73 research outputs found
Local exact exchange potentials within the all-electron FLAPW method and a comparison with pseudopotential results
We present a general numerical approach to construct local Kohn-Sham
potentials from orbital-dependent functionals within the all-electron
full-potential linearized augmented-plane-wave (FLAPW) method, in which core
and valence electrons are treated on an equal footing. As a practical example,
we present a treatment of the orbital-dependent exact-exchange (EXX) energy and
potential. A formulation in terms of a mixed product basis, which is
constructed from products of LAPW basis functions, enables a solution of the
optimized-effective-potential (OEP) equation with standard numerical algebraic
tools and without shape approximations for the resulting potential. We find
that the mixed product and LAPW basis sets must be properly balanced to obtain
smooth and converged EXX potentials without spurious oscillations. The
construction and convergence of the exchange potential is analyzed in detail
for diamond. Our all-electron results for C, Si, SiC, Ge, GaAs semiconductors
as well as Ne and Ar noble-gas solids are in very favorable agreement with
plane-wave pseudopotential calculations. This confirms the adequacy of the
pseudopotential approximation in the context of the EXX-OEP formalism and
clarifies a previous contradiction between FLAPW and pseudopotential results.Comment: 12 pages, 7 figures, 5 table
Precise response functions in all-electron methods: Application to the optimized-effective-potential approach
The optimized-effective-potential (OEP) method is a special technique to
construct local Kohn-Sham potentials from general orbital-dependent energy
functionals. In a recent publication [M. Betzinger, C. Friedrich, S. Bl\"ugel,
A. G\"orling, Phys. Rev. B 83, 045105 (2011)] we showed that uneconomically
large basis sets were required to obtain a smooth local potential without
spurious oscillations within the full-potential linearized augmented-plane-wave
method (FLAPW). This could be attributed to the slow convergence behavior of
the density response function. In this paper, we derive an incomplete-basis-set
correction for the response, which consists of two terms: (1) a correction that
is formally similar to the Pulay correction in atomic-force calculations and
(2) a numerically more important basis response term originating from the
potential dependence of the basis functions. The basis response term is
constructed from the solutions of radial Sternheimer equations in the
muffin-tin spheres. With these corrections the local potential converges at
much smaller basis sets, at much fewer states, and its construction becomes
numerically very stable. We analyze the improvements for rock-salt ScN and
report results for BN, AlN, and GaN, as well as the perovskites CaTiO3, SrTiO3,
and BaTiO3. The incomplete-basis-set correction can be applied to other
electronic-structure methods with potential-dependent basis sets and opens the
perspective to investigate a broad spectrum of problems in theoretical
solid-state physics that involve response functions.Comment: 17 pages, 7 figures, 3 table
A simple, efficient, and general treatment of the singularities in Hartree-Fock and exact-exchange Kohn-Sham methods for solids
We present a general scheme for treating the integrable singular terms within
exact exchange (EXX) Kohn-Sham or Hartree-Fock (HF) methods for periodic
solids. We show that the singularity corrections for treating these
divergencies depend only on the total number and the positions of k-points and
on the lattice vectors, in particular the unit cell volume, but not on the
particular positions of atoms within the unit cell. The method proposed here to
treat the singularities constitutes a stable, simple to implement, and general
scheme that can be applied to systems with arbitrary lattice parameters within
either the EXX Kohn-Sham or the HF formalism. We apply the singularity
correction to a typical symmetric structure, diamond, and to a more general
structure, trans-polyacetylene. We consider the effect of the singularity
corrections on volume optimisations and k-point convergence. While the
singularity corrections clearly depends on the total number of k-points, it
exhibits a remarkably small dependence upon the choice of the specific
arrangement of the k-points.Comment: 24 pages, 5 Figures, re-submitted to Phys. Rev. B after revision
Competition for Graphene: Graphynes with Direction-Dependent Dirac Cones
The existence of Dirac cones in the band structure of two-dimensional materials accompanied by unprecedented electronic properties is considered to be a unique feature of graphene related to its hexagonal symmetry. Here, we present other two-dimensional carbon materials, graphynes, that also possess Dirac cones according to first-principles electronic structure calculations. One of these materials, 6,6,12-graphyne, does not have hexagonal symmetry and features two self-doped nonequivalent distorted Dirac cones suggesting electronic properties even more amazing than that of graphene
Exact-Exchange Kohn-Sham formalism applied to one-dimensional periodic electronic systems
The Exact-Exchange (EXX) Kohn-Sham formalism, which treats exchange
interactions exactly within density-functional theory, is applied to
one-dimensional periodic systems. The underlying implementation does not rely
on specific symmetries of the considered system and can be applied to any kind
of periodic structure in one to three dimensions. As a test system,
-polyacetylene, both in form of an isolated chain and in the bulk
geometry has been investigated. Within the EXX scheme, bandstructures and
independent particle response functions are calculated and compared to
experimental data as well as to data calculated by several other methods.
