Neural Canonical Transformation for the Spectra of Fluxional Molecule CH5+

Protonated methane, CH5+, is a highly fluxional molecule with large spatial motions of the hydrogen atoms. The molecule's anharmonic effects and the scrambling of the hydrogen atoms significantly affect the excitation spectrum of the molecule. The neural canonical transformation (NCT) approach, which we previously developed to solve the vibrational spectra of molecules and solids, is a powerful method that effectively treats nuclear quantum effects and anharmonicities. Using NCT with wavefunctions in atomic coordinates rather than normal coordinates, we successfully calculate the ground and excited states of CH5+. We found that the wavefunctions for the ground state, as well as for low- and high-energy excited states, show preferences for the three stationary points on the potential energy surface. Furthermore, the dynamics of all these states are characterized by continuous hydrogen swapping. This work extends the applicability of the NCT approach for calculating excited states to fluxional molecules without fixed geometry.