Correcting overbinding in local-density-approximation calculations

We introduce a semiempirical method to correct the systematic equilibrium lattice parameters underestimation present in first principles calculations based on the local density approximation. The method consists in performing calculations under a negative pressure such that the calculated equilibrium volume matches the experimentally observed one. We find that elastic properties obtained under these conditions are typically in better agreement with experiment. We also observe that the negative pressure which needs to be applied to crystalline compound can be reliably interpolated by taking the concentration-weighted average of the pressures determined from pure crystals made of each of the elements present in the compound. In a large class of materials, the knowledge of one pressure per element is thus sufficient to correct most of the bias in lattice constants and elastic properties. We finally propose a simple model of the nonlocal contribution to the exchange-correlations energy that is able to explain the observed linear dependence between the required negative pressure and concentration.