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

Abstract

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=±2l←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=3u←±1l. 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.