Adaptive Finite Element Approximations for a Class of Nonlinear Eigenvalue Problems in Quantum Physics

In this paper, we study an adaptive finite element method for a class of nonlinear eigenvalue problems resulting from quantum physics that may have a nonconvex energy functional. We prove the convergence of adaptive finite element approximations and present several numerical examples of micro-structure of matter calculations that support our theory.     

Convergence properties of methods for effective operator calculations studied in a simple many-body model

Several methods for effective interaction and operator calculations based on the Rayleigh-Schrödinger and Brillouin-Wigner perturbation expansions are studied. Special emphasis is given to the use of Padé approximants for effective operator calculations. The convergence properties of the methods are studied numerically in a Lipkin many-body model. Among the various methods using Padé-approximants, the method based on a variational approach in the BW scheme is found to give most encouraging results for the present model.     

Theoretical ROVibrational Energies (TROVE): A robust numerical approach to the calculation of rovibrational energies for polyatomic molecules

We present a new computational method with associated computer program TROVE (Theoretical ROVibrational Energies) to perform variational calculations of rovibrational energies for general polyatomic molecules of arbitrary structure in isolated electronic states. The (approximate) nuclear kinetic energy operator is represented as an expansion in terms of internal coordinates. The main feature of the computational scheme is a numerical construction of the kinetic energy operator, which is an integral part of the computation process. Thus the scheme is self-contained, i.e., it requires no analytical pre-derivation of the kinetic energy operator. It is also general, since it can be used in connection with any internal coordinates. The method represents an extension of our model for pyramidal XY₃ molecules reported previously [S.N. Yurchenko, M. Carvajal, P. Jensen, H. Lin, J.J. Zheng, W. Thiel, Mol. Phys. 103 (2005) 359]. Non-rigid molecules are treated in the Hougen-Bunker-Johns approach [J.T. Hougen, P.R. Bunker, J.W.C. Johns, J. Mol. Spectrosc. 34 (1970) 136]. In this case, the variational calculations employ a numerical finite basis representation for the large-amplitude motion using basis functions that are generated by Numerov-Cooley integration of the appropriate one-dimensional Schrödinger equation.     

Bestimmung der Abschirmung der magnetischen Kernresonanz und der magnetischen Suszeptibilität durch Berechnung der Stromdichte diamagnetischer Moleküle mit der Methode der finiten Elemente

Determination of the NMR-Shielding and of Magnetic Susceptibility by Calculation of the Current Density of Diamagnetic Molecules by the Finite Element Method In paper [20] the finite element method was initiated for calculations of diamagnetic properties of molecules on the basis of a semiclassical approach [18, 19]. In the present work this method is used in the frame of the uncoupled Hartree-Fock-perturbation theory. It is shown that the proposed approach is applicable to localized orbitals, the susceptibility and the shielding being divided into incrementary contributions. Furthermore the relationship to the semiclassical approach and to the approach of Rebane [7] is shown. The H₂-molecule, the threedimensional anisotropic harmonic oscillator and the CH₄-molecule serve as examples to present the possibilities of this method.     

Comparative first-principles analysis of the absorption spectra of ZnAl2S4 and ZnGa2O4 crystals doped with Cr3+

Systematic first-principles analysis of the energy level schemes and ground state absorption spectra of trivalent chromium in ZnAl₂S₄ and ZnGa₂O₄ crystals has been performed in the present paper. The recently developed first-principles approach to the analysis of the absorption spectra of impurity ions in crystals based on the discrete variational multi-electron (DV-ME) method [K. Ogasawara et al., Phys. Rev. B 64, 115413 (2001)] was used in the calculations. The method is based on the numerical solution of the Dirac equation; no phenomenological parameters are used in the calculations. As a result, complete energy level schemes of the Cr³⁺ ion and its absorption spectra in both crystals were calculated, assigned and compared with experimental data. By performing analysis of the molecular orbital (MO) population, it was shown that the covalency of the chemical bonds between the Cr³⁺ and S^2- ions is more significant than that one between the Cr³⁺ and O^2- ions.     

First-principles study of the optical properties of PbFX (X = Cl,Br, I) compounds in its matlockite-type structure

We present the results of the ab initio theoretical study of the optical properties for PbFX (X = Cl, Br, I) compounds in its matlockite-type structure using the full potential linearized augmented plane wave (FP-LAPW) method as implemented in the WIEN2K code. We employed generalized gradient approximation (GGA), which is based on exchange-correlation energy optimization to calculate the total energy. Also we have used the Engel-Vosko GGA formalism, which optimizes the corresponding potential for band structure calculations. Our calculations show that the valence band maximum (VBM) and conduction band minimum (CBM) are located at Z resulting in a direct energy gap. We present calculations of the frequency-dependent complex dielectric function ε( ω) and its zero-frequency limit ε₁ ( 0 ). We find that the values of ε₁ ( 0 ) increases with decreasing the energy gap. The reflectivity spectra and absorption coefficient has been calculated and compared with the available experimental data. The optical properties are analyzed and the origin of some of the peaks in the spectra is discussed in terms of the calculated electronic structure.     

