Partitioning the electronic wave function using deep variational Monte Carlo

Abstract: We propose a novel wave function partitioning method that integrates deep-learning variational Monte Carlo with ans\"atze based on generalized product functions. This approach effectively separates electronic wave functions (WFs) into multiple partial WFs representing, for example, the core and valence domains or different electronic shells. Although our ans\"atze do not explicitly include correlations between individual electron groups, we show that they accurately reproduce the underlying physics and chemical properties, such as dissociation curve, dipole moment, reaction energy, ionization energy, or atomic sizes. We identify the optimal number of core electrons and define physical core sizes for Li to Mg atoms. Our results demonstrate that core electrons can be effectively decoupled from valence electrons. We show that the core part of the WF remains nearly constant across different molecules and their geometries, enabling the transfer and reuse of the core part in WFs of more complex systems. This work provides a general framework for WF decomposition, offering potential advantages in computing and studying larger systems, and possibly paving the way for ab-initio development of effective core potentials. Though currently limited to small molecules due to scaling, we highlight several directions for extending our method it to larger systems.