Modified conjugated gradient method for diagonalising large matrices

We present an iterative method to diagonalise large matrices. The basic idea is the same as the conjugated gradient (CG) method, i.e, minimizing the Rayleigh quotient via its gradient and avoiding reintroduce errors to the directions of previous gradients. Each iteration step is to find lowest eigenvector of the matrix in a subspace spanned by the current trial vector and the corresponding gradient of the Rayleigh quotient, as well as some previous trial vectors. The gradient, together with the previous trail vectors, play a similar role of the conjugated gradient of the original CG algorithm. Our numeric tests indicate that this method converges significantly faster than the original CG method. And the computational cost of one iteration step is about the same as the original CG method. It is suitably for first principle calculations.Comment: 6 Pages, 2EPS figures. (To appear in Phys. Rev. E

Acceleration Schemes for Ab-Initio Molecular Dynamics and Electronic Structure Calculations

We study the convergence and the stability of fictitious dynamical methods for electrons. First, we show that a particular damped second-order dynamics has a much faster rate of convergence to the ground-state than first-order steepest descent algorithms while retaining their numerical cost per time step. Our damped dynamics has efficiency comparable to that of conjugate gradient methods in typical electronic minimization problems. Then, we analyse the factors that limit the size of the integration time step in approaches based on plane-wave expansions. The maximum allowed time step is dictated by the highest frequency components of the fictitious electronic dynamics. These can result either from the large wavevector components of the kinetic energy or from the small wavevector components of the Coulomb potential giving rise to the so called {\it charge sloshing} problem. We show how to eliminate large wavevector instabilities by adopting a preconditioning scheme that is implemented here for the first-time in the context of Car-Parrinello ab-initio molecular dynamics simulations of the ionic motion. We also show how to solve the charge-sloshing problem when this is present. We substantiate our theoretical analysis with numerical tests on a number of different silicon and carbon systems having both insulating and metallic character.Comment: RevTex, 9 figures available upon request, to appear in Phys. Rev.

Anomalous enhancement of tetragonality in PbTiO3 induced by negative pressure

Using a first-principles approach based on density-functional theory, we find that a large tetragonal strain can be induced in PbTiO3 by application of a negative hydrostatic pressure. The structural parameters and the dielectric and dynamical properties are found to change abruptly near a crossover pressure, displaying a ``kinky'' behavior suggestive of proximity to a phase transition. Analogous calculations for BaTiO3 show that the same effect is also present there, but at much higher negative pressure. We investigate this unexpected behavior of PbTiO3 and discuss an interpretation involving a phenomenological description in terms of a reduced set of relevant degrees of freedom.Comment: 9 pages, with 9 postscript figures embedded. Uses REVTEX and epsf macros. Also available at http://www.physics.rutgers.edu/~dhv/preprints/st_pbti/index.htm

Ab initio study of the beta$-tin->Imma->sh phase transitions in silicon and germanium

We have investigated the structural sequence of the high-pressure phases of silicon and germanium. We have focussed on the cd->beta-tin->Imma->sh phase transitions. We have used the plane-wave pseudopotential approach to the density-functional theory implemented within the Vienna ab-initio simulation package (VASP). We have determined the equilibrium properties of each structure and the values of the critical parameters including a hysteresis effect at the phase transitions. The order of the phase transitions has been obtained alternatively from the pressure dependence of the enthalpy and of the internal structure parameters. The commonly used tangent construction is shown to be very unreliable. Our calculations identify a first-order phase transition from the cd to the beta-tin and from the Imma to the sh phase, and they indicate the possibility of a second-order phase-transition from the beta-tin to the Imma phase. Finally, we have derived the enthalpy barriers between the phases.Comment: 12 pages, 16 figure

Superhard Phases of Simple Substances and Binary Compounds of the B-C-N-O System: from Diamond to the Latest Results (a Review)

The basic known and hypothetic one- and two-element phases of the B-C-N-O system (both superhard phases having diamond and boron structures and precursors to synthesize them) are described. The attention has been given to the structure, basic mechanical properties, and methods to identify and characterize the materials. For some phases that have been recently described in the literature the synthesis conditions at high pressures and temperatures are indicated.Comment: Review on superhard B-C-N-O phase

Thermodynamic model of hardness: Particular case of boron-rich solids

A number of successful theoretical models of hardness have been developed recently. A thermodynamic model of hardness, which supposes the intrinsic character of correlation between hardness and thermodynamic properties of solids, allows one to predict hardness of known or even hypothetical solids from the data on Gibbs energy of atomization of the elements, which implicitly determine the energy density per chemical bonding. The only structural data needed is the coordination number of the atoms in a lattice. Using this approach, the hardness of known and hypothetical polymorphs of pure boron and a number of boron-rich solids has been calculated. The thermodynamic interpretation of the bonding energy allows one to predict the hardness as a function of thermodynamic parameters. In particular, the excellent agreement between experimental and calculated values has been observed not only for the room- temperature values of the Vickers hardness of stoichiometric compounds, but also for its temperature and concentration dependencies

Theoretical study of a five-coordinated silica polymorph

Theoretical calculations are performed to study transformations in silica as a function of nonhydrostatic stress. Molecular-dynamics calculations reveal a crystalline-to-crystalline transition from alpha-quartz to a phase with five-coordinated silicon (Si-V) at high pressure in the presence of deviatoric stress. The phase, which appears for specific orientations of the stress tensor relative to the crystallographic axes of quartz, is a crystalline polymorph of silica with five-coordinated silicon. The structure possesses P3(2)21 space-group symmetry. First-principles calculations within the local-density approximation, as well as molecular dynamics and energy minimization with interatomic potentials, find this phase to be mechanically and energetically stable with respect to quartz at high pressure. The calculated x-ray diffraction pattern and vibrational properties of the phase are reported. Upon decompression, the Si-V phase reverts to alpha-quartz through an intermediate four-coordinated phase and an unusual isosymmetrical phase transformation. The results suggest the importance of application of nonhydrostatic stress conditions in the design and synthesis of novel materials

Bandstructure approach to near edge structure

We review the current state of the art in EELS fingerprinting by computer simulation, focusing on the bandstructure approach to the problem. Currently calculations are made using a one electron theory, but we describe in principle the way to go beyond this to include final state effects. We include these effects within the one electron framework using the Slater transition state formula and assess the errors involved. Two examples are then given which illustrate the use of the one electron approximation within density functional theory. Our approach is to combine predicted atomic structure with predicted electronic structure to assist in fingerprinting of complex crystal structures