The $Na+–H2$ cation complex: Rotationally resolved infrared spectrum, potential energy surface, and rovibrational calculations

The rotationally resolved infrared spectrum of the $Na+–H2$ cation complex is recorded in the H–H stretch region $(4067–4118cm−1)$ by monitoring the production of $Na+$ photofragments. Altogether 42 lines are identified, 40 of which are assigned to $Ka=1-1$ transitions (associated with complexes containing ortho-$H2$⁠) and two tentatively assigned to $Ka=0-0$ transitions (associated with complexes containing para-$H2$⁠). The $Ka=1-1$ subband lines were fitted using a Watson $A$-reduced Hamiltonian, yielding effective spectroscopic constants. The band origin is estimated as $4094.6cm−1$⁠, a shift of $−66.6cm−1$ with respect to the $Q1(0)$ transition of the free $H2$ molecule. The results demonstrate that $Na+–H2$ has a T-shaped equilibrium configuration with the $Na+$ ion attached to a slightly perturbed $H2$ molecule but that large-amplitude vibrational motions significantly influence the rotational constants derived from the asymmetric rigid rotor analysis. The vibrationally averaged intermolecular separation in the ground vibrational state is estimated as $2.493Å$⁠, increasing slightly (by $0.002Å$⁠) when the $H2$ subunit is vibrationally excited. A new three-dimensional potential energy surface is developed to describe the $Na+–H2$ complex. Ab initio points calculated using the CCSD(T) method and aug-cc-pVQZ basis set augmented by bond functions are fitted using a reproducing kernel Hilbert space method [Ho et al., J. Chem. Phys. 104, 2584 (1996)] to give an analytical representation of the potential energy surface. Ensuing variational calculations of the rovibrational energy levels demonstrate that the potential energy surface correctly predicts the frequency of the $νHH$ transition (to within $2.9cm−1$⁠) and the dissociation energies [$842cm−1$ for $Na+–H2(para)$ and $888cm−1$ for $Na+–H2(ortho)$]. The $B$ and $C$ rotational constants are slightly underestimated (by 1.7%), while the vibrationally averaged intermolecular separation is overestimated by $0.02Å$⁠.