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The calculations of electronic transport coefficients and optical propertiesrequire a very dense interpolation of the electronic band structure inreciprocal space that is computationally expensive and may have issues withband crossing and degeneracies. Capitalizing on a recently developedpseudo-atomic orbital projection technique, we exploit the exact tight-bindingrepresentation of the first principles electronic structure for the purposes of(1) providing an efficient strategy to explore the full band structure$E_n({\bf k})$, (2) computing the momentum operator differentiating directlythe Hamiltonian, and (3) calculating the imaginary part of the dielectricfunction. This enables us to determine the Boltzmann transport coefficients andthe optical properties within the independent particle approximation. Inaddition, the local nature of the tight-binding representation facilitates thecalculation of the ballistic transport within the Landauer theory for systemswith hundreds of atoms. In order to validate our approach we study themulti-valley band structure of CoSb$_3$ and a large core-shell nanowire usingthe ACBN0 functional. In CoSb$_3$ we point the many band minima contributing tothe electronic transport that enhance the thermoelectric properties; for thecore-shell nanowire we identify possible mechanisms for photo-currentgeneration and justify the presence of protected transport channels in thewire.

Accurate $ab~initio$ tight-binding Hamiltonians: effective tools for electronic transport and optical spectroscopy from first principles