Choosing k Points in the Brillouin Zone

TABLE 3.2 Results from Computing the Total Energy of fee Cu with M x M x M k Points Generated Using the Monkhorst Pack Method 

The last column in Table 3.2 lists the computational time taken for the total energy calculations, normalized by the result for M 1. Note that getting what we just defined to be a converged result takes at least 20 times longer than a calculation involving just one k point. An initially curious feature of these results is that if M is an odd number, then the amount of time taken for the calculations with either M or (M + 1) was close to the same. This occurs because the calculations take full advantage of the many symmetries that exist in a 

Tn some situations such as examining electronic structure, it can be important to include a k point at the T point. 

There are many examples where it is useful to use supercells that do not have the same length along each lattice vector. As a somewhat artificial example, imagine we wanted to perform our calculations for bulk Cu using a supercell that had lattice vectors 

---