Compared to results from the local-density approximation, the EXX method leads
to an increased value for the band gap, in line with similar observations for
three-dimensional semiconductors. An inclusion of correlation potentials within
the local density approximation or generalized gradient approximations leads to
only negligible effects in the bandstructure. The EXX band gaps are in good
agreement with experimental data for bulk -polyacetylene. Packing
effects of the chains in bulk -polyacetylene are found to lower the band
gap by about 0.5 eV
The contact of graphene with Ni(111) surface: description by modern dispersive forces approaches
Here we present a Density Functional Theory (DFT) study on the suitability of modern corrections for the inclusion of dispersion related terms (DFT-D) in treating the interaction of graphene and metal surfaces, exemplified by the graphene/Ni(111) system. The Perdew-Burke-Ernzerhof (PBE) exchange-correlation functional is used as basis, on top of which we tested the family of Grimme corrections (D2 and D3, including Becke-Jonson damping and Andersson approach) as well as different flavors of the approach by Tkatchenko and Scheffler (TS). Two experimentally observed chemisorbed states, top-fcc and bridge-top conformations, were examined, as well as one physisorbed situation, the hcp-fcc state. Geometric, energetic, and electronic properties were compared to sets of experimental data for our model system of graphene/Ni(111), but also for available data of bulk Ni, graphite, and free-standing graphene. Results show that two of the most recent approximations, the fully ab initio TS-MBD, and the semi-empirical Grimme D3 correction are best suited to describe graphene↔metal contacts, yet, comparing to earlier studies, the Rev-vdW-DF2 functional is also a good option, whereas optB86-vdW and optB88b-vdW functionals are fairly close to experimental values to be harmless used. The present results highlight how different approaches for the approximate treatment of dispersive forces yield different results, and so fine-tuning and testing of the envisioned approach for every specific system is advisable. The present survey clears the path for future accurate and affordable theoretical studies of nanotechnologic devices based on graphene-metal contacts
Exact Kohn-Sham exchange kernel for insulators and its long-wavelength behavior
We present an exact expression for the frequency-dependent Kohn-Sham
exact-exchange (EXX) kernel for periodic insulators, which can be employed for
the calculation of electronic response properties within time-dependent (TD)
density-functional theory. It is shown that the EXX kernel has a
long-wavelength divergence behavior of the exact full exchange-correlation
kernel and thus rectifies one serious shortcoming of the adiabatic
local-density approximation and generalized-gradient approximations kernels. A
comparison between the TDEXX and the GW-approximation-Bethe-Salpeter-equation
approach is also made.Comment: two column format 6 pages + 1 figure, to be publisehd in Physical
Review
Precise determination of graphene functionalization by in situ Raman spectroscopy
The verification of a successful covalent functionalization of graphene and
related carbon allotropes can easily be carried out by Raman spectroscopy.
Nevertheless, the unequivocal assignment and resolution of individual lattice
modes associated with the covalent binding of addends was elusive up to now.
Here we present an in situ Raman study of a controlled functionalization of
potassium intercalated graphite, revealing several new bands appearing in the
D-region of the spectrum. The evolution of these bands with increasing degree
of functionalization from low to moderate levels provides a basis for the
deconvolution of the different components towards quantifying the extent of
functionalization. By complementary DFT calculations we were able to identify
the vibrational changes in the close proximity of the addend bearing lattice
carbon atoms and to assign them to specific Raman modes. The experimental in
situ observation of the developing functionalization along with the
reoxidation of the intercalated graphite represents an important step towards
an improved understanding of the chemistry of graphene
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