van der Waals Interactions in Ionic and Semiconductor Solids

Abstract

van der Waals (vdW) energy corrected density-functional theory [Phys. Rev. Lett. 102, 073005 (2009)] is applied to study the cohesive properties of ionic and semiconductor solids (C, Si, Ge, GaAs, NaCl, and MgO). The required polarizability and dispersion coefficients are calculated using the dielectric function obtained from time-dependent density-functional theory. Coefficients for "atoms in the solid" are then calculated from the Hirshfeld partitioning of the electron density. It is shown that the Clausius-Mossotti equation that relates the polarizability and the dielectric function is accurate even for covalently-bonded semiconductors. We find an overall improvement in the cohesive properties of Si, Ge, GaAs, NaCl, and MgO, when vdW interactions are included on top of the Perdew-Burke-Ernzerhof or Heyd-Scuseria-Ernzerhof functionals. The relevance of our findings for other solids is discussed.

First-Principles Models for van der Waals Interactions in Molecules and Materials: Concepts, Theory, and Applications

“…For instance, Zhang et al demonstrated a substantial linear dependence of α Si and C 6 Si−Si in zinc blende silicon on the lattice constant using TD-DFT calculations. 80 This behavior cannot be explained by the coordination of the silicon, because this is unchanged throughout the lattice contraction, but rather can be related to the change in the electronic band gap. Nonlinear dependence of vdW parameters on the lattice constant can be observed in semiconductors, such as Ge, where the small band gap becomes zero upon the metallic phase transition induced by the lattice contraction.…”

“…The other limit assumes Na + and Cl − ions, yielding a significantly reduced polarizability of 21.6. 80 The large difference between these two limits is caused by the change in the polarizability from 167.7 for neutral Na atom to 0.9 for Na + . Measurements of dielectric properties 81 and high-level calculations 82 demonstrate that the polarizability of NaCl solid is in fact closer to the sum of Na + and Cl − ions.…”

“…Bucǩo et al applied electrodynamic screening from eq 18 to the atomic C 6 coefficients, leading to improvements in the description of layered materials. 207 Zhang et al and Ruiz et al 76,80 used the dielectric function of bulk materials to define atomic polarizabilities in solids as an alternative to the free-atom reference data used in eq 57. Such renormalized bulk reference parameters can be used to investigate cohesion in solids 80,208 and adsorption of molecules on surfaces.…”

“…207 Zhang et al and Ruiz et al 76,80 used the dielectric function of bulk materials to define atomic polarizabilities in solids as an alternative to the free-atom reference data used in eq 57. Such renormalized bulk reference parameters can be used to investigate cohesion in solids 80,208 and adsorption of molecules on surfaces. 76,77,101,209 Furthermore, the TS approach was also extended from DFT 60 to the density-functional tight-binding (DFTB) method, 210 as well as classical force fields.…”

Recent development of atom‐pairwise van der waals corrections for density functional theory: From molecules to solids

“…[56,57] For an accurate description of all of the non-covalent interactions, a method must therefore be able to address the whole range of interactions. Accordingly, the vdW correction methods are tested for ionic crystals of LiH, LiF, LiCl, NaF, NaCl, NaI, KCl, KI, and MgO.…”