Accurate and transferable extended Hückel-type tight-binding parameters

Abstract

We show how the simple extended Hückel theory can be easily parametrized in order to yield accurate band structures for bulk materials, while the resulting optimized atomic orbital basis sets present good transferability properties. The number of parameters involved is exceedingly small, typically ten or eleven per structural phase. We apply the method to almost fifty elemental and compound bulk phases.

Extended Hückel theory for band structure, chemistry, and transport. I. Carbon nanotubes

“…In the following, we apply this EHT parametrization scheme 21 by benchmarking it to a two-dimensional graphene sheet 22,23 and extending it to obtain the band structure, density of states, and electronic transmission of carbon nanotubes ͑CNTs͒ of varying chiralities. We show that the same bulk-optimized EHT parameters ͑onsite energies and AObasis functions͒ are transferable to small diameter CNT band structures, capturing even curvature-induced band gap effects for larger than 1%-3% tube deformation, in quantitative agreement with STS data.…”

“…Such theories, widely used in the past to describe the equilibrium properties of isolated molecules, 19 have recently been applied to molecular conduction 20 and also extended to solids using transferable atomic-orbital ͑AO͒ basis sets for calculating the electronic structure of various compounds benchmarked with detailed DFT calculations within the local density approximation ͑LDA͒ or generalized gradient ͑GGA͒ approximation. 21 Given a geometry, one uses the explicit EHT basis functions to calculate a nonorthogonal overlap matrix S, which along with separately fitted onsite Hamiltonian matrix elements yields the corresponding off-diagonal hopping elements of the Hamiltonian. Within the standard Hückel prescription, structural changes are simply accounted for by recalculating the overlap and hopping elements but leaving the basis sets and onsite elements unchanged.…”

“…The use of basis functions that are not too localized turns out to be a key issue for achieving a good transferability. 21 Admittedly, the use of a direction independent K EHT function is a drastic assumption that can be relaxed by making the constant orbital dependent, but we make the simplifying assumption that the orientation dependence arises principally from the corresponding overlap functionals.…”

“…For instance, the Fermi level of most metals is set to E F = −10 eV in the paper in Ref. 21, which means that each dispersion curve needs to be individually shifted to bring its Fermi level up to the experimental value, through the transformation H → H + V c S for each subsystem. The correct alignment of the levels relative to each other becomes particularly important when studying compound systems such as metal-semiconductor junctions or molecular components attached on nanowires and nanotubes.…”

Theories of scanning probe microscopes at the atomic scale

“…When the surface structure is known, its electronic structure has to be computed with sophisticated methods, and existing codes more and more rely on firstprinciples density-functional theory (Wimmer et al, 1985;Kresse and Hafner, 1993;Kresse and Furthmü ller, 1996), or, in case of tight-binding models (Turchi et al, 1998), they obtain their parameters from a fit to DFT data (Cerda and Soria, 2000). The fit is not without ambiguities, since it is unknown whether the density of states used for the fit is really unique.…”