The calculation time of ab initio calculations varies — to first order — as the cube of the number of atoms or equivalently of electrons (the famous N3 dependence) in the cell. If a fine к-point sampling is needed, this dependence is reduced to N2 as the number of к points decreases in inverse proportion with the size of the cell. On the other hand, the number of self­consistent cycles needed to reach convergence tends to increase with N. Anyway, the variation of calcula­tion time with the size of the cell is huge and thus strongly limits the number of atoms and also the cell size that can be considered. On one hand, calculations on the unit cell of simple crystalline materials (with a small number of atoms per unit cell) are fast and can easily be performed on a common laptop. On the other hand, when larger simulation cells are needed, the calculations quickly become more demanding. The present upper limit in the number of atoms that can be considered is of the order of a few hundreds. The exact limit of course depends on the code and also on the number of electrons per atoms and other technicalities (number of basis functions, к points, available computer power, etc.), so it is not possible to state it precisely. Considering such large cells leads anyway to very heavy calculations in which the use of parallel versions of the codes is almost mandatory. Various parallelization schemes are possible: on k points, fast Fourier transform, bands, spins; the parallelization schemes actually available depend on the code.

The situation gets even worse when one notes that a relaxation roughly involves at least ten ground-state calculations, a saddle point calculation needs about ten complete relaxations, and that each molecular dynamics simulation time step (of about 1 fs) needs a complete ground-state calculation. Overall, one can understand that the CPU time needed to complete an ab initio study (which most of the time involves vari­ous starting geometry) may amount up to hundreds of thousands or millions of CPU hours.