The Raman signal from a hindered hydrogen rotor*

We present a method for calculation of Raman modes of hydrogen and deuterium in the solid phases. We use the mean-field assumption that the quantized excitations are localized on one molecule. This is done by explicit solution of the time-dependent Schroedinger equation in an angle-dependent potential, and direct calculation of the polarization. Our method generates the full Raman signal through Fourier transform of the time response of the system, using a single parameter for the decorrelation time that we obtain from AIMD. We show that in the free rotor limit, the H₂ and D₂ frequencies differ by a factor of 2, which evolves toward √2 as the modes acquire librational character due to stronger interactions. The ratio overshoots √2 if anharmonic terms weaken the harmonic potential. When the applied potential breaks the degeneracy of the free rotor states, new ‘re-orientational’ Raman active modes emerge from the Rayleigh line. The intensity of these modes is entirely suppressed in back scatter for a single crystal with C-axis parallel to the incident beam. We demonstrate good agreement between theory and experiment for phase I of hydrogen and deuterium.