Linearized augmented plane wave method utilizing the quadratic energy expansion of radial wave functions

Conclusions The developed version of the augmented plane wave method yields eigenvalues and eigenfunctions with higher accuracy than the standard LAPW, preserving its computational efficiency.The approximation of the exact radial solution by the Taylor expansion involving also the second energy derivative of the radial function, except for the first derivative, has two advantages. First, the energy dependence of the logarithmic derivatives atr=R is better described and, therefore, the method is less sensitive to the choice of the centre of expansionE ₀ or, equivalently, acceptably accurate eigenvalues are obtained for the broader energy region aroundE ₀. The other and probably more important advantage is that the approximate radial solutions are remarkably closer to the exact radial functions inside the muffin-tin sphere. This can be of use when evaluating the measurable quantities depending on the wave functions.     

On the accuracy of the wavefunctions calculated by LAPW method

The accuracy and the convergence properties of LAPW wavefunctions are studied using Be metal as an example. We show that radial part of thes-component of wavefunction inside the muffin-tin sphere differs substantially from the exact solution to the radial Schrodinger equation. We find that LAPW method underestimates the energy expectation value in the interstitial region. The inaccuracy of the well-converged wavefunctions occasionally produces significant errors in momentum matrix elements.     

Energy bands and electron densities of Li3N

Self-consistent band-structure calculations on the fast ionic conductor lithium nitride are performed by means of the linearized augmented plane wave (LAPW) method within the local density formalism. The corresponding density of states is decomposed into local (inside spheres), partial (l-like) and symmetry (p _x p _y ;p _z ) components from which an only very small covalent contribution to the bonding in Li₃N can be deduced. Electron density maps reveal Li₃N to be highly ionic (near Li⁺ and N^3–). A simple Watson model, although a good first approximation, cannot account for all details. For instance a remarkable non-spherical electrons density is found around N which may explain the high electric field gradient experimentally observed on this site; furthermore a reduced electron density around the Li-sites appears in contrast to a simple supper-possition of N^3– ionic densities. However, calculated x-ray structure factors and difference electron densities are in good qualitative agreement with recent x-ray diffraction experiments.This work has been supported by the Hochschuljubiläumsstiftung der Stadt Wien. All calculations were carried out at the Rechenzentrum der Technischen Universität Wien     

Electronic Properties of MoSi2-Type Hf2X Intermetallic Compounds (X=Pd,Ag, Cd)

The Hf z coordinate and the value of the electric field gradient (efg) main component (V _zz ), were calculated for three Hf₂X compounds (X = Pd, Ag, Cd) on a first-principle basis, using the full potential linear augmented plane wave (LAPW) method. Exchange and correlation effects were treated either by the local spine density approximation (LSDA) or by the more advanced generalized gradient approximation (GGA). The calculated V _zz values, in the Hf site, were in very good agreement with available ¹⁸¹Hf TDPAC experimental results. This revised version was published online in September 2006 with corrections to the Cover Date.     

Conductance through atomic point contacts between fcc(100) electrodes of gold

Electrical conductance through various nanocontacts between gold electrodes is studied by using the density functional theory, scalar-relativistic pseudopotentials, generalized gradient approximation for the exchange-correlation energy and the recursion-transfer-matrix method along with channel decomposition. The nanocontact is modeled with pyramidal fcc(100) tips and 1 to 5 gold atoms between the tips. Upon elongation of the contact by adding gold atoms between the tips, the conductance at Fermi energy E_F evolves from G ≈ 3G₀ to G ≈ 1G₀ (G₀ = 2e/h²). Formation of a true one-atom point contact, with G ≈ 1G₀ and only one open channel, requires at least one atom with coordination number 2 in the wire. Tips that share a common vertex atom or tips with touching vertex atoms have three partially open conductance channels at E_F, and the symmetries of the channels are governed by the wave functions of the tips. The long 5-atom contact develops conductance oscillations and conductance gaps in the studied energy range -3 ≤ E-E_F ≤ 5 eV, which reflects oscillations in the local density of electron states in the 5-atom linear “gold molecule" between the electrodes, and a weak coupling of this “molecule" to the tips.     

