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We devise a framework to compute accurate phonons in molecular crystals evenin case of strong quantum anharmonicity. Our approach is based on thecalculation of the static limit of the phononic Matsubara Green's function frompath integral molecular dynamics simulations. Our method enjoys a remarkablylow variance, which allows one to compute accurate phonon frequencies after afew picoseconds of nuclear dynamics, and it is further stabilized by the use ofappropriate constrained displacement operators. We applied it to solid hydrogenat high pressure. For phase III, our predicted infrared (IR) and Raman activevibrons agree very well with experiments. We then characterize the crystallinesymmetry of phase IV by direct comparison with vibrational data and wedetermine the character of its Raman and IR vibron peaks.

Hydrogen phase-IV characterization by full account of quantum anharmonicity