For example, if I have a unit cell with 56 atoms the DFT calculation would take x time, but if create a supercell (e.g. 2x2x2) I would have 448 atoms, but I don't know the number of k-points, only the mesh (3x3x3 or 6x6x6).
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Actually, it is possible, in principle, to estimate the duration of ONE iteration of self-consistent cycle (taking into account the dimension fo the basic used, the speed of concrete CPU, etc.). However, the problem is that the QUANTITY of iterations required for the cycle to converge is a priori practically unpredictable.
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For example, if I have a unit cell with 56 atoms the DFT calculation would take x time, but if create a supercell (e.g. 2x2x2) I would have 448 atoms, but I don't know the number of k-points, only the mesh (3x3x3 or 6x6x6).
How can estimate time duration for DFT caculation?.
Depends on computational formalism, in particular, how the basic used in computations is formed. Let us suppose, for simplicity, the dimension of basic is proportional to the number of atomic valence states. Then, if we assume that the dimension of basic for cell with 56 atoms is M, the dimension of basic for 2x2x2 supercell will be 8*M.
The most of computational time typically is spent for the diagonalization of matrix defined for EACH k-point. This time is proportional to (dimension of basic)3. So, in the present example the computational time PER ONE k-point and FOR ONE cycle iteration is expected to increase about (8)3 =512 times .
Knowing the k-mesh for the cell 56 atoms (not specified in the sample above) and the k-mesh for 2x2x2 cell we can take time x and to estimate the time required for one iteration for 2x2x2 cell.
Note, some standard DFT-packages generate before-start output files where the actulal dimension N of used basic is specified. Keeping in mind that computational time ~N3, we can estimate the time required for one iteration of supercell as compared with ordinary cell. However, it does not provide the possibility to estimate a priori a NUMBER of required iterations, as I have already mentioned.
It is very difficult to calculate the actual time, because it depends on many factors. For example, number of K-points, cut off energy, max. stress, rate of convergence, max. force per atom, number of cores, types of calculation ( memory, default or speed) etc.