50 research outputs found
Exact exchange-correlation potential of a ionic Hubbard model with a free surface
We use Lanczos exact diagonalization to compute the exact
exchange-correlation (xc) potential of a Hubbard chain with large binding
energy ("the bulk") followed by a chain with zero binding energy ("the
vacuum"). Several results of density functional theory in the continuum
(sometimes controversial) are verified in the lattice. In particular we show
explicitly that the fundamental gap is given by the gap in the Kohn-Sham
spectrum plus a contribution due to the jump of the xc-potential when a
particle is added. The presence of a staggered potential and a nearest-neighbor
interaction V allows to simulate a ionic solid. We show that in the ionic
regime in the small hopping amplitude limit the xc-contribution to the gap
equals V, while in the Mott regime it is determined by the Hubbard U
interaction. In addition we show that correlations generates a new potential
barrier at the surface
Random-phase approximation and its applications in computational chemistry and materials science
The random-phase approximation (RPA) as an approach for computing the
electronic correlation energy is reviewed. After a brief account of its basic
concept and historical development, the paper is devoted to the theoretical
formulations of RPA, and its applications to realistic systems. With several
illustrating applications, we discuss the implications of RPA for computational
chemistry and materials science. The computational cost of RPA is also
addressed which is critical for its widespread use in future applications. In
addition, current correction schemes going beyond RPA and directions of further
development will be discussed.Comment: 25 pages, 11 figures, published online in J. Mater. Sci. (2012
On-surface synthesis of graphene nanoribbons with zigzag edge topology
Graphene-based nanostructures exhibit a vast range of exciting electronic
properties that are absent in extended graphene. For example, quantum
confinement in carbon nanotubes and armchair graphene nanoribbons (AGNRs) leads
to the opening of substantial electronic band gaps that are directly linked to
their structural boundary conditions. Even more intriguing are nanostructures
with zigzag edges, which are expected to host spin-polarized electronic edge
states and can thus serve as key elements for graphene-based spintronics. The
most prominent example is zigzag graphene nanoribbons (ZGNRs) for which the
edge states are predicted to couple ferromagnetically along the edge and
antiferromagnetically between them. So far, a direct observation of the
spin-polarized edge states for specifically designed and controlled zigzag edge
topologies has not been achieved. This is mainly due to the limited precision
of current top-down approaches, which results in poorly defined edge
structures. Bottom-up fabrication approaches, on the other hand, were so far
only successfully applied to the growth of AGNRs and related structures. Here,
we describe the successful bottom-up synthesis of ZGNRs, which are fabricated
by the surface-assisted colligation and cyclodehydrogenation of specifically
designed precursor monomers including carbon groups that yield atomically
precise zigzag edges. Using scanning tunnelling spectroscopy we prove the
existence of edge-localized states with large energy splittings. We expect that
the availability of ZGNRs will finally allow the characterization of their
predicted spin-related properties such as spin confinement and filtering, and
ultimately add the spin degree of freedom to graphene-based circuitry.Comment: 15 pages, 4 figure
Long-wavelength behavior of the exchange-correlation kernel in the Kohn-Sham theory of periodic systems
The polarization dependence of the exchange-correlation (re) energy functional of periodic insulators within Kohn-Sham (KS) density-functional theory requires a O(1/q(2)) divergence in the re kernel for small vectors q. This behavior, exemplified for a one-dimensional model semiconductor, is also observed when an insulator happens to be described asa KS metal, or vice versa. Although it can occur in the exchange-only kernel, it is not found in the usual local, semilocal, or even nonlocal approximations to KS theory. We also show that the test-charge and. electronic definitions of the macroscopic dielectric constant differ from one another in exact KS theory, but are equivalent in the above-mentioned approximations