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Author(s): Ji Feng [1, 4]; Richard G. Hennig [2]; N. W. Ashcroft (corresponding author) [3]; Roald Hoffmann (corresponding author) [1] High pressure is known to influence electronic structure and crystal [...]

Author(s): Kurt A. Johnson; N. W. Ashcroft (corresponding author) The possibility that steadily compressed hydrogen might undergo a transition from a proton-paired insulator to a monatomic metal was first suggested [...]

Though hydrogen and lithium have been assigned a common column of the periodic table, their crystalline states under common conditions are drastically different: the former at temperatures where it is crystalline is a molecular insulator, whereas the latter is a metal that takes on simple structures. On compression, however, the two come to share some structural and other similarities associated with the insulator-to-metal and metal-to-insulator transitions, respectively. To gain a deeper understanding of differences and parallels in the behaviors of compressed hydrogen and lithium, we performed an ab initio comparative study of these systems in selected identical structures. Both elements undergo a continuous pressure-induced s-p electronic transition, though this is at a much earlier stage of development for H. The valence charge density accumulates in interstitial regions in Li but not in H in structures examined over the same range of compression. Moreover, the valence charge density distributions or electron localization functions for the same arrangement of atoms mirror each other as one proceeds from one element to the other. Application of the virial theorem shows that the kinetic and potential energies jump across the first-order phase transitions in H and Li are opposite in sign because of non-local effects in the Li pseudopotential. Finally, the common tendency of compressed H and Li to adopt three-fold coordinated structures as found is explained by the fact that such structures are capable of yielding a profound pseudogap in the electronic densities of states at the Fermi level, thereby reducing the kinetic energy. These results have implications for the phase diagrams of these elements and also for the search for new structures with novel properties. [ABSTRACT FROM AUTHOR]

We discuss the high-pressure phases of crystalline lithium hydroxide, LiOH. Using first-principles calculations, and assisted by evolutionary structure searches, we reproduce the experimentally known phase transition under pressure, but we suggest that the high-pressure phase LiOH-III be assigned to a new hydrogen-bonded tetragonal structure type that is unique amongst alkali hydroxides. LiOH is at the intersection of both ionic and hydrogen bonding, and we examine the various ensuing structural features and their energetic driving mechanisms. At P = 17 GPa, we predict another phase transition to a new phase, Pbcm-LiOH-IV, which we find to be stable over a wide pressure range. Eventually, at extremely high pressures of 1100 GPa, the ground state of LiOH is predicted to become a polymeric structure with an unusual graphitic oxygen-hydrogen net. However, because of its ionic character, the anticipated metallization of LiOH is much delayed; in fact, its electronic band gap increases monotonically into the TPa pressure range. [ABSTRACT FROM AUTHOR]

In order to explain the intricate dance of intramolecular (intra-proton-pair) H-H separations observed in a numerical laboratory of calculationally preferred static hydrogen structures under pressure, we examine two effects through discrete molecular models. The first effect, we call it physical, is of simple confinement. We review a salient model already in the literature, that of LeSar and Herschbach, of a hydrogen molecule in a spheroidal cavity. As a complement, we also study a hydrogen molecule confined along a line between two helium atoms. As the size of the cavity/confining distance decreases (a surrogate for increasing pressure), in both models the equilibrium proton separation decreases and the force constant of the stretching vibration increases. The second effect, which is an orbital or chemical factor, emerges from the electronic structure of the known molecular transition metal complexes of dihydrogen. In these the H-H bond is significantly elongated (and the vibron much decreased in frequency) as a result of depopulation of the σg bonding molecular orbital of H2, and population of the antibonding σu* MO. The general phenomenon, long known in chemistry, is analyzed through a specific molecular model of three hydrogen molecules interacting in a ring, a motif found in some candidate structures for dense hydrogen. [ABSTRACT FROM AUTHOR]

A preliminary discussion of the general problem of localization of wave functions, and the way it is approached in theoretical condensed matter physics (Wannier functions) and theoretical chemistry (localized or fragment orbitals) is followed by an application of the ideas of Paper II in this series to the structures of hydrogen as they evolve under increasing pressure. The idea that emerges is that of simultaneously operative physical (reduction of available space by an increasingly stiff wall of neighboring molecules) and chemical (depopulation of the σg bonding molecular orbital of H2, and population of the antibonding σu* MO) factors. The two effects work in the same direction of reducing the intermolecular separation as the pressure increases, but compete, working in opposite directions, in their effect on the intramolecular (nearest neighbor, intra-pair) distance. We examine the population of σg and σu* MOs in our numerical laboratory, as well as the total electron transfer (small), and polarization (moderate, where allowed by symmetry) of the component H2 molecules. From a molecular model of two interacting H2 molecules we find a linear relationship between the electron transfer from σg to σu* of a hydrogen molecular fragment and the intramolecular H-H separation, and that, in turn, allows us to estimate the expected bond lengths in H2 under pressure if the first effect (that of simple confinement) was absent. In essence, the intramolecular H-H separations under pressure are much shorter than they would be, were there no physical/confinement effect. We then use this knowledge to understand how the separate E and PV terms contribute to hydrogen phase changes with increasing pressure. [ABSTRACT FROM AUTHOR]

