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+.