Quantum Theory of Advanced Materials

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.

We show that the continuous feedback approach is highly effective for controlling chaotic systems. The control design for the Lorenz system is presented as an example to demonstrate the strength of this approach. The proposed control is able to eliminate chaos and bring the system toward any of the three steady states. Two different control input locations are considered. Only one system variable is used in the feedback. The control scheme can tolerate both measurement noise and modeling uncertainty as long as they are bounded.

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.

The phase stability is studied for the beta-phase YH2+x system based on first-principles total energy calculations. Our study predicts that the D0(22), ''40'', and D1a structures are stable near x = 0. 25, 0.5, and 0.8, respectively. Using the effective cluster interactions obtained from the first-principles total-energy data, the phase diagram for the D0(22) and ''40'' ordered phases is calculated by the cluster variational method. The calculated order-disorder transition temperature at x = 0.1 for the D0(22) structure is around 280 K, which is consistent with the recent observation of the metal-semiconductor transition near 230-280 K and resistivity anomalies near 200-250 K for the system with x near 0.1 [Daou and Vajda, Phys. Rev. B 45, 10 907 (1992)].

We present a tight-binding model for silicon which incorporates two-center intra-atomic parameters. The model is fitted to density-functional theory band structures for silicon in the diamond structure over a number of volumes. It is shown that with only a two-center, orthogonal basis, reasonable total energies can be obtained for many different structures. Thus it eliminates the need to use structure-dependent terms in the total-energy model.

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 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.

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.

The asymmetry in the phase diagram of the H/Ru(001) system is studied by assuming a lattice gas model for the chemisorbed hydrogen and using the cluster variation method. Ground state analysis of the ordered structures shows that the effective pair interaction for the next-nearest neighbors has to be repulsive. We also found that the order-disorder transition temperatures and hence the phase diagram are very sensitive to upsilon3, the ratio of the effective next-nearest to nearest neighbor interactions of H adatoms. The asymmetry in the phase diagram, which cannot be accounted for by the adsorbate relaxation model by Persson [Surf. Sci. 258 (1991) 451], is attributed to the coverage dependence of the effective pair interactions. By assuming a simple piecewise linear dependence of upsilon3 on the chemical potential, we constructed an asymmetric phase diagram which is in excellent agreement with the experimental data. The model studied can be applied to the H/Pd(111) system directly and can be easily generalized for other close-packed metal surfaces.

Using tight-binding models, the energies of a number of silicon and germanium (111) surfaces are studied. These include reconstructed surfaces with dimers and stacking faults (DS), simple adatom surfaces such as 2x2 and c(2x8), and more complicated cases with dimers, adatoms, and stacking faults (DAS). For reconstructed surfaces containing adatoms, it is found that a simple correction term dependent on the adatom concentration is needed in the present total-energy model to account for the unusual geometry. Similarities between the silicon and germanium reconstructions are seen and compare well with ab initio results. There are also some differences between silicon and germanium, for example, the DS surfaces are lower in energy than the relaxed (1x1) for silicon, but higher for germanium. Si(111) reconstructs into the DAS structure while Ge(111) goes to the simple adatom c(2x8) surface. The c(2x8), 7x7 DAS, (1x1), and 7x7 DS surface reconstructions of Ge(111) were studied with in-plane strain. For these surfaces, a strain of about 2% was sufficient to make the 7x7 DAS/DS surface lower in energy than the c(2x8)/(1x1) surface. An analysis of the energy per atom showed that the dimer-row and associated first-layer atoms played a major part in the differing energy behavior, in agreement with an earlier proposal. An expansive strain was applied to the 2x2, 7x7 DAS, (1x1), and 7x7 DS surface reconstructions of Si(111). With a strain of about 2.5% the adatom surfaces switched relative energies, while the adatom free surfaces required only about 1.5% strain. As for germanium, the dimer-row and associated atoms were of major importance in the differing energy change.

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.

By accurately fitting tight-binding parameters to ab initio band structures from 14 different tetrahedral volumes, tight-binding parametric formulas have been developed for silicon and germanium. The distance dependences for these orthogonal, nearest-neighbor parameters range from r-2.5 to r-3.3. Repulsive potentials are added in order to reproduce the total energies for a number of bulk structures. It is found that the repulsive potential needed has the simple form of a pairwise interaction multiplied by a structure-dependent constant. Transferability is shown with good bulk and cluster results.

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.

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.

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 have performed tight-binding calculations on a model of an amorphous silicon sample generated previously by a molecular-dynamics simulation employing the Stillinger-Weber potential. The sample consists of 588 atoms and contains a high density of floating-bond defects. Two tight-binding calculations are presented, one using the widely accepted Chadi parameters, which include only nearest-neighbor interactions, and the other using the parameters recently proposed by Allen, Broughton, and McMahan (ABM) [Phys. Rev. B 34, 859 (1986)] for a nonorthogonal basis set. Comparison of the densities of states shows similar behavior in the valence band, but the electron density near a defect is less localized with the ABM parameters. It is also found that the projected density of states on the fivefold-coordinated atoms is very close to that on the fourfold-coordinated atoms, while the projected density of states on the threefold-coordinated atoms is distinctly different and has more states in the gap.