New stable thorium decahydride 3 ̅ -ThH10, a record high-temperature superconductor with TC up to 241 K (-32 о С), critical field HC up to 71 T and superconducting gap Δ0 = 52 meV at 80-100 GPa was predicted by evolutionary algorithm USPEX. Another phase 2 1 / -ThH7 was found to be a high-temperature superconductor with TC ~ 65 K. Analysis of superconducting state was performed within Eliashberg formalism and the dependencies of HC(T), Δ(T), TC(P) together with jump in the specific heat at critical temperature were calculated. Several other new thorium hydrides were predicted to be stable under pressure including ThH3, Th3H10, ThH4, ThH6. Thorium (which has s 2 d 2 electronic configuration) forms high-TC polyhydrides similar to those formed by s 2 d 1 metals (Y-La-Ac). Thoriumis the next member in Mg-Ca-Sc-Y-La-Ac family of elements forming high-TC superconducting hydrides.

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We study the stability of the hydrogen molecule interacting with the environment according to the balanced gain and loss energy scheme. We determined the properties of the molecule taking into account all electronic interactions, where the parameters of the Hamiltonian have been computed by using the variational method. The interaction of the hydrogen molecule with the environment was modeled parametrically (γ) with the help of the non-hermitian operator. We have shown that the hydrogen molecule is dynamically unstable. The dissociation time (TD) decreases, if the γ parameter increases (for γ → 0, we get TD → +∞). At the dynamic instability of the hydrogen molecule overlaps its static instability as the coupling constant γ increases. We observed the decrease in the dissociation energy and the existence of the metastable state of the molecule (γMS = 0.659374 Ry). The hydrogen molecule is statically unstable for γ > γD = 1.024638 Ry. One can also observed the PT symmetry breaking effect for the electronic Hamiltonian (γPT = 0.520873 Ry). However, it does not affect the properties of the hydrogen molecule, such as: the electronic Hamiltonian parameters, the phonon and rotational energy, and the values of the electron-phonon coupling constants.

The H5S2 and H2S compounds are the two candidates for the low-temperature phase of compressed sulfur-hydrogen system. We have shown that the value of Coulomb pseudopotential (μ*) for H5S2 ([TC]exp = 36 K and p = 112 GPa) is anomalously high. The numerical results give the limitation from below to μ* that is equal to 0.402 (μ* = 0.589), if we consider the first order vertex corrections to the electron-phonon interaction). Presented data mean that the properties of superconducting phase in the H5S2 compound can be understood within the classical framework of Eliashberg formalism only at the phenomenological level (μ* is the parameter of matching the theory to the experimental data). On the other hand, in the case of H2S it is not necessary to take high value of Coulomb pseudopotential to reproduce the experimental critical temperature relatively well (μ* = 0.15). In our opinion, H2S is mainly responsible for the observed superconductivity state in the sulfur-hydrogen system at low temperature.

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