Classical, Thermostated Ring Polymer, and Quantum VSCF/VCI Calculations of IR Spectra of H7O3+ and H9O4+ (Eigen) and Comparison with Experiment.

We report vibrational IR spectra of the protonated water clusters H7O3+ and H9O4+ (Eigen) in the range from 0 to 4000 cm-1, from classical molecular dynamics (MD) and thermostated ring polymer molecular dynamics (TRPMD) calculations, using recent high-level ab initio potential and dipole moments surfaces. The MD spectra are done at 20 and 100 K, whereas the computationally intensive TRPMD spectra are done at 100 K. These spectra are compared with previous quantum vibrational self-consistent field/virtual state configuration interaction (VSCF/VCI) and quasi-classical MD calculations, using the same potential and dipole moment surfaces, and with experimental spectra for cold (∼20 K) clusters. As expected, the 20 K MD spectra have vibrational bands close to the harmonic ones, and at 100 K some downshifting of the bands is seen along with significant broadening. The TRPMD calculations, using two different thermostats (path integral Langevin equation and generalized Langevin Equation thermostat), show substantial downshifting relative to the classical spectrum at 100 K, especially for the intense proton-stretch bands. However, the downshifting is not sufficient to produce quantitative agreement with the VSCF/VCI (and experimental) band positions. An analysis of these positions is given based on a previously reported linear correlation between the hydronium O-H bond length and the harmonic frequency.