Exploring the Spectral Signatures of Large Amplitude Motions in the CH Stretching Region of the Vibrational Spectrum of CH 5 +

The spectra of CH5+ and its deuterated analogues are challenging to interpret due to the very flat potential surface and the highly delocalized ground state wave function. In this work, an approach is developed to model the spectra of CH5+ and CH4D+. In this approach, several thousand geometries are sampled from the ground-state probability density, which is evaluated using diffusion Monte Carlo. For each structure, the potential energy is minimized with respect to the five CH bond lengths, and the frequencies and intensities for the five 1-0 transitions involving the CH or CD stretching vibrations are then evaluated using a five-dimensional harmonically coupled anharmonic oscillator model and a sum of one-dimensional cuts through the dipole moment surface. This information is used to obtain the spectrum by two approaches. To model the lower-resolution laser-induced reaction spectrum, the calculated spectrum is obtained by convoluting the spectra obtained at all of the sampled structures. To model the helium droplet spectrum, in which the individual CH vibrational transitions are resolved, the spectrum is obtained by averaging the Hamiltonian matrices and transition moment vectors over the sampled structures. We find that these approaches reproduce the reported spectra. Analysis of the helium droplet spectrum leads us to conclude that, in this environment, the isomerization of CH5+ in its ground state is restricted compared to the gas phase. Overall, this approach provides a simple and physically transparent way to connect fluxional structures to CH-stretch spectral patterns, and offers frameworks for interpreting future spectroscopic studies.