Inelastic neutron scattering spectra of a hydrogen molecule in a nanocavity: Methodology for quantum calculations incorporating the coupled five-dimensional translation-rotation eigenstates

Abstract

We present an in-depth description of the methodology for accurate quantum calculation of the inelastic neutron scattering (INS) spectra of an H${}_{2}$ molecule confined inside a nanosize cavity of an arbitrary shape. This methodology was introduced in a recent work [M. Xu, L. Ulivi, M. Celli, D. Colognesi, and Z. Ba\ifmmode \check{c}\else \v{c}\fi{}i\ifmmode \acute{c}\else \'{c}\fi{}, Phys. Rev. B 83, 241403(R) (2011)], where the INS spectra of para- and ortho-H${}_{2}$ in the small cage of the structure II clathrate hydrate were simulated and compared with the measured spectra. The key distinctive feature of our approach, and its main strength and advantage, is the use of the coupled quantum 5D translation-rotation (TR) energy levels and wave functions of the entrapped H${}_{2}$ molecule, rigorously calculated on the 5D intermolecular potential energy surface (PES), as the initial and the final states of the INS transitions. In this work, we describe the implementation of the 5D TR wave functions within the quantum INS formalism, and obtain the working expressions for the matrix elements required to compute the INS spectra of the nanoconfined H${}_{2}$ molecule. The computational approach devised for efficient calculation of the 5D TR eigenstates in the compact contracted basis, indispensable for our quantum simulation of the INS spectra, is presented as well. Since the TR coupling is fully taken into account, the computed INS spectra exhibit a uniquely high degree of realism and faithfully reflect the quantum dynamics of H${}_{2}$ on the PES of the host environment.