Quantum Theory of Advanced Materials

The structural and electronic properties of hydrogen in yttrium are studied using the pseudopotential method within the local-density-functional approximation (LDA). Different concentration regions are considered for the alpha and beta phases. The binding energies associated with different interstitial sites are evaluated as well as the diffusion energy barrier and local vibrational modes. It is found that the occupation of the tetrahedral site is energetically more favorable than that of the octahedral site in the alpha phase. The calculated vibrational frequency is in excellent agreement with the value observed in neutron scattering experiments. Possibility of pairing is also examined from the consideration of energetics.

The Hofstadter butterfly spectrum for Landau levels in a two-dimensional periodic lattice is a rare example exhibiting fractal properties in a truly quantum system. However, the observation of this physical phenomenon in a conventional material will require a magnetic field strength several orders of magnitude larger than what can be produced in a modern laboratory. It turns out that for a specific range of rotational angles twisted bilayer graphene serves as a special system with a fractal energy spectrum under laboratory accessible magnetic field strengths. This unique feature arises from an intriguing electronic structure induced by the interlayer coupling. Using a recursive tight-binding method, we systematically map out the spectra of these Landau levels as a function of the rotational angle. Our results give a complete description of LLs in twisted bilayer graphene for both commensurate and incommensurate rotational angles and provide quantitative predictions of magnetic field strengths for observing the fractal spectra in these graphene systems.

The structural properties of hexagonal-close-packed yttrium are studied by using the plane-wave basis within the pseudopotential method and local-density-functional approximation. By employing a "soft" pseudopotential proposed by Troullier and Martins, satisfactory convergence is achieved with a plane-wave energy cutoff of 30-40 Ry for this early-transition-metal element. The overall results for the structural properties are in good agreement with experiment. It is found that the charge overlap between core and valence electrons has a substantial effect on the accuracy of the calculated structural properties. Two different calculations are performed with and without the outer-core 4p orbital included as a valence state. In addition, as found in some other local-density calculations, the uncertainty in the results due to different exchange-correlation energy functionals may not be negligible in transition metals.

We studied total energies of various ordered structures of PdHx (in which hydrogen occupies the octahedral sites within the fee Pd lattice) using the pseudopotential method and a plane-wave basis within the local-density-functional approximation. The structures considered include the (420)-plane ordering of hydrogen atoms at different concentrations. For x greater than or equal to 1/2 we found that the NiMo- and Ni4Mo (D1(a))-type structures at x=1/2 and x=4/5, respectively, were energetically favored phases, in agreement with the superlattice reflections found in previous neutron-scattering measurements. For the intermediate concentrations, linear variation of the formation energy as a function of x in several (420)-ordered structures explained the observed short-range order. In contrast to an earlier proposal, we did not find the Fermi surface imaging effect responsible in this case. The overall energy variation in different phases indicates the importance of going beyond pairwise interactions between interstitial hydrogen atoms in this system.

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The solid-solution phase of hydrogen in hexagonal close-packed yttrium (a-YH(x)) is studied using the pseudopotential method within the local-density-functional approximation with a plane-wave basis. The binding energies associated with different interstitial sites are evaluated for several ordered structures: YH0.5, YH0.25, and YH0.167. It is found that the occupation of the tetrahedral site is always energetically favorable. The hydrogen potential-energy curves around the tetrahedral sites along the c axis and along the path connecting the adjacent octahedral sites are also calculated for YH0.25. In particular, the local vibrational mode along the c axis is estimated to be 100 meV, in excellent agreement with that measured in neutron-scattering experiments. Finally, the intriguing pairing phenomenon is investigated by calculating the total energy for various pairing configurations. The possibility of pairing between nearest-neighbor tetrahedral sites is excluded due to the high energy. It is found that the pairing of hydrogen across a metal atom is indeed energetically favorable compared with other kinds of pairs considered and also with isolated tetrahedral hydrogen atoms. The connection with the electronic structure of the system is also examined.

Aluminum hydride (alane) AlH(3) is an important material in hydrogen storage applications. It is known that AlH(3) exists in multiply forms of polymorphs, where alpha-AlH(3) is found to be the most stable with a hexagonal structure. Recent experimental studies on gamma-AlH(3) reported an orthorhombic structure with a unique double-bridge bond between certain Al and H atoms. This was not found in alpha-AlH(3) or other polymorphs. Using density functional theory, we have investigated the energetics, and the structural, electronic, and phonon vibrational properties for the newly reported gamma-AlH(3) structure. The current calculation concludes that gamma-AlH(3) is less stable than alpha-AlH(3) by 1.2 KJ/mol, with the zero-point energy included. Interesting binding features associated with the unique geometry of gamma-AlH(3) are discussed from the calculated electronic properties and phonon vibrational modes. The binding of H-s with higher energy Al-p,d orbitals is enhanced within the double-bridge arrangement, giving rise to a higher electronic energy for the system. Distinguishable new features in the vibrational spectrum of gamma-AlH(3) were attributed to the double-bridge and hexagonal-ring structures.

The cubic YH2+x system with an extended hydrogen composition is studied using the pseudopotential method and the local-density-functional approximation with a plane-wave basis. The study focuses on the beta phase with the metal atoms forming a face-centered-cubic lattice and the octahedral sites partially occupied by hydrogen for 0 < x < 1. The self-consistent total-energy calculation is performed by employing the supercell modeling method. The structural property, in particular, the volume contraction with increasing x, is investigated by analyzing the energy changes for different site occupation. It is found that the lattice contracts mainly to increase the interaction of the additional electron and the metal d potential. In addition, the (420)-plane ordering of the x-excess hydrogen is examined for YH2.25 and is confirmed by energetics studies.

