The projection of the eigenfunctions obtained in standard plane-wave first-principle electronic-structure calculations into atomic-orbital basis sets is proposed as a formal and practical link between the methods based on plane waves and the ones based on atomic orbitals. Given a candidate atomic basis, ({\it i}) its quality is evaluated by its projection into the plane-wave eigenfunctions, ({\it ii}) it is optimized by maximizing that projection, ({\it iii}) the associated tight-binding Hamiltonian and energy bands are obtained, and ({\it iv}) population analysis is performed in a natural way. The proposed method replaces the traditional trial-and-error procedures of finding appropriate atomic bases and the fitting of bands to obtain tight-binding Hamiltonians. Test calculations of some zincblende semiconductors are presented.

https://arxiv.org/pdf/cond-mat/9505075.pdf

Projection of plane-wave calculations into atomic orbitals

Oxidation of metals and alloys

The most relevant, and often utilized, methods and techniques for obtaining energy levels of confined one- and two-electron atoms are reviewed. We discuss how the electronic states of hydrogen and helium atoms are remarkably modified when subjected to extreme pressure regimes. For the hydrogen atom confined in a spherical box of impenetrable walls, we present the exact solutions and the energy eigenvalues obtained with very high accuracy. A few wave function properties calculated for the confined hydrogen atom, such as pressure, polarizability and the Fermi contact term, are discussed in some detail. Some accurate energy calculations for the hydrogen atom confined in a penetrable spherical box and when subjected to Neumann boundary conditions, are also presented. In addition, for the spherically confined helium atom we present the most accurate calculations reported to date.

The Hydrogen and Helium Atoms Confined in Spherical Boxes

The hydrogen atom confined by an infinite spherical potential barrier is studied employing a variational procedure based on the p-version of the finite element method. In such a procedure, the spherical spatial confinement is imposed straightforwardly by removing a local basis function. The calculations have been performed for estimating the energy spectrum, the dipole polarizability and the effective pressure for various confinement radii. The effect of the spatial confinement on these quantities is analysed. The results obtained are compared with those previously published in the literature and the efficiency of the finite element method to treat confined quantum systems is discussed.

A study of the confined hydrogen atom using the finite element method

We discuss the boundary effects on a quantum system by examining the problem of a hydrogen atom in a spherical well. Using an approximation method which is linear in energy we calculate the boundary corrections to the ground-state energy and wavefunction. We obtain the asymptotic dependence of the ground-state energy on the radius of the well.

https://iopscience.iop.org/article/10.1088/0143-0807/21/3/309/pdf

Hydrogen atom in a spherical well: linear approximation

We discuss the boundary effects on a quantum system by examining the problem of a hydrogen atom in a spherical well. By using an approximation method which is linear in energy we calculate the boundary corrections to the ground-state energy and wave function. We obtain the asymptotic dependence of the ground-state energy on the radius of the well.

We have used a full-potential linear muffin-tin orbital method to calculate the effects of oxygen impurities on the electronic structure of NiAl. Using the supercell method with a 16-atom supercell we have investigated the cases where an oxygen atom is substitutionally placed at either a nickel or an aluminum site. Full relaxation of the atoms within the supercell was allowed. We found that oxygen prefers to occupy a nickel site over an aluminum site with a site selection energy of 138 mRy (21 370 K). An oxygen atom placed at an aluminum site is found to cause a substantial relaxation of its nickel neighbors away from it. In contrast, this steric repulsion is hardly present when the oxygen atom occupies the nickel site and is surrounded by aluminum neighbors. We comment on the possible relation of this effect to the pesting degradation phenomenon (essentially spontaneous disintegration in air) in nickel aluminides.

Oxygen impurities in NiAl: Relaxation effects

We have performed a systematic first-principles computational study of the effects of impurity atoms (boron, carbon, nitrogen, oxygen, silicon, phosporus, and sulfur) on the orbital hybridization and bonding properties in the intermetallic alloy NiAl using a full-potential linear muffin-tin orbital method. The matrix elements in momentum space were used to calculate real-space properties: onsite parameters, partial densities of states, and local charges. In impurity atoms that are empirically known to be embrittler (N and O) we found that the $2s$ orbital is bound to the impurity and therefore does not participate in the covalent bonding. In contrast, the corresponding $2s$ orbital is found to be delocalized in the cohesion enhancers (B and C). Each of these impurity atoms is found to acquire a net negative local charge in NiAl irrespective of whether they sit in the Ni or Al site. The embrittler therefore reduces the total number of electrons available for covalent bonding by removing some of the electrons from the neighboring Ni or Al atoms and localizing them at the impurity site. We show that these correlations also hold for silicon, phosporus, and sulfur.

Systematic first-principles study of impurity hybridization in NiAl

We have examined a method of direct extraction of accurate tight-binding parameters from an ab-initio band-structure calculation. The linear muffin-tin potential method, in its full-potential implementation, has been used to provide the hamiltonian and overlap matrix elements in the momentum space. These matrix elements are Fourier transformed to real space to produce the tight-binding parameters. The feasibility of this method has been tested on the intermetallic alloy NiAl, using spd orbitals for each atom. The parameters generated for this alloy have been used as input to a real-space calculation of the local density of states using the recursion method.

David Djajaputra

Papers

Hydrogen atom in a spherical well: linear approximation

Hydrogen atom in a spherical well: linear approximation

Oxygen impurities in NiAl: Relaxation effects

Systematic first-principles study of impurity hybridization in NiAl

Tight-binding parameters from the full-potential linear muffin-tin orbital method: A feasibility study on NiAl