Hybrid density functionals with screened Hartree-Fock exchange at long range have become popular for modeling solids. I'm curious as to what the reasoning is behind this functional form. I understand that exchange interactions are expensive to compute and so eliminating long range ones can help to maintain low scaling for larger systems. My initial intuition would say that screening these interactions would reduce the accuracy, but I have heard that full exchange at long range is actually unphysical. What makes long range exchange incorrect for solids?
I think the rationale is pretty well explained in the paper by Heyd, Scuseria and Ernzerhof, i.e. Journal of Chemical Physics 118, 8207 (2003)
For insulators there is a large gap, and the density matrix and the exchange interactions decay exponentially when you go farther and farther from the cell at the origin. (This means that in this case, you can easily also apply further screening to the exchange.)
For metals there is no gap, which leads to a divergence in Hartree-Fock. (This problem is just an issue of Hartree-Fock, as it neglects correlation which should become significant for metals!) However, if you switch to short-range only exchange, you kill the divergence, thus making the functional better behaved.