A numerically exact calculation of vibration–rotation–tunneling levels of water dimer on a new accurate potential energy surface: Achieving sub-cm−1 accuracy from the terahertz to the infrared

Abstract

Numerically exact vibrational–rotational–tunneling (VRT) levels of (H2O)2 and (D2O)2 have been computed in full dimensionality on a new highly accurate two-body potential energy surface (PES). Inter-molecular levels are computed with a basis of products of contracted intra-molecular basis functions and inter-molecular functions that are products of Wigner functions. Intra-molecular levels are computed with a product of contracted intra-molecular basis functions and contracted inter-molecular basis functions. We use a two-body PES that is fitted using the fundamental-invariant neural network method using 740 000 ab initio points. Energies for points near the bottom of the well are computed without the frozen-core approximation. The PES has a root-mean-square fitting error of only 0.70 cm−1. All the experimental VRT fork origins and tunneling splittings in the terahertz region (up to 150 cm−1) are in excellent agreement with our calculated levels. The largest error is 0.44 cm−1 for (H2O)2 and 0.85 cm−1 for (D2O)2. The calculated levels also agree very well with the 22, of a possible 24, observed OD stretch vibration–tunneling levels of (D2O)2 [Barclay et al., J. Chem. Phys. 150, 164307 (2019) and Barclay et al., 160, 114314 (2024)], with the largest error being 0.35 cm−1. Coupling, which causes predissociation, makes OH stretch states of (H2O)2 difficult to observe and their assignment is controversial. Our calculations resolve the controversy. For the only rotationally resolved experimental OH stretch state, the as[A] “2s” state [Huang and Miller, J. Chem. Phys 91, 6613 (1989)], near 3738 cm−1, the 3 observed vibrational–tunneling levels agree with the calculated levels to within 0.35 cm−1.