Experimental, theoretical and computational investigation of the inelastic neutron scattering spectrum of a homonuclear diatomic molecule in a nearly spherical trap: H2@C60.

Salvatore Mamone,Mark R Johnson,Mónica Jiménez-Ruiz,Anthony J Horsewill,Stéphane Rols

doi:10.1039/c6cp06059e

Abstract

In this paper we report a methodology for calculating the inelastic neutron scattering spectrum of homonuclear diatomic molecules confined within nano-cavities of spherical symmetry. The method is based on the expansion of the confining potential into multipoles of the coupled rotational and translational angular variables. The Hamiltonian and the INS transition probabilities are evaluated analytically. The method affords a fast and computationally inexpensive way to simulate the inelastic neutron scattering spectrum of molecular hydrogen confined in fullerene cages. The potential energy surface is effectively parametrized in terms of few physical parameters comprising an harmonic term, anharmonic corrections and translation-rotation couplings. The parameters are refined by matching the simulations against the experiments and the excitation modes are identified for transfer energies up to 215 meV.

Highlights

The topic of confined particles lies at the foundations of quantum mechanics and textbook examples of a particle confined in a well or moving in a harmonic trap provides the starting point for a deeper understanding of many quantum systems
In the range 30–60 meV the resolution function is typically two times better than the previously published IN4 spectrum,24 enabling TR fine structure to be resolved for the first time in the high energy modes
The basis was defined by nmax = 11 and jmax = 7, giving rise to 10 192 para states and 13 104 ortho states, of which only 800 distinct reduced para states and 972 reduced ortho states were necessary for the evaluation of the Hamiltonian and of the inelastic neutron scattering (INS) transition probability

Summary

Introduction

The topic of confined particles lies at the foundations of quantum mechanics and textbook examples of a particle confined in a well or moving in a harmonic trap provides the starting point for a deeper understanding of many quantum systems. With the advent of ‘‘molecular surgery’’ techniques in organic synthesis, pioneered in the laboratories of Komatsu, Murata and more recently Whitby, molecular complexes have become available in which a variety of quantum rotors may be fully enclosed and confined inside a fullerene cage. These are the small molecule endofullerenes, of which H2@C60 is the primary example, representing a model system of its kind.. With its unique ability to induce transitions between ortho- and para-spinisomers, inelastic neutron scattering (INS) is a prime technique for studying confined hydrogen.

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Discussion

Conclusion