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