66 research outputs found
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
Solution of the Schrodinger equation for quasi-one-dimensional materials using helical waves
We formulate and implement a spectral method for solving the Schrodinger
equation, as it applies to quasi-one-dimensional materials and structures. This
allows for computation of the electronic structure of important technological
materials such as nanotubes (of arbitrary chirality), nanowires, nanoribbons,
chiral nanoassemblies, nanosprings and nanocoils, in an accurate, efficient and
systematic manner. Our work is motivated by the observation that one of the
most successful methods for carrying out electronic structure calculations of
bulk/crystalline systems -- the plane-wave method -- is a spectral method based
on eigenfunction expansion. Our scheme avoids computationally onerous
approximations involving periodic supercells often employed in conventional
plane-wave calculations of quasi-one-dimensional materials, and also overcomes
several limitations of other discretization strategies, e.g., those based on
finite differences and atomic orbitals. We describe the setup of fast
transforms to carry out discretization of the governing equations using our
basis set, and the use of matrix-free iterative diagonalization to obtain the
electronic eigenstates. Miscellaneous computational details, including the
choice of eigensolvers, use of a preconditioning scheme, evaluation of
oscillatory radial integrals and the imposition of a kinetic energy cutoff are
discussed. We have implemented these strategies into a computational package
called HelicES (Helical Electronic Structure). We demonstrate the utility of
our method in carrying out systematic electronic structure calculations of
various quasi-one-dimensional materials through numerous examples involving
nanotubes, nanoribbons and nanowires. We also explore the convergence, accuracy
and efficiency of our method. We anticipate that our method will find numerous
applications in computational nanomechanics and materials science
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Symmetry-adapted real-space density functional theory for cylindrical geometries: Application to large group-IV 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 plane-wave 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, other than the armchair and zigzag type III carbon variants, for which we find a vanishingly small bandgap, indicative of metallic behavior. 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, while considering radii of curvature up to
5
nm
. 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. Overall, the current work opens an avenue for the efficient ab initio study of 1D nanostructures with large radii as well as 1D/2D nanostructures under uniform bending
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
Bicrystallography-informed Frenkel-Kontorova model for interlayer dislocations in strained 2D heterostructures
In recent years, van der Waals (vdW) heterostructures and homostructures,
which consist of stacks of two-dimensional (2D) materials, have risen to
prominence due to their association with exotic quantum phenomena. Atomistic
scale relaxation effects play an extremely important role in the electronic
scale quantum physics of these systems. We investigate such structural
relaxation effects in this work using atomistic and mesoscale models, within
the context of twisted bilayer graphene -- a well-known heterostructure system
that features moire patterns arising from the lattices of the two graphene
layers. For small twist angles, atomic relaxation effects in this system are
associated with the natural emergence of interface dislocations or strain
solitons, which result from the cyclic nature of the generalized stacking fault
energy (GSFE), that measures the interface energy based on the relative
movement of the two layers. In this work, we first demonstrate using atomistic
simulations that atomic reconstruction in bilayer graphene under a large twist
also results from interface dislocations, although the Burgers vectors of such
dislocations are considerably smaller than those observed in small-twist
systems. To reveal the translational invariance of the heterointerface
responsible for the formation of such dislocations, we derive the translational
symmetry of the GSFE of a 2D heterostructure using the notions of coincident
site lattices (CSLs) and displacement shift complete lattices (DSCLs). The
workhorse for this exercise is a recently developed Smith normal form
bicrystallography framework. Next, we construct a bicrystallography-informed
and frame-invariant Frenkel-Kontorova model, which can predict the formation of
strain solitons in arbitrary 2D heterostructures, and apply it to study a
heterostrained, large-twist bilayer graphene system
Electronic Structure Prediction of Multi-million Atom Systems Through Uncertainty Quantification Enabled Transfer Learning
The ground state electron density - obtainable using Kohn-Sham Density
Functional Theory (KS-DFT) simulations - contains a wealth of material
information, making its prediction via machine learning (ML) models attractive.
However, the computational expense of KS-DFT scales cubically with system size
which tends to stymie training data generation, making it difficult to develop
quantifiably accurate ML models that are applicable across many scales and
system configurations. Here, we address these fundamental challenges using
Bayesian neural networks and employ transfer learning to leverage the
multi-scale nature of the training data. Our ML models employ descriptors
involving simple scalar products, comprehensively sample system configurations
through thermalization, and quantify uncertainty in electron density
predictions. We show that our models incur significantly lower data generation
costs while allowing confident - and when verifiable, accurate - predictions
for a wide variety of bulk systems well beyond training, including systems with
defects, different alloy compositions, and at unprecedented, multi-million-atom
scales
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