Ab Initio rovibrational spectrum of the NaH₂ ⁺ ion–quadrupole complex

Abstract

The electronic and rovibrational structure of (¹A₁) NaH₂ ⁺ has been investigated using a relativistically-corrected, all-electron coupled-cluster with singles, doubles and perturbative triples (CCSD(T)) ansatz. For the electronic ground state this ansatz yielded equilibrium Na–H bond lengths (R _e ) of 2.4208 Å and an equilibrium H–Na–H bond angle (θ_e) of 17.8°. An analytical potential energy surface (PES) was embedded in the rovibrational Hamiltonian. The PES was constructed using 118 CCSD(T) points and exhibited a residual error of 1.2 cm⁻¹. The rovibrational Hamiltonian was diagonalised using variational techniques. The vibrational and rovibrational eigenvectors were assigned using a configuration weight scheme in terms of normal modes and the Mulliken assignment scheme, respectively. For the ground vibrational state of (¹A₁) NaH₂ ⁺, the vibration-averaged bond lengths 〈R〉 and angle 〈θ〉 were 2.4995 Å and 17.1°, respectively. The ab initio (¹A₁) NaH₂ ⁺ PES yielded a dissociation energy (D ₀) value of 10.3 kJ mol⁻¹, which is in excellent agreement with the experimental value of 10.3 ± 0.8 kJ mol⁻¹ (Bushnell et al. in J Phys Chem 98:2044, 1994). An analytical dipole moment surface was constructed using 90 CCSD(T) points. Rovibrational spectra of (¹A₁) NaH₂ ⁺, (¹A′) NaHD⁺ and (¹A₁) NaD₂ ⁺ for v ≤ 10, J ≤ 5 were constructed using rovibrational transition moment matrix elements calculated in a novel manner that employs the analytical dipole moment surface (DMS). The rovibrational structure of the Na⁺–H₂ v _HH = 1 ← v _HH = 0 band was calculated and compared to that of Li⁺–H₂.