In this paper, we examine the transition from a molecular to monatomic solid in hydrogen over a wide pressure range. This is achieved by setting up two models in which a single parameter δ allows the evolution from a molecular structure to a monatomic one of high coordination. Both models are based on a cubic Bravais lattice with eight atoms in the unit cell; one belongs to space group [formula], the other to space group [formula]. In [formula] one moves from effective 1-coordination, a molecule, to a simple cubic 6-coordinated structure but through a very special point (the golden mean is involved) of 7-coordination. In [formula], the evolution is from 1 to 4 and then to 3 to 6-coordinate. If one studies the enthalpy as a function of pressure as these two structures evolve (δ increases), one sees the expected stabilization of minima with increased coordination (moving from 1 to 6 to 7 in the [formula] structure, for instance). Interestingly, at some specific pressures, there are in both structures relatively large regions of phase space where the enthalpy remains roughly the same. Although the structures studied are always higher in enthalpy than the computationally best structures for solid hydrogen - those emerging from the Pickard and Needs or McMahon and Ceperley numerical laboratories - this result is suggestive of the possibility of a microscopically non-crystalline or 'soft' phase of hydrogen at elevated pressures, one in which there is a substantial range of roughly equi-enthalpic geometries available to the system. A scaling argument for potential dynamic stabilization of such a phase is presented. [ABSTRACT FROM AUTHOR]

In the first of a series of four papers on hydrogen under pressure, and its transitions from an initiating molecular state, we begin by defining carefully the problem, and setting the distance scale of interactions of protons and electrons in molecular aggregates of the first of the elements. Following a review of the experimental situation, in particular the phase diagram of hydrogen, in as much as it is known, and the behavior of its vibrons and rotons, we move onto the setting up of a numerical laboratory for probing the underlying physics and chemistry of interactions in hydrogen as the pressure increases. The laboratory consists of the preferred static structures emerging from calculations on the system in the range of 1 atm to 500 GPa, those of Pickard and Needs. The intermolecular (inter-pair) H···H separations naturally decrease with increasing pressure, first rapidly so, then more slowly. The intramolecular (intra-pair) H-H distances vary over a much smaller scale (0.05 Å) as the pressure increases, first decreasing, then increasing, and finally decreasing. We define an equalization function to gauge the approach to equality of the first neighbor and shortest next neighbor H (proton) separations in this numerical laboratory. And we find that metallization is likely to occur before bond equalization. [ABSTRACT FROM AUTHOR]

Under normal conditions, sodium forms a 1:1 stoichiometric compound with indium, and also with thallium, both in the double-diamond structure. But sodium does not combine with aluminum at all. Could NaAl exist? If so, under what conditions and in which structural types? Instead of beginning with a purely computational and first-principles structure search, we are led to apply the early Brillouin and higher (Jones) zone ideas of the physics determining structural selection. We begin with a brief recapitulation of the higher zone concept as applied to the stability of metals and intermetallic compounds. We then discuss the extension of this concept to problems where density becomes a primary variable, within the second-order band structure approximation. An analysis of the range of applicability of pressure-induced Jones zone activation is presented. The simple NaAl compound serves us as a numerical laboratory for the application of this concept. Higher zone arguments and chemical intuition lead quite naturally to the suggestion that 1:1 compound formation between sodium and aluminum should be favored under pressure and specifically in the double-diamond structure. This is confirmed computationally by density functional theoretic methods within the generalized gradient approximation. [ABSTRACT FROM AUTHOR]

An extension of the modified weighted-density approximation (MWDA) is presented which retains the key features of the original MWDA in that it continues to describe the nonuniform system through the use of low-order correlation functions of the uniform counterpart. However, the approximate free energy functional is now exact up to third order in the functional expansion of the free energy, and therefore requires as input both the second- and third-order direct correlation functions of the uniform liquid, as well as its excess free energy per particle. The theory has been applied previously to the problem of isochoric freezing of the classical one-component plasma, and is here applied to the well-known problem of isobaric freezing of hard spheres. We use two different approaches to describe the less well-known third-order direct correlation function of the uniform liquid. The first approach is representative of a class of models for this function that are derived through three functional density differentiations of an approximate free energy model. The second is a factorization ansatz based on liquid-state diagrammatic expansions. The results are quite sensitive to these choices: The first leads to an improvement over the already satisfactory results of the original MWDA for the hard-sphere system, whereas the second does not lead to freezing at all. These differences are traced to the ways in which the approximations treat long-range and short-range potentials. [ABSTRACT FROM AUTHOR]