Bound state solutions of the two-electron Dirac-Coulomb equation

We present a variational method for solving the two-electron Dirac-Coulomb equation. When the expectation value of the Dirac-Coulomb Hamiltonian is made stationary for all possible variations of the different components of a well-behaved trial function one obtains solutions representative of the physical bound state wave functions. The ground state wave function is derived from the application of a minimax principle. Since the trial function remains well-behaved, the method remains safe from the twin demons of variational collapse and continuum dissolution. The ground state wave function thus derived can be interpreted as a linear combination of different configurations. In particular, the admixing of intermediate states having one (two) electron(s) deexcited to a negative-energy orbital (orbitals) contributes a second-order level shiftE ₀₋ ⁽²⁾ which can be identified with the second-order shift due to the Pauli blocking of the production of one (or two) virtual electron-positron pair(s). Thus the minimax solution corresponds to the renormalized ground state in quantum electrodynamics, with deexcitations to negative-energy orbitals taking the place of the avoidance of virtual pairs. If one extends the relativistic configuration interaction (RCI) treatment by additionally including negative-energy and mixed-energyeigenvectors of the Dirac-Hartree-Fock hamiltonian matrix in the two-electron basis, the calculated energy will be shifted from the conventional RCI value by an amount that is much smaller thanE ₀₋ ⁽²⁾ . For two-electron atoms, we have derived expressions for the all-spinor limit (δE) and thes-spinor limit (δE _s) of this shift in leading orders. The all-spinor limit (δE) is of orderα ⁴ Z ^{4 1/3} whereas thes-spinor limit (δE _s) is of orderα ⁴ Z ^{3 2/3}. leading components are related to the 1-pair component ofE ₀₋ ⁽²⁾ in a simple way, and the relationships offer the possibility of computing energy due to virtual pairs. Numerical results are discussed.     

幂函数叠加势的径向薛定谔方程的解析解

研究多种正幂势函数与逆幂势函数紧密耦合条件下薛定谔径向方程解析解的求解方法.对势函数为V（r）=α₁r⁸＋α₂r³+α₃r²+β₃r^-1＋β₂r^-3＋β₁r^-4的径向薛定谔方程存在解析解的条件以及精确的解析解进行了研究. 根据量子系统波函数必须满足单值、有界和连续的标准条件,首先求出径向坐标r→∞以及r→0时的渐近解,然后采用非正则奇点邻域附近的波函数级数解法与求得的渐近解相结合,通过幂级数系数比较法得到径向薛定谔方程在势函数系数紧密耦合条件下的一系列定态波函数解析解以及相应的能级结构,并作适当讨论与结论. 关键词： 级数解法 幂势函数 径向波函数 渐近解     

Distribution Radiale de la Densité des Atomes Métastables dans les Plasmas Produits par un Champ Electrique Continu ou de Haute-Fréquence

The radial density distribution of metastable Ar(³P₂) and resonant Ar(¹P₁) atoms is determined experimentally in two types of electrical discharges of cylindrical shape: the positive column plasma of a DC discharge and the plasma produced by an electromagnetic surface wave. The exitation and deexcitation rates for Ar(³P₂) by electron collisions are determined as a function of radius from the measured radial population density profile using a population density balance equation. These rate coefficients are obtained for various electron density values on the axis. The published values for these coefficients in the positive column plasma assume that they are independent of the discharge current. In this work, it is shown that these coefficients actually decrease as the electron density increases. In a more general way, the results obtained indicate that the examination of the radial density distributions of exited atoms is a powerful method for determining the kinetics of their creation and destruction.     

High Pressure Study of HfNi Crystallographic and Electronic Structure

The crystallographic structure and electronic properties of HfNi were studied as a function of pressure by combining X-ray diffraction results with the full potential linearized augmented plane wave (LAPW) calculations. No phase transition was observed up to a pressure of 35.3 GPa, with a total volume contraction of V/V ₀ = 0.85, a bulk modulus value of B ₀ = 52 ± 3 GPa and B ₀ ^′ = 1.29 ± 0.26. The calculated linear increase in the V _zz value as a function of the pressure induced volume reduction at the hafnium site was attributed mainly to the p–p contribution, while in the nickel site, a non negligible d–d contribution to V _zz is also observed, and attributed to the high 3d-partial DOS near the nickel nucleus. Based on the total electronic DOS at E _Fermi calculated for 0 K (N(E ⁰ _Fermi)), a value of 6.85 and 5.03 (mJ/mol/k²) was calculated for the band contribution (γ _band) to the electronic specific heat coefficient (γ) at a pressure of 0 and 35.3 GPa, respectively.     

