Vibrational infrared and Raman spectra of the methanol molecule with equivariant neural-network property surfaces

Electric dipole and polarizability surfaces are developed for the methanol (CH${}_3$OH) molecule using ab initio electronic structure data, computed at the CCSD/aug-cc-pVTZ level of theory, and equivariant neural networks. These property surfaces are used to compute vibrational infrared and Raman intensities with variational vibrational energies and wave functions. The energies and wave functions, fully accounting for the large-amplitude motion and tunneling splitting states, are from continued variational vibrational computations, based on earlier work [Sunaga et al., J. Chem. Phys., 2025, 163, 064101], up to 3700 cm${}^{-1}$ beyond the zero-point vibration, now reaching the O-H stretching fundamental. All vibrational fundamentals, combination and overtone bands are in excellent agreement with available (gas-phase) experimental data, with a 2.2 cm${}^{-1}$ root-mean-squared deviation of the fundamentals from experiment. These developments constitute an important step towards a quantitative and comprehensive exact quantum dynamics model of the methanol molecule, and a linelist for astrophysical applications.