Torsional States and Tunneling Probability in HOSOH, DOSOD, and DOSOH Molecules Analyzed at the CBS Limit

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 H3O+, H3O-, and H3O

Splitting of the ground state and some excited symmetric bending vibrational states due to inversion tunneling of the oxygen atom in the H₃O⁺, H₃O^- ions and in the H₃O 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 H₃O⁺ at the CCSD(T)/aug-cc-pVTZ and CCSD(T)-F12/cc-pVTZ-F12 levels of theory. The same 2D PES for the H₃O^- anion and H₃O 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 H₃¹⁶O⁺, D₃¹⁶O⁺, T₃¹⁶O⁺, H₃¹⁸O⁺, D₃¹⁸O⁺, T₃¹⁸O⁺. The tunneling splittings for the H₃O^-, D₃O^-, T₃O^- anions and H₃O, D₃O, T₃O 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 H₃¹⁶O⁺ and D₃¹⁶O⁺ cations.