A numerical evaluation of Rayleigh's theory applied to scattering by randomly rough dielectric surfaces

Abstract

We present a numerical simulation of scattering by one-dimensional randomly rough surfaces. It is based on the use of plane-wave expansions to describe the Melds on the surface (i.e. Rayleigh hypothesis). Accuracy and convergence properties of two different numerical implementations are studied. Some examples of results for a dielectric and a metallic Gaussian rough surface are shown to be in good agreement with calculations by a rigorous numerical method. The Rayleigh method appears to be a fast computation tool for dielectric surfaces with slopes of less than 0.2.     

A second order self-consistent IMEX method for radiation hydrodynamics

We present a second order self-consistent implicit/explicit (methods that use the combination of implicit and explicit discretizations are often referred to as IMEX (implicit/explicit) methods ,  and ) time integration technique for solving radiation hydrodynamics problems. The operators of the radiation hydrodynamics are splitted as such that the hydrodynamics equations are solved explicitly making use of the capability of well-understood explicit schemes. On the other hand, the radiation diffusion part is solved implicitly. The idea of the self-consistent IMEX method is to hybridize the implicit and explicit time discretizations in a nonlinearly consistent way to achieve second order time convergent calculations. In our self-consistent IMEX method, we solve the hydrodynamics equations inside the implicit block as part of the nonlinear function evaluation making use of the Jacobian-free Newton Krylov (JFNK) method ,  and . This is done to avoid order reductions in time convergence due to the operator splitting. We present results from several test calculations in order to validate the numerical order of our scheme. For each test, we have established second order time convergence.     

Satellite phenomena in the X-ray photoelectron spectra of lanthanide trihydroxides

Using the direct CI method perturbation corrections to the Koopmans ionization energies have been obtained up to order 10 for the molecules CN^? and H₂O. The results are compared with those from the fully converged CI and B_k-type calculations. The convergence of the perturbation series is found to be quite slow although substantial improvement is possible using a variation-perturbation method.     

Electronic structure of a thermoelectric material: CsBi4Te6

We have calculated the electronic structure of CsBi₄Te₆ by means of first-principles self-consistent total-energy calculations within the local-density approximation using the full-potential linear-muffin-tin-orbital method. From our calculated electronic structure we have calculated the frequency dependent dielectric function. Our calculations shows that CsBi₄Te₆ a semiconductor with a band gap of 0.3 eV. The calculated dielectric function is very anisotropic. Our calculated density of state support the recent experiment of Chung et al. [Science 287 (2000) 1024] that CsBi₄Te₆ is a high performance thermoelectric material for low temperature applications.     

Structural properties of zinc-blende Ga<Subscript>x</Subscript>In<Subscript>1-x</Subscript>N: ab initio calculations

We present a theoretical study of the structural properties, namely lattice constant, bulk modulus and its pressure derivative of zinc-blende Ga_xIn_1-xN. The calculations are performed using first-principles calculations in the framework of the density-functional-theory within the local density approximation under the virtual crystal approximation. The computed values are in good agreement with the available experimental data. The composition dependence of the studied quantities is examined. Besides, the deviation of the alloy lattice constant from Vegard's law is evaluated.     

Luminescence studies on nitride quaternary alloys double quantum wells

We present theoretical photoluminescence (PL) spectra of undoped and p-doped Al_xIn_1−x−yGa_yN/Al_XIn_1−X−YGa_YN double quantum wells (DQWs). The calculations were performed within the k.p method by means of solving a full eight-band Kane Hamiltonian together with the Poisson equation in a plane wave representation, including exchange-correlation effects within the local density approximation. Strain effects due to the lattice mismatch are also taken into account. We show the calculated PL spectra, analyzing the blue and red-shifts in energy as one varies the spike and the well widths, as well as the acceptor doping concentration. We found a transition between a regime of isolated quantum wells and that of interacting DQWs. Since there are few studies of optical properties of quantum wells based on nitride quaternary alloys, the results reported here will provide guidelines for the interpretation of forthcoming experiments.     

Optical spectrum and local lattice structure for ruby

We perform ab initio calculations using a pseudo-potential plane-wave method based on density functional theory, within the local density approximation and generalized gradient approximation, in order to determine and predict the pressure dependence of structural and elastic properties of spinel compounds: MgAl₂O₄, MgGa₂O₄ and MgIn₂O₄. The results are in agreement with the available experimental data and other theoretical calculations.     

