Dear Dario, this is an issue related to the fact that a shifted grid in the fcc Bravais lattice has lower symmetry than cubic... just think of the simplest 1 1 1 1 1 1 grid that should contains one single point L=(1/2 1/2 1/2) but actually represents the 4 (rotationally but not translationally) equivalent points (1/2 1/2 1/2), (-1/2,-1/2,1/2), (-1/2,1/2,-1/2),(1/2,-1/2,-1/2) . The argument can be easily extended to denser grids and shows that the shifted grid represents 4*N^3 points in the fcc BZ. This explains why the shifted grid appears more accurate (it is actually denser than you think) and why the number of points it contains is larger than you may have thought ... In fact avoiding high symmetry points like the Gamma point, contained in the unshifted grid, should help reducing the number of inequivalent points while instead the number of shifted points for a given nominal density is larger than the number of unshifted ones... true, but the corresponding parent grid is actually 4 times denser than you may have thought...and the "symmetry reductions" factor is indeed larger for the shifted grid for example: shifted 4*4*4 -> 256 points in the full BZ -> 10 points in the IW => sym. red. fact. = 25.6 unshifted 4*4*4 -> 64 points in the full BZ -> 8 points in the IW => sym. red. fact. = 8 Some time (especially if your system does not have much symmetry to start with) you don't really care about sampling the BZ according to a fully cubic symmetry but a regular grid in the 3 directions is enough.. in this case the use of shifted grids may results in a large amount of "un-needed" k-points which you may want NOT to include in the calculation... this annoying fact is the origin of the infamous nosym=.true. options that much confusion generates in most users until they realize what its meaning and purpose really is ... there are many threads on that in the archive....
As to the fact that total energy are less sensitive than dielectric properties to k-points sampling this is a well known fact [see for instance S.Baroni and R. Resta, PRB 33, 7017 (1986)] Hope this helps, stefano -- Stefano de Gironcoli - SISSA and DEMOCRITOS dario rocca wrote: > Dear Users > I have an issue related to the convergence of the static dielectric > matrix using the PH code. I have performed calculations > on bulk silicon using different k point meshes and I have obtained the > following results: > > k grid diagonal component of number of k points in > the dielectric tensor the > irreducible Brillouin zone > > 4*4*4 23.668350065 8 > 6 *6*6 16.297485614 16 > 8 *8*8 14.044830694 29 > 10 *10*10 13.288531964 47 > 12*12*12 13.029602882 72 > 16 *16*16 12.908820645 145 > 20 *20*20 12.894538380 256 > > k grid+ 1 1 1 shift diagonal component of number of > k points in > the dielectric > tensor the irreducible Brillouin zone > > 4*4*4 13.840844632 > 10 > 6*6*6 > 12.997009732 28 > 8*8*8 > 12.903849607 60 > 10*10*10 > 12.893711596 110 > 12*12*12 > 12.892685597 182 > 16*16*16 > 12.892482798 408 > 20*20*20 > 12.892537346 770 > > I was surprised of the improvement in the convergence due to the shift > of the grid. I don't think this is related to the number of k points > in the IBZ (at least not exclusively). > I have observed a similar behavior in diamond. > The ground state energy convergence also benefits from the shift, but > the improvement is not so striking. > Does someone has any hint on why the shift of the grid improves the > calculation of the dielectric properties of silicon? > Thanks a lot > Dario Rocca, dept. of chemistry, UC Davis > > ------------------------------------------------------------------------ > > _______________________________________________ > Pw_forum mailing list > Pw_forum at pwscf.org > http://www.democritos.it/mailman/listinfo/pw_forum >
