Note: On the inclusion of a diagonal Born-Oppenheimer correction in the reduced dimensional treatment of the H₂O–para-H₂ complex

In this note, we propose an improvement of the so-called adiabatic-hindered-rotor (AHR) approximation that was recently proposed for the quantum treatment of both bound states and inelastic scattering of the H₂O–para-H₂ complex.^1,2 Within the standard AHR scheme, we separate out the five body-fixed internal degrees of freedom ${R,𝜃,ϕ,𝜃′,ϕ′}$ (see Fig. 1 in Ref. 2 for a representation of the coordinates) into two subgroups as follows:

This decoupling is analogous to the Born-Oppenheimer separation of electronic and nuclear motion. The AHR approximation scheme then consists of repetitively solving the two-dimensional (2D) rotational equation for the q-hydrogen coordinates at each intermolecular coordinates Q,