10 research outputs found
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.Comment: REVTeX file, 27 pages with 4 uuencoded postscript figure
A novel multigrid method for electronic structure calculations
A general real-space multigrid algorithm for the self-consistent solution of
the Kohn-Sham equations appearing in the state-of-the-art electronic-structure
calculations is described. The most important part of the method is the
multigrid solver for the Schroedinger equation. Our choice is the Rayleigh
quotient multigrid method (RQMG), which applies directly to the minimization of
the Rayleigh quotient on the finest level. Very coarse correction grids can be
used, because there is no need to be able to represent the states on the coarse
levels. The RQMG method is generalized for the simultaneous solution of all the
states of the system using a penalty functional to keep the states orthogonal.
The performance of the scheme is demonstrated by applying it in a few molecular
and solid-state systems described by non-local norm-conserving
pseudopotentials.Comment: 9 pages, 3 figure
A Real-Space Full Multigrid study of the fragmentation of Li11+ clusters
We have studied the fragmentation of Li11+ clusters into the two
experimentally observed products (Li9+,Li2) and (Li10+,Li) The ground state
structures for the two fragmentation channels are found by Molecular Dynamics
Simulated Annealing in the framework of Local Density Functional theory.
Energetics considerations suggest that the fragmentation process is dominated
by non-equilibrium processes. We use a real-space approach to solve the
Kohn-Sham problem, where the Laplacian operator is discretized according to the
Mehrstellen scheme, and take advantage of a Full MultiGrid (FMG) strategy to
accelerate convergence. When applied to isolated clusters we find our FMG
method to be more efficient than state-of-the-art plane wave calculations.Comment: 9 pages + 6 Figures (in gzipped tar file
Real-Space Mesh Techniques in Density Functional Theory
This review discusses progress in efficient solvers which have as their
foundation a representation in real space, either through finite-difference or
finite-element formulations. The relationship of real-space approaches to
linear-scaling electrostatics and electronic structure methods is first
discussed. Then the basic aspects of real-space representations are presented.
Multigrid techniques for solving the discretized problems are covered; these
numerical schemes allow for highly efficient solution of the grid-based
equations. Applications to problems in electrostatics are discussed, in
particular numerical solutions of Poisson and Poisson-Boltzmann equations.
Next, methods for solving self-consistent eigenvalue problems in real space are
presented; these techniques have been extensively applied to solutions of the
Hartree-Fock and Kohn-Sham equations of electronic structure, and to eigenvalue
problems arising in semiconductor and polymer physics. Finally, real-space
methods have found recent application in computations of optical response and
excited states in time-dependent density functional theory, and these
computational developments are summarized. Multiscale solvers are competitive
with the most efficient available plane-wave techniques in terms of the number
of self-consistency steps required to reach the ground state, and they require
less work in each self-consistency update on a uniform grid. Besides excellent
efficiencies, the decided advantages of the real-space multiscale approach are
1) the near-locality of each function update, 2) the ability to handle global
eigenfunction constraints and potential updates on coarse levels, and 3) the
ability to incorporate adaptive local mesh refinements without loss of optimal
multigrid efficiencies.Comment: 70 pages, 11 figures. To be published in Reviews of Modern Physic