A pseudopotential local-density calculation is performed for YH3 to study the unusual hydrogen displacements previously found in neutron diffraction. These displacements are identified as Peierls distortions associated with (hydrogen) lattice instability in this 3D system. The wave vector of these displacements is close to the vector connecting the electron and hole pockets in the undistorted system. With other electron and hole pockets at GAMMA that still overlap after distortion, the possibility of the existence of an excitonic insulator phase will be discussed.

A small amount of catalyst, such as Ti, was found to greatly improve the kinetics of hydrogen reactions in the prototypical hydrogen storage compound sodium alanate (NaAlH(4)). We propose a near-surface alloying mechanism for the rehydrogenation cycle based on a detailed analysis of available experimental data as well as first-principles calculations. The calculated results indicate that the catalyst remains at subsurface sites near the Al surface, reducing the dissociation energy barrier of H(2). The binding between Ti and Al modifies the surface charge distribution, which facilitates hydrogen adsorption and enhances hydrogen mobility on the surface.

Recently it was discovered that a total of 5.6 wt. % H-2 could be released from the 1:2 mixture of lithium amide and magnesium hydride at temperatures as low as 150 degrees C. With a reaction enthalpy of 44 KJ/mol H-2, this system has high potential for on-board hydrogen storage applications. The fully desorbed product is believed to be a mixed lithium and magnesium imide Li2Mg(NH)(2). In this work, the crystal structure of this mixed imide is studied from total-energy density-functional calculations. Based on a recent experimentally established space group, possible ordered configurations are examined. Important local orderings are identified for the experimentally observed disordered phase at room temperature. These unique local arrangements are also connected with the observed structural transitions above room temperature. In addition, the local ordering in Mg(NH2)(2) is analyzed. The similarity and difference of local arrangements among hydrogen, cations, and vacancies are discussed for the three amide (imide) systems: LiNH2, Mg(NH2)(2), and Li2Mg(NH)(2). The identification of the cation and hydrogen local orderings are expected to facilitate the design of new mixed imides and amides as hydrogen storage materials with desired physical properties.

We propose a simple method to evaluate the energies of ideal metal surfaces as a function of orientation based on cluster energy expansion. By symmetry only clusters with even-number corners will be present. It is found that the energy expansion converges rapidly and in most cases can be truncated at the pair interaction level. The parameters can be determined from a limited number of low-index surface energies obtained from first-principles calculations. The equilibrium crystal shape at T = O is then predicted and the step energy on major facets is derived for some fee metals.

We report first-principles calculations of Pb (100) films up to 22 monolayers to study variations in the surface energy and work function as a function of film thickness. An even-odd oscillation is found in these two quantities, while a jelliumlike model for this s-p metal predicts a periodicity of about three monolayers. This unexpected result is explained by considering a coherent superposition of contributions from quantum-well states centered at both the Gamma and M points in the two-dimensional Brillouin zone, demonstrating the importance of crystal band structure in studying the quantum size effect in metal thin films.

We have carried out first-principles calculations of Pb (111) films up to 25 monolayers to study the oscillatory quantum size effects exhibited in the surface energy and work function. These oscillations are correlated with the thickness dependence of the energies of confined electrons, which can be properly modeled by an energy-dependent phase shift of the electronic wave function upon reflection at the interface. It is found that a quantitative description of these quantum size effects requires a full consideration of the crystal band structure.

We present the calculation of the full phonon spectrum for silicon and germanium with the pseudopotential method and the local-density approximation without using linear-response theory. The interplanar-force constants for three high-symmetry orientations [(100), (110), and (111)] are evaluated by supercell calculations using the Hellmann-Feynman theorem. By considering the symmetry of the crystal, three-dimensional interatomic-force-constant matrices are determined by a least-squares fit. Interactions up to the eighth nearest neighbors are included. The dynamical matrix, which is the Fourier transform of the force constant matrix, is hence constructed and diagonalized for any arbitrary wave vector in the Brillouin zone, yielding the phonon dispersion. In this paper we will present the calculation details and discuss various aspects of convergence. Phonon dispersions of Si and Ge calculated are in excellent agreement with experiments.

We present a method to calculate the full phonon spectrum using the local-density approximation and Hellmann-Feynman forces. By a limited number of supercell calculations of the planar force constants, the interatomic force constant matrices are determined. One can then construct the dynamical matrix for any arbitrary wave vector in the Brillouin zone. We describe in detail the procedure for elements in the diamond structure and derive the phonon dispersion curves for Si. The anharmonic effects can also be studied by the present method.

We have studied the properties of quantum well states in supported Ag(100) films on the Fe substrate by first-principles density-functional calculations. The energies of these quantum well states as a function of thickness N are examined in terms of the characteristic phase shift of the electronic wave function at the interface. These energy-dependent phase shifts are determined numerically for both the film-substrate and film-vacuum interfaces. It is also found that the substrate has a major effect on film stability, enhancing the stability of the N=5 film and reversing that of the N=2 film.

We report the first implementation of orthonormal wavelet bases in self-consistent electronic structure calculations within the local-density approximation. These local bases of different scales efficiently describe localized orbitals of interest. As an example, we studied two molecules, H-2 and O-2, using pseudopotentials and supercells. Considerably fewer bases are needed compared with conventional plane-wave approaches, yet calculated binding properties are similar. Our implementation employs fast wavelet and Fourier transforms, avoiding evaluating any three-dimensional integral numerically.

A model interaction is introduced for quantum many-body simulations of Coulomb systems using periodic I boundary conditions. The interaction gives much smaller finite size effects than the standard Ewald interaction and is also much faster to compute. Variational quantum Monte Carlo simulations of diamond-structure silicon with up to 1000 electrons demonstrate the effectiveness of our method.