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

## TL;DR

This paper introduces a Cartesian dynamics-based semiclassical method to analyze the vibrational spectrum of the Zundel cation, effectively handling floppy, anharmonic molecules and providing results close to experimental and high-level quantum calculations.

## Contribution

It presents a divide-and-conquer semiclassical approach with Cartesian dynamics and reduced rovibrational coupling, improving spectral analysis of complex protonated water clusters.

## Key findings

- Achieved a mean absolute error of ~29 cm^{-1} compared to MCTDH calculations.
- Obtained a ~14 cm^{-1} MAE relative to experimental excitations.
- Demonstrated promising scalability for larger protonated water clusters.

## Abstract

We study the vibrational spectrum of the protonated water dimer, by means of a divide-and-conquer semiclassical initial value representation of the quantum propagator, 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 employ fully Cartesian dynamics and carefully reduce the coupling to global rotations in the definition of normal modes. We apply the time-averaging filter and obtain clean power spectra relative to suitable reference states, that highlight the spectral peaks corresponding to the fundamental excitations of the system. Our trajectory-based approach allows us for physical interpretation of the very challenging proton transfer modes. We find that it is important, for such a floppy molecule, to selectively avoid to initially excite lower energy modes, in order to obtain cleaner spectra. The estimated vibrational energies display a mean absolute error (MAE) of $\sim29\text{cm}^{-1}$ with respect to available Multi-Configuration time-dependent Hartree calculations and $\text{MAE}\sim14\text{cm}^{-1}$ when compared to the optically active experimental excitations of the Ne-tagged Zundel cation. The reasonable scaling in the number of trajectories for Monte Carlo convergence is promising for applications to higher dimensional protonated cluster systems.