Special points for Brillouin-zone integrations

The efficiency of two different methods for obtaining "special" points useful for Brillouin-zone integrations of periodic functions is compared. We find that for some Bravais lattices (such as body-centered cubic and hexagonal), the method suggested by Monkhorst and Pack leads to different and sometimes less efficient point sets than those previously obtained by Chadi and Cohen. For a two-dimensional oblique lattice, special points twice as efficient as those suggested by Cunningham are given.