Quantum-Chemical and Quantum-Graph Models of the Dynamical Structure of CH₅

Experimental and computational results about the structure, dynamics, and rovibrational spectra of protonated methane have challenged a considerable number of traditional chemical concepts. Hereby theoretical and computational results are provided about the dynamical structure of CH₅⁺. It is shown that the ground vibrational state investigated thus far by computations, forbidden by nuclear-spin statistics, has a structure similar to the first allowed vibrational state and, in fact, the structures of all vibrational states significantly below 200 cm^-1 are highly similar. Spatial delocalization of the nuclei, determined by nuclear densities computed from accurate variational vibrational wave functions, turns out to be limited when viewed in the body-fixed frame, confirming that the effective structure of CH₅⁺ is well described as a CH₃⁺ tripod with a H₂ unit on top of it. The interesting and unusual qualitative aspects of the sophisticated state-dependent variational results receive full explanation via simple quantum-graph models.