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We present a scheme to controllably improve the accuracy of tight-bindingHamiltonian matrices derived by projecting the solutions of plane-wave abinitio calculations on atomic orbital basis sets. By systematically increasingthe completeness of the basis set of atomic orbitals, we are able to optimizethe quality of the band structure interpolation over wide energy rangesincluding unoccupied states. This methodology is applied to the case ofinterlayer and image states, which appear several eV above the Fermi level inmaterials with large interstitial regions or surfaces such as graphite andgraphene. Due to their spatial localization in the empty regions inside oroutside of the system, these states have been inaccessible to traditionaltight-binding models and even to ab initio calculations with atom-centeredbasis functions.

Accurate Tight-Binding Hamiltonians for 2D and Layered Materials