Plane-wave Results Research Articles

Generalized stacking-faults and screw-dislocation core-structure in bcc iron: A comparison between ab initio calculations and empirical potentials

Generalized stacking fault energies and screw dislocation core structures are reported for two sets of models for iron: density functional theory (DFT) calculations and empirical potentials. A thorough comparison between various DFT approaches has been performed on {110} and {211} γ-lines, which give a first indication on dislocation properties: (i) the effect of the exchange-correlation functional, LDA versus GGA, is significant in the pseudopotential approximation but not in the PAW approximation or in paramagnetic calculations; and (ii) the discrepancy due to the basis set between SIESTA and plane-wave results is rather small. Three empirical potentials for iron have been benchmarked on these DFT results. They all yield similar energies, but different shapes for the γ-lines. Using the criterion suggested by Duesbery and Vitek, the γ-line results point to non-degenerate core structures for the DFT calculations and for the Ackland and Ackland–Mendelev potentials but not for the Dudarev–Derlet potential. The direct calculations of the dislocation core structures show that the Ackland potential is an exception to the Duesbery–Vitek rule. More insight into the stability of the core structure can be gained by looking at the response to the polarization of the core. The Dudarev–Derlet and Ackland potentials have similar polarizations, but the energy difference between degenerate and non-degenerate cores is much larger with the Dudarev–Derlet potential, as expected from the γ-lines. The polarizability of the non-degenerate core is smaller with the Ackland–Mendelev potential than in DFT, indicating that the energy landscape is flatter in this direction.

Quasiatomic orbitals forab initiotight-binding analysis

Wave functions obtained from plane-wave density-functional theory (DFT) calculations using norm-conserving pseudopotential, ultrasoft pseudopotential, or projector augmented-wave method are efficiently and robustly transformed into a set of spatially localized nonorthogonal quasiatomic orbitals (QOs) with pseudoangular momentum quantum numbers. We demonstrate that these minimal-basis orbitals can exactly reproduce all the electronic structure information below an energy threshold represented in the form of environment-dependent tight-binding Hamiltonian and overlap matrices. Band structure, density of states, and the Fermi surface are calculated from this real-space tight-binding representation for various extended systems (Si, SiC, Fe, and Mo) and compared with plane-wave DFT results. The Mulliken charge and bond order analyses are performed under QO basis set, which satisfy sum rules. The present work validates the general applicability of Slater and Koster's scheme of linear combinations of atomic orbitals and points to future ab initio tight-binding parametrizations and linear-scaling DFT development.

Theoretical Simulations of 0.25 Monolayer Iodine Adsorption on Cu(100)

Simulations of adsorption 0.25 monolayer of iodine on Cu(100) were performed using a local-orbital minimal basis technique based on density functional theory and compared with plane-wave basis results. It was found that iodine adsorption changes the spacings between surface layers of copper substrate and can cause the reconstruction of this surface to rhombus-like arrangement with a stable threefold hollow adsorption site. The calculated structure of I/Cu(100) is presented together with the simulated scanning tunneling microscopy images of this surface. The obtained results are discussed in comparison with experimental results.

Benchmark density functional theory calculations for nanoscale conductance

We present a set of benchmark calculations for the Kohn-Sham elastic transmission function of five representative single-molecule junctions. The transmission functions are calculated using two different density functional theory methods, namely an ultrasoft pseudopotential plane-wave code in combination with maximally localized Wannier functions and the norm-conserving pseudopotential code SIESTA which applies an atomic orbital basis set. All calculations have been converged with respect to the supercell size and the number of k|| points in the surface plane. For all systems we find that the SIESTA transmission functions converge toward the plane-wave result as the SIESTA basis is enlarged. Overall, we find that an atomic basis with double zeta and polarization is sufficient (and in some cases, even necessary) to ensure quantitative agreement with the plane-wave calculation. We observe a systematic downshift of the SIESTA transmission functions relative to the plane-wave results. The effect diminishes as the atomic orbital basis is enlarged; however, the convergence can be rather slow.

Density functional theory study of mercury adsorption on metal surfaces

Density functional theory (DFT) calculations are used to characterize the interaction of mercury with copper, nickel, palladium, platinum, silver, and gold surfaces. Mercury binds relatively strongly to all the metal surfaces studied, with binding energies up to $\ensuremath{\sim}1\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ for Pt and Pd. DFT calculations underestimate the energy of adsorption with respect to available experimental data. Plane-wave DFT results using the local density approximation and the Perdew-Wang 1991 and Perdew-Burke-Ernzerhof parametrizations of the generalized gradient approximation indicate that binding of mercury at hollow sites is preferred over binding at top or bridge sites. The interaction with mercury in order of increasing reactivity over the six metals studied is $\mathrm{Ag}<\mathrm{Au}<\mathrm{Cu}<\mathrm{Ni}<\mathrm{Pt}<\mathrm{Pd}$. Binding is stronger on the (001) faces of the metal surfaces, where mercury is situated in fourfold hollow sites as opposed to the threefold hollow sites on (111) faces. In general, mercury adsorption leads to decreases in the work function; adsorbate-induced work function changes are particularly dramatic on Pt.

