[Pw_forum] slow relaxing

[Axel Kohlmeyer]

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
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SB> 
SB> 
SB> 
SB> 
SB> 

-- 
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Axel Kohlmeyer   akohlmey at cmm.chem.upenn.edu   http://www.cmm.upenn.edu
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