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arXiv1995

Towards a Linear-Scaling DFT Technique: The Density Matrix Approach

A recently proposed linear-scaling scheme for density-functional pseudopotential calculations is described in detail. The method is based on a formulation of density functional theory in which the ground state energy is determined by minimization with respect to the density matrix, subject to the condition that the eigenvalues of the latter lie in the range [0,1]. Linear-scaling behavior is achieved by requiring that the density matrix should vanish when the separation of its arguments exceeds a chosen cutoff. The limitation on the eigenvalue range is imposed by the method of Li, Nunes and Vanderbilt. The scheme is implemented by calculating all terms in the energy on a uniform real-space grid, and minimization is performed using the conjugate-gradient method. Tests on a 512-atom Si system show that the total energy converges rapidly as the range of the density matrix is increased. A discussion of the relation between the present method and other linear-scaling methods is given, and some problems that still require solution are indicated.

mtrl-th↗

arXiv1996

Vibrational Spectra of Defects in Silicon: An Orbital Radii Approach

A phenomenological approach to the stretching mode vibrational frequencies of defects in semiconductors is proposed. A novel quantum scale is defined in terms of the first principles pseudopotential based orbital radius and the principal quantum number of the element concerned. A universal linear relationship between the Sanderson electronegativity and this quantum scale is established. Next, we show that the stretching mode vibrational frequencies of hydrogen and chlorine in the silicon network scale linearly with this quantum scale. Predictions and identifications of defect environments around the Si-H and Si-Cl are possible. The assignments of vibrational modes in porous silicon are critically examined. We discuss our proposed scale in the context of Mendeleveyan scales in general, and suggest justifications for it. We believe that our approach can be gainfully extended to the vibrational spectra of other semiconductors.

mtrl-th↗

arXiv1996

Selfconsistent order-N density-functional calculations for very large systems

We present a method to perform fully selfconsistent density-functional calculations, which scales linearly with the system size and which is well suited for very large systems. It uses strictly localized pseudoatomic orbitals as basis functions. The sparse Hamiltonian and overlap matrices are calculated with an $O(N)$ effort. The long range selfconsistent potential and its matrix elements are computed in a real-space grid. The other matrix elements are directly calculated and tabulated as a function of the interatomic distances. The computation of the total energy and atomic forces is also done in $O(N)$ operations using truncated, Wannier-like localized functions to describe the occupied states, and a band-energy functional which is iteratively minimized with no orthogonality constraints. We illustrate the method with several examples, including carbon and silicon supercells with up to 1000 Si atoms and supercells of $β$-C$_3$N$_4$. We apply the method to solve the existing controversy about the faceting of large icosahedral fullerenes by performing dynamical simulations on C$_{60}$, C$_{240}$, and C$_{540}$.

cond-mat↗

arXiv1995

Strongly-interacting model for antiferromagnetism in one-dimensional C60-polymers: A1C60

We study the antiferromagnetic phase of the C60-polymer doped with one electron per one C60 by using a tight-binding model with long-range Coulomb interactions. The model is solved by the unrestricted Hartree-Fock approximation, and a phase diagram is obtained by changing Coulomb interaction strengths and a conjugation parameter between C60 molecules. We find that the antiferromagnetism is well described by the present model. The comparison with the photoemission studies shows that the new band around the Fermi energy of the A1C60 phase can be explaind by the extremely large intrusion of an energy level into the gap of the neutral system. This indicates that the interaction effects among electrons are important in doped C60-polymers.

cond-mat↗

arXiv1995

First-principles investigation of 180-degree domain walls in BaTiO_3

We present a first-principles study of 180-degree ferroelectric domain walls in tetragonal barium titanate. The theory is based on an effective Hamiltonian that has previously been determined from first-principles ultrasoft-pseudopotential calculations. Statistical properties are investigated using Monte Carlo simulations. We compute the domain-wall energy, free energy, and thickness, analyze the behavior of the ferroelectric order parameter in the interior of the domain wall, and study its spatial fluctuations. An abrupt reversal of the polarization is found, unlike the gradual rotation typical of the ferromagnetic case.

mtrl-th↗

arXiv1995

Linear-Response Calculation of Electron-Phonon Coupling Parameters

An ab initio method for calculating electron-phonon coupling parameters is presented. The method is an extension of the plane-wave-based linear-response method for the calculation of lattice dynamics. Results for the mass enhancement parameter and the electron-phonon spectral function for Al, Pb and Li are presented. Comparisons are made to available experimental data.

