We use first principles calculations to study structural, vibrational and superconducting properties of H2S at pressures P ≥ 200 GPa. The inclusion of zero point energy leads to two different possible dissociations of H2S, namely 3H2S → 2H3S + S and 5H2S → 3H3S + HS2, where both H3S and HS2 are metallic. For H3S, we perform non-perturbative calculations of anharmonic effects within the self-consistent harmonic approximation and show that the harmonic approximation strongly overestimates the electron-phonon interaction (λ ≈ 2.64 at 200 GPa) and Tc. Anharmonicity hardens H-S bond-stretching modes and softens H-S bond-bending modes. As a result, the electronphonon coupling is suppressed by 30% (λ ≈ 1.84 at 200 GPa). Moreover, while at the harmonic level Tc decreases with increasing pressure, the inclusion of anharmonicity leads to a Tc that is almost independent of pressure. High pressure hydrogen sulfide is a strongly anharmonic superconductor.Cuprates [1] have for many years held the world record for the highest superconducting critical temperature (T c = 133 K) [2]. However, despite almost 30 years of intensive research, the physical mechanism responsible for such a high T c is still elusive, although the general consensus is that it is highly non-conventional. The discovery by Drozdov et al.[3] of T c = 190 K in a diamond anvil cell loaded with hydrogen sulfide (H 2 S) and compressed to about 200 GPa breaks the cuprates record and overturns the conventional wisdom that such a high T c cannot be obtained via phonon-mediated pairing.The claim that hydrogen at high pressure could be superconducting is not new [4] and it was recently supported by first principles calculations based on the harmonic approximation applied to dense hydrogen [5][6][7][8] and several hydrides [9][10][11][12][13][14][15]. More recently, two theoretical papers predicted the occurrence of high T c superconductivity in high-pressure sulfur-hydrides [16,17]. However, as shown in Refs. [18,19], anharmonicity can be crucial in these systems. For example, in PdH, the electron-phonon coupling λ parameter is found to be 1.55 at the harmonic level, while a proper inclusion of anharmonic effects leads to λ = 0.40 [18], in better agreement with experiments. Thus, in hydrogen-based compounds, the phonon spectra are strongly affected by anharmonic effects.Several first principles calculations [16,17,20,26] suggested that decomposition of the H 2 S sample occurs within the diamond-anvil cell at high pressures. The high-T c superconducting material is therefore very unlikely to be H 2 S, while H 3 S is the obvious candidate for the H-rich decomposition product.Here we study the structural, vibrational and superconducting properties of H 2 S above 200 GPa, where the highest T c occurs. We show that the inclusion of zero point motion in the convex hull at 200 and 250 GPa stabilizes two metallic structures, H 3 S and HS 2 . Finally, we show that, contrary to suggestions in previous work [16,20], the harmonic approximation does not explain the measured T c ...

Harmonic calculations based on density-functional theory are generally the method of choice for the description of phonon spectra of metals and insulators. The inclusion of anharmonic effects is, however, delicate as it relies on perturbation theory requiring a considerable amount of computer time, fast increasing with the cell size. Furthermore, perturbation theory breaks down when the harmonic solution is dynamically unstable or the anharmonic correction of the phonon energies is larger than the harmonic frequencies themselves. We present here a stochastic implementation of the self-consistent harmonic approximation valid to treat anharmonicity at any temperature in the non-perturbative regime. The method is based on the minimization of the free energy with respect to a trial density matrix described by an arbitrary harmonic Hamiltonian. The minimization is performed with respect to all the free parameters in the trial harmonic Hamiltonian, namely, equilibrium positions, phonon frequencies and polarization vectors. The gradient of the free energy is calculated following a stochastic procedure. The method can be used to calculate thermodynamic properties, dynamical properties and even anharmonic corrections to the Eliashberg function of the electron-phonon coupling. The scaling with the system size is greatly improved with respect to perturbation theory. The validity of the method is demonstrated in the strongly anharmonic palladium and platinum hydrides. In both cases we predict a strong anharmonic correction to the harmonic phonon spectra, far beyond the perturbative limit. In palladium hydrides we calculate thermodynamic properties beyond the quasiharmonic approximation, while in PtH we demonstrate that the high superconducting critical temperatures at 100 GPa predicted in previous calculations based on the harmonic approximation are strongly suppressed when anharmonic effects are included.