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

TL;DR

This paper introduces an exactly solvable one-dimensional quantum model for CH5+ vibrational states, revealing symmetries and providing analytic solutions based on a graph-theoretic approach.

Contribution

It presents a novel 1D model using a 60-vertex graph to analytically describe CH5+ vibrational levels, linking quantum states to graph combinatorics.

Findings

Analytic solutions for CH5+ vibrational states

Explanation of observed symmetries in vibrational spectra

Graph-based model simplifies understanding of complex vibrational dynamics

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 ${\Gamma}_{60}$ 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+.