Exactly solvable 1D model explains the low-energy vibrational level structure of protonated methane

A new one-dimensional model is proposed for the low-energy vibrational quantum dynamics of CH5+ based on the motion of an effective particle confined to a 60-vertex graph Gamma(60) with a single edge length parameter. Within this model, the quantum states of CH5+ are obtained in analytic form and are related to combinatorial properties of Gamma(60). The bipartite structure of Gamma(60) gives a simple explanation for curious symmetries observed in numerically exact variational calculations on CH5+.

Automated summary

This study presents a new one-dimensional model for the low-energy vibrational quantum dynamics of CH5+, based on the motion of an effective particle on a 60-vertex graph Gamma(60) with a single edge length parameter. The quantum states of CH5+ are obtained analytically within this model and are linked to combinatorial properties of Gamma(60). The bipartite structure of Gamma(60) provides a simple explanation for the curious symmetries observed in numerically exact variational calculations on CH5+.