2,730 research outputs found
A spectral scheme for Kohn-Sham density functional theory of clusters
Starting from the observation that one of the most successful methods for
solving the Kohn-Sham equations for periodic systems -- the plane-wave method
-- is a spectral method based on eigenfunction expansion, we formulate a
spectral method designed towards solving the Kohn-Sham equations for clusters.
This allows for efficient calculation of the electronic structure of clusters
(and molecules) with high accuracy and systematic convergence properties
without the need for any artificial periodicity. The basis functions in this
method form a complete orthonormal set and are expressible in terms of
spherical harmonics and spherical Bessel functions. Computation of the occupied
eigenstates of the discretized Kohn-Sham Hamiltonian is carried out using a
combination of preconditioned block eigensolvers and Chebyshev polynomial
filter accelerated subspace iterations. Several algorithmic and computational
aspects of the method, including computation of the electrostatics terms and
parallelization are discussed. We have implemented these methods and algorithms
into an efficient and reliable package called ClusterES (Cluster Electronic
Structure). A variety of benchmark calculations employing local and non-local
pseudopotentials are carried out using our package and the results are compared
to the literature. Convergence properties of the basis set are discussed
through numerical examples. Computations involving large systems that contain
thousands of electrons are demonstrated to highlight the efficacy of our
methodology. The use of our method to study clusters with arbitrary point group
symmetries is briefly discussed.Comment: Manuscript submitted (with revisions) to Journal of Computational
Physic
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
Three real-space discretization techniques in electronic structure calculations
A characteristic feature of the state-of-the-art of real-space methods in
electronic structure calculations is the diversity of the techniques used in
the discretization of the relevant partial differential equations. In this
context, the main approaches include finite-difference methods, various types
of finite-elements and wavelets. This paper reports on the results of several
code development projects that approach problems related to the electronic
structure using these three different discretization methods. We review the
ideas behind these methods, give examples of their applications, and discuss
their similarities and differences.Comment: 39 pages, 10 figures, accepted to a special issue of "physica status
solidi (b) - basic solid state physics" devoted to the CECAM workshop "State
of the art developments and perspectives of real-space electronic structure
techniques in condensed matter and molecular physics". v2: Minor stylistic
and typographical changes, partly inspired by referee comment
Electronic damping of molecular motion at metal surfaces
A method for the calculation of the damping rate due to electron-hole pair
excitation for atomic and molecular motion at metal surfaces is presented. The
theoretical basis is provided by Time Dependent Density Functional Theory
(TDDFT) in the quasi-static limit and calculations are performed within a
standard plane-wave, pseudopotential framework. The artificial periodicity
introduced by using a super-cell geometry is removed to derive results for the
motion of an isolated atom or molecule, rather than for the coherent motion of
an ordered over-layer. The algorithm is implemented in parallel, distributed
across both and space, and in a form compatible with the
CASTEP code. Test results for the damping of the motion of hydrogen atoms above
the Cu(111) surface are presented.Comment: 10 pages, 3 figure
Symmetry-adapted real-space density functional theory for cylindrical geometries: application to large X (X=C, Si, Ge, Sn) nanotubes
We present a symmetry-adapted real-space formulation of Kohn-Sham density
functional theory for cylindrical geometries and apply it to the study of large
X (X=C, Si, Ge, Sn) nanotubes. Specifically, starting from the Kohn-Sham
equations posed on all of space, we reduce the problem to the fundamental
domain by incorporating cyclic and periodic symmetries present in the angular
and axial directions of the cylinder, respectively. We develop a high-order
finite-difference parallel implementation of this formulation, and verify its
accuracy against established planewave and real-space codes. Using this
implementation, we study the band structure and bending properties of X
nanotubes and Xene sheets, respectively. Specifically, we first show that
zigzag and armchair X nanotubes with radii in the range 1 to 5 nm are
semiconducting. In particular, we find an inverse linear dependence of the
bandgap with respect to the radius for all nanotubes, other than the armchair
and zigzag type III carbon variants, for which we find an inverse quadratic
dependence. Next, we exploit the connection between cyclic symmetry and uniform
bending deformations to calculate the bending moduli of Xene sheets in both
zigzag and armchair directions. We find Kirchhoff-Love type bending behavior
for all sheets, with graphene and stanene possessing the largest and smallest
moduli, respectively. In addition, other than graphene, the sheets demonstrate
significant anisotropy, with larger bending moduli along the armchair
direction. Finally, we demonstrate that the proposed approach has very good
parallel scaling and is highly efficient, enabling ab initio simulations of
unprecedented size for systems with a high degree of cyclic symmetry. In
particular, we show that even micron-sized nanotubes can be simulated with
modest computational effort.Comment: 24 pages, 8 figures, 4 table
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