Real or Artificial Stability of \({\text{CH}}_{5}^{ + }\) Ions and Deuterated Variants \({\mathbf{C}}{{{\mathbf{H}}}_{x}}{\mathbf{D}}_{{\left( {5 - x} \right)}}^{ + }\) Based on Ab Initio Calculation and Rotational Spectrum

Abstract

Protonated methane, \({\text{CH}}_{5}^{ + }\), has unusual vibrational and rotational behavior because its three nonequivalent equilibrium structures have nearly identical energies and its five protons scramble freely. The highly flexible \({\text{CH}}_{5}^{ + }\), molecular ion has been shown by ab initio calculations to have 120 symmetrically equivalent minima of Cs symmetry in its ground electronic state. Complete proton rearrangement, making all minima accessible to each other, is possible as a result of two large-amplitude internal motions: an internal rotation about the C₃ axis with an ab initio barrier of 30 cm^–1 and an internal flip motion with an ab initio barrier of 300 cm^–1 that exchanges protons between the H₂ and \({\text{CH}}_{3}^{ + }\) groups. We calculate the structure of the J = 2 \( \leftarrow \)1 and 1 \( \leftarrow \) 0 rotational transitions of \({\text{CH}}_{5}^{ + }\), \({\text{CD}}_{5}^{ + }\) and also other variants containing \({\text{C}}{{{\text{H}}}_{x}}{\text{D}}_{{(5 - x)}}^{ + }\). Although many theoretical papers have been published on the quantum mechanics of these systems, a better understanding requires spectral and conformational analysis. Post Hartree-Fock, Møller-Plesset and DFT calculation with the correlation consistent polarized valence double and triple zeta basis sets have done for the zero-point energies of \({\text{C}}{{{\text{H}}}_{x}}{\text{D}}_{{(5 - x)}}^{ + }\). The present results indicates the mode 8, 12, and 10 agree with qualitative of \({\text{CH}}_{5}^{ + }\), which is highly fluxional and has a complex spectrum while the C–X bonds which are broken and reformed all the time. The spectrum of mode 12 is highly complex with huge red-and some blue shifts. In particular, they can be attributed to the rapid coupling of the original CH-stretching normal mode to motions more closely related to isomerization, i.e., bending or rocking. There has thus been a long debate whether \({\text{CH}}_{5}^{ + }\) has a structure at all or not and is it real rotational motions or artificial. In addition, we include the contribution to the torsional barrier from the zero point energies of the other (high-frequency) vibrations, the effect of centrifugal distortion, and the effect of second-order rotation-vibration interactions.