equivariant density-matrix learning model with analytic refinement, enabling faster SCF workflows and accurate electronic properties prediction.

Findings

Refined 1-RDMs reduce SCF iteration steps by 4981%.

Model accurately predicts total energies and atomic forces without force supervision.

Demonstrates general applicability across multiple molecular systems.

Abstract

We present \textsc{dm-PhiSNet}, a physically constrained \textsc{PhiSNet}-based equivariant model that predicts one-electron reduced density matrices (1-RDMs) directly from molecular geometries in an atomic-orbital (AO) basis for accelerated self-consistent field (SCF) workflows. 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 in the AO metric, and regularizes the occupation spectrum of the L\"owdin-orthogonalized density. Across six closed-shell systems -- H$_2$O, CH$_4$, NH$_3$, HF, ethanol, and NO$_3^-$ -- 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 workflows.