mtrl-th↗

arXiv1995

Atomic and electronic structure of ideal and reconstructed $α$-Sn (111) surface

We have carried out an ab-initio study of $α$-Sn (111), with the aim of predicting and understanding its structure, reconstructions, and electronic states. We consider a variety of structural possibilities, and optimize them by moving atoms according to Hellmann-Feynman forces. Our results indicate that the unreconstructed surface is highly unstable, while a variety of reconstructions compete for the true ground state. Extrapolated trends from diamond to Si to Ge are well borne out, with a $2\times 1 π$-bonded chain reconstruction prevailing in the absence of adatoms, and a $c(4\times 2)$ or $(2\times 2)$ basic adatom-restatom unit reconstruction otherwise. Accompanying surface bucklings are in both cases larger than in Si and Ge, with consequently large ionic charge transfers predicted. Search for a $β$-Sn-like metallic state of the surface turned out to be inconclusive.

cond-mat↗

arXiv1996

Charge transfer excitons in optical absorption spectra of C60-dimers and polymers

Charge-transfer (CT) exciton effects are investigated for the optical absorption spectra of crosslinked C60 systems by using the intermediate exciton theory. We consider the C60-dimers, and the two (and three) molecule systems of the C60-polymers. We use a tight-binding model with long-range Coulomb interactions among electrons, and the model is treated by the Hartree-Fock approximation followed by the single-excitation configuration interaction method. We discuss the variations in the optical spectra by changing the conjugation parameter between molecules. We find that the total CT-component increases in smaller conjugations, and saturates at the intermediate conjugations. It decreases in the large conjugations. We also find that the CT-components of the doped systems are smaller than those of the neutral systems, indicating that the electron-hole distance becomes shorter in the doped C60-polymers.

cond-mat↗

arXiv1996

Correlation effects in MgO and CaO: Cohesive energies and lattice constants

A recently proposed computational scheme based on local increments has been applied to the calculation of correlation contributions to the cohesive energy of the CaO crystal. Using ab-initio quantum chemical methods for evaluating individual increments, we obtain 80% of the difference between the experimental and Hartree-Fock cohesive energies. Lattice constants corrected for correlation effects deviate by less than 1% from experimental values, in the case of MgO and CaO.

mtrl-th↗

arXiv1996

Third order dielectric susceptibility in a model quantum paraelectric

In the context of perovskite quantum paraelectrics, we study the effects of a quadrupolar interaction $J_q$, in addition to the standard dipolar one $J_d$. We concentrate here on the nonlinear dielectric response $χ_{P}^{(3)}$, as the main response function sensitive to quadrupolar (in our case antiquadrupolar) interactions. We employ a 3D quantum four-state lattice model and mean-field theory. The results show that inclusion of quadrupolar coupling of moderate strength ($J_q \sim {{1}\over{4}} J_d$) is clearly accompanied by a double change of sign of $χ_{P}^{(3)}$ from negative to positive, near the quantum temperature $T_Q$ where the quantum paraelectric behaviour sets in. We fit our $χ_{P}^{(3)}$ to recent experimental data for SrTiO$_3$, where the sign change is identified close to $T_Q \sim 37 K$.

mtrl-th↗

arXiv1995

Separable Dual Space Gaussian Pseudo-potentials

We present pseudo-potential coefficients for the first two rows of the periodic table. The pseudo potential is of a novel analytic form, that gives optimal efficiency in numerical calculations using plane waves as basis set. At most 7 coefficients are necessary to specify its analytic form. It is separable and has optimal decay properties in both real and Fourier space. Because of this property, the application of the nonlocal part of the pseudo-potential to a wave-function can be done in an efficient way on a grid in real space. Real space integration is much faster for large systems than ordinary multiplication in Fourier space since it shows only quadratic scaling with respect to the size of the system. We systematically verify the high accuracy of these pseudo-potentials by extensive atomic and molecular test calculations.

mtrl-th↗

arXiv1996

Surprises in the Orbital Magnetic Moment and g-Factor of the Dynamic Jahn-Teller Ion C_{60}^-

We calculate the magnetic susceptibility and g-factor of the isolated C_{60}^- ion at zero temperature, with a proper treatment of the dynamical Jahn-Teller effect, and of the associated orbital angular momentum, Ham-reduced gyromagnetic ratio, and molecular spin-orbit coupling. A number of surprises emerge. First, the predicted molecular spin-orbit splitting is two orders of magnitude smaller than in the bare carbon atom, due to the large radius of curvature of the molecule. Second, this reduced spin-orbit splitting is comparable to Zeeman energies, for instance, in X-band EPR at 3.39KGauss, and a field dependence of the g-factor is predicted. Third, the orbital gyromagnetic factor is strongly reduced by vibron coupling, and so therefore are the effective weak-field g-factors of all low-lying states. In particular, the ground-state doublet of C_{60}^- is predicted to show a negative g-factor of \sim -0.1.

cond-mat↗

arXiv1996

The Structure, Dynamics and Electronic Structure of Liquid Ag-Se Alloys Investigated by Ab Initio Simulation

