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The water trimer, as the smallest water cluster in which the three-body interactions can manifest, is arguably the most important hydrogen-bonded trimer. Accurate, fully coupled quantum treatment of its excited intermolecular vibrations has long been an elusive goal. Here, we present the methodology that for the first time allows rigorous twelve-dimensional (12D) quantum calculation of the intermolecular vibration-tunneling eigenstates of the water trimer, with the monomers treated as rigid. These 12D eigenstates are used to simulate the low-frequency absorption spectrum of the trimer for direct comparison with the measured far-infrared (FIR) spectrum of the water trimer in helium nanodroplets. The 12D calculations reveal weak coupling between the large-amplitude torsional and intermolecular stretching vibrations. The calculated torsional tunneling splittings are in excellent agreement with spectroscopic results. There are visible differences between the spectrum simulated using the 12D eigenstates and that based on our earlier 9D calculations where the stretching vibrations are not included. The peaks in the 12D spectrum are generally shifted to slightly lower energies relative to those in the 9D spectrum, as well as the measured FIR spectrum, and are often split by intermolecular stretch–bend Fermi resonances that the 9D treatment cannot capture. 

We present fully coupled, full-dimensional quantum calculations of the inter- and intra-molecular vibrational states of HCl trimer, a paradigmatic hydrogen-bonded molecular trimer. They are performed utilizing the recently developed methodology for the rigorous 12D quantum treatment of the vibrations of the noncovalently bound trimers of flexible diatomic molecules [Felker and Bačić, J. Chem. Phys. 158, 234109 (2023)], which was previously applied to the HF trimer by us. In this work, the many-body 12D potential energy surface (PES) of (HCl)3 [Mancini and Bowman, J. Phys. Chem. A 118, 7367 (2014)] is employed. The calculations extend to the intramolecular HCl-stretch excited vibrational states of the trimer with one- and two-quanta, together with the low-energy intermolecular vibrational states in the two excited v = 1 intramolecular vibrational manifolds. They reveal significant coupling between the intra- and inter-molecular vibrational modes. The 12D calculations also show that the frequencies of the v = 1 HCl stretching states of the HCl trimer are significantly redshifted relative to those of the isolated HCl monomer. Detailed comparison is made between the results of the 12D calculations on the two-body PES, obtained by removing the three-body term from the original 2 + 3-body PES, and those computed on the 2 + 3-body PES. It demonstrates that the three-body interactions have a strong effect on the trimer binding energy as well as on its intra- and inter-molecular vibrational energy levels. Comparison with the available spectroscopic data shows that good agreement with the experiment is achieved only if the three-body interactions are included. Some low-energy vibrational states localized in a secondary minimum of the PES are characterized as well.