On Sun, 11 May 2008, Stefano Baroni wrote: perhaps one more comment on top of that mentioning a subject that is easily forgotten.
i noticed that in the example input the wavefunction cutoff was chosen somewhat low (if not too low at 60ry) for norm-conserving pseudopotentials on an oxygen containing system. with a low (density) cutoff there will be a residual "ripples" on the density since you are missing high frequency components. as a consequence the minimum your system "sees" may actually change with the displacement of atoms or the whole system. this artefact will of course interfere with the geometry convergence behavior, particularly for gradient corrected functionals, and particularly for systems where you have "vacuum" areas in which those oscillations will have the largest relative impact. in part the latter effect is handled by a cutoff to not compute XC functionals if the densities, but it still is an effect to consider. in conclusion, the more tightly you want to converge your geometry, the higher cutoff you need. one has to keep in mind, though, that there are also the systematic errors of DFT to be considered and that it is of little use to converge geometries (far) beyond. cheers, axel. SB> a few remarks for the benefit of the less experienced members of the forum: SB> SB> On May 11, 2008, at 10:22 AM, Nicola Marzari wrote: SB> SB> >ideally, if you have 18 atoms, i.e. 56 degrees of freedom (or 53, if you SB> >remove traslations) a conjugate gradient algorithms should bring you to SB> >the minimum in 53 steps. SB> SB> this is strictly true for a quadratic function. a non quadratic one may SB> require more iterations. SB> SB> also, the number of degrees of freedon should be considered as an upper SB> bound for the number of iterations needed to minimize a quadratic functional SB> using CG's. this upper limit is only reached for very ill-conditioned SB> functionals (those whose quadratic form has eigenvalues of wildly different SB> order of magnitude). well conditioned functionals (whose quadratic form has SB> eigenvalues all of about the same magnitude) usually converge much faster. SB> SB> to some extent, the above two facts (non quadraticity, better condition of SB> the quadratic form) and may compensate, I guess. SB> SB> Stefano SB> SB> --- SB> Stefano Baroni - SISSA & DEMOCRITOS National Simulation Center - Trieste SB> [+39] 040 3787 406 (tel) -528 (fax) / stefanobaroni (skype) SB> SB> La morale est une logique de l'action comme la logique est une morale de la SB> pens?e - Jean Piaget SB> SB> Please, if possible, don't send me MS Word or PowerPoint attachments SB> Why? See: http://www.gnu.org/philosophy/no-word-attachments.html SB> SB> SB> SB> SB> SB> -- ======================================================================= Axel Kohlmeyer akohlmey at cmm.chem.upenn.edu http://www.cmm.upenn.edu Center for Molecular Modeling -- University of Pennsylvania Department of Chemistry, 231 S.34th Street, Philadelphia, PA 19104-6323 tel: 1-215-898-1582, fax: 1-215-573-6233, office-tel: 1-215-898-5425 ======================================================================= If you make something idiot-proof, the universe creates a better idiot.
