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We study the vibrational spectrum of the protonated water dimer, by means ofa divide-and-conquer semiclassical initial value representation of the quantumpropagator, as a first step in the study of larger protonated water clusters.We use the potential energy surface from [Huang et al., J. Chem. Phys. 122,044308 (2005)]. To tackle such an anharmonic and floppy molecule, we employfully Cartesian dynamics and carefully reduce the coupling to global rotationsin the definition of normal modes. We apply the time-averaging filter andobtain clean power spectra relative to suitable reference states, thathighlight the spectral peaks corresponding to the fundamental excitations ofthe system. Our trajectory-based approach allows us for physical interpretationof the very challenging proton transfer modes. We find that it is important,for such a floppy molecule, to selectively avoid to initially excite lowerenergy modes, in order to obtain cleaner spectra. The estimated vibrationalenergies display a mean absolute error (MAE) of $\sim29\text{cm}^{-1}$ withrespect to available Multi-Configuration time-dependent Hartree calculationsand $\text{MAE}\sim14\text{cm}^{-1}$ when compared to the optically activeexperimental excitations of the Ne-tagged Zundel cation. The reasonable scalingin the number of trajectories for Monte Carlo convergence is promising forapplications to higher dimensional protonated cluster systems.

Reduced Rovibrational Coupling Cartesian Dynamics for Semiclassical Calculations: Application to the Spectrum of the Zundel Cation