Calculation of Rotation–Vibration Energy Levels of the Water Molecule with Near-Experimental Accuracy Based on an ab Initio Potential Energy Surface

A recently computed, high-accuracy ab initio Born–Oppenheimer (BO) potential energy surface (PES) for the water molecule is combined with relativistic, adiabatic, quantum electrodynamics, and, crucially, nonadiabatic corrections. Calculations of ro-vibrational levels are presented for several water isotopologues and shown to have unprecedented accuracy. A purely ab initio calculation reproduces some 200 known band origins associated with seven isotopologues of water with a standard deviation (σ) of about 0.35 cm–1. Introducing three semiempirical scaling parameters, two affecting the BO PES and one controlling nonadiabatic effects, reduces σ below 0.1 cm–1. Introducing one further rotational nonadiabatic parameter gives σ better than 0.1 cm–1 for all observed ro-vibrational energy levels up to J = 25. We conjecture that the energy levels of closed-shell molecules with roughly the same number of electrons as water, such as NH3, CH4, and H3O+, could be calculated to this accuracy using an analogous procedure. This means that near-ab initio calculations are capable of predicting transition frequencies with an accuracy only about a factor of 5 worse than high resolution experiments.