Charge of C atoms in graphite

[yoshi]

I am studying electronic structure of graphite by using VASP code.
I calculated the charges on C atoms in graphite in differnt NGXF, NGYF, and NGZF grids.
I thought that all C atoms might have charge of 4.0000, so I increased the FFT grids of CHGCAR.
But I could not get the reasonable results.
For example, in C1 atom, 3.9451 ==> 4.0255 ==> 4.0520 ==> 3.9849
The results seem to oscillate.
Please teach me why each charge of C atoms is different and not convergent to 4.000, and what I should do to equal all charges on C atoms.
Thank you.

[Case 1] NGXF = 50, NGYF = 50, NGZF = 100
# X Y Z CHARGE MIN DIST
----------------------------------------------------------------
1 1.2233 0.0000 0.0000 3.9451 0.6361
2 2.4465 0.7062 0.0000 4.0549 0.6497
3 1.2233 0.0000 3.3216 3.9451 0.6361
4 1.2233 1.4125 3.3216 4.0549 0.6497
----------------------------------------------------------------
NUMBER OF ELECTRONS: 16.00000

[Case 2] NGXF = 100, NGYF = 100, NGZF = 200
# X Y Z CHARGE MIN DIST
----------------------------------------------------------------
1 1.2233 0.0000 0.0000 4.0255 0.6780
2 2.4465 0.7062 0.0000 3.9745 0.6710
3 1.2233 0.0000 3.3216 4.0255 0.6780
4 1.2233 1.4125 3.3216 3.9745 0.6710
----------------------------------------------------------------
NUMBER OF ELECTRONS: 16.00000

[Case 3] NGXF = 150, NGYF = 150, NGZF = 300
# X Y Z CHARGE MIN DIST
----------------------------------------------------------------
1 1.2233 0.0000 0.0000 4.0520 0.6922
2 2.4465 0.7062 0.0000 3.9480 0.6780
3 1.2233 0.0000 3.3216 4.0520 0.6922
4 1.2233 1.4125 3.3216 3.9480 0.6780
----------------------------------------------------------------
NUMBER OF ELECTRONS: 16.00000

[Case 3] NGXF = 200, NGYF = 200, NGZF = 400
# X Y Z CHARGE MIN DIST
----------------------------------------------------------------
1 1.2233 0.0000 0.0000 3.9849 0.6886
2 2.4465 0.7062 0.0000 4.0151 0.6921
3 1.2233 0.0000 3.3216 3.9849 0.6886
4 1.2233 1.4125 3.3216 4.0151 0.6921
----------------------------------------------------------------
NUMBER OF ELECTRONS: 16.00000

[andri]

Are you using the lastest (v0.25a 06/12/08) version of the code?

[graeme]

Also, are you writing the core charges (LAECHG=.True.) and using this as described at:
http://theory.cm.utexas.edu/bader/vasp.php

[yoshi]

I used the latest version of bader, but did not use the latest VASP code.
Seeing the charge density map of graphite, I found that the maximum charge densities, which are llocated at 2 points on the C-C line, are approximately 0.22 e/A3 (covalent bond).
On the other hand, the charge density on 4 C atoms are approximately 0.21e/A3.
I will recalculate using the latest VASP.

[yoshi]

I report the charges of C atoms in graphite calculated by the latest version VASP(4.6.34 5Dec07) and bader(v0.25a 06/12/08).
I added "LAECHG=.TRUE." in INCAR.
I relaxed 4 C atoms in graphite under the condition of potpaw(C), LDA, Ecut = 800eV, and KPOINTS=(15 15 4).
After that, I excuted "/chgsum.pl AECCAR0 AECCAR2" to make CHGCAR_sum, and executed "/bader CHGCAR -ref CHGCAR_sum" according to your web site.
The obtained ACF.dat files are as follows.
The results of new case 1 and new case 3 were the same as case 1 and case 2(using old version VASP).
It was found that the charges of C atoms still seem to oscillate.
(for example, for C1 atom, 3.9451==> 3.9734 ==>4.0521 ==>4.0474)
Do I need more NGXF, NGYF, and NGZF to obtain the charge of 4.0000 on C atom, or Would I mistake the calculation conditions ?
I wonder if the bader analysis works well because the C-C bond has two maximal and three minimal vcharge densities on the C-C axis.
Thank you.

[New case 1] NGXF = 50, NGYF = 50, NGZF = 100
# X Y Z CHARGE MIN DIST
----------------------------------------------------------------
1 1.2233 0.0000 0.0000 3.9451 0.6361
2 2.4465 0.7062 0.0000 4.0549 0.6497
3 1.2233 0.0000 3.3216 3.9451 0.6361
4 1.2233 1.4125 3.3216 4.0549 0.6497
----------------------------------------------------------------
NUMBER OF ELECTRONS: 16.00000

[New case 2] NGXF = 100, NGYF = 100, NGZF = 200
# X Y Z CHARGE MIN DIST
----------------------------------------------------------------
1 1.2233 0.0000 0.0000 3.9734 0.6780
2 2.4465 0.7062 0.0000 4.0266 0.6710
3 1.2233 0.0000 3.3216 3.9734 0.6780
4 1.2233 1.4125 3.3216 4.0266 0.6710
----------------------------------------------------------------
NUMBER OF ELECTRONS: 16.00000

[New case 3] NGXF = 150, NGYF = 150, NGZF = 300
# X Y Z CHARGE MIN DIST
----------------------------------------------------------------
1 1.2233 0.0000 0.0000 4.0521 0.6922
2 2.4465 0.7062 0.0000 3.9479 0.6780
3 1.2233 0.0000 3.3216 4.0521 0.6922
4 1.2233 1.4125 3.3216 3.9479 0.6780
----------------------------------------------------------------
NUMBER OF ELECTRONS: 16.00000


[New case 4] NGXF = 200, NGYF = 200, NGZF = 400
# X Y Z CHARGE MIN DIST
----------------------------------------------------------------
1 1.2233 0.0000 0.0000 4.0474 0.6992
2 2.4465 0.7062 0.0000 3.9526 0.6816
3 1.2233 0.0000 3.3216 4.0474 0.6992
4 1.2233 1.4125 3.3216 3.9526 0.6816
----------------------------------------------------------------
NUMBER OF ELECTRONS: 16.00000

[graeme]

It sounds like you are doing everything in the best way we have. I would not, however, conclude that the charges are oscillating as you increase the grid density. The values on each C seem to be converging to a value (+-0.01 e), it is just not equal for each C atom. Perhaps 1 more grid size of 250^3 would help convince us if this were true.

Are you sure that each C should (perhaps by symmetry) have the same charge? Could there be some perturbation which distinguishes 2 of them from the other 2.

But anyways, I don't see a problem with the analysis based upon the data that you have provided. If you are worried about additional maxima in the charge density along the C-C bonds, you could look at the BCF file, and see if you have any small Bader volumes centered between atoms. I agree that such a topology would cause problems -- but this would not be a problem with the method, but rather a problem with the Bader partitioning.