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We study the structural and vibrational properties of the high-temperaturesuperconducting sulfur trihydride and trideuteride in the high-pressure$Im\bar{3}m$ and $R3m$ phases by first-principles density-functional-theorycalculations. On lowering pressure, the rhombohedral transition $Im\bar{3}m\rightarrow R3m$ is expected, with hydrogen bond desymmetrization andoccurrence of trigonal lattice distortion. In hydrostatic conditions we findthat, contrary to what suggested in some recent experiments, if therhombohedral distortion exists it affects mainly the hydrogen-bonds, whereasthe resulting cell distortion is minimal. We estimate that the occurrence of astress anisotropy of approximately $10\%$ could explain this discrepancy.Assuming hydrostatic conditions, we calculate the critical pressure at whichthe rhombohedral transition occurs. Quantum and anharmonic effects, which arerelevant in this system, are included at nonperturbative level with thestochastic self-consistent harmonic approximation (SSCHA). Within thisapproach, we determine the transition pressure by calculating the free energyHessian. We find that quantum anharmonic effects are responsible for a strongreduction of the critical pressure with respect to the one obtained with theclassical harmonic approach. Moreover, we observe a prominent isotope effect,as we estimate higher pressure transition for D${}_3$S than for H${}_3$S.Finally, within SSCHA we calculate the anharmonic phonon spectral functions inthe $Im\bar{3}m$ phase. The strong anharmonicity of the system is confirmed bythe occurrence of very large anharmonic broadenings leading to complexnon-Lorentzian line shapes. However, for the vibrational spectra at zonecenter, accessible e.g. by infrared spectroscopy, the broadenings are verysmall (linewidth at most around 2~meV) and anharmonic phonon quasiparticles arewell defined.

physical review. b./physical review. b

High-pressure phase diagram of hydrogen and deuterium sulfides from  first principles: structural and vibrational properties including quantum and  anharmonic effects