Theoretical Calculations of Infrared Bands of CH3+and CH5+

Abstract

Existing theoretical calculations predict that infrared spectra of the two most fundamental reactive carbo-ions, methyl cation <TEX>$CH{_3}^+$</TEX> with <TEX>$D_{3h}$</TEX> symmetry and protonated methyl cation <TEX>$CH{_5}^+$</TEX> with <TEX>$C_s(I)$</TEX>, <TEX>$C_s(II)$</TEX>, and <TEX>$C_{2v}$</TEX> symmetries, appear together in the 7-<TEX>${\mu}m$</TEX> region corresponding to the C-H bending modes. Vibrational band profiles of <TEX>$CH{_3}^+$</TEX> and <TEX>$CH{_5}^+$</TEX> have been compared by ab initio calculation methods that use the basis sets of MP2/aug-cc-pVTZ and CCSD(T)/cc-pVTZ. Our results indicate that the bands of rotation-vibration transitions of <TEX>$CH{_3}^+$</TEX> and <TEX>$CH{_5}^+$</TEX> should overlap not only in the 3-<TEX>${\mu}m$</TEX> region corresponding to the C-H stretching modes but also in the 7-<TEX>${\mu}m$</TEX> region corresponding to the C-H bending modes. Five band intensities of <TEX>$CH{_5}^+$</TEX> among fifteen vibrational transitions between 6 and 8 <TEX>${\mu}m$</TEX> region are stronger than those of the <TEX>${\nu}_2$</TEX> and <TEX>${\nu}_4$</TEX> bands in <TEX>$CH{_3}^+$</TEX>. Ultimate near degeneracy of the two bending vibrations <TEX>${\nu}_2$</TEX> and <TEX>${\nu}_4$</TEX> of <TEX>$CH{_3}^+$</TEX>along with the stronger intensities of <TEX>$CH{_5}^+$</TEX> in the three hydrogen scrambling structures may cause extreme complications in the analysis of the high-resolution carbo-ion spectra in the 7-<TEX>${\mu}m$</TEX> region.