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

Abstract

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 Γ₆₀ 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 Γ₆₀. The bipartite structure of Γ₆₀ gives a simple explanation for curious symmetries observed in numerically exact variational calculations on CH₅⁺.