Machine Learned Fock Matrix.

This work introduces a novel machine learning integral-based self-consistent field method, called miSCF, designed for the efficient prediction of molecular electronic structures. By incorporating detailed information from the atomic information and geometric features to predict the molecular Fock matrix, this approach enhances data sharing among similar systems and facilitates effective data transfer within chemically analogous systems. This enables precise predictions of various electronic properties of the systems with only a small amount of training data, significantly reducing computational costs while maintaining high accuracy. Testing results on some representative small molecules, H2 and H2O chain as well as ice structures, demonstrate that miSCF shows good performance in the prediction of energies, wave function, and electron densities, showcasing high precision, efficiency, and good transferability. Thus, the miSCF method provides an efficient tool for quantum chemical calculations, laying a solid foundation for further applications in potential energy surface construction, ab initio molecular dynamics, and chemical reaction simulations.