Solid LiH Research Articles

Electron Correlation in the Condensed Phase from a Resolution of Identity Approach Based on the Gaussian and Plane Waves Scheme.

The second-order Møller-Plesset perturbation energy (MP2) and the Random Phase Approximation (RPA) correlation energy are increasingly popular post-Kohn-Sham correlation methods. Here, a novel algorithm based on a hybrid Gaussian and Plane Waves (GPW) approach with the resolution-of-identity (RI) approximation is developed for MP2, scaled opposite-spin MP2 (SOS-MP2), and direct-RPA (dRPA) correlation energies of finite and extended system. The key feature of the method is that the three center electron repulsion integrals (μν|P) necessary for the RI approximation are computed by direct integration between the products of Gaussian basis functions μν and the electrostatic potential arising from the RI fitting densities P. The electrostatic potential is obtained in a plane waves basis set after solving the Poisson equation in Fourier space. This scheme is highly efficient for condensed phase systems and offers a particularly easy way for parallel implementation. The RI approximation allows to speed up the MP2 energy calculations by a factor 10 to 15 compared to the canonical implementation but still requires O(N(5)) operations. On the other hand, the combination of RI with a Laplace approach in SOS-MP2 and an imaginary frequency integration in dRPA reduces the computational effort to O(N(4)) in both cases. In addition to that, our implementations have low memory requirements and display excellent parallel scalability up to tens of thousands of processes. Furthermore, exploiting graphics processing units (GPU), a further speedup by a factor ∼2 is observed compared to the standard only CPU implementations. In this way, RI-MP2, RI-SOS-MP2, and RI-dRPA calculations for condensed phase systems containing hundreds of atoms and thousands of basis functions can be performed within minutes employing a few hundred hybrid nodes. In order to validate the presented methods, various molecular crystals have been employed as benchmark systems to assess the performance, while solid LiH has been used to study the convergence with respect to the basis set and system size in the case of RI-MP2 and RI-dRPA.

Second-Order Møller-Plesset Perturbation Theory in the Condensed Phase: An Efficient and Massively Parallel Gaussian and Plane Waves Approach.

A novel algorithm, based on a hybrid Gaussian and plane waves (GPW) approach, is developed for the canonical second-order Møller-Plesset perturbation energy (MP2) of finite and extended systems. The key aspect of the method is that the electron repulsion integrals (ia|λσ) are computed by direct integration between the products of Gaussian basis functions λσ and the electrostatic potential arising from a given occupied-virtual pair density ia. The electrostatic potential is obtained in a plane waves basis set after solving the Poisson equation in Fourier space. In particular, for condensed phase systems, this scheme is highly efficient. Furthermore, our implementation has low memory requirements and displays excellent parallel scalability up to 100 000 processes. In this way, canonical MP2 calculations for condensed phase systems containing hundreds of atoms or more than 5000 basis functions can be performed within minutes, while systems up to 1000 atoms and 10 000 basis functions remain feasible. Solid LiH has been employed as a benchmark to study basis set and system size convergence. Lattice constants and cohesive energies of various molecular crystals have been studied with MP2 and double-hybrid functionals.

Approaching the theoretical limit in periodic local MP2 calculations with atomic-orbital basis sets: The case of LiH

The atomic orbital basis set limit is approached in periodic correlated calculations for solid LiH. The valence correlation energy is evaluated at the level of the local periodic second order Møller-Plesset perturbation theory (MP2), using basis sets of progressively increasing size, and also employing "bond"-centered basis functions in addition to the standard atom-centered ones. Extended basis sets, which contain linear dependencies, are processed only at the MP2 stage via a dual basis set scheme. The local approximation (domain) error has been consistently eliminated by expanding the orbital excitation domains. As a final result, it is demonstrated that the complete basis set limit can be reached for both HF and local MP2 periodic calculations, and a general scheme is outlined for the definition of high-quality atomic-orbital basis sets for solids.

