Gauge-including neural-network quantum Monte Carlo for molecules in magnetic fields

Abstract

External magnetic fields, through their coupling to orbital and spin motion, complicate the correlated electronic states and impose coordinate-dependent phases on the wavefunction, thereby making accurate electronic structure calculations substantially more demanding. Recently, neural network-based quantum Monte Carlo (NNQMC) has emerged as a highly accurate approach to study nucleus-free systems in magnetic fields. For molecular systems, however, things get more complicated as the magnetic field would introduce a rapidly varying phase in the region far from the gauge origin. Here we introduce a gauge-including phase factor that acts directly on the full many-electron wavefunction and accounts for the prescribed magnetic phase, leaving a smoother correlated residual for the network to learn. This factor greatly improves molecular translation consistency and size consistency, providing a route for studying systems in magnetic fields with NNQMC. Upon this approach, we reproduce weak-field magnetizabilities and strong-field bond contraction in \ce{H2}. We further apply the method to selected transitions in the \ce{CN} red and \ce{C2} Swan systems at magnetic fields relevant to white dwarfs. The \ce{CN} transition exhibits a much larger field-induced shift than its \ce{C2} counterpart, suggesting its potential as a probe of white-dwarf magnetic fields.