32 research outputs found
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