10 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
Periodic Pulay method for robust and efficient convergence acceleration of self-consistent field iterations
Pulay's Direct Inversion in the Iterative Subspace (DIIS) method is one of
the most widely used mixing schemes for accelerating the self-consistent
solution of electronic structure problems. In this work, we propose a simple
generalization of DIIS in which Pulay extrapolation is performed at periodic
intervals rather than on every self-consistent field iteration, and linear
mixing is performed on all other iterations. We demonstrate through numerical
tests on a wide variety of materials systems in the framework of density
functional theory that the proposed generalization of Pulay's method
significantly improves its robustness and efficiency.Comment: Version 2 (with minor edits from version 1
Parallel eigensolvers in plane-wave Density Functional Theory
We consider the problem of parallelizing electronic structure computations in
plane-wave Density Functional Theory. Because of the limited scalability of
Fourier transforms, parallelism has to be found at the eigensolver level. We
show how a recently proposed algorithm based on Chebyshev polynomials can scale
into the tens of thousands of processors, outperforming block conjugate
gradient algorithms for large computations
The Effect of Structural Phase Changes on Fermi Level Shifts and Optoelectronic Properties of Lead-Free CsSnI3 Perovskites
The work carried out first-principles calculations within the framework of
density functional theory to study the structural stability of the CsSnI3
compound and the influence of phase transitions on their electronic and optical
properties. Using the GGA and SCAN functionals, the relaxed structures of the
CsSnI3 phases were obtained and their geometric characteristics were assessed.
Using the Phonopy code based on VASP, calculations of phonon and thermodynamic
properties were performed, and the temperatures of phase transitions of CsSnI3
were determined. Electronic properties and Fermi level shifts as a result of
phase transformations of CsSnI3 were assessed using the HSE06 functional and
machine learning prediction. The values of the complex dielectric constant and
the refractive index of all phases of the CsSnI3 were determined.Comment: 16 pages, 11 figures, 4 table
Two-level Chebyshev filter based complementary subspace method: pushing the envelope of large-scale electronic structure calculations
We describe a novel iterative strategy for Kohn-Sham density functional
theory calculations aimed at large systems (> 1000 electrons), applicable to
metals and insulators alike. In lieu of explicit diagonalization of the
Kohn-Sham Hamiltonian on every self-consistent field (SCF) iteration, we employ
a two-level Chebyshev polynomial filter based complementary subspace strategy
to: 1) compute a set of vectors that span the occupied subspace of the
Hamiltonian; 2) reduce subspace diagonalization to just partially occupied
states; and 3) obtain those states in an efficient, scalable manner via an
inner Chebyshev-filter iteration. By reducing the necessary computation to just
partially occupied states, and obtaining these through an inner Chebyshev
iteration, our approach reduces the cost of large metallic calculations
significantly, while eliminating subspace diagonalization for insulating
systems altogether. We describe the implementation of the method within the
framework of the Discontinuous Galerkin (DG) electronic structure method and
show that this results in a computational scheme that can effectively tackle
bulk and nano systems containing tens of thousands of electrons, with chemical
accuracy, within a few minutes or less of wall clock time per SCF iteration on
large-scale computing platforms. We anticipate that our method will be
instrumental in pushing the envelope of large-scale ab initio molecular
dynamics. As a demonstration of this, we simulate a bulk silicon system
containing 8,000 atoms at finite temperature, and obtain an average SCF step
wall time of 51 seconds on 34,560 processors; thus allowing us to carry out 1.0
ps of ab initio molecular dynamics in approximately 28 hours (of wall time).Comment: Resubmitted version (version 2
Cyclic Density Functional Theory : A route to the first principles simulation of bending in nanostructures
We formulate and implement Cyclic Density Functional Theory (Cyclic DFT) -- a
self-consistent first principles simulation method for nanostructures with
cyclic symmetries. Using arguments based on Group Representation Theory, we
rigorously demonstrate that the Kohn-Sham eigenvalue problem for such systems
can be reduced to a fundamental domain (or cyclic unit cell) augmented with
cyclic-Bloch boundary conditions. Analogously, the equations of electrostatics
appearing in Kohn-Sham theory can be reduced to the fundamental domain
augmented with cyclic boundary conditions. By making use of this symmetry cell
reduction, we show that the electronic ground-state energy and the
Hellmann-Feynman forces on the atoms can be calculated using quantities defined
over the fundamental domain. We develop a symmetry-adapted finite-difference
discretization scheme to obtain a fully functional numerical realization of the
proposed approach. We verify that our formulation and implementation of Cyclic
DFT is both accurate and efficient through selected examples.
