13,889 research outputs found
Linear-scaling DFT+U with full local orbital optimization
We present an approach to the DFT+U method (Density Functional Theory +
Hubbard model) within which the computational effort for calculation of ground
state energies and forces scales linearly with system size. We employ a
formulation of the Hubbard model using nonorthogonal projector functions to
define the localized subspaces, and apply it to a local-orbital DFT method
including in situ orbital optimization. The resulting approach thus combines
linear-scaling and systematic variational convergence. We demonstrate the
scaling of the method by applying it to nickel oxide nano-clusters with sizes
exceeding 7,000 atoms.Comment: 10 pages, 4 figures. This version (v3) matches that accepted for
Physical Review B on 30th January 201
ELSI: A Unified Software Interface for Kohn-Sham Electronic Structure Solvers
Solving the electronic structure from a generalized or standard eigenproblem
is often the bottleneck in large scale calculations based on Kohn-Sham
density-functional theory. This problem must be addressed by essentially all
current electronic structure codes, based on similar matrix expressions, and by
high-performance computation. We here present a unified software interface,
ELSI, to access different strategies that address the Kohn-Sham eigenvalue
problem. Currently supported algorithms include the dense generalized
eigensolver library ELPA, the orbital minimization method implemented in
libOMM, and the pole expansion and selected inversion (PEXSI) approach with
lower computational complexity for semilocal density functionals. The ELSI
interface aims to simplify the implementation and optimal use of the different
strategies, by offering (a) a unified software framework designed for the
electronic structure solvers in Kohn-Sham density-functional theory; (b)
reasonable default parameters for a chosen solver; (c) automatic conversion
between input and internal working matrix formats, and in the future (d)
recommendation of the optimal solver depending on the specific problem.
Comparative benchmarks are shown for system sizes up to 11,520 atoms (172,800
basis functions) on distributed memory supercomputing architectures.Comment: 55 pages, 14 figures, 2 table
Parallel, linear-scaling building-block and embedding method based on localized orbitals and orbital-specific basis sets
We present a new linear scaling method for the energy minimization step of
semiempirical and first-principles Hartree-Fock and Kohn-Sham calculations. It
is based on the self-consistent calculation of the optimum localized orbitals
of any localization method of choice and on the use of orbital-specific basis
sets. The full set of localized orbitals of a large molecule is seen as an
orbital mosaic where each tessera is made of only a few of them. The orbital
tesserae are computed out of a set of embedded cluster pseudoeigenvalue coupled
equations which are solved in a building-block self-consistent fashion. In each
iteration, the embedded cluster equations are solved independently of each
other and, as a result, the method is parallel at a high level of the
calculation. In addition to full system calculations, the method enables to
perform simpler, much less demanding embedded cluster calculations, where only
a fraction of the localized molecular orbitals are variational while the rest
are frozen, taking advantage of the transferability of the localized orbitals
of a given localization method between similar molecules. Monitoring single
point energy calculations of large poly(ethylene oxide) molecules and three
dimensional carbon monoxide clusters using an extended Huckel Hamiltonian are
presented.Comment: latex, 15 pages, 10 figures, accepted for publication in J.Chem.Phy
Electronic structure calculations and molecular dynamics simulations with linear system-size scaling
We present a method for total energy minimizations and molecular dynamics
simulations based either on tight-binding or on Kohn-Sham hamiltonians. The
method leads to an algorithm whose computational cost scales linearly with the
system size. The key features of our approach are
(i) an orbital formulation with single particle wavefunctions constrained to
be localized in given regions of space, and (ii) an energy functional which
does not require either explicit orthogonalization of the electronic orbitals,
or inversion of an overlap matrix.
The foundations and accuracy of the approach and the performances of the
algorithm are discussed, and illustrated with several numerical examples
including Kohn-Sham hamiltonians. In particular we present calculations with
tight-binding hamiltonians for diamond, graphite, a carbon linear chain and
liquid carbon at low pressure. Even for a complex case such as liquid carbon --
a disordered metallic system with differently coordinated atoms -- the
agreement between standard diagonalization schemes and our approach is very
good. Our results establish the accuracy and reliability of the method for a
wide class of systems and show that tight binding molecular dynamics
simulations with a few thousand atoms are feasible on small workstations
Low complexity method for large-scale self-consistent ab initio electronic-structure calculations without localization
A novel low complexity method to perform self-consistent electronic-structure
calculations using the Kohn-Sham formalism of density functional theory is
presented. Localization constraints are neither imposed nor required thereby
allowing direct comparison with conventional cubically scaling algorithms. The
method has, to date, the lowest complexity of any algorithm for an exact
calculation. A simple one-dimensional model system is used to thoroughly test
the numerical stability of the algorithm and results for a real physical system
are also given
SCDM-k: Localized orbitals for solids via selected columns of the density matrix
The recently developed selected columns of the density matrix (SCDM) method
[J. Chem. Theory Comput. 11, 1463, 2015] is a simple, robust, efficient and
highly parallelizable method for constructing localized orbitals from a set of
delocalized Kohn-Sham orbitals for insulators and semiconductors with
point sampling of the Brillouin zone. In this work we generalize the SCDM
method to Kohn-Sham density functional theory calculations with k-point
sampling of the Brillouin zone, which is needed for more general electronic
structure calculations for solids. We demonstrate that our new method, called
SCDM-k, is by construction gauge independent and is a natural way to describe
localized orbitals. SCDM-k computes localized orbitals without the use of an
optimization procedure, and thus does not suffer from the possibility of being
trapped in a local minimum. Furthermore, the computational complexity of using
SCDM-k to construct orthogonal and localized orbitals scales as O(N log N )
where N is the total number of k-points in the Brillouin zone. SCDM-k is
therefore efficient even when a large number of k-points are used for Brillouin
zone sampling. We demonstrate the numerical performance of SCDM-k using systems
with model potentials in two and three dimensions.Comment: 25 pages, 7 figures; added more background sections, clarified
presentation of the algorithm, revised the presentation of previous work,
added a more high level overview of the new algorithm, and mildly clarified
the presentation of the results (there were no changes to the numerical
results themselves
Generalized Wannier functions: a comparison of molecular electric dipole polarizabilities
Localized Wannier functions provide an efficient and intuitive means by which
to compute dielectric properties from first principles. They are most commonly
constructed in a post-processing step, following total-energy minimization.
Nonorthogonal generalized Wannier functions (NGWFs) [Skylaris et al., Phys.
Rev. B 66, 035119 11 (2002); Skylaris et al., J. Chem. Phys. 122, 084119
(2005)] may also be optimized in situ, in the process of solving for the
ground-state density. We explore the relationship between NGWFs and
orthonormal, maximally localized Wannier functions (MLWFs) [Marzari and
Vanderbilt, Phys. Rev. B 56, 12847 (1997); Souza, Marzari, and Vanderbilt,
ibid. 65, 035109 (2001)], demonstrating that NGWFs may be used to compute
electric dipole polarizabilities efficiently, with no necessity for
post-processing optimization, and with an accuracy comparable to MLWFs.Comment: 5 pages, 1 figure. This version matches that accepted for Physical
Review B on 4th May 201
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