[Pw_forum] Question for electron phonon coulping

[Yanming ma]

Dear Stefano de Gironcoli,

Thanks very much for your excellent comments.
I am not sure if I can understand 100 percent of your comments .
I try to follow your comments in order to make sure I can do the calculation 
in a right way.

>Do a calculation with a given set of k points and calculate el-ph as a
>function of sigma

In practise,
I choose a 8x8x8 k mesh and a q point (say 0.5 0.5 0.0). I set nsig =4, 8, 
12, 16, 20, 24...respectively. I calculate the lambdas at this q point with 
this k mesh and with different nsigs. Concerning the lambda value, For 
example, for nsig=4 and 8, the final lambda values are choosen as the final 
step gaussian broadening (step 4 for nsig=4, step 8 for nsig=8).
Then I can get a curve for nsig.vs.lambda at this q point.


>Do again the same calculation increasing the number of k-points and the
>same set of values for sigma.

Repeat the calculation with a larger k mesh, for example, 12x12x12.

>You will notice that for sufficiently large values of sigma the two
>curves will agrees. This means that
>the k-points mesh is sufficiently accurate for sigmas larger than that
>but may not be good for smaller values.

I compare the two curves and get a reliable nsig value, which the two curves 
start to agree.

>Repeating the calculation for even larger set of k-points (same set of
>sigma) you will see that from a value
>of sigma that is smaller than the previous one the most accurate
>calculation (the one using more k-points)
>will agree with the second-best (and with the first, less accurate,
>calculation when these last two agree)

if I repeat the calculation with more denser k mesh (say 16x16x16), I will 
get a smaller reliable nsig by comparing the two more denser k mesh.


>Trust only the curve in the region in which the calculation is converged
>with respect to k-ponts summation.

In practise, how can I decide the calculation is converged with respect to k 
points summation?
At a q point, with the same nsig, The calculated lambdas are same within 
some errors for two K points mesh. Does this mean convergence?

>For sufficiently large set of k-points the SAFE region will approach
>enough the limit of sigma going to zero
>that you can stop the procedure.
>

I can not understand this paragraph. Sigma going to zero...?

Any comments?
Thanks in advance.

Yanming Ma

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