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 ${\mathrm{HHe}}_3^{+}$ . The equilibrium structure of ${\mathrm{HHe}}_3^{+}$ is planar and T-shaped, one He atom solvating the quasi-linear He-H⁺ -He core. The dynamical structure of ${\mathrm{HHe}}_3^{+}$ , 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 ${\mathrm{HHe}}_2^{+}$ chomophore, but freely orbits the central proton, forming a three-dimensional torus around the ${\mathrm{HHe}}_2^{+}$ 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.

Keywords: nuclear delocalization; nuclear density (ND); path integral molecular dynamics (PIMD); spatial distribution functions (SDF); variational nuclear-motion computations.