Comparison of localized basis and plane-wave basis for density-functional calculations of organic molecules on metals

Localized pseudoatomic orbitals (PAOs) are mainly optimized and tested for the strong chemical bonds within molecules and solids with their proven accuracy and efficiency, but are prone to significant basis set superposition error (BSSE) for weakly interacting systems. Here we test the accuracy of PAO basis in comparison with the BSSE-free plane-wave basis for the physisorption of pentacene molecule on Au (001) by calculating the binding energy, adsorption height, and energy level alignment. We show that both the large cutoff radius for localized PAOs and the counter-poise correction for BSSE are necessary to obtain well-converged physical properties. Thereby obtained results are as accurate as the plane-wave basis results. The comparison with experiment is given as well.

Reconstruction of mono-vacancies in carbon nanotubes: Atomic relaxation vs. spin polarization

We have investigated the reconstruction of mono-vacancies in carbon nanotubes using density functional theory (DFT) geometry optimization and electronic structure calculations, employing a numerical basis set. We considered mono-vacancies in achiral nanotubes with diameter range ≈ 4 –9 Å. Contrary to previous tight-binding calculations, our results indicate that mono-vacancies could have several metastable geometries, confirming the previous plane-wave DFT results. Formation energy of mono-vacancies is 4.5– 5.5 eV , increasing with increasing tube diameter. Net magnetic moment decreases from ideal mono-vacancy value after reconstruction, reflecting the reduction of the number of dangling bonds. In spite of the existence of a dangling bond, ground state of mono-vacancies in semiconducting tubes have no spin polarization. Metallic carbon nanotubes show net magnetic moment for most stable structure of mono-vacancy, except for very small diameter tubes.

Transient Reflection Properties of a Dispersive and Lossy Bi-Isotropic Slab With an Anisotropic Laminated Composite Backing

This paper presents a detailed analysis of the transient reflection from a general bi-isotropic slab backed by a laminated composite. Either a nonreciprocally Tellegen medium or a reciprocally dispersive chiral medium with losses is considered as the bi-isotropic slab. The laminated composite is a graphite-fiber-reinforced-plastic composite (GFRPC), which has been widely used as a replacement for metals and may be treated as a multilayered anisotropic medium from the electromagnetic point of view. For the analysis, a theoretical model is developed based on a state-equation approach. On the basis of this model, both the time-domain and the frequency-domain plane-wave reflection results are obtained and studied. The factors affecting the results, such as the material parameters of the bi-isotropic slab and the fiber-orientation pattern of the GFRPC, are investigated in detail. Some special reflection properties, such as the twist-polarizer reflection and the antireflection, are observed based on this investigation. The properties may lead to a novel transient absorber technology for electromagnetic compatibility (EMC) applications.

PlanarN=4 gauge theory and the Inozemtsev long range spin chain

We investigate whether the (planar, two complex scalar) dilatation operator of N=4 gauge theory can be, perturbatively and, perhaps, non-perturbatively, described by an integrable long range spin chain with elliptic exchange interaction. Such a chain was introduced some time ago by Inozemtsev. In the limit of sufficiently ``long'' operators a Bethe ansatz exists, which we apply at the perturbative two- and three-loop level. Spectacular agreement is found with spinning string predictions of Frolov and Tseytlin for the two-loop energies of certain large charge operators. However, we then go on to show that the agreement between perturbative gauge theory and semi-classical string theory begins to break down, in a subtle fashion, at the three-loop level. This corroborates a recently found disagreement between three-loop gauge theory and near plane-wave string theory results, and quantitatively explains a previously obtained puzzling deviation between the string proposal and a numerical extrapolation of finite size three-loop anomalous dimensions. At four loops and beyond, we find that the Inozemtsev chain exhibits a generic breakdown of perturbative BMN scaling. However, our proposal is not necessarily limited to perturbation theory, and one would hope that the string theory results can be recovered from the Inozemtsev chain at strong 't Hooft coupling.

