where n is the band index, n e is the number of electrons, and N is the number of bands considered below and above the band index n e /2, which in the case of a semiconductor will correspond to the index of the valence band. O n,k is the occupation of the band n at a specific k-point. Here, P is a Boolean function of O n,k . For bands with indices n 1 through n e /2, if O n,k < 2 (assuming doubly occupied bands), P = 1 otherwise P = 0. Similarly, for band indices n e /2 + 1 through n 2 , P = 1 if O n,k > . We use N = 3 and occupation tolerance = 10 3 to calculate R. R varies between 0 and 1, with R = 0 representing a semiconductor and large R indicating that the phase is likely a metal (Figure ). We classified materials with 0 < R  0.1 (GGA-PBE electronic structure) as potential narrow-gap semiconductors and semimetals because of the small overlap between the nominally valence and conduction bands. Among the 650 Zintl phases, we identify 44 that have R  0.1.