Fig. 2: Histograms of the decrease in band gap energy from electronic band structures calculated using the LM approach compared to the previous conventions by SC and Hinuma et al.

The histograms labeled “shorter paths” correspond to space groups with a negative value of the average increase in the number of path segments in Fig. 1. For the majority of band structures calculated with longer k-paths from the new method, the band gap is shown to either be unchanged or decreased in value. This confirms that in most cases the increased sampling of reciprocal space via the maximally inclusive high-symmetry criteria provides a better description of the electronic band structure. The smaller band gaps shown in the histogram can be seen to primarily result from calculations with shorter paths, further indicating the necessary inclusion of additional segments from previous conventions to the newly generated paths for tetragonal and trigonal systems with low symmetry.