Ab Initio Study of the Geometries, Jahn–Teller Distortions, and Electronic Charge Distribution in the CH4+ Ion

Abstract

The CH₄⁺ ion is known to be involved in many ion–molecule reactions, presumably including those leading to the precursors of life, but little experimental information about it is available. In the present investigation, the energy of CH₄⁺ in various geometries is calculated by the restricted SCF MO method using a Gaussian basis set. The ion is distorted from the regular tetrahedron because of the Jahn–Teller effect. Two stable geometries are found: tetragonal ${\mathrm{(D}}_{\text{2d}}{\mathrm{),\; R}}_{\mathrm{CH}}\text{\hspace{0.17em}=\hspace{0.17em}2.0943}\mathrm{bohr}$ , dihedral angle = 53.3°, $\text{E\hspace{0.17em}=\hspace{0.17em}−39.74593}\mathrm{hartree}$ ; trigonal ${\mathrm{(C}}_{\text{3υ}}{\mathrm{),\; R}}_{{\mathrm{CH}}_1}{\text{\hspace{0.17em}=\hspace{0.17em}2.5859, R}}_{{\mathrm{CH}}_{\text{2,3,4}}}\text{\hspace{0.17em}=\hspace{0.17em}2.0121}$ , H₁CH₂ angle = 98.28°, $\text{E\hspace{0.17em}=\hspace{0.17em}−\hspace{0.17em}39.74156}$ hartree. Other geometries investigated are, in order of decreasing energy, regular tetrahedron, square plane, and CH₃⁺ + H. The relations among these geometries are discussed in terms of orbital energies, energy components, and population analysis.