van der Waals density functional for solids

The recent nonlocal correlation functional of Vydrov and van Voorhis [J. Chem. Phys. 133, 244103 (2010)] is investigated and two new versions of the functional are suggested as being appropriate for describing van der Waals interactions in solids. A refitting of the original functional is demonstrated to result in very accurate interlayer binding energies for weakly bonded layered solids. A VV10 functional based on the generalized gradient approximation by Armiento and Mattsson [Phys. Rev. B 72, 085108 (2005)], while performing slightly worse for interlayer binding, is highly successful in describing the equilibrium geometries of both weakly bonded and close packed solids.

Figure 1

Binding energy curves for three representative compounds from the set used for optimizing the VV10 functional for solids, for the GGA functionals AM05, PBEsol, and PW86R. The units of the $x$ axis are the deviation of the $c$ axis length from the experimental geometry, and the units of the $y$ axis are meV/Å${}^2$, both normalized by the number of layers per unit cell. The calculated values of $(c-c_{\text{expt}})/\text{layers}$ extend out to 15.0 Å. In the examples shown here, AM05 has no binding at all for MoS${}_2$ and TiSe${}_2$, although for TiSe${}_2$ there is a local minimum near the experimental geometry, whereas PbO has a small binding energy of about 1.5 meV/Å${}^2$. By contrast, PW86R always gives a small binding energy with the minimum in the vicinity of the experimental lattice constant and PBEsol gives a much deeper minimum close to the experimental lattice constant. Note also the lower slope of AM05 in the compressive region to the left of the experimental equilibrium lattice constant.