Ab initio molecular-dynamics simulations have been used to investigate the structure, dynamics and electronic properties of the liquid alloy Ag(1-x)Se(x) at 1350 K and at the three compositions x=0.33, 0.42 and 0.65. The calculations are based on density-functional theory in the local density approximation and on the pseudopotential plane-wave method. The reliability of the simulations is confirmed by detailed comparisons with very recent neutron diffraction results for the partial structure factors and radial distribution functions (RDF) of the stoichiometric liquid Ag2Se. The simulations show a dramatic change of the Se-Se RDF with increasing Se content. This change is due to the formation of Se clusters bound by covalent bonds, the Se-Se bond length being almost the same as in pure c-Se and l-Se. The clusters are predominantly chain-like, but for higher x a large fraction of 3-fold coordinated Se atoms is also found. It is shown that the equilibrium fractions of Se present as isolated atoms and in clusters can be understood on a simple charge-balance model based on an ionic interpretation. The Ag and Se diffusion coefficients both increase with Se content, in spite of the Se clustering. An analysis of the Se-Se bond dynamics reveals surprisingly short bond lifetimes of less than 1 ps. The changes in the density of states with composition arise directly from the formation of Se-Se covalent bonds. Results for the electronic conductivity obtained using the Kubo-Greenwood approximation are in adequate agreement with experiment for l-Ag2Se, but not for the high Se contents. Possible reasons for this are discussed.

mtrl-th↗

arXiv1996

Semiempirical Hartree-Fock calculations for KNbO3

In applying the semiempirical intermediate neglect of differential overlap (INDO) method based on the Hartree-Fock formalism to a cubic perovskite-based ferroelectric material KNbO3, it was demonstrated that the accuracy of the method is sufficient for adequately describing the small energy differences related to the ferroelectric instability. The choice of INDO parameters has been done for a system containing Nb. Based on the parametrization proposed, the electronic structure, equilibrium ground state structure of the orthorhombic and rhombohedral phases, and Gamma-TO phonon frequencies in cubic and rhombohedral phases of KNbO3 were calculated and found to be in good agreement with the experimental data and with the first-principles calculations available.

mtrl-th↗

arXiv1996

Calculated optical properties of Si, Ge, and GaAs under hydrostatic pressure

The macroscopic dielectric function in the random-phase-approximation without local field effect has been implemented using the local density approximation with an all electron, full-potential linear muffin-tin orbital basis-set. This method is used to investigate the optical properties of the semiconductors Si, Ge, and GaAs under hydrostatic pressure. The pressure dependence of the effective dielectric function is compared to the experimental data of Goñi and coworkers, and an excellent agreement is found when the so called ``scissors-operator'' shift (SOS) is used to account for the correct band gap at $Γ$. The effect of the $3d$ semi-core states in the interband transitions hardly changes the static dielectric function, $ε_\infty$; however, their contribution to the intensity of absorption for higher photon energies is substantial. The spin-orbit coupling has a significant effect on $ε_\infty$ of Ge and GaAs, but not of Si. The $E_1$ peak in the dynamical dielectric function is strongly underestimated for Si, but only slightly for Ge and GaAs, suggesting that excitonic effects might be important only for Si.

cond-mat↗

arXiv1995

Theoretical study of O adlayers on Ru(0001)

Recent experiments performed at high pressures indicate that ruthenium can support unusually high concentrations of oxygen at the surface. To investigate the structure and stability of high coverage oxygen structures, we performed density functional theory calculations, within the generalized gradient approximation, for O adlayers on Ru(0001) from low coverage up to a full monolayer. We achieve quantitative agreement with previous low energy electron diffraction intensity analyses for the (2x2) and (2x1) phases and predict that an O adlayer with a (1x1) periodicity and coverage of 1 monolayer can form on Ru(0001), where the O adatoms occupy hcp-hollow sites.

mtrl-th↗

arXiv1996

Solitonic-exchange mechanism of surface~diffusion

We study surface diffusion in the framework of a generalized Frenkel-Kontorova model with a nonconvex transverse degree of freedom. The model describes a lattice of atoms with a given concentration interacting by Morse-type forces, the lattice being subjected to a two-dimensional substrate potential which is periodic in one direction and nonconvex (Morse) in the transverse direction. The results are used to describe the complicated exchange-mediated diffusion mechanism recently observed in MD simulations [J.E. Black and Zeng-Ju Tian, Phys. Rev. Lett. {\bf 71}, 2445-2448(1993)].

patt-sol↗

arXiv1996

Mobility and diffusivity in a generalized Frenkel-Kontorova model

Molecular dynamics simulations are used to investigate the atomic mobility and diffusivity of a generalized Frenkel-Kontorova model which takes into account anharmonic (exponential) interaction of atoms subjected to a three-dimensional substrate potential periodic in two dimensions and nonconvex (Morse) in the third dimension. The numerical results are explained by a phenomenological theory which treats a system of strongly interacting atoms as a system of weakly interacting quasiparticles (kinks). Model parameters are chosen close to those for {\bf K}-{\bf W}(112) adsorption system.

patt-sol↗