Quantum Nuclear Delocalization and its Rovibrational Fingerprints

Abstract

Quantum mechanics dictates that nuclei must undergo some delocalization. In this work, emergence of quantum nuclear delocalization and its rovibrational fingerprints are discussed for the case of the van der Waals complex HHe3+. The equilibrium structure of HHe3+ is planar and T‐shaped, one He atom solvating the quasi‐linear He‐H+‐He core. The dynamical structure of HHe3+, in all of its bound states, is fundamentally different. As revealed by spatial distribution functions and nuclear densities, during the vibrations of the molecule the solvating He is not restricted to be in the plane defined by the instantaneously bent HHe3+ chomophore, but freely orbits the central proton, forming a three‐dimensional torus around the HHe2+ chromophore. This quantum delocalization is observed for all vibrational states, the type of vibrational excitation being reflected in the topology of the nodal surfaces in the nuclear densities, showing, for example, that intramolecular bending involves excitation along the circumference of the torus.

Unusual Dynamics and Vibrational Fingerprints of van der Waals Dimers Formed by Linear Molecules and Rare-Gas Atoms

“…As shown in Figures a–c, S10, and S11, the nuclear densities form double tori for the pure T-bend states, where the two tori are divided by a nodal surface perpendicular to the bent chromophore’s plane. The results shown for CO 2 ·Ne (Figure b) and OCS·Ar (Figure c) corroborate findings documented in ref for HHe 3 + (see also Figure a). For the same chromophore, the thickness of these tori decreases with the size of the solvating atom, just as expected.…”

“…Nonetheless, for the purposes of this investigation, the uncertainty of the 4D e model, 5–10 cm –1 , is considered to be good. At this level of accuracy, the deviations between the 4D e results of the present study and those of ref (green in Figure a) are deemed insignificant. Similar to the CO 2 ·Ar case, the 4D e → 2D e,0 replacement does not improve the computed vibrational energies.…”

“…The accuracy of the six reduceddimensional models, exploiting our 4D PES and its LD cuts, was also evaluated against 6D, 4D e , and 4D 0 quasi-variational results reported for HHe 3 + . 5 These reference computations involved a 6D PES obtained at the aug-cc-pVQZ-OPTRI DF-CCSD(T*)-F12b level, 5 supposedly delivering an accuracy better than 1 cm −1 for the vibrational energies. A comparison of the results is given in Table S9 and Figure 5.…”

“…In recent studies involving our group, 1−5 interesting structural, dynamical, and spectroscopic results have been reported for the HHe n + and He n + systems, whereby either a proton or a positive charge is "solvated" by He atoms, respectively. In particular, results obtained for HHe 3 + , 5 where a He atom solvates the formally linear HHe 2 + cation, led us to the present study of the structure, dynamics, and vibrational fingerprints for a collection of van der Waals (vdW) dimers, composed of neutral or charged linear chromophores and a single rare-gas (Rg) atom, Rg = He, Ne, and Ar.…”

“…95 In the last case, the exact kinetic-energy operators as well as newly developed four-dimensional (4D) PESs and their 2D/3D cuts are employed, where the intermonomer bond lengths are kept fixed. Nuclear densities, that is the spatial distributions of the nuclei in a body-fixed Cartesian-coordinate system, 5,96 are also obtained for all bound states. To constrain the length of the main text, most of the numerical data are deposited in the Supporting Information, while some technical details are moved to table footnotes and figure captions.…”