Supplementary Discussion: To evaluate the activity of the edges, we calculated the free energies of H adsorption on TaS 2 and NbS 2 edges. Although the structures of TaS 2 and NbS 2 edges at working condition are unknown, and very likely they keep changing during the reaction as the materials are broken into small pieces, we take the most common structure of the MoS 2 edge at HER condition (as shown in the Supplementary figure 18 below) 1,2 , as a representative model for TaS 2 and NbS 2 edges.Our calculations show that the free energies of H adsorption on this specific type of edges are -0.13 eV/H for TaS 2 and -0.26 eV/H for NbS 2 . Compared with the free energies of H adsorption on the basal plane, 0.17 eV/H for TaS 2 and 0.01 eV/H for NbS 2 , this specific type of edges likely does have some level of activity. However, we point out that these edges are less active than the MoS 2 edge (0.05 eV/H; A closer-to-zero free energy suggests a higher activity, see the main text), which suggests that the better overall performance of NbS 2 and TaS 2 compared to MoS 2 must have significant contributions from other factors. The most likely explanation is basal-plane activity, as our calculations indicate.

It is generally assumed 1,2,3 that solid hydrogen will transform into a metallic alkali-like crystal at sufficiently high pressure. However, some theoretical models 4,5 have also suggested that compressed hydrogen may form an unusual two-component (protons and electrons) metallic fluid at low temperature, or possibly even a zero-temperature liquid ground state. The existence of these new states of matter is conditional on the presence of a maximum in the melting temperature versus pressure curve (the 'melt line'). Previous measurements 6,7,8 of the hydrogen melt line up to pressures of 44 GPa have led to controversial conclusions regarding the existence of this maximum. Here we report ab initio calculations that establish the melt line up to 200 GPa. We predict that subtle changes in the intermolecular interactions lead to a decline of the melt line above 90 GPa. The implication is that as solid molecular hydrogen is compressed, it transforms into a low-temperature quantum fluid before becoming a monatomic crystal. The emerging low-temperature phase diagram of hydrogen and its isotopes bears analogies with the familiar phases of 3 He and 4 He, the only known zero-temperature liquids, but the long-range Coulombic interactions and the large component mass ratio present in hydrogen would ensure dramatically different properties 9,10 .The possible existence of low-temperature liquid phases of compressed hydrogen has been rationalized with arguments based on the nature of effective pair interactions and of the quantum dynamics at high density, resulting in proton-proton correlations insufficient for the stabilization of a crystalline phase 5 . But so far there has been no conclusive evidence establishing whether hydrogen metallizes at low temperature as a solid (the more widely accepted view to date) or as a liquid. Measurements and theoretical predictions of the near-ground state high-pressure phases 3 of hydrogen have proven to be difficult because of the light atomic mass, significant quantum effects and strong electron-ion interactions. In this regard, the finite temperature liquid-solid phase boundary predicted here is especially valuable for understanding the manner in which hydrogen metallizes.The appearance of a maximum melting temperature in hydrogen is in itself a manifestation of an unusual physical phenomenon. The few systems with a negative melt slope involve either open crystalline structures, such as water and graphite, or in the case of closed packed solids, a promotion of valence electrons to higher orbitals upon compression (6s to 5d in cesium 11 , for example). In these cases, the liquid is denser than the solid when they coexist, possibly because of structural or electronic transitions taking place continuously in the liquid, as a function of pressure, but only at discrete pressure intervals in the solid.In contrast, recent experiments 8 have shown that hydrogen phase I -a solid structure with rotationally-free molecules associated with the sites of a hexagonal closed packed (hcp) lattice -persist...

We present a theoretical study of solid carbon dioxide (CO2) up to 50 GPa and 1500 K using firstprinciples calculations. In this pressure-temperature range, interpretations of recent experiments have suggested the existence of CO2 phases which are intermediate between molecular and covalentbonded solids. We reexamine the concept of intermediate phases in the CO2 phase diagram and propose instead molecular structures, which provide an excellent agreement with measurements.

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All elements, except for helium, appear to solidify into crystalline forms at zero temperature, and it is generally assumed that the introduction of lattice defects results in an increase in internal energy. beta-Rhombohedral boron, a thermodynamically stable form of elemental boron at high temperature, is known to have a large amount of partial occupied sites, seemingly in conflict with our common knowledge. By using lattice Monte Carlo techniques combined with ab initio calculations, we find that the beta-phase is stabilized by a macroscopic amount of intrinsic defects that are responsible not only for entropic effects but also for a reduction in internal energy. These defects enable the conversion of two-center to three-center bonds and are accompanied by the presence of localized, nonconductive electronic states in the optical gap. In addition we find that the ab initio Ising model describing the partial occupancy of beta-boron has macroscopic residual entropy, suggesting that boron is a frustrated system analogous to ice and spin ice.