Density functional simulation of small Fe nanoparticles

We calculate from first principles the electronic structure, relaxation and magnetic moments in small Fe particles, applying the numerical local orbitals method in combination with norm-conserving pseudopotentials. The accuracy of the method in describing elastic properties and magnetic phase diagrams is tested by comparing benchmark results for different phases of crystalline iron to those obtained by an all-electron method. Our calculations for the bipyramidal Fe_5 cluster qualitatively and quantitatively confirm previous plane-wave results that predicted a non-collinear magnetic structure. For larger bcc-related (Fe_35) and fcc-related (Fe_38, Fe_43, Fe_62) particles, a larger inward relaxation of outer shells has been found in all cases, accompanied by an increase of local magnetic moments on the surface to beyond 3 mu_B.

First-principles study of the ferroelastic phase transition inCaCl2

First-principles density-functional calculations within the local-density approximation and the pseudopotential approach are used to study and characterize the ferroelastic phase transition in calcium chloride (CaCl_2). In accord with experiment, the energy map of CaCl_2 has the typical features of a pseudoproper ferroelastic with an optical instability as ultimate origin of the phase transition. This unstable optic mode is close to a pure rigid unit mode of the framework of chlorine atoms and has a negative Gruneisen parameter. The ab-initio ground state agrees fairly well with the experimental low temperature structure extrapolated at 0K. The calculated energy map around the ground state is interpreted as an extrapolated Landau free-energy and is successfully used to explain some of the observed thermal properties. Higher-order anharmonic couplings between the strain and the unstable optic mode, proposed in previous literature as important terms to explain the soft-phonon temperature behavior, are shown to be irrelevant for this purpose. The LAPW method is shown to reproduce the plane-wave results in CaCl_2 within the precision of the calculations, and is used to analyze the relative stability of different phases in CaCl_2 and the chemically similar compound SrCl_2.

All-electron magnetic response with pseudopotentials: NMR chemical shifts

A theory for the ab initio calculation of all-electron NMR chemical shifts in insulators using pseudopotentials is presented. It is formulated for both finite and infinitely periodic systems and is based on an extension to the Projector Augmented Wave approach of Bloechl [P. E. Bloechl, Phys. Rev. B 50, 17953 (1994)] and the method of Mauri et al [F. Mauri, B.G. Pfrommer, and S.G. Louie, Phys. Rev. Lett. 77, 5300 (1996)]. The theory is successfully validated for molecules by comparison with a selection of quantum chemical results, and in periodic systems by comparison with plane-wave all-electron results for diamond.

Some physical implications of the Weyl-Dirac theory

The solution of a wave equation in the Gauss-Mainardi-Codazzi formalism of Weyl-Dirac theory is obtained in terms of the elliptic function. In particular, by degenerating the elliptic function, plane-wave, wavepacket, kink and soliton results. Each particular solution corresponds to certain values of the curvature scalar and of the cosmological constant, so that the entity manifests different wave-particle properties in different geometric situations. Associating a superconducting behaviour to matter, by means of the kink solution, we find the dependences on the reduced temperature of the superconducting parameters, in other words, we develop a thermodynamics of the isolated particle. Using the soliton solution we show that for any particle we can define a particular waveguide.

Singly resonant cavity-enhanced frequency tripling

We use a plane-wave analysis to examine a singly resonant, cavity-enhanced, frequency doubler containing an intracavity sum-frequency interaction that frequency sums the resonant fundamental with the second harmonic to produce the third harmonic of the resonant field. We derive expressions for the steady-state performance of the device. We determine the input coupler intensity reflectivity and the ratio of nonlinear drives between the second-harmonic generation (SHG) and sum-frequency generation (SFG) stages for optimum third-harmonic conversion efficiency. We also examine the optimum SHG interaction length under conditions of limited total interaction length. We find that numerical simulations modeling three spatial dimensions can be closely approximated by appropriately scaled plane-wave results. As an example, we consider frequency tripling of a 350-mW, 1319-nm, cw laser in two consecutive nonlinear gratings in periodically poled lithium niobate and find third-harmonic power-conversion efficiency of 85.3% when first-order quasi-phase-matching (QPM) is used for the SFG process and 51.0% when third-order SFG QPM is used. We also consider frequency tripling of a 20-W, 1064-nm, continuous-wave mode-locked laser in two lithium triborate crystals and find a time-averaged third-harmonic power-conversion efficiency of 56.0% from modeling three spatial dimensions.

Non-stationary scattering of wave-packets

Potential scattering of free-electron wave packets is considered in the framework of non-stationary quantum-mechanical theory. The general expression for the average angle of scattering is obtained. The traditional quantum-mechanical plane-wave approximation and classical results are shown to be incorporated in the results derived.

