French Fries or Onions? Improving integration in DFT calculations

The amount of recent cpu time ($>100$ mega cpu hours) spent in our group on high-throughput materials prediction led us to re-examine convergence issues in standard DFT calculations. Calculations for metals typically take 100 times longer than calculations for semiconductors. By improving the integration technique can we shrink the``metal deficit''? Conceptually one can attack the problem in the typical ``rectangle" fashion (french fries) or by integrating in energy space (onions). The standard approach converges very slowly in the case of metals. Revisiting the k-point integration issue in light of modern DFT practice, we demonstrate that this ``metal deficit'' can be reduced to only a factor of 5--10 worse than semiconductors.