Gradual collapse of nuclear wave functions regulated by frequency tuned X-ray scattering

Nina Ignatova,Vinícius V Cruz,Michael Odelius,Freddy F Guimarães,Victor Kimberg,Rafael C Couto,Emelie Ertan,Sergey Polyutov,Faris Gel’Mukhanov,Andrey Zimin,Hans Ågren

doi:10.1038/srep43891

Abstract

As is well established, the symmetry breaking by isotope substitution in the water molecule results in localisation of the vibrations along one of the two bonds in the ground state. In this study we find that this localisation may be broken in excited electronic states. Contrary to the ground state, the stretching vibrations of HDO are delocalised in the bound core-excited state in spite of the mass difference between hydrogen and deuterium. The reason for this effect can be traced to the narrow “canyon-like” shape of the potential of the state along the symmetric stretching mode, which dominates over the localisation mass-difference effect. In contrast, the localisation of nuclear motion to one of the HDO bonds is preserved in the dissociative core-excited state . The dynamics of the delocalisation of nuclear motion in these core-excited states is studied using resonant inelastic X-ray scattering of the vibrationally excited HDO molecule. The results shed light on the process of a wave function collapse. After core-excitation into the state of HDO the initial wave packet collapses gradually, rather than instantaneously, to a single vibrational eigenstate.

Highlights

Delocalisation of vibrations in the asymmetric isotopomer HDO can be found in the competition between the symmetric shape of the potential energy surface (PES) and the asymmetric kinetic energy operator, which allows for a coexistence of localised and delocalised nuclear motions in the same molecule
In spite of the fact that the electronic structure of HDO is equivalent to H2O, the nuclear dynamics along the O-H and O-D bonds is asymmetric due to the mass difference which introduces an asymmetry in the nuclear Hamiltonian of the stretching motion via the kinetic energy operator K
It is here instructive to look at the spatial shape of the nuclear wave functions, which directly indicates if the vibration is localised on one bond or it is delocalised over the both bonds

Summary

Introduction

Delocalisation of vibrations in the asymmetric isotopomer HDO can be found in the competition between the symmetric shape of the potential energy surface (PES) and the asymmetric kinetic energy operator, which allows for a coexistence of localised and delocalised nuclear motions in the same molecule. Employing a pump IR pulse one can selectively populate a particular localised vibrational level of the ground electronic state, for example the ψ1,0 state localised in the O-D bond, Fig. 1a. A probe X-ray photon promotes the system into a core-excited state, where the nuclear motion may be localised along in the tchaeseseolfetchteedboOu-nDdb1oan1−d12inb21thestcaatese(roigf htht epadnisesloicniaFtiigv.e1b1)a.1−S1u4bas1e1qsuteantet (left panel of Fig. 1b) and delocalised decay back into the ground electronic state will populate vibrations localised either only on the selected O-D bond or on both O-D and O-H bonds, depending on the degree of delocalisation in the core-excited state. The final population of the ground state vibrational modes, which are localised on different bonds, gives direct information about the degree of delocalisation in the core-excited state. One should notice that in the H2O molecule the delocalised character of the ground state vibrational wave functions is preserved in the vibrational functions of the investigated core-excited states (Fig. 1b)

Methods

Results

Conclusion