[Pw_forum] Hubbard U of Zn in ZnO

[Matteo Cococcioni]

Hi,

Yu Xue wrote:
> Hello,all,
>
> I am trying to use LDA+U to do some calculations on ZnO.
> First,I need to decide Hubbard U of Zn in the scheme of Dr.Cococcioni,see 
> PRB 71,035105(2005)-----(*)
> Everything looks good,just the result is unreasonable:
>
>   

what is that looks good then?

> d(alpha)/d(n)=-440.3838054 eV
> d(alpha_0)/d(n_0)= -2.2765143 eV
> U=(-d(alpha)/d(n))-(-d(alpha_0)/d(n_0))=2.2765143-440.3838054=-438.1072911 
> eV
>
>   

You seem to be inverting just two diagonal element of the response 
matrices dn^I/dalpha^J or dn_0^I/dalpha^J instead of taking
the diagonal element of the difference between their inverses as the 
method above says.
Also the difference between the two numbers is very large and sounds 
wrong to me. Are you sure:
1) your calculation is well converged (cut offs, smearing, k-points etc)?
2) you are using a big enough supercell?
3) when you run the perturbed calculations (with alpha =/= 0) you are 
setting  diago_thr_init to a value close or smaller to the last ethr of the
unperturbed scf calculation of which you read converged wavefunctions 
and potential?

If you are sure of all this and your results still look unreasonable 
(because Zn has filled d bands) then you may try to use alpha values
that are not centered in zero but around a small positive value x. This 
means you run a well converged scf calculation with the alpha on one
Zn atom fixed at value of x then, starting from converged wfcs and 
potential you run perturbed calculations with Hubbard_alpha on the same Zn
equal to x+0.01,  x-0.01 x+0.02 x-0.02 x+0.05 x-0.05 etc etc.
You should find a more stable number. Then maybe you can study the 
convergence of this number  (the U) with x --> 0)
> In Shujun Hu's paper,PRB 73, 245205(2006),he mentioned that "The method 
> mentioned above is invalid to gain the Hubbard Uzn since diagonal elements 
> indicating the Zn sites in Eq(19) of (*) are close to zero due to fully 
> occupying of Zn 3d states. "

That U is close to 0 is not totally unreasonable because the d bands are 
full and you don't need to do much to encourage their occupation to be 1.

>  So he uses Uzn as a fitting parameter.I don't 
> quite understand that,and wonder,then we can't use  
> constrained-density-functional and linear response scheme to calculate 
> Hubbard U of Zn?Do we have some tricks to gain Uzn using this scheme?
>
>   
I don't understand either. In the sense that either you want to fit a 
value for U to a specific property and use it in your "non ab-initio" 
calculations,
or you want to do everything "ab-initio". That was the reason why we 
tried to compute U. Probably it's not a perfect method, but it's not 
fitting.
Also beware that U varies a lot  when you change pseudopotential, if you 
distort the unit cell etc. So there is not a universal value  to be used 
and keep in mind it is a correction whose strength depends on what you 
want to corerect. If you believe in the ab-initio way you should compare 
instead your results  with experiments or  more refined calculations.  
That will tell you  about the quality of  your  calculations. Not the 
value of U itself, how close it is to 0 or to any other fitted value.
Our linear response should be equivalent to a constraint DFT 
calculation. you could actually use the response matrices to learn how 
to constraint your system in such a way that only one atomic occupation 
changes.

Hope this helps. Let us know.

> I appreciate any suggestions from you
>   

and the forum would appreciate to know more about you and your 
affiliation. Thanks.

Matteo

> Thanks a lot
>
> Sally
>
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