Ab initionuclear momentum distributions in lithium hydride: Assessing nonadiabatic effects

Theoretical nuclear momentum distributions for solid lithium hydride and lithium deuteride are presented. Electronic-structure calculations were performed within the framework of plane-wave density functional theory, followed by the computation of phonon-dispersion relations and vibrational densities of states. The generalized-gradient-approximation functional of Perdew, Burke, and Ernzerhof was used in these first-principles calculations. Our computational results are compared with existing neutron Compton scattering and inelastic neutron scattering experiments on solid LiH. We find an excellent agreement between theory and experiment within the harmonic Born-Oppenheimer approximation. On the basis of the above, we estimate an upper conservative bound of $~$2 to 3% for the effects of nonadiabatic dynamics on the second moment and Laplacian of the atomic momentum distributions in this benchmark system. We close by discussing the implications of this study on future theoretical studies of atomic momentum distributions from isolated molecules and extended condensed-matter systems.

Comment on “Accurate Hartree-Fock energy of extended systems using large Gaussian basis sets”

In a recent paper on Hartree-Fock (HF) calculations on solid LiH with large Gaussian-type basis sets, Paier et al. [Phys. Rev. B 80, 174114 (2009)] report a comment that we dispute: that similar calculations appear unlikely to be feasible using the CRYSTAL code. Here we show that using a full HF approach within periodic boundary conditions as implemented in the CRYSTAL code the same total energy is obtained as from the schemes adopted by Paier et al.

Accurate Hartree-Fock energy of extended systems using large Gaussian basis sets

Calculating highly accurate thermochemical properties of condensed matter via wave function-based approaches (such as e.g. Hartree-Fock or hybrid functionals) has recently attracted much interest. We here present two strategies providing accurate Hartree-Fock energies for solid LiH in a large Gaussian basis set and applying periodic boundary conditions. The total energies were obtained using two different approaches, namely a supercell evaluation of Hartree-Fock exchange using a truncated Coulomb operator and an extrapolation toward the full-range Hartree-Fock limit of a Pad\'e fit to a series of short-range screened Hartree-Fock calculations. These two techniques agreed to significant precision. We also present the Hartree-Fock cohesive energy of LiH (converged to within sub-meV) at the experimental equilibrium volume as well as the Hartree-Fock equilibrium lattice constant and bulk modulus.

Isotopic Effects in Solid LiH and LiD at Very Low Temperature

The ground state of the ionic solids LiD and LiH is theoretically studied using the Variational Monte Carlo (VMC) method. Our main focus has been the calculation of relevant properties of the H− and D− ions using a fully quantum approach. In particular, we report results on their kinetic energies, mean-squared displacements, Einstein frequencies, radial distribution functions, and density profiles around the sites. The microscopic results obtained for both isotopes show corrections beyond trivial isotopic effects due to their quantum behavior. Finally, the VMC results are compared with predictions from self consistent average phonon (SCAP) theory at T = 0 K.

A new path to ultracold hydrogen

Ultracold hydrogen offers unique possibilities for precision spectroscopy, studies of atomic interactions, and the creation of quantum fluids containing mixtures of hydrogen and deuterium. Current techniques for trapping and cooling hydrogen have produced large condensates with N ∼ 109 atoms, but suffer from a variety of experimental limitations. Among these are the slow evaporative cooling rate due to the small H–H elastic-scattering cross section, the need for a superfluid helium film in the initial thermalization process, a geometry that severely limits detection efficiency, and the inability to trap deuterium. We are constructing a new apparatus based on buffer-gas cooling that will overcome these problems. To accelerate evaporative cooling, the thermalization rate is increased by simultaneously loading lithium and hydrogen into a 4.2 T anti-Helmholtz trap. Lithium accelerates evaporative cooling because the Li–H elastic-scattering cross section is ∼1200 times larger than that of H–H. Hydrogen and lithium will be produced by laser ablation of solid LiH in a 3He buffer gas held at temperatures of ∼350 mK. Because no wall collisions are needed for initial thermalization, ablating a solid sample of LiD should enable studies of deuterium. The apparatus is in the final stages of construction. We report on results of initial tests and discuss the new scientific opportunities made possible by this approach.PACS No.: 32.80.Pj

Quantum hydrogen vibrational dynamics in LiH: Neutron-scattering measurements and variational Monte Carlo simulations

Hydrogen single-particle dynamics in solid LiH at $T=20\mathrm{K}$ has been studied through the incoherent inelastic neutron-scattering technique. A careful analysis of the scattering data has allowed for the determination of a reliable hydrogen-projected density of phonon states and, from this, of three relevant physical quantities: mean-squared displacement, mean kinetic energy, and Einstein frequency. In order to interpret these experimental findings, a fully quantum microscopic calculation has been carried out using the variational Monte Carlo method. The agreement achieved between neutron-scattering data and Monte Carlo estimates is good. In addition, a purely harmonic calculation has been also performed via the same Monte Carlo code, but anharmonic effects in H dynamics were not found relevant. The possible limitations of the present semiempirical potentials are finally discussed.

