Practical integration of machine learning into <i>ab initio</i> calculations and workflows: Accelerating the SCF cycle via density matrix predictions

Data-driven approaches offer great potential for accelerating ab initio electronic structure calculations of molecules and materials, but their transferability is often limited due to the vast amount of data needed for training, including the need to fine-tune universal models for each specific system to be studied. Here, we demonstrate how contributions from system-specific electronic structure machine learning (ESML) models may be combined ("stitched") to deliver density matrices of entire systems of interest, improving the initial guess for the self-consistent field cycle and delivering gains in computational efficiency. The "stitching" of density matrices is demonstrated for sequential calculations, such as geometry optimization and molecular dynamics, and we show that the synergistic use of ESML models and density matrix extrapolation algorithms can accelerate standard computational calculations. The algorithms are demonstrated for test cases relating to water clusters and a methane clathrate cage, with the benefits discussed. The future opportunities for hybrid quantum mechanical and ML (QM/ML), and also ML/ML paradigms, are broad-ranging with significant computational speed-up attainable.