Orthogonalized Plane Wave Research Articles

Supplemented-orthogonalized-plane-wave expansion for energy-band calculations

We study the convergence of a plane-wave expansion supplemented (SOPW) by $d$ basis functions for $d$ states in iron [for hybridized states orthogonalized plane waves (OPW's) would be used]. We find a $d$ basis function which leads to convergence with only two sets of plane waves (to within 0.021 Ry), whereas the $d$ basis functions proposed by Deegan and Twose are 0.069 Ry from convergence. The advantages of the SOPW expansion over the augmented-plane-wave expansion for thin-film calculations are discussed.

Constrained variational calculations of closed shell nuclei with the reid potential

Lowest-order constrained variational calculations with harmonic oscillator wave functions are carried out for 4He, 16O, and 40Ca nuclei with the Reid potential. The results obtained with this simple method are in very close agreement with those obtained by renormalized Brueckner-Hartree-Fock theory with orthogonalized plane wave intermediate states. The A-dependence of the difference between the experimental and calculated binding energies for A = 2, 3, 4, 16, 40 and ∞ can be explained by a three-body cluster term coming either from a wrong off-energy-shell behavior of the Reid potential or a three-body force. The calculated radii of 16O and 40Ca are ≈ 10% too small, indicating that the Reid potential may not be very realistic.

Anisotropic relaxation times for impurity scattering on the Fermi surface

A theoretical calculation is described for the anisotropic relaxation time due to impurity scattering on the Fermi surface of simple metals. The calculation is based on a multiple plane wave scattering formalism using pseudopotentials and phase shifts. The pseudowavefunctions and the Fermi surface are obtained from a four orthogonalised plane wave calculation while the scattering pseudopotentials are taken from form factors which are locally rescreened and corrected for lattice distortion around impurities. Detailed results are presented for impurity in Al. Calculated Dingle temperatures are in reasonable agreement with experimental results. A phase shift model is introduced which allows the Dingle temperature to be expressed in terms of impurity phase shifts and pseudowavefunction amplitudes. These amplitudes have been calculated for several orbits on the Fermi surfaces of Al, In and Pb. The influence of impurities on the low field Hall effect is also discussed.

Oscillatory magnetostriction and the stress dependence of the Fermi surface of aluminum, indium, zinc, and magnesium

Oscillatory magnetostriction and de Haas-van Alphen measurements have been made in aluminum, indium, zinc, and magnesium between 1.3 and 4.2K and in magnetic fields up to 22 kOe. From these results we determined the stress dependence of several orbits on the third band Fermi surfaces of aluminum and indium and some orbits on the Fermi surfaces of zinc and magnesium. The experimental values are in agreement with the results of simple OPW (orthogonalized plane wave) calculations in which the stress dependence of the pseudopotential is obtained from the Heine-Abarenkov-Animalu form factor in a local screening approximation. We observed angular constancy in the stress dependence of the orbits, and a model is presented to account for this. We also discuss the possibility of stress-induced Lifshitz transitions, and show how the free-electron model should be used to predict changes in the Fermi surface under hydrostatic pressure and uniaxial stress.

Magnetoconductivity of Indium

The components of the electrical magnetoconductivity and magnetoresistivity tensors of indium were calculated by the path integral method with a formulation used previously for aluminum. Results presented for longitudinal and transverse magnetoresistance, the longitudinal–transverse components and the Hall term are compared with previous calculations for aluminum and with available experimental results of indium. The magnetoconductivity of aluminum for a four orthogonalized plane wave (OPW) pseudopotential Fermi surface model is reported for comparison with the single OPW calculations.