Influence of transverse effects on self-induced polarization changes in an isotropic Kerr medium

Allowing for an isotropic optical nonlinearity of third order, we derive approximate Gaussian solutions of the paraxial wave equation. They describe a monochromatic elliptically polarized light signal of finite extension both in space and in time. In contrast to plane-wave results, the state of polarization is found to be strongly nonuniform in the transverse direction. Both the orientation and the shape of the polarization ellipse are not conserved. For low intensities, parameters measuring the induced optical activity depend on the intensity quadratically instead of linearly. For high intensities, saturation sets in. It is argued that by means of nonlinear ellipsometry one can evaluate two tensor components, namely, Re χxyyx(3) and Re χxxxx(3). Upon taking into account transverse as well as temporal effects, the magnitude of these components may decrease by a factor of 10.

Structure and elasticity of MgO at high pressure

The structural and elastic properties of MgO periclase were studied up to 150 GPa with the first-principles pseudopotential method within the local density approximation. The calculated lattice constant of the B1 phase over the pressure range studied is within 1% of experimental values. The observed B1 phase of MgO was found to be stable up to 450 GPa, precluding the B1-B2 phase transition within the lower mantle. The calculated transition pressure is less than one-half of the previous pseudopotential prediction but is very close to the linearized augmented plane-wave result. All three independent elastic constants, c(11), c(12), and c(44) for the B1 phase are calculated from direct computation of stresses generated by small strains. The calculated zero-pressure values of the elastic moduli and wave velocities and their initial pressure dependence are in excellent agreement with experiments. MgO was found to be highly anisotropic in its elastic properties, with the magnitude of the anisotropy first decreasing between 0 and 15 Gpa and then increasing from 15 to 150 GPa. Longitudinal and shear-wave velocities were found to vary by 23 and 59%, respectively, with propagation direction at 150 Gpa. The character of the anisotropy changes qualitatively with pressure. At zero pressure longitudinal and shear-wave propagations are fastest along [111] and [100], respectively, whereas above 15 GPa, the corresponding fast directions are [100] and [110]. The Cauchy condition was found to be strongly violated in MgO, reflecting the importance of noncentral many-body forces.

Ab Initio Investigation of the High Pressure Elasticity of Mg2SiO4 Forsterite and Ringwoodite

ABSTRACTWe discuss the behavior of two minerals of the same composition, Mg2SiO4 but different structures: forsterite and ringwoodite. Ab initio plane-wave pseudopotential results are discussed in terms of the full elastic constant tensors of these phases and their elastic anisotropy. The structures of the two minerals, based on pseudo-hep and pseudo-fee packing of oxygens, respectively, show very different behavior at high pressure. While the elastic anisotropy of olivine depends weakly on pressure between 0 and 25 GPa, the anisotropy of ringwoodite decreases with pressure initially, vanishing at 17 GPa before increasing again at higher pressure. This unusual behavior is understood in terms of a change of sign of the combination of elastic constants c2+2c44-c11, and a resulting interchange of fast and slow directions of acoustic wave propagation. To gain insight into the origin of their elastic behavior, the ab initio results are compared with a simple model based on the O sub-lattice.

Optical pressure exerted on a dielectric film in the evanescent field of a Gaussian beam

We theoretically investigate the optical pressure for a dielectric film located in the evanescent field of a Gaussian beam. In our approach, we derive the electromagnetic fields at the boundaries of the film by solving the boundary-value problem for a system of four stratified media with the incidence of a Gaussian beam. We also formulate analytically the optical pressure exerted on a dielectric film by using the derived electromagnetic fields. Numerical results of the optical pressure by a Gaussian beam-generated evanescent wave are presented in comparison with the plane-wave results.

Analysis of atomic orbital basis sets from the projection of plane-wave results

The projection of the eigenfunctions obtained in standard plane-wave first-principles calculations is used for analysing atomic orbital basis sets. The `spillage' defining the error in such a projection allows the evaluation of the quality of an atomic orbital basis set for a given system and its systematic variational optimization. The spillage is shown to correlate with the mean square error in the energy bands obtained from the projected Hamiltonian matrix. The method is applied to the characterization of finite-range pseudo-atomic orbitals (Sankey O F and Niklewski D J 1989 Phys. Rev. B 40 3979) in comparison to infinite-range pseudo-atomic and Slater-type orbitals. The bases are evaluated and optimized for several zinc-blende semiconductors and for aluminium; the finite-range orbitals display high quality in spite of the limited range. A simple scheme is proposed to systematically enlarge the basis without increasing its range.