Advancing Natural Orbital Functional Calculations through Deep Learning-Inspired Techniques for Large-Scale Strongly Correlated Electron Systems

Natural orbital functional (NOF) theory provides a valuable framework for studying strongly correlated systems at an affordable computational cost, with an accuracy comparable to highly demanding wave-function-based methods. However, its widespread adoption in cases involving a large number of correlated electrons has been limited by the extensive iterations required for convergence. In this Letter, we present an approach that integrates the techniques used for optimization in deep learning into NOF calculations, enabling a substantial expansion in the scale of accessible systems. The proposed procedure employs an adaptive momentum-based technique for orbital optimization, alternated with the optimization of occupation numbers, significantly improving the computational feasibility of challenging calculations. We illustrate the capabilities of our approach through three challenging test cases: (i) the symmetric dissociation of a large hydrogen cluster with 1000 electrons, (ii) an analysis of occupancy distributions in fullerenes, and (iii) a study of the singlet-triplet energy gap in linear acenes. These examples demonstrate the method's applicability to large-scale systems and strongly correlated electron phenomena, extending the reach of NOF theory to increasingly complex systems.