Intensity and Shape of the X-Ray-Edge Singularity

The singularity at the Fermi edge in the soft-x-ray spectra of metals is known to be described by a factor ${|\frac{{\ensuremath{\xi}}_{0}}{\ensuremath{\epsilon}}|}^{\ensuremath{\alpha}}$ multiplying the one-electron intensity. Using a separable potential, Nozi\`eres and deDominicis showed that $\ensuremath{\alpha}$ is a function of the Fermi-electron phase shifts. However, ${\ensuremath{\xi}}_{0}$, treated until now as a constant, has not yet been derived. We extend the above factor to other frequencies, writing it in the form $G(\ensuremath{\epsilon}){|\frac{\ensuremath{\xi}(\ensuremath{\epsilon})}{\ensuremath{\epsilon}}|}^{\ensuremath{\alpha}}$. Using simplified diagrams we can introduce a realistic potential and orthogonalized plane waves and we determine $G(\ensuremath{\epsilon})$ and $\ensuremath{\xi}(\ensuremath{\epsilon})$ in a range of about 3 eV from the edge. The calculations are applied to $\mathrm{Na}{L}_{2,3}$, $\mathrm{Li}K$, and $\mathrm{Be}K$ bands. The factor $G(\ensuremath{\epsilon})$, related to the open-line part of the problem, presents a singularity in the slope at $\ensuremath{\epsilon}=0$. This fact, important in the $K$ bands, was not realized before. However, the edge singularity does not appear to be strong enough to explain the premature peak in the $K$-emission bands. The $p$-scattering resonance discussed by Allotey is probably dominant here.

Combined OPW-TB Method for the Band Calculation of Layer-Type Crystals. II. The Band Structure of Graphite

The band calculations are made for graphite by the orthogonalized-plane-wave(OPW) representation in the parallel direction to the layer and by the tight-binding(TB) one in the normal direction. The calculated σ as well as π bands of a monolayer of graphite explain fairly. well the various structures observed in the imaginary part of dielectric constant. The band parameters of the Slonczewski-Weiss Hamiltonian, which describes the Fermi surface of three-dimensional graphite, are calculated by this method, but they are found not in good agreement with those determined by experiments. The spin-orbit coupling constant is also calculated by this method, and the negative value is obtained.

Inverse Problem with Constraints

In a recent letter of the same title by Ernst, Monahan, Shakin, and Thaler, a procedure is presented for constructing a solution to the inverse problem with a set of prescribed wave functions. It is pointed out here that their procedure had in fact already been described in three previous publications, under the name of the method of 'completely orthogonalized plane waves.'' (auth)

Orbital-Correction Method

A method for calculating the total energy of complex systems, such as molecules, is proposed. It is a perturbation expansion with two novel features. First, the starting point is an approximate state (rather than an approximate Hamiltonian) and the expansion is in the orbital correction to that state (rather than in a perturbing Hamiltonian). This permits application to complicated molecules where there is no soluble unperturbed Hamiltonian resembling the real system. The second feature is the evaluation of the total energy without the diagonalization of a Hamiltonian matrix. This is accomplished in a way analogous to, but basically different from, the use of the invariance of a trace under a similarity transformation. This permits the treatment of arbitrarily large systems. The principal approximations in the theory are a self-consistent-field approximation to the electron-electron interaction and the truncation at second order of an expansion which would be exact if carried to all orders. If the method were applied to metals, with the approximate starting states taken as orthogonalized plane waves, the theory becomes rigorous nonlocal pseudopotential theory. In molecules linear-combination-of-atomic-orbitals (LCAO) starting states are envisaged and the theory is a systematic improvement upon (as well as simplification of) LCAO theory. Pseudopotentials do not play a central role in the application to molecules, though their use will improve the accuracy and the improvement may be an important one. The results of application of the method to the central hydrides, methane and hydrogen fluoride, by Meserve are given.

Magnetic field-modulated magnetoreflectance of europium chalcogenides

The optical constants of EuO and EuS single crystals have been determined at 300 K by means of a Kramers-Kronig analysis of the reflectivity for photon energies up to 12 eV. For EuS the optical constants have also been determined above and below the Curie temperature in the energy region from 1.5 to 5.7 eV. A first tentative assignment of optical structure to interband transitions has been attempted on the basis of recent orthogonal plane wave (OPW) and earlier augmented plane wave (APW) band structure calculations. For photon energies from 1.2 to 3.8 eV a low magnetic field-modulated magnetoreflectance has been measured using circularly polarized light. By use of the Kramers-Kronig relation for the differential reflectance spectra in conjunction with our data of the optical constants, a detailed analysis of the magnetoreflectance spectra of EuS was carried out for the first time.

