Temperature Dependence of Intramolecular Vibrational Bands in Small Water Clusters

Cyclic water clusters are pivotal for understanding atmospheric reactions as well as liquid water, yet the temperature (T) dependence of their dynamics and spectroscopy is poorly studied. The development of highly accurate water potentials, such as MB-pol, partly rectifies this. It remains to account for the quantum nuclear effects (NQE), because quantum nuclear dynamics become increasingly inaccurate at low temperatures. From a practical point of view, we find that NQE can be accounted for simply by subtracting a constant from the frequencies obtained from the velocity autocorrelation functions (VACF) of classical nuclear dynamics, resulting in unprecedented agreement with experiment, mostly within 5 cm^-1. We have performed classical simulations of (H₂O)_n clusters (n = 2-5) from 20 K and up to their melting temperature, calculating both all-atom and partial VACF, thus generating the temperature dependence of the vibrational frequencies (IR and Raman bands). Focusing on the hydrogen-bonded (HBed) OH stretch and HOH bend, we find opposing T dependencies. The HBed OH modes blue shift linearly with T, attributed to ring expansion rather than any specific conformational change. The lowest-frequency Raman concerted mode is predicted to show the largest such shift. In contrast, the HOH bend undergoes a red-shift, with the highest frequency concerted band undergoing the largest red-shift. These results can be explained by a coupled-oscillator model for n hydrogen atoms on a ring, constrained to move either tangentially (stretch) or perpendicularly (bend) to the ring. With increasing temperature and weakening of HBs, the intrinsic force constant increases (stretch) or remains constant (bend), while the nearest-neighbor coupling constant decreases, and this results in the interesting behavior revealed herein. T-dependent Raman studies are required for testing some of these predictions.