A known identity relating the functional density derivative of the pair distribution function g(12) of nonuniform liquids to the triplet distribution function g(123) is obtained within the grand canonical ensemble, but then generalized to the case of nonuniform liquid mixtures with either short- or long-range forces. The resulting identities are easily applied to the case of uniform one- or multicomponent liquids, and when applied to the case of a binary Coulomb mixtures, they yield the canonical sum rules relating the n-point to the (n+1)-point distribution functions. Finally, when applied to the one-component plasma (OCP), taken as a particular limiting case, the expected result that the total compressibility of the OCP must vanish in the thermodynamic limit is obtained. [ABSTRACT FROM AUTHOR]

The crystalline phase of a system of classical rigid spheres is treated using an adaptation of the Kikuchi cluster-variation approximation in the variational formulation of Morita. The theory is developed for an arbitrary choice of basic clusters, but the numerical calculations that are presented are carried out for two sets of basic clusters, namely nearest neighbor pairs and a combination of isosceles and equilateral triangles. The integrations required in the evaluation of the clusters are performed using Monte Carlo techniques, which permit the use of moderately large clusters, and in consequence fairly general parametrizations of the density functions. No symmetry conditions need to be imposed beyond those already inherent in an assumed fcc crystal. Numerical results are given for the entropy and density functions, the latter being presented in a parametrized form suitable for use in a variational calculation which takes the hard sphere crystal as a reference system. [ABSTRACT FROM AUTHOR]

A systematic structure search in the La-H and Y-H systems under pressure reveals some hydrogen-rich structures with intriguing electronic properties. For example, LaH10 is found to adopt a sodalite-like face-centered cubic (fcc) structure, stable above 200 GPa and LaH8 a C2/m space group structure. Phonon calculations indicate both are dynamically stable; electron phonon calculations coupled to Bardeen-Cooper-Schrieffer (BCS) arguments indicate they might be high-Tc superconductors. In particular, the superconducting transition temperature Tc calculated for LaH10 is 274-286 K at 210 GPa. Similar calculations for the Y-H system predict stability of the sodalite-like fcc YH10 and a c above room temperature, reaching 305-326 K at 250 GPa. The study suggests that dense hydrides consisting of these and related hydrogen polyhedral networks may represent new classes of potential very hightemperature superconductors. [ABSTRACT FROM AUTHOR]

Atomic and cationic radii have been calculated for the first 96 elements, together with selected anionic radii. The metric adopted is the average distance from the nucleus where the electron density falls to 0.001 electrons per bohr3, following earlier work by Boyd. Our radii are derived using relativistic all-electron density functional theory calculations, close to the basis set limit. They offer a systematic quantitative measure of the sizes of non-interacting atoms, commonly invoked in the rationalization of chemical bonding, structure, and different properties. Remarkably, the atomic radii as defined in this way correlate well with van der Waals radii derived from crystal structures. A rationalization for trends and exceptions in those correlations is provided. [ABSTRACT FROM AUTHOR]

Compressed hydrides of the heavy group-15 elements Bi and Sb are investigated using ab initio methods. Whde the hydrides of Bi and Sb are known to be quite unstable at one atmosphere, our calculations predict that they can be stabilized at high pressures. Thus, at the composition of XH3 (X = Bi or Sb), possible Bi hydrides are BiH2(Pnma) + H beyond 105 GPa and BiH3(I41/amd) beyond 250 GPa; for Sb hydrides, SbH2 + H hardly appears, and SbH3(Pnma) is stabilized beyond 150 GPa. All of these hydrides are metallic with very dispersive electronic structures, this being in accordance with the predictions of the Goldhammer-Herzfeld criterion. Superconducting transition temperatures have also been estimated from the extended McMillan equation, and they turn out to be 39 K for BiH2 at 125 GPa, 65 K for BiH3 at 270 GPa, and 68 K for SbH3 at 170 GPa. [ABSTRACT FROM AUTHOR]

The isotopes of hydrogen provide a unique exploratory laboratory for examining the role of zero point energy (ZPE) in determining the structural and dynamic features of the crystalline ices of water. There are two critical regions of high pressure: (i) near 1 TPa and (ii) near the predicted onset of metallization at around 5 TPa. At the lower pressure of the two, we see the expected small isotopic effects on phase transitions. Near metallization, however, the effects are much greater, leading to a situation where tritiated ice could skip almost entirely a phase available to the other isotopomers. For the higher pressure ices, we investigate in some detail the enthalpics of a dynamic proton sublattice, with the corresponding structures being quite ionic. The resistance toward diffusion of single protons in the ground state structures of high-pressure H2O is found to be large, in fact to the point that the ZPE reservoir cannot overcome these. However, the barriers toward a three-dimensional coherent or concerted motion of protons can be much lower, and the ensuing consequences are explored. [ABSTRACT FROM AUTHOR]