[Pw_forum] How to achieve the convergence of Ecutrho?

[Guido Fratesi]

Dear Plato Tao,

as for any convergence parameter, the criterion is analogue to the 
epsilon-delta definition in calculus.
  Namely, if Q is the quantity you want to have converged (say, the 
total energy) within an accuracy \epsilon (the value of \epsilon 
depending on your own needs), with respect to a convergence parameter x 
(say, the cutoff):

if   |Q(\infty) - Q(x)| < \epsilon   for all x >= x',

then x' is the value of the parameter ensuring you convergence. Notice 
that this does not imply anything about how fast you reach convergence, 
so a criterion only based on differences between consecutive steps 
(x,x+dx,x+2dx...) is ill defined as it depends on dx. You have to 
estimate the value of Q(\infty), e.g. by extrapolation to large values 
of x, and see when your error with respect to this virtually exact 
result is lower than the accuracy you want to achieve.

Best wishes,
Guido

Il 12/13/2011 08:43 AM, 陶鹏 ha scritto:
> Dear all,
>
> I've asked sevral people about the convergence criteria of Ecutrho test. They point out that the convergence will be achieved when the difference between two adjacent scf calculation is smaller than 0.1 meV. However, they are not very sure about the step length. From my view, the step length may pose huge effects on our calculation. Consider the cases of step lengths are 100 Ry and 0.00001Ry respectively, the latter will be convergent immediately while the former will not be so fast.
>
> For the resons above, I'm really confused now. And could any nice guy show me the strict judgement of the convergence for Ecutrho? Thank you very much!
>
> Yours,
> Plato Tao
>
> --
> -------------------------------------------------------------------
> PH.D. candidate Peng Tao
> Magnetism and Magnetic Materials Division
> National Laboratory for Material Science
> Institute of Metal Research, Chinese Academy of Sciences
> Phone  +86-024-83978751
> -------------------------------------------------------------------
>
>
>
>
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-- 
Guido Fratesi

Dipartimento di Scienza dei Materiali
Universita` degli Studi di Milano-Bicocca
via Cozzi 53, 20125 Milano, Italy