VUV spectroscopy of solids at low temperature using synchrotron radiation

The normal-incidence monochromator beamline at the 550 MeV electron storage ring MAX in Lund has been utilized for VUV spectroscopy of solids at low temperatures. The experimental setup is described in some detail. The first results include reflectivity and luminescence excitation spectra for the high Tc superconductor Y-Ba-Cu-O and for solid LiH. The results agree with and extend previous optical data for these systems.

First-principles calculation of the shock-wave equation of state of isotopic lithium hydrides

The equations of state (EOS) of solid LiH in the B1 (NaCl-type) and B2 (CsCl-type) structures have been calculated within the local-density approximation (LDA), using the augmented-plane-wave method with Ceperley-Alder's form for the exchange-correlation energy. Using the EOS obtained by the LDA, the volume dependencies of the Debye temperatures for both phases have been determined. The calculated Debye temperatures in the B1 phase at zero pressure and zero temperature are 1246 K for $^{7}\mathrm{LiH}$ and 972 K for $^{7}\mathrm{LiD}$ in agreement with the experimental values in the T=0 K limit at normal pressure which are 1190\ifmmode\pm\else\textpm\fi{}80 K for $^{7}\mathrm{LiH}$ and 1030\ifmmode\pm\else\textpm\fi{}50 K for $^{7}\mathrm{LiD}$, respectively. The calculated lattice constants for isotopic LiH at zero pressure are in agreement with the experimental values at T=83 K by 1.9%. With these results the shock-wave equations of state (the Hugoniot) for both phases have been calculated. The Hugoniots for the B1 phase are in agreement with the experiment by Marsh.

Pressure induced insulator-metal transition of solid LiH

The equation of state and the electronic band structure of solid LiH have been calculated using the local-density functional theory with Ceperley and Alder's exchange-correlation potential in the muffin-tin approximation. The band gap is the direct gap with the X 1 minus; X′ 4 symmetries up to the band closing at V M =3.35 cm 3 mole −1. At further compression, the band crossing occurs between the state with the Z 1 symmetry and that of the Z 3 symmetry. The transition pressure of metallization is estimated to be P M =226 GPa. Using the Debye model, the zero-point pressure is also calculated with the Debye temperature theoretically determined. The Debye temperature of 7LiH at normal density is 1115 K in agreement with the experimental value 1190 ± 80 K.

Electric and electrochemical properties of solid LiH 2PO 4

Electrical and electrochemical properties of solid LiH 2PO 4 conductor were investigated in the temperature range from room temperature to 373 K. It was found that high conductivity throughout the temperature range, with activation energy 17.23 kJ/mol, originates from the movement of hydrogen ions (protons). The movement of protons in the correlation with phosphate groups rotation was considered. The slopes of Tafel lines and exchange current densities both for cathodic hydrogen and anodic oxygen evolution were determined (by means of usual electrochemical kinetic methods) at various temperatures. The energy of activation at the equilibrium potentials both for the cathodic and the anodic processes have been assessed to be 17.23 kJ/mol (0.18 eV) and 2.9 kJ/mol (0.03 eV), respectively.

An NMR investigation of anion and cation diffusion in solid lithium hydride

AbstractNuclear spin‐lattice relaxation rates and nmr absorption linewidths of 1H and 7Li in solid LiH have been measured up to 620 C. For both species motional narrowing is observed which is shifted under the influence of MgH2 additions in opposite directions. Above 300°C spin‐lattice relaxation is exclusively determined by dipole interactions originating from translational diffusion. The calculated peak relaxation rates are in excellent agreement with the observed ones. ‐ For LiH containing Li2O or small additions of MgH2, the mean jump frequency of hydrogen by far exceeds that of lithium in the whole temperature range. Between 400 and 620°C for LiH in equilibrium with Li2O the mean jump frequencies are given bymagnified imageFor the “pure” material investigated (with an estimated oxygen content of 300 ppm) the activation energy for v(H) is (0.97 ± 0.07) eV. The numerical values of v(H) and v(Li) are not very sensitive to variations in oxygen content. With large additions of MgH2 (> 1000 ppm), v(Li) by far exceeds v(H) in the whole temperature range; the activation energy for v(Li) above 250°C is 0.55 eV in agreement with results derived from conductivity data for LiH doped with MgH2. — For LiH without MgH2 additions, the nmr results are in agreement with diffusion data but deviate from conductivity measurements in temperature dependence and in numerical value. — The present results are interpreted on the basis of Schottky disorder with an enthalpy of formation of 2eV and migration enthalpies of 0.3–0.4eV and 0.55 eV for H− and Li+ ions, respectively. Strong association between O2− impurities and anion vacancies must be assumed. With O2− impurities present, the H− jumps by means of associated vacancies probably play an important role for the diffusion process. For this type of diffusion a nmr correlation factor is to be expected which differs by a factor of 0.5 from the corresponding correlation factor for tracer diffusion.