Hulthén势散射态的解析解

在任意l波的离心项1/r²用λ²e^-λr/(1-e^-λr)²近似表达的条件下,对Hulthén势的径向Schrdinger方程作自变量指数变换,使此转化为超几何微分方程,获得了Hulthén势s波散射态的精确解和非s波散射态的近似解析解.给出了相移的解析表达式和按“k/2π标度”归一化的用超几何函数表示的径向波函数.讨论了解析解的意义.     

Time-dependent quantum wave packet and quasiclassical trajectory studies of the Au(2S) + H2(X1∑+g) → AuH(X1∑+g) + H(2S) reaction

The time-dependent quantum wave packet (TDWP) and quasiclassical trajectory calculations (QCT) are carried out for the Au(²S) + H₂(X¹∑⁺_g) → AuH(X¹∑⁺_g) + H(²S) reaction on a global potential energy surface. The reaction probabilities at a series of J values, integral cross sections (ICSs) and differential cross sections of the title reaction are calculated by the TDWP method. For reaction probabilities, there are a mass of sharp oscillations at low collision energy, which can be attributed to resonances supported by the potential well. Due to the endothermicity of the title reaction, the total ICS shows a threshold about 1.53 eV. In order to further investigate the reactive mechanism, the lifetime of complex is calculated by QCT method. At the low collision energy, most intermediate complexes are long lived, which implies that the reaction is governed by indirect reactive mechanism. With the collision energy increasing, the direct reactive mechanism occupies the dominant position. Due to the change of the reactive mechanism, the angular distribution shifts toward the forward direction with collision energy increasing. The isotopic variant, Au + D₂→AuD + D reaction, is also calculated by TDWP method. The calculated reaction probabilities and ICSs show that the isotope effect reduces the reactivity.     

Modifications in high energy higher order Born approximation

A systematic study is made to find out the differential scattering cross-section in the case of electron-atom collisions. The first and the second Born terms ofO(1/k _i ) are calculated in the framework of Yates high energy higher order Born approximation. The second Born term ofO(1/k _i ² ) is calculated using the second order Wallace term, the third term is calculated using the Glauber-eikonal series of Yates. The method is applied to the elastic scattering of electrons by atomic hydrogen in the energy range 100–400 eV and by helium for energies 200 eV and 400 eV. Comparison is made with other theoretical results and the experimental data.     

Electronic structure and magnetism of R(Fe,Si)12 (R = Y, Nd)

The newly developed full-potential linearized augmented plane wave (LAPW) and local orbitals (lo) based on standard APW methods are briefly introduced, and the structure and magnetic properties of R(Fe, Si)₁₂ compounds (R = Y, Nd) are calculated using the method. The distribution of Si at different sites is analyzed based on total energy of one crystal unit with structure having been optimized. The characters of magnetic moments, total density of states (TDOS) and partial density of states (PDOS) for different crystal sites Si occupies are obtained and analyzed. The results show that the total magnetic moments of RFe₁₀Si₂ (R = Y, Nd) are larger than those of RFe₁₀ M ₂ (M = Ti, V, Cr, Mn, Mo and W) and the hybridization mechanism is seen as follows. Si(8j) reduce the magnetic moments of Fe at three sites, however, Si(8f) mainly reduce the magnetic moments of Fe(8i) and Fe(8j) atoms. The Curie temperature is markedly enhanced by the introduction of Si atoms according to spin fluctuation of DOS at Fermi level.     

Radial excitations of heavy-light mesons

The recent discovery of D_s states suggests the existence of radial excitations. Our semirelativistic quark potential model succeeds in reproducing these states within one to two percent of accuracy compared with the experiments, D _s0(2860) and D _s ^*(2715), which are identified as 0⁺ and 1^- radial excitations (n = 2). We also present calculations of radial excitations for B/B _s heavy mesons. The relation between our formulation and the modified Goldberger-Treiman relation is also described.     

