Neural wavefunction calculations of hyperfine coupling constants relevant to μSR spectroscopy with quantum muons and protons

Accurate prediction of muon hyperfine constants at zero temperature is useful for interpreting muon spin spectroscopy data, yet standard methods, such as density functional theory (DFT), evaluate these constants within the Born–Oppenheimer approximation, in which the electronic wavefunction is calculated with the muon and nuclei held as clamped point charges. This treatment may be inadequate for the muon because of its small mass. To overcome this limitation, we use the variational quantum Monte Carlo method with neural-network trial wavefunctions, a highly accurate and flexible approach recently applied to other quantum chemical problems. Within this framework, the muon can either be clamped or included explicitly in the many-particle electron-muon wavefunction, in which case the fully quantum-mechanical pair density is obtained directly. We calculate zero-temperature vacuum muon hyperfine constants in muoniated methyl and ethyl radicals for both clamped and quantum-mechanical muons. The hyperfine constants obtained from our clamped-muon calculations in the methyl and ethyl radicals differ significantly from the corresponding DFT results, highlighting the limitations of DFT even when the muon is clamped. The results with quantum muons are closer to experiment after accounting for environmental and temperature effects. These findings suggest that explicitly calculating the quantum-mechanical muon-electron pair density improves the accuracy of muon hyperfine constant predictions.