Vibrational quantum graphs and their application to the quantum dynamics of CH5+

Abstract

The first application of quantum graphs to the vibrational quantum dynamics of molecules is reported. The quantum-graph model is applied to the quasistructural molecular ion CH₅⁺, whose nuclear dynamics challenges the traditional understanding of chemical structures and molecular spectra. The vertices of the quantum graph represent versions of the equilibrium structure with distinct atom numbering, while the edges refer to collective nuclear motions transforming the versions of the equilibrium structure into one another. These definitions allow the mapping of the complex vibrational quantum dynamics of CH₅⁺ onto the motion of a particle confined in a quantum graph. The quantum-graph model provides a simple understanding of the low-energy vibrational quantum dynamics of CH₅⁺ and is able to reproduce the low-lying vibrational energy levels of CH₅⁺ (and CD₅⁺) with remarkable accuracy.