Structural, mechanical, thermodynamic, and electronic properties of thorium hydrides from first principles Bao-Tian Wang, 1, 2 Ping Zhang, 2, 3,$_{∗}$ Hongzhou Song, 2 Hongliang Shi, 2, 4 Dafang Li, 2 and Wei-Dong Li 1 $^{1}$Institute of Theoretical Physics and Department of Physics, Shanxi University, Taiyuan 030006, People’s Republic of China $^{2}$LCP, Institute of Applied Physics and Computational Mathematics, Beijing 100088, People’s Republic of China $^{3}$Center for Applied Physics and Technology, Peking University, Beijing 100871, People’s Republic of China $^{4}$SKLSM, Institute of Semiconductors, Chinese Academy of Sciences, People’s Republic of China We perform first-principles calculations of the structural, electronic, mechanical, and thermody- namic properties of thorium hydrides (ThH 2 and Th 4 H 15 ) based on the density functional theory with generalized gradient approximation. The equilibrium geometries, the total and partial densities of states, charge density, elastic constants, elastic moduli, Poisson’s ratio, and phonon dispersion curves for these materials are systematically investigated and analyzed in comparison with exper- iments and previous calculations. These results show that our calculated equilibrium structural parameters are well consistent with experiments. The Th − H bonds in all thorium hydrides exhibit weak covalent character, but the ionic properties for ThH 2 and Th 4 H 15 are different due to their different hydrogen concentration. It is found that while in ThH 2 about 1.5 electrons transfer from each Th atom to H, in Th 4 H 15 the charge transfer from each Th atom is around 2.1 electrons. Our calculated phonon spectrum for the stable body-centered tetragonal phase of ThH 2 accords well with experiments. In addition we show that ThH 2 in the fluorite phase is mechanically and dynamically unstable. PACS numbers: 71.27.+a, 71.15.Mb, 71.20.-b, 63.20.dk hydrides. Also, the stability of the metastable phase of ThH$_{2}$ (fluorite structure with space group Fm ¯ 3 m ) is an- alyzed and our calculated results show that the fluorite- type ThH$_{2}$ is mechanically unstable. We perform the Bader analysis 6,7 of thorium hydrides and find that about 1.5 (2.1) electrons transfer from each Th atom to H for ThH$_{2}$ (Th$_{4}$H$_{15}$). Thorium is one kind of important nuclear materials and together with its compounds has been widely investi- gated both experimentally and theoretically. Among tho- rium compounds, thorium hydrides (ThH$_{2}$ and Th$_{4}$H$_{15}$) are metallic solids and have potential use for advanced nuclear fuels. In addition, Th$_{4}$H$_{15}$ has been reported to have superconductivity with transition temperatures T$_{c}$ ∼ 8 K 1 and has been considered as promising candidates for hydrogen storage since its large hydrogen-to-metal ratio $^{2}$. ThH$_{2}$ is not superconducting above 1 K $^{3}$. Despite the abundant research on thorium hydrides, relatively little is known regarding their chemical bond- ing, mechanical properties, and phonon dispersion. Only the optical phonon density of states of ThH$_{2}$ and Th$_{4}$H$_{15}$ was measured through inelastic neutron scattering 4 and the bulk modulus of ThH$_{2}$ was calculated by linear muffin-tin orbital (LMTO) method $^{5}$. Until now the elas- tic properties, which relate to various fundamental solid- state properties such as interatomic potentials, equation of state, phonon spectra, and thermodynamical proper- ties, are unknown for ThH$_{2}$ and Th$_{4}$H$_{15}$. In addition, although the electronic properties as well as the chemi- cal bonding in thorium hydrides have been calculated re- cently by Shein et al. 2 through the full-potential LAPW (FLAPW) method, the study of the bonding nature of Th − H bond involving its mixed ionic/covalent charac- ter is still lacking. These facts, as a consequence, in- hibit deep understanding of thorium hydrides. Motivated by these observations, in this paper, we present a first- principles study by calculating the structural, electronic, mechanical, and thermodynamic properties of thorium In present work, the theoretical equilibrium volume, Our total energy calculations are carried out by em- ploying the plane-wave basis pseudopotential method as implemented in Vienna ab initio simulation package (VASP) $^{8}$. The exchange and correlation effects are de- scribed by the density functional theory (DFT) within generalized gradient approximation (GGA) $^{9}$. The pro- jected augmented wave (PAW) method of Bl¨ ochl 10 is implemented in VASP with the frozen-core approxima- tion. The thorium 6s $^{2}$7s$^{2}$6p$^{6}$6d$^{1}$5f1 and the hydrogen 1s 1 electrons are treated as valence electrons. Note that although the 5 f states are empty in elemental Th, this level turns to evolve into a hybridization with the hydro- gen orbitals both in the valence band and the conduc- tion band, as well as to prominently contribute to the conduction band (see Fig. 3 below). 9 × 9 × 9 and 5 × 5 × 5 Monkhorst-Pack 11 k point-meshes in the full wedge of the Brillouin zone are used for ThH$_{2}$ and Th$_{4}$H$_{15}$, re- spectively. Electron wave function is expanded in plane waves up to a cutoff energy of 450 eV, and all atoms are fully relaxed until the Hellmann-Feynman forces become less than 0.02 eV/ ˚ A. arXiv:1001.1481v1 [cond-mat.mtrl-sci] 10 Jan 2010 II. COMPUTATIONAL METHODS I. INTRODUCTION