A convenient set of vibrational coordinates for 2D calculation of the tunneling splittings of the ground state and some excited vibrational states for the inversion motion in HO, HO, and HO.

Splitting of the ground state and some excited symmetric bending vibrational states due to inversion tunneling of the oxygen atom in the HO, HO ions and in the HO radical are analyzed by numerically solving the vibrational Schrödinger equation of restricted (2D) dimensionality. As two vibrational coordinates, we used 1) the distance of the oxygen atom from the plane of a regular triangle formed by three hydrogen atoms and 2) a symmetry coordinate composed of three distances between chemically non-bonded hydrogen atoms. The kinetic energy operator in this case takes the simplest form. The 2D potential energy surface (PES) in the given coordinates was calculated for HO at the CCSD(T)/aug-cc-pVTZ and CCSD(T)-F12/cc-pVTZ-F12 levels of theory. The same 2D PES for the HO anion and HO radical were calculated at the CCSD(T)/aug-cc-pVQZ, CCSD(T)/d-aug-cc-pVQZ and UCCSD(T)/aug-cc-pVQZ, UCCSD(T)/d-aug-cc-pVQZ levels of theory, respectively. The tunneling splittings were calculated for the cations HO, DO, TO, HO, DO, TO. The tunneling splittings for the HO, DO, TO anions and HO, DO, TO radicals were calculated for the first time. The results of calculations demonstrate good agreement with experimental values of the tunneling splittings in the ground state and in some excited vibrational states of the HO and DO cations.