Intermolecular Bending States and Tunneling Splittings of Water Trimer from Rigorous 9D Quantum Calculations: I. Methodology, Energy Levels, and Low-Frequency Spectrum

We present the computational methodology that enables the first rigorous nine-dimensional (9D) quantum calculations of the intermolecular bending states of the water trimer, as well as its low-frequency spectrum for direct comparison with experiment. The water monomers, treated as rigid, have their centers of mass (cm's) at the corners of an equilateral triangle, and the intermonomer cm-to-cm distance is set to a value slightly larger than that in the equilibrium geometry of the trimer. The remaining nine strongly coupled large-amplitude bending (angular) degrees of freedom (DOFs) enter the 9D bend Hamiltonian of the three coupled 3D rigid-water hindered rotors. Its 9D eigenstates encompass excited librational vibrations of the trimer, as well as their torsional and bifurcation tunneling splittings which have been the subject of much interest. For this reason, the calculation of these eigenstates by diagonalizing the 9D bend Hamiltonian represents the most rigorous high-dimensional quantum treatment to date of the intermolecular vibrational states of the water trimer and its excited-state tunneling splittings. Such calculations are extremely demanding, and a sophisticated computational scheme is developed that exploits the molecular symmetry group of the water trimer, G48, in order to make them feasible in a reasonable amount of time. The spectrum of the low-frequency vibrations of the water trimer simulated using the eigenstates of the 9D bend Hamiltonian agrees remarkably well with the experimentally observed far-infrared (FIR) spectrum of the trimer in helium nanodroplets over the entire frequency range of the measurements from 70 to 620 cm−1. This shows that most peaks in the experimental FIR spectrum are associated with the intermolecular bending vibrations of the trimer. Moreover, the ground-state torsional tunneling splittings from the present 9D calculations are in excellent agreement with the spectroscopic data. These results demonstrate the high quality of the ab initio 2+3-body PES employed for the DOFs included in the bound-state calculations.