Quantum Reorientational Excitations in the Raman Spectrum of Hydrogen

Abstract

Low-frequency Raman peaks, below 250 cm-1, are observed in hydrogen between 2-174 GPa and 13-300 K. The origin of these features is attributed to reorientational transitions (DeltaJ = 0; Q0-branch), which shift from the Rayleigh line as anisotropic intermolecular interactions lift the mJ degeneracy. This family of excitations closely follows the behavior of the S0-branches, sharing their dependence on pressure, temperature, and ortho-H2 concentration. Above 65 K, spectra corrected by the Bose-Einstein population factor reveal a broad continuum arising from populated higher J-states and increased ortho-para disorder. Upon entering phase III, where molecular rotation is inhibited, this continuum is quenched, giving way to well-established optical phonons. Below 25 K, equilibrated samples demonstrate a fine structure from isolated and pair excitations from impurity ortho-H2 molecules in a parahydrogen lattice, the latter a sensitive probe to anisotropic intermolecular interactions relevant to the quantum modeling of solid H2.

Figures (6)

• Figure 1: 532 nm excited Raman spectroscopy of H$_2$ during isothermal compressions; (1) left panels (a,b), room temperature from 0.2-27.3 GPa and (2) right panels (c,d) at 66 K from 20-60 GPa. Fluid H$_2$ and solid H$_2$ are plotted with orange and black traces respectively. Top panels (a) and (c) present a raw Raman spectrum at 20 GPa (gray), the BEP corrected spectrum (blue) and the mirrored corrected Stokes spectrum (dashed red). Bottom panels (b) and (d), are waterfall plots of the corrected spectra, with the average temperature and its error bar (one standard deviation (SD)) determined spectroscopically from the BEP correction. Dashed horizontal lines mark the zero-intensity baselines for each spectrum. Dots and crosses denote the maxima of the $Q_0$-branches and the frequency of the $E_{2g}$ phonon peak, respectively. The rotational excitations are highlighted as $S_0(J)$ and $O_0(J)$, for Stokes and anti-Stokes, respectively.
• Figure 2: (a) Raman logarithmic intensity heat map as a function of time measured at 17 K and 29 GPa. (b) Raw Raman measurements, normalized to the unstressed diamond edge, taken upon reaching the base temperature (red trace) and 24 hours later (black trace). (b) Inset shows the normalized integrated intensity over time for the $Q_0^+$, $S_0(0)$ and $S_0(1)$ branches shown in panels (a,b).
• Figure 3: Selected BEP corrected Raman spectra, excited by a 532 nm laser, of the $Q_0$-branch and the $S_0(0)$-branch for a compression (39-59 GPa) followed by decompression (59-4 GPa) of a 2$\%$ ortho-H$_2$ concentration sample. Measurements were performed over the course of several hours while the temperature as temperature increased from 13$\rightarrow$25 K due to the exhaustion of L-He.
• Figure 4: Pressure dependency of low frequency excitations, P$_{1-7}$ (denoted in Fig \ref{['Fig3']}), from parahydrogen containing $2\%$ ortho-H$_2$ at 13-25 K. Black solid and empty circles denote measurements carried out on compression and decompression, respectively. The solid black traces are fits to a linear function for P$_1$ and a global stretched exponential function for P$_{2-7}$ (see End Matter for functional details), with extrapolations to ambient pressure shown as dashed traces. The empty red circles are taken from 9 ortho-H$_2$ pair excitations reported from microwave measurements on hydrogen at 1.2 K and ambient pressure Hardy1975 and the red bar represents the theoretical frequency range of the manifold Harris1977Silvera1980. The empty blue circle is the experimentally determined value of an isolated ortho-H$_2$ molecule in parahydrogen from infrared measurements at ambient pressure and low temperatures Dickson1996. The gray hatched region represents frequencies which are inaccessible due to the width of the notch filters used $\pm8$ cm$^{-1}$.
• Figure 5: Raman spectra, excited by a 660 nm laser, of solid hydrogen measured upon compression between 13-54 GPa at room temperature. (a) Raw Raman spectrum at 20 GPa (gray), the BEP corrected spectrum (blue) and the mirrored corrected Stokes spectrum (dashed red). (b) Waterfall of the raw Raman spectrum upon compression. (c) Waterfall of the BEP corrected spectra from panel (b), with the average temperature and its error bar (one SD) determined spectroscopically from the BEP corrections. Dashed horizontal lines mark the zero-intensity baselines for each spectrum. In panels (b) and (c), dots and crosses denote the maxima of the $Q_0$-branch and the frequency of the $E_{2g}$ phonon peak, respectively.