CH 5 + : The story goes on. An explicitly correlated coupled-cluster study

CCSD(T)-R12 calculations (as well as R12 calculations at lower CC and MPn level) with large basis sets have been performed for the three lowest stationary structures of CH${}_5^{+},$ for CH${}_4$ , and for CH${}_3^{+}$ + H${}_2$ . The basis set limit of the total energy at all levels of the treatment of correlation is reached within $\text{∼1}$ kcal/mol. At the CCSD(T)-R12 level the same accuracy is achieved for CH${}_4$ with respect to its “experimental’’ non-relativistic energy. Accordingly, energy differences should be correct to within a small fraction of a kcal/mol. In agreement with the most accurate previous calculations, the $C_s\text{(1)}$ structure of CH${}_5^{+}$ is lowest, followed by $C_s\text{(2)}$ and $C_{\text{2v}}.$ For the relative energies of the two latter structures we predict energy differences of 0.1 and 0.8 kcal/mol respectively. The possibility of a vibrational stabilization of the $C_{\text{2v}}$ -structure is discussed. Accurate predictions of the proton affinity of CH${}_4$ and the binding energy between CH${}_3^{+}$ and H${}_2$ are also given.