Microscopic Analysis of 5d States Splitting and Charge Transfer Energies Dependence on Interionic Distance in Alkaline Earth Fluorides Doped with Light Trivalent Lanthanides

A first principles fully relativistic analysis (K. Ogasawara et al., Phys. Rev. B 2001, 64, 115413) of the dependence of 5d orbitals splitting (10Dq) and charge transfer (CT) energies on interionic distance has been performed for light lanthanides (Ce³⁺, Pr³⁺, Nd³⁺) in CaF₂, SrF₂, BaF₂ crystals. The salient feature of the method is that four‐component molecular orbitals (MO) composed of atomic wave functions are used as the basis set. Without any fitting parameter, the power dependencies for 10Dq and linear dependencies for the CT energies on the distance between rare‐earth (RE) ions and ligands were obtained. A comparison with experimental values is discussed.     

Relation between vortex excitation and thermal conductivity in superconductors

Thermal conductivity κ _xx(T) under a field is investigated in d _{x2 - y2}-wave superconductors and isotropic s-wave superconductors by the linear response theory, using a microscopic wave function of the vortex lattice states. To study the origin of the different field dependence of κ_xx(T) between higher and lower temperature regions, we analyze the spatially-resolved thermal conductivity around a vortex at each temperature, which is related to the spectrum of the local density of states. We also discuss the electric conductivity in the same formulation for a comparison. Received 8 December 2001 and Received in final form 20 March 2002 Published online 6 June 2002     

Surface optical waves at the boundary with a nonlinear Kerr medium

A rigorous solution consistent with a plane wave approximation is given to the boundary problem for Maxwell’s equations for surface optical waves at the boundary with a nonlinear Kerr medium. Exact formulas for the flux intensity (J ₀) and energy density (W ₀) of these waves are derived depending on the parameters of the adjacent media and the propagation constant (ξ). It is shown that these variables as functions of ξ have minima. Thus, J ₀ and W ₀ increase sharply as the propagation constant deviates from the minimum value ξ_min. Their values are greater, the larger the difference between the dielectric constants of the linear and nonlinear media is. An expression for the propagation velocity of a nonlinear surface wave is also obtained.     

A Construction of Blow up Solutions for Co-rotational Wave Maps

The existence of co-rotational finite time blow up solutions to the wave map problem from ${\mathbb{R}^{2+1} \to N}The existence of co-rotational finite time blow up solutions to the wave map problem from \mathbbR²⁺¹ ? N{\mathbb{R}^{2+1} \to N} , where N is a surface of revolution with metric d ρ ² + g(ρ)² dθ², g an entire function, is proven. These are of the form u(t,r)=Q(l(t)t)+R(t,r){u(t,r)=Q(\lambda(t)t)+\mathcal{R}(t,r)} , where Q is a time independent solution of the co-rotational wave map equation −u _tt  + u _rr  + r ⁻¹ u _r  = r ⁻² g(u)g′(u), λ(t) = t ^−1-ν, ν > 1/2 is arbitrary, and R{\mathcal{R}} is a term whose local energy goes to zero as t → 0.     

Spectral/hp least-squares finite element formulation for the Navier–Stokes equations

We consider the application of least-squares finite element models combined with spectral/hp methods for the numerical solution of viscous flow problems. The paper presents the formulation, validation, and application of a spectral/hp algorithm to the numerical solution of the Navier–Stokes equations governing two- and three-dimensional stationary incompressible and low-speed compressible flows. The Navier–Stokes equations are expressed as an equivalent set of first-order equations by introducing vorticity or velocity gradients as additional independent variables and the least-squares method is used to develop the finite element model. High-order element expansions are used to construct the discrete model. The discrete model thus obtained is linearized by Newton’s method, resulting in a linear system of equations with a symmetric positive definite coefficient matrix that is solved in a fully coupled manner by a preconditioned conjugate gradient method. Spectral convergence of the L₂ least-squares functional and L₂ error norms is verified using smooth solutions to the two-dimensional stationary Poisson and incompressible Navier–Stokes equations. Numerical results for flow over a backward-facing step, steady flow past a circular cylinder, three-dimensional lid-driven cavity flow, and compressible buoyant flow inside a square enclosure are presented to demonstrate the predictive capability and robustness of the proposed formulation.