Reduced rovibrational coupling Cartesian dynamics for semiclassical calculations: Application to the spectrum of the Zundel cation

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 ∼ 29cm −1 with respect to available Multi-Configuration time-dependent Hartree calculations and MAE ∼ 14cm −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.The Zundel cation is the most representative member of the family of protonated water clusters, towards which many computational efforts are being devoted, mainly motivated by a flourishing of experimental results, 11-16 and the request for higher accuracy. [17][18][19][20][21] In this respect, this molecule is a prototypical example that has been tackled by various approaches, given the great biological relevance of the charge transport mechanism in aqueous solutions. [22][23][24][25][26][27] On the experimental side, the vibrational spectrum of the Zundel cation has been investigated by infrared multiphoton photodissociation spectroscopy 28,29 and noble gases predissociation spectroscopy, in particular Argon and Neon. [30][31][32] The theoretical literature about the vibrational spectrum of the Zundel cation is quite vast, since its strong anharmonicity provides the ideal test-bed for theoretical methods. The PES computed at the level of coupled cluster theory and devised in Ref. 33, has been employed by a plethora of methods for vibrational calculations, such as vibrational configuration interaction (VCI), 34 diffusion Monte Carlo, 32,35 classical molecu-

How many water molecules are needed to solvate one?

“…However, it also shows that, as expected, the spectroscopic features of the water dimer (especially at high frequency) are not compatible with those of bulk water, confirming that more elaborated structures are necessary to mimick the bulk. Semiclassical methods have been applied successfully in a range going from small molecules, [32][33][34] including fluxional ones, 35 to medium-large systems. 36 For this work we employed the multiple coherent states divide-and-conquer semiclassical initial value representation technique (MC-DC SCIVR), 37 which has permitted to solve open issues concerning protonated glycine supramolecular systems 38 and has already been applied to the vibrational in-vestigation of small water clusters.…”

Anharmonic quantum nuclear densities from full dimensional vibrational eigenfunctions with application to protonated glycine

“…The multiple coherent time averaging semiclassical initial value representation (MC SCIVR) [38][39][40][41] can successfully simulate anharmonic vibrational spectra for large systems [42][43][44][45][46] , even in extreme anharmonic cases [47][48][49] . MC SCIVR can be rigorously derived from the stationary phase approximation of the exact Feynman's path integral, and expresses the quantum timeevolution propagator in terms of a few classical trajectories, whose energy is close to the vibrational eigenvalues of the system (see Supplementary Methods).…”

Improved semiclassical dynamics through adiabatic switching trajectory sampling

“…The initial setup would require a particular care in defining normal modes and the conversion matrix between them and Cartesian coordinates, as largely debated in Ref. 16.…”

“…As an alternative, it has been proposed to keep trajectories up to the instant when numerical instability kicks in, possibly by weighing their contributions appropriately. [16,59] A different way to tackle the problem is by approximating or regularizing the prefactor. [60][61][62][63] However, none of these approaches is able to provide a way to restrict the semiclassical calculation to non-chaotic trajectories beforehand.…”