10 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.
Electron localization : band-by-band decomposition, and application to oxides
Using a plane wave pseudopotential approach to density functional theory we
investigate the electron localization length in various oxides. For this
purpose, we first set up a theory of the band-by-band decomposition of this
quantity, more complex than the decomposition of the spontaneous polarization
(a related concept), because of the interband coupling. We show its
interpretation in terms of Wannier functions and clarify the effect of the
pseudopotential approximation. We treat the case of different oxides: BaO,
-PbO, BaTiO and PbTiO. We also investigate the variation of the
localization tensor during the ferroelectric phase transitions of BaTiO as
well as its relationship with the Born effective charges
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
Interatomic force constants from first-principles: the case of alpha-quartz
We describe a method for calculating the interatomic force constants in crystalline insulators, from first principles, with explicit inclusion of the long-ranged anisotropic dipole-dipole interaction. Using this technique, the dynamics of α-quartz, a model for tetrahedrally bonded silica, is investigated: we examine the range of interatomic forces, their anisotropy, their longitudinal and transverse character, and the importance of the dipole-dipole contribution. These force constants provide an extensive database for testing semiempirical interatomic potentials used in silica molecular-dynamics simulations