Learning the One-Electron Reduced Density Matrix at SCF Convergence Thresholds

Machine learning of the one-electron reduced density matrix (1-RDM) provides a computationally efficient surrogate to conventional electronic structure methods. In this work, we train models that map the electron–nuclear interaction potential to the 1-RDM with such an accuracy that predicted 1-RDMs deviate from fully converged ones by no more than a standard self-consistent field (SCF) threshold. Through targeted model optimization strategies, we demonstrate that training set sizes substantially smaller than those required in our previous work [Shao et al., Nat. Commun., 14, 6281 (2023)] are sufficient to reach this accuracy. Furthermore, we introduce a force-correction algorithm that enables stable ab initio molecular dynamics powered by the machine learned 1-RDMs, extending the applicability of the surrogate electronic structure methods to molecules as large as biphenyl.