To classify a band as fully occupied, partially occupied, or fully unoccupied, we define an energy window and label the band based on its location relative to this window, as shown in Figure . We define the smearing window such that any band whose occupation f falls within 10 -6 < f < 1 -10 -6 is considered partially occupied. Consequently, occupations less than 0 (greater than 1), as can occur using MP1 broadening, are counted as fully unoccupied (occupied). We note that if a band is fully occupied or unoccupied at some k-points but partially occupied at others, it is counted as partially occupied.