Quantitative characterization of the (D₂O)₃ torsional manifold by terahertz laser spectroscopy and theoretical analysis

We report the measurement of two new perpendicular (D₂O)₃ torsional bands by terahertz laser vibration-rotation-tunneling (VRT) spectroscopy of a planar pulsed supersonic expansion. The first (28.0 cm^-1) band corresponds to the k = ± 2^l←0 transition, and is the lowest frequency vibrational spectrum observed for a water cluster. The second (81.8 cm^-1) band originates in the first excited torsional state, and has been assigned as k = 3^u← ± 1^l. An effective three-dimensional Hamiltonian is derived to describe the rotational structure of each torsional state. Degenerate torsional levels with k = ± 1 and k =± 2 exhibit a Coriolis splitting linear in K implying the presence of vibrational angular momentum, and a second-order splitting from off-diagonal coupling between degenerate sublevels with + |k| and - |k|. With this effective Hamiltonian we fit a total of 554 rovibrational transitions in five different bands connecting the lowest nine torsional states, with a rms residual of 1.36 MHz. The data set comprises the two new VRT bands together with the 41.1 cm^-1 parallel band, the 89.6 cm^-1 parallel band, and the 98.1 cm^-1 perpendicular band. This analysis provides a comprehensive characterization of the torsional energy levels in (D₂O)₃ up to 100 cm^-1 above the zero-point energy, and confirms the torsional assignments for all five (D₂O)₃ VRT bands observed to date. Moreover, it vindicates the adiabatic separation of the trimer torsional and hydrogen bond stretch/bend vibrational modes which underlies the torsional model.