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 CH 5 + based on the motion of an effective particle confined to a 60-vertex graph Γ 60 with a single edge length parameter. Within this model, the quantum states of CH 5 + are obtained in analytic form and are related to combinatorial properties of Γ 60 . The bipartite structure of Γ 60 gives a simple explanation for curious symmetries observed in numerically exact variational calculations on CH 5 + . We present a simple, one-dimensional, exactly solvable model which explains not one but the first 60 vibrational eigenstates of the 6-atom molecule CH 5 + .