Infrared Peak Splitting from Phonon Localization in Solid Hydrogen

We show that the isotope effect leads to a completely different spectroscopic signal in hydrogen-deuterium mixtures, compared to pure elements that have the same crystal structure. This is particularly true for molecular vibrations, which are the main source of information about the structure of high-pressure hydrogen. Mass disorder breaks translational symmetry, meaning that vibrations are localized almost to single molecules, and are not zone-center phonons. In mixtures, each observable infrared (IR) peak corresponds to a collection of many such molecular vibrations, which have a distribution of frequencies depending on local environment. Furthermore discrete groups of environments cause the peaks to split. We illustrate this issue by considering the IR spectrum of the high-pressure phase III structure of hydrogen, recently interpreted as showing novel phases in isotopic mixtures. We calculate the IR spectrum of hydrogen-deuterium mixtures in the $C2/c$ and $Cmca\text{−}12$ structures, showing that isotopic disorder gives rise to mode localization of the high-frequency vibrons. The local coordination of the molecules leads to discrete IR peaks. The spread of frequencies is strongly enhanced with pressure, such that more peaks become resolvable at higher pressures, in agreement with the recent measurements.

Figure 1

Upper panels show the two most intense IR-active vibron modes at 250 GPa in pure hydrogen, assuming (a) $C2/c$ and (b) $Cmca\text{−}12$ structures (24 atoms). The unit cells comprise two layers, shown separately for clarity ($L_1$, orange, and $L_2$, yellow). (c) Displacements corresponding to IR-active vibrons from the $C2/c$ cell (288 atoms) of disordered mixture at 250 GPa: orange, H; cyan, D. Isotopic symmetry breaking means that all modes obtain some IR activity. The highly localized vibron modes shown are representative examples for the spectrum generated by mixtures.

Figure 2

Stacked plot of simulated vibronic infrared signal at different pressures (shown on the $y$ axis) for the two candidate structures $C2/c$ and $Cmca\text{−}12$. Intensities are calculated so spectra at different pressure points are comparable. On the left is pure hydrogen as (a) $Cmca\text{−}12$ and (b) $C2/c$. Normal-mode linewidths narrower than experimental resolution [17] are chosen to emphasize the impossibility of resolving the two $C2/c$ modes below 230 GPa. On the right we show the data for 50:50 hydrogen-deuterium mixtures (c) $Cmca\text{−}12$ and (d) $C2/c$. Comparison in Fig. 4 (and Supplemental Material) shows that $C2/c$ is a better candidate than $Cmca\text{−}12$. At low pressures $C2/c$ has six distinct peaks, two for each molecular type (${\mathrm{H}}_2$, HD, and ${\mathrm{D}}_2$). The two peaks per molecule type here are not connected to the distinct peaks in the pure hydrogen spectra, but rather a signature of local molecular environments. This splitting is an indirect indication of mode localization, which confers some IR activity to all modes [28].

Figure 3

Method used to calculate spectra in mixtures at 250 GPa from 288 atom calculations, explained in detail in Supplemental Material [27]. (a) mixture data binned up in a histogram for comparison with experiment. (b) dot for the intensity of each of 144000 localized modes generated from 1000 random samples of hydrogen-deuterium mixtures. (c) IR spectrum of pure hydrogen $C2/c$.

Figure 4

Comparison of calculated IR in $C2/c$ mixtures (see also Fig. 2) to the recent raw experimental data [1]. We have removed the Gaussian fits made to the data by Dias et al. since this approach is invalid to describe localized modes. Theoretically calculated spectra are systematically some $200{\mathrm{cm}}^{-1}$ softer than experimental spectra, due to a combination of errors including neglect of temperature, zero-point effects in calculated pressure, calibration of the experimental pressure, and choice of exchange-correlation functional [7, 10, 28]. (a) $C2/c$ spectra at 300 GPa from 3000 randomized samples: gray dots are individual modes, and the red line is a histogram. (b) Comparison of the calculations to the digitized experimental data at 307 GPa [1, 31]. (c) Color map showing the calculated pressure dependence of the IR intensity compared to the equivalent experimental data [1].