The connection of cyclic symmetries with uniform bending deformations
provides an elegant route to the ab-initio study of bending in nanostructures
using Cyclic DFT. As a demonstration of this capability, we simulate the
uniform bending of a silicene nanoribbon and obtain its energy-curvature
relationship from first principles. A self-consistent ab-initio simulation of
this nature is unprecedented and well outside the scope of any other systematic
first principles method in existence. Our simulations reveal that the bending
stiffness of the silicene nanoribbon is intermediate between that of graphene
and molybdenum disulphide. We describe several future avenues and applications
of Cyclic DFT, including its extension to the study of non-uniform bending
deformations and its possible use in the study of the nanoscale flexoelectric
effect.Comment: Version 3 of the manuscript, Accepted for publication in Journal of
the Mechanics and Physics of Solids,
http://www.sciencedirect.com/science/article/pii/S002250961630368
Density functional theory method for twisted geometries with application to torsional deformations in group-IV nanotubes
We present a real-space formulation and implementation of Kohn-Sham Density
Functional Theory suited to twisted geometries, and apply it to the study of
torsional deformations of X (X = C, Si, Ge, Sn) nanotubes. Our formulation is
based on higher order finite difference discretization in helical coordinates,
uses ab intio pseudopotentials, and naturally incorporates rotational (cyclic)
and screw operation (i.e., helical) symmetries. We discuss several aspects of
the computational method, including the form of the governing equations,
details of the numerical implementation, as well as its convergence, accuracy
and efficiency properties.
The technique presented here is particularly well suited to the first
principles simulation of quasi-one-dimensional structures and their
deformations, and many systems of interest can be investigated using small
simulation cells containing just a few atoms. We apply the method to
systematically study the properties of single-wall zigzag and armchair group-IV
nanotubes, as they undergo twisting. For the range of deformations considered,
the mechanical behavior of the tubes is found to be largely consistent with
isotropic linear elasticity, with the torsional stiffness varying as the cube
of the nanotube radius. Furthermore, for a given tube radius, this quantity is
seen to be highest for carbon nanotubes and the lowest for those of tin, while
nanotubes of silicon and germanium have intermediate values close to each
other. We also describe different aspects of the variation in electronic
properties of the nanotubes as they are twisted. In particular, we find that
akin to the well known behavior of armchair carbon nanotubes, armchair
nanotubes of silicon, germanium and tin also exhibit bandgaps that vary
periodically with imposed rate of twist, and that the periodicity of the
variation scales in an inverse quadratic manner with the tube radius
Ab initio framework for systems with helical symmetry: theory, numerical implementation and applications to torsional deformations in nanostructures
We formulate and implement Helical DFT -- a self-consistent first principles
simulation method for nanostructures with helical symmetries. Such materials
are well represented in all of nanotechnology, chemistry and biology, and are
expected to be associated with unprecedented material properties. We rigorously
demonstrate the existence and completeness of special solutions to the single
electron problem for helical nanostructures, called helical Bloch waves. We
describe how the Kohn-Sham Density Functional Theory equations for a helical
nanostructure can be reduced to a fundamental domain with the aid of these
solutions. A key component in our mathematical treatment is the definition and
use of a helical Bloch-Floquet transform to perform a block-diagonalization of
the Hamiltonian in the sense of direct integrals. We develop a symmetry-adapted
finite-difference strategy in helical coordinates to discretize the governing
equations, and obtain a working realization of the proposed approach. We verify
the accuracy and convergence properties of our numerical implementation through
examples. Finally, we employ Helical DFT to study the properties of zigzag and
chiral single wall black phosphorus (i.e., phosphorene) nanotubes. We use our
simulations to evaluate the torsional stiffness of a zigzag nanotube ab initio.
Additionally, we observe an insulator-to-metal-like transition in the
electronic properties of this nanotube as it is subjected to twisting. We also
find that a similar transition can be effected in chiral phosphorene nanotubes
by means of axial strains. Notably, self-consistent ab initio simulations of
this nature are unprecedented and well outside the scope of any other
systematic first principles method in existence. We end with a discussion on
various future avenues and applications