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The evolutionary algorithm USPEX (1416) is a powerful tool for predicting thermodynamically stable compounds of given elements at a given pressure. We performed variable-composition searches in the U-H system at 0, 5, 25, 50, 100, 200, 300, 400, and 500 GPa. The first generation (120 structures) was created using a random symmetric generator, while all subsequent generations contained 20% of random structures, and 80% of structures created using heredity, soft mutation, and transmutation operators. Within USPEX runs, structure relaxations were performed at the generalized gradient approximation level [with the functional from ref. (21)] of density functional theory using the projector-augmented wave method (22) as implemented in the Vienna Ab initio Simulation Package (VASP) code (2325). Plane-wave kinetic energy cutoff was set to 600 eV, and the Brillouin zone was sampled by the Γ-centered k-mesh with a resolution of 2π × 0.05 Å−1.

To establish stability fields of the predicted phases, we recalculated their enthalpies with increased precision at various pressures with a smaller pressure increment (from 1 to 10 GPa), recalculating the thermodynamic convex hull at each pressure. The phases that were located on the convex hull are the ones stable at given pressure. Stable structures of elemental H and U were taken from USPEX calculations and from (26) and (27), respectively.

The superconducting properties were calculated using the QUANTUM ESPRESSO (QE) package (28). The phonon frequencies and EPC coefficients were computed using density-functional perturbation theory (29) using the plane-wave pseudopotential method and Perdew-Burke-Ernzerhof exchange correlation functional (21). Convergence tests showed that 60 rydberg (Ry) is a suitable kinetic energy cutoff for the plane-wave basis set. Electronic band structures of UH7 and UH8 were calculated using both VASP and QE and demonstrated good consistency. Comparison of the phonon densities of states calculated using the finite displacement method [VASP and PHONOPY (30)] and density-functional perturbation theory (QE) showed perfect agreement between these methods.

Critical temperature was calculated from the Eliashberg equation (31), which is based on the Fröhlich Hamiltonian Embedded Image where c+ and b+ relate to creation operators of electrons and phonons, respectively. The matrix element of electron-phonon interaction Embedded Image calculated within the harmonic approximation in QE can be defined as Embedded Image, where uq is the displacement of an atom with mass M in the phonon mode q,j. Within the framework of Gor’kov (32) and Migdal (33) approach, the correction to the electron Green’s function Embedded Image caused by interaction can be calculated by taking into account only the first terms of the expansion of electron-phonon interaction in series of (ωlog/EF). As a result, it will lead to integral Eliashberg equations (31). These equations can be solved using an iterative self-consistent method for the real part of the order parameter Δ(T, ω) (superconducting gap) and the mass renormalization function Z(T, ω) (for more details, see the supplementary materials) (34).

In our calculations of the EPC parameter λ, the first Brillouin zone was sampled using a 2 by 2 by 2 q-points mesh and a denser 24 by 24 by 24 k-points mesh (with Gaussian smearing and σ = 0.03 Ry, which approximates the zero-width limits in the calculation of λ). The superconducting transition temperature Tc was also estimated using the Allen-Dynes–modified McMillan equation (35).Embedded Image(1)where ωlog is the logarithmic average frequency, and μ* is the Coulomb pseudopotential for which we used widely accepted lower and upper bound values of 0.10 and 0.15. The EPC constant λ and ωlog were calculated asEmbedded Image(2)andEmbedded Image(3)

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