Nuclear magnetic resonance measurements and the energy band structure of PtSn

Nuclear magnetic resonance measurements of the Knight shift and spin-lattice relaxation time for 195Pt and 119Sn in PtSn are reported. The energy band structure as determined by the relativistic orthogonalized plane wave method is also presented. The band model developed has holes in the Pt d-band but does not have a large density of states associated therewith.

A study of charge density in beryllium

Abstract The x-ray structure amplitudes for the 27 lowest-angle Bragg reflections of beryllium metal have been measured on an absolute scale. These can be used to deduce the charge density. The measured structure amplitudes are compared with those predicted both by the free atom Hartree-Foch wave functions and by a free electron orthogonalized plane wave model. For both models the predicted value for the lowest angle reflection is close to that observed, but the structure amplitudes of subsequent reflections given by the models are significantly greater than those observed. To account for these discrepancies a model of beryllium involving 2p-like tight binding functions is proposed.

Computation of electronic properties of solids

A large number of physical properties of solids can be understood in terms of the one-electron picture. This implies an enormous simplification in the description of both static and dynamic properties. However, even this reduction in complexity is generally not sufficient to obtain solutions of the one-electron problems in analytical form. A survey is presented of several important methods for the computation of energy band structures. The knowledge of these is basic for the understanding of an important class of phenomena. An account is given of the following methods: Light bonding, augmented plane wave, Green's function, orthogonalized plane wave, empirical pseudopotential method. Their mutual relations as well as their ranges of applicability are discussed. It is indicated how the results of these various methods can be used in the calculation of electron density distributions, photoemission spectra, ϵ 2(ω)-spectra etc.

Orthogonalized plane wave calculation of the conduction band of CuCl

Calculations of the conduction band of CuCl by OPW method upto 6th neighbouring points in the reciprocal space have been made along three high symmetry directions Δ, Λ, and Σ. The calculated band structure agrees well with the u.v. absorption spectrum.

Relativistic Pseudopotential Method

A relativistic pseudopotential is defined for the Dirac Hamiltonian with the use of relativistic orthogonalized plane waves. In the standard representation, the leading new terms in the Dirac pseudo-Hamiltonian are a mass-change term, a change in the timelike component of the vector potential, and spatial components of bivector and pseudovector contributions. The former two give rise to the "repulsive" part of the pseudopotential in the nonrelativistic limit. The latter are "rotational" energy contributions due to core overlap which give rise to the spinorbit corrections of the more usual treatments. The nature of the spin-orbit interaction is discussed in some detail.

Rainfall crosspolarisation of linearly and circularly polarised waves at microwave frequencies

The isolation between right- and left-hand circularly polarised plane waves is evaluated and compared with that between orthogonal linear plane waves for propagation through rain with nonspherical drops. It is seen that the linear orthogonal mode of propagation will give superior isolation when a distribution of raindrop canting angles is considered.

Mutually Orthogonal Orthogonalized Plane Waves

A basis set of mutually orthogonal orthogonalized plane waves (OPW's) is constructed. As an example of the utility of this basis set, these orthogonal OPW's are applied in the simplification of the secular equation of the one-electron problem in a periodic potential.

On the orthogonalized plane wave method

AbstractThe overcompleteness of the system of orthogonalized plane waves and related problems in the OPW method are discussed.

On the asymptotic linear dependence of orthogonalized plane waves

AbstractThe influence of the linear dependence of orthogonalized plane waves on energy band calculations is investigated. One of the modifications of the method is analysed. Calculations for diamond illustrate the general considerations.

Equivalent Two-Body Interactions with Specified Bound-State Wave Functions

The correspondence between the recent Letter of the same title by Monahan, Shakin, and Thaler, and the method of "completely orthogonalized plane waves" is pointed out, and the geometrical significance of the corresponding transformation is elucidated. The analysis of Monahan, Shakin, and Thaler is generalized and simplified.