Magnetic mirror confinement of laser-produced LiH plasmas

The results of measurement and analysis of the decay of mirror-confined lithium hydride plasmas are reported. The plasmas are produced by laser irradiation of a solid LiH particle suspended at the center of a mimimum-B magnetic field. In the initial state, the ratio of the Li3+ energy to H+ energy is 7 to 1, the mean energy of lithium ions is about 2000 eV, and the electrons are cold. In the subsequent decay of the mirror-confined plasmas from 3×1013 to 1012 cm−3, the H+ lifetime is sufficiently shorter than the lifetime of the Li3+ ions so that the plasma evolves to a lithium plasma. The density decay is faster than classical but quiescent for the first 250 μsec. After that time, there are sudden increases in the plasma decay rate and in the rf emission at the central cyclotron frequency of lithium ions, interpreted as evidence of the onset of the drift cyclotron loss cone instability. The quiescent behavior is correlated with the observation of optical radiation from the plasma between 70 and 250 μsec. The plasma luminosity is interpreted as evidence for the creation of cold plasma by ionization of cold neutral reflux from the walls of the baseball coil. A quasi-linear Fokker–Planck calculation of the ion distributions and the growth and damping of the drift cyclotron loss cone mode yielded results consistent with an explanation of the quiescent decay as the suppression of the instability by the cold plasma.

Decomposition pressures in the (α + β) fields of the Li-LiH, Li-LiD, and Li-LiT systems

Decomposition (“plateau”) pressures of H 2, D 2, and T 2 over Li-LiH, Li-LiD, and Li-LiT alloys were determined between 600 and 850°C, for pressures ranging from 3 to 460 Torr, and for alloy compositions falling within the (α + β) miscibility gaps. The measurements were carried out separately for each hydrogen isotope using the same lithium sample and experimental procedures. For each system the ln P vs. 1/ T data form a pair of linear segments, the intersection of which represents the monotectic temperature (694°C for Li-LiH, 690°C for Li-LiD, and 688°C for Li-LiT). For a given temperature plateau pressures were in the order P T 2 > P D 2 > P H 2 . The D H and T H isotope effects in pressures varied from 1.48 and 1.74 at 600°C to 1.34 and 1.45 at 850°C. The results were used to calculate the standard free energies of formation of solid LiH, LiD, and LiT. The tritium gas used in this study had significant amounts of hydrogen and deuterium. A method for correcting the plateau pressures of this mixture to those of pure tritium is presented.

On the direct calculation of localized HF orbitals in molecule clusters, layers and solids

It is shown that the computational effort involved in HF calculations can be considerably reduced by applying the following concepts: 1) the use of a localization operator for the direct determination of localized non-orthogonal HF orbitals, 2) the approximation of the interaction potential between different localization centres by a Hartree-like ansatz, 3) the successive calculation of many-body corrections to molecular properties such as the total energy. A numerical application to LiH layers and solid LiH is described.

Infrared Absorption Wavelengths for Solid LiH and LiD

The infrared absorption spectrum of thin films of LiH and LiD was obtained at room temperature for the region 12.5-25 \ensuremath{\mu}. The primary feature of the spectrum is a broad but definite absorption peak which occurs at 17.0 \ensuremath{\mu} for LiH and at 22.4 \ensuremath{\mu} for LiD. The observed ratio of the wavelengths is 1.32\ifmmode\pm\else\textpm\fi{}0.02, in excellent accord with the ratio of the square root of the reduced masses, 1.33. This agreement is a confirmation of the elementary Born theory of lattice vibrations.