Calculating the Raman signal of solid hydrogen beyond perturbation theory

Abstract

The study of the solid phases of hydrogen has become an area of intense interest in recent decades. The majority of this work has been focused on obtaining a solid metallic phase, famously predicted to exist by Wigner and Huntington in 1935. As a result of the search for metallic hydrogen, a rich phase diagram has gradually been uncovered and hydrogen is now believed to form at least five solid phases. Powerful computational techniques, utilising density functional theory (DFT), have been used to predict several structural candidates for each of these phases. However, owing to experimental constraints imposed by working with hydrogen at high pressure, none of the proposed candidates have been unequivocally verified. The most common experimental technique used to characterise the solid hydrogens is Raman spectroscopy. Analysis of the Raman spectra for a given system can often elucidate its precise structure and the nature of the excited states. Vibrational Raman transitions in solid hydrogen have been well described by DFT based methods, but the rotational spectra are not obtainable in this way. Significant nuclear quantum effects (NQEs) in hydrogen, cause the diatomic molecule to form a quantum rotor. The ground state has a spherically symmetric wavefunction and the angular momentum is quantised.

In this thesis I present a single molecule method for predicting the rotational Raman signal of various systems of quantum rotors. I firstly apply this method to a diatomic molecule in a range of model mean-field potentials, and evaluate the evolution of the associated Raman spectra with field strength. This reveals that dramatic changes occur in the appearance of the Raman spectrum for a diatomic molecule without any associated change in the symmetry of the surrounding potential. I show that the ground state corresponds to a quantum rotor at low field strength and a quantum oscillator at high field strength. However, there are also ‘re-orientational’ modes and many mixed modes which are neither rotons nor librons. The mass-dependence of the various states is different - rotors, oscillators and reorientations have 1/m, 1/√m and weaker mass dependence respectively. This may allow one to identify the character of the mode with isotope spectroscopy. However, it is complicated by mixed modes and transitions between two different eigenstates with different character. I demonstrate that with these simple potentials, all of which are simpler than those expected for any solid phase of hydrogen, interpretation of the Raman spectra is already overwhelming complex. Significant changes in the Raman spectra are seen even in a simple fixed symmetry potential, leading to the conclusion that such changes in isolation are not sufficient evidence for a phase transition in a diatomic solid.

I adapt the method to recreate the experimental Raman signal for phase I in hydrogen and deuterium. I fit a parameterised mean-field consisting of long range electrostatic and short range steric terms to experimental data. The fitted potential reveals a large repulsion out of the A-B plane, consistent with recent neutron scattering data but in opposition to previous theoretical models. By incorporating experimental geometry into the model, I reveal the importance of such effects in predicting Raman spectra for experiments using DACs. This has wider implications for previous Raman spectra prediction with other methods. Moving to phase II, I analyse single molecule excitations for various structure candidates from the literature. This is motivated by the appearance of low frequency peaks in the experimental data at the phase I-II transition. Previous predictions of Raman spectra for phase II structural candidates have focused on delocalised collective excitations, but previous experiments on deuterium and hydrogen mixtures suggest these peaks are not associated with long range order. I use molecular dynamics trajectories with a classical hydrogen forcefield to generate mean-field potentials. I then incorporate nuclear quantum effects to these potentials by rescaling the temperature. I predict that in the case of hydrogen the ground state exhibits preferred orientation but is only weakly bound. A previously unassigned Raman active peak may be explained by a re-orientation transition from the first excited state. The nature of the modes predicted in this regime is inconsistent with the canonical view of Raman transitions as either vibrons, librons or phonons, rather the excitations correspond to either a re-orientation of the molecule or mixed modes between the rotor and librator regime.

Overall, the quantum treatment developed in this thesis reveals the complexity of interpreting Raman spectra for diatomic molecular solids. I demonstrate that the simplified view of rotons and librons is insufficient to describe the solid phases of hydrogen. Furthermore, perturbative approaches fail to predict the existence of low frequency modes in the ordered phases. In some cases these peaks can be assigned to single molecule modes in the heavily hindered rotor regime. Finally I find that details such as the geometry of the experiment and ortho:para ratio of the sample can significantly effect the observed modes in the signal. The method developed here is applicable to any system containing diatomic molecules and could be further adapted to include higher numbers of atoms.