\textit{Atoms in Solids} Perspective on Polarizabilities and van der Waals Coefficients in Semiconductors

The calculation of response properties of solids including their polarizabilities and van der Waals (vdW) coefficients usually requires the knowledge of the full electronic bandstructure. For non-covalently bound solids, such as noble-gas and ionic crystals, atoms-in-solids model can be successfully utilized to define their polarizabilities. Here we critically assess the atoms-in-solids model for covalently-bound solids, ranging from wide-gap ($\sim$10 eV) to narrow-gap ($\sim$1 eV) semiconductors. We model their response by assigning a single quantum harmonic oscillator to every atom, where the parameters of the oscillators are defined as functionals of the electron density, following the Tkatchenko-Scheffler method [1]. The response function is then calculated by solving self-consistent screening equations of classical electrodynamics, without any explicit information about the electronic bandstructure [2]. The calculated polarizabilities and vdW coefficients for 23 semiconductors are compared with TDDFT and experimental benchmark data, revealing an overall agreement within 10\%. We demonstrate the crucial role of vdW interactions in the cohesive properties of the 23 semiconductors.\\[4pt] [1] Tkatchenko and Scheffler, PRL (2009);\\[0pt] [2] Tkatchenko, DiStasio, Car, Scheffler, PRL (2012).