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A computationally inexpensive k.p-based interpolation scheme is developedthat can extend the eigenvalues and momentum matrix elements of a sparselysampled k-point grid into a densely sampled one. Dense sampling, often requiredto accurately describe transport and optical properties of bulk materials, canbe demanding to compute, for instance, in combination with hybrid functionalsin density functional theory (DFT) or with perturbative expansions beyond DFTsuch as the $GW$ method. The scheme is based on solving the k.p method andextrapolating from multiple reference k-points. It includes a correction termthat reduces the number of empty bands needed and ameliorates banddiscontinuities. We show how the scheme can be used to generate accurate bandstructures, density of states, and dielectric functions. Several examples aregiven, using traditional and hybrid functionals, with Si, TiNiSn, and Cu asmodel materials. We illustrate that d-electron and semi-core states, which areparticular challenging for the k.p method, can be handled with the correctionscheme if the sparse grid is not too sparse.

Enabling accurate first-principle calculations of electronic properties with a corrected k.p scheme