Quantum chemical modelling of ‘green’ luminescence in self activated perovskite-type oxides

We discuss the origin of the intrinsic visible band emission of ABO₃ perovskite oxides (so-called ‘green luminescence’) which remains a topic of high interest during the last quarter of the century. We present a theoretical calculation modelling of this emission in the framework of a concept of charge transfer vibronic excitons [Phys. Solid State, 40 (1998) 834], i.e. as a result of radiative recombination of correlated (bound) self-trapped electron and hole polarons in the highly polarizable ABO₃-type matrix. The Intermediate Neglect of Differential Overlap method combined with the Large Unit Cell periodic defect model was used for quantum chemical calculations and theoretical simulation of the green emission for a series of model ABO₃ perovskites. The ‘green’ luminescence energies for PbTiO₃, SrTiO₃, BaTiO₃, KNbO₃ and KTaO₃ perovskite-type crystals agree well with those experimentally observed earlier.     

Electron Scattering without Spin Sums

Using the spacetime algebra formulation of the Dirac equation, we demonstrate how to perform cross-section calculations following a method suggested by Hestenes (1982). Instead of an S-matrix, we use an operator that rotates the initial states into the scattered states. By allowing the scattering operator to become a function of the initial spin, we can neatly handle spin-dependent calculations. When the operator is independent of spin, we can provide manifestly spin-independent results. We use neither spin basis nor spin sums, instead handling the spin orientation directly. As examples, we perform spin-dependent calculations in Coulomb scattering to second order, and briefly consider more complicated calculations in QED.     

Neutron-neutron scattering length from the reaction γd → πnn employing chiral perturbation theory

We discuss the possibility to extract the neutron-neutron scattering length a_nn from experimental spectra on the reaction γd → π⁺ nn . The transition operator is calculated to high accuracy from chiral perturbation theory. We argue that for properly chosen kinematics, the theoretical uncertainty of the method can be as low as 0.1 fm.     

Calculation of absolute electron-impact ionization cross-sections of dimers and trimers

We report calculations of the electron-impact ionization cross-sections of selected dimers (homonuclear diatomic molecules) and trimers (homonuclear triatomic molecules) using a method which relies only on macroscopic quantities in conjunction with a “defect concept”. The empirically determined defect describes the deviation of the cluster (dimer, trimer) cross-sections from a simple linear dependence on the cluster size. We compare the calculated cross-sections to experimental data for the dimers S₂ and F₂ and the trimer O₃ and we present predictions for the ionization cross-sections of Br₂, I₂, C₂ and C₃ for which no experimental data are available. Lastly, we extend the method to the calculation of ionization cross-sections for the fullerenes C₆₀ and C₇₀. Received 6 December 1999 and Received in final form 10 April 2000     

First principles study of structural,magnetic and electronic properties of half-metallic CrO<Subscript>2</Subscript> under pressure

A first-principles tight-binding linear muffin tin orbital (TB-LMTO) method within the local-density approximation is used to calculate the total energy, lattice parameter, bulk modulus, magnetic moment, density of states and energy band structures of half-metallic CrO₂ at ambient as well as at high pressure. The magnetic and structural stabilities are determined from the total energy calculations. From the present study we predict a magnetic transition from ferromagnetic (FM) state to a non-magnetic (NM) state at 65 GPa, which is of second order in nature. We also observe from our calculations that CrO₂ is more stable in tetragonal phase (rutile-type) at ambient conditions and undergoes a transition to an orthorhombic structure (CaCl₂-type) at 9.6 GPa, which is in good agreement with the experimental results. We predict a second structural phase transition from CaCl₂- to fluorite-type structure at 89.6 GPa with a volume collapse of 7.3%, which is yet to be confirmed experimentally. Interestingly, CrO₂ shows half metallicity under ambient conditions. After the first structural phase transition from tetragonal to orthorhombic, half metallicity has been retained in CrO₂ and it vanishes at a pressure of 41.6 GPa. Ferromagnetism is quenched at a pressure of 65 GPa.     

Algebraic aspects of the Hirzebruch signature operator and applications to transitive Lie algebroids

The index of the classical Hirzebruch signature operator on a manifold M is equal to the signature of the manifold. The examples of Lusztig ([10], 1972) and Gromov ([4], 1985) present the Hirzebruch signature operator for the cohomology (of a manifold) with coefficients in a flat symmetric or symplectic vector bundle. In [6], we gave a signature operator for the cohomology of transitive Lie algebroids. In this paper, firstly, we present a general approach to the signature operator, and the above four examples become special cases of a single general theorem.