Pressure dependence of energy gaps within local density functional formalism

From a precise first principles evaluation of pressure within local density functional formalism a detailed study of the pressure dependence of the energy gaps has been made, for prototype semiconductor Si. It is shown that although the correct gaps for semiconductors cannot be obtained within local-density functional their pressure variation is still well accounted for. In particular $\text{dE}{}_{\mathrm{g}}\text{dP}$ for the minimum gap is very well reproduced. This suggests that the proposed correction Δ=E_g-ε_g, between the minimum gap E_g and the exact density functional Kohn-Sham gap, ε_g, determined by derivative discontinuities of the exchange correlation energy across the gap is pressure independent (assuming that local density functional gives a good approximation to ε_g).