Giant splitting of the hydrogen rotational eigenenergies in the C$_2$ filled ice

TL;DR

This study combines theoretical calculations and experimental measurements to reveal a giant splitting of hydrogen rotational energy levels in the C$_2$ phase of hydrogen hydrate, highlighting strong hydrogen-water interactions.

Contribution

It provides the first direct quantum mechanical calculation and experimental validation of large rotational energy splitting in hydrogen hydrate C$_2$ phase.

Findings

Giant energy splitting of ±3.2 meV for hydrogen rotational states.

Excellent agreement between theory and inelastic neutron scattering measurements.

Hydrogen-water interactions significantly influence hydrogen rotational dynamics.

Abstract

Hydrogen hydrates present a rich phase diagram influenced by both pressure and temperature, with the so-called C$_2$ phase emerging prominently above 2.5 GPa. In this phase, hydrogen molecules are densely packed within a cubic ice-like lattice and the interaction with the surrounding water molecules profoundly affects their quantum rotational dynamics. Herein, we delve into this intricate interplay by directly solving the Schr\"{o}dinger's equation for a quantum H$_2$ rotor in the C$_2$ crystal field at finite temperature, generated through Density Functional Theory. Our calculations reveal a giant energy splitting relative to the magnetic quantum number of $\pm$3.2 meV for $l=1$. Employing inelastic neutron scattering, we experimentally measure the energy levels of H$_2$ within the C$_2$ phase at 6.0 and 3.4 GPa and low temperatures, finding remarkable agreement with our theoretical predictions. These findings underscore the pivotal role of hydrogen--water interactions in dictating the rotational behavior of the hydrogen molecules within the C$_2$ phase and indicate heightened induced-dipole interactions compared to other hydrogen hydrates.