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Based on evolutionary crystal structure searches in combination with abinitio calculations, we predict an unusual structural phase of thesuperconducting LaH$_{10}$ that is stable from about 250 GPa to 425 GPapressure. This new phase belongs to a trigonal $R\bar{3}m$ crystal lattice withan atypical cell angle, $\alpha_{rhom}$ $\sim$ 24.56$^{\circ}$. We find thatthe new structure contains three units of LaH$_{10}$ in its primitive cell,unlike the previously known trigonal phase, where primitive cell contains onlyone LaH$_{10}$ unit. In this phase, a 32-H atoms cage encapsulates La atoms,analogous to the lower pressure face centred cubic phase. However, the hydrogencages of the trigonal phase consist of quadrilaterals and hexagons, in contrastto the cubic phase, that exhibits squares and regular hexagons. Surprisingly,the shortest H-H distance in the new phase is shorter than that of the lowerpressure cubic phase and of atomic hydrogen metal. We find a structural phasetransition from trigonal to hexagonal at 425 GPa, where the hexagonal crystallattice coincides with earlier predictions. Solving the anisotropicMigdal-Eliashberg equations we obtain that the predicted trigonal phase (forstandard values of the Coulomb pseudopotential) is expected to becomesuperconducting at a critical temperature of about 175 K, which is less than$T_c \sim$250 K measured for cubic LaH$_{10}$.

Prediction of an unusual trigonal phase of superconducting LaH$_{\bf 10}$ stable from 250 to 425 GPa pressure