Bader charge analysis with -ref to CHGCAR_sum

[zahra]

Dear all,

I have followed the steps in the website to calculate bader charges of my atoms in my system. As it is outlined, I have generated AECCAR0 and AECCAR2. I have then found the summation of core and valence charges and then calculated charge of individual atoms.
I have two questions:

1. If we are using -ref CHGCAR_sum, shouldn't it give the total charge of each atom rather than its valence electrons. If not, what is the point of using -ref CHGCAR_sum at all?

2. How to get reliable and converged total numbers of electrons at atoms, which parameters to watch? How close the total number of electrons in the system should be to the integer to make sure that everything is correct? Let's say, the ideal number of electrons 950 and I get 949.55, is it ok or not?

I appreciate if you can help me with these questions.

Best,
Zahra

[graeme]

the command "bader CHGCAR -ref CHGCAR_sum" will determine the Bader volumes from the CHGCAR_sum file but then integrate the charge from the CHGCAR file in those Bader volumes. The total charge should be accurate, because the normalization of the CHGCAR file is based upon the sum of the charge density elements.

[zahra]

Thanks a lot for your reply. Now it is clear for me what -ref does.
I have another question as well:
To get accurate core charges it is needed to increase the grid point. In my calcualtions, also this shows a huge difference in core charge calculations, when doing it by default values of NGXF,... and when doing the bader analysis using higher values of grid points.
Now, what confuses me is that, no matter what I have for grid points when I use: ./bader CHGCAR -ref CHGCAR_sum, I get the same valence electrons. However, using ./bader CHGCAR_sum gives dramatically different results (for example smaller grid gives 75 as total charge for Au while the bigger one gives 78).
So:
1. Why grid sampling only affects core charge? and how it does so?
2. If valence electronsplay the most important role in bond formation, etc. why core charges at all?
3. If density of grid points changes core charge a lot but valence charge is not affected, how can we trust the results for valence charges?
Here is one example:

./bader CHGCAR_sum ./bader CHGCAR -ref CHGCAR_sum
____________________________________________________________________________________________
NG(X,Y,Z)=112 (default) Au 75.1152 !!! 10.8
NG(X,Y,Z,)F=150 (default) Br 52.22 !!!! 7.35


./bader CHGCAR_sum ./bader CHGCAR -ref CHGCAR_sum
_____________________________________________________________________________________________
NG(X,Y,Z)=212 Au 78.29 !!! 10.79
NG(X,Y,Z,)F=250 Br 34.09 !!! 7.35

Thanks for your help in advance!
Zahra

[graeme]

The valence charge is normalized so that the sum of the values at the grid points in the CHGCAR file gives the total (valence) charge.

There is no such normalization for the total charge. The integrated total charge is highly sensitive to the grid density because of the cusps at the nuclear centers.

The problem with analyzing just the valence charge (bader CHGCAR) is that the CHGCAR data does not have the correct structure in the atomic cores. The Bader analysis requires charge density maxima at the atomic centers.

The problem with analyzing just the total charge (bader CHGCAR_sum) is that the CHGCAR_sum data has peaks at the atomic centers and does not integrate to the constant value unless you use a ridiculously fine charge density grid.

Our solution is to use the CHGCAR_sum to define the bader volumes and then integrate the valence charge in those volumes from the CHGCAR file. You should find that these integrated valence charges have the correct normalization and converge with grid density. Using (bader CHGCAR -ref CHGCAR_sum) avoids the problems associated with analyzing either file individually.

[zahra]

Thanks a lot for your reply! This is very helpful.

Zahra