Vibrational analysis of methyl cation - rare gas atom complexes: CH$_3^+$-Rg (Rg=He, Ne, Ar, Kr)

The vibrational spectra of simple CH$_3^+$-Rg (Rg=He, Ne, Ar, Kr) complexes have been studied by vibrational configuration interaction (VCI) theory relying on multidimensional potential energy surfaces (PES) obtained from explicitly correlated coupled cluster calculations, CCSD(T)-F12a. In agreement with experimental results, the series of rare gas atoms leads to rather unsystematic results and indicates huge zero point vibrational energy effects for the helium complex. In order to study these sensitive complexes more consistently, we also introduce configuration averaged vibrational self-consistent field theory (CAVSCF), which is a generalization of standard VSCF theory to several configurations. The vibrational spectra of the complexes are compared to that of the methyl cation, for which corrections due to scalar-relativistic effects, high-level coupled-cluster terms, i.e. CCSDTQ, and core-valence correlation have explicitly been accounted for. The occurrence of tunneling splittings for the vibrational ground-state of CH$_3^+$-He has been investigated on the basis of semiclassical instanton theory. These calculations and a direct comparison of the energy profiles along the intrinsic reaction coordinates (IRC) with that of the hydronium cation, H$_3$O$^+$, suggest that tunneling effects for vibrationally excited states should be very small.