Charge partitioning issues in cell with vacuum

[jefflowe]

Hello,

I have a fairly simple system: a surface slab with 40 lithium atoms that has been relaxed in VASP. However, when computing the Bader charges, there is a very uneven partitioning of the charges. My ACF.dat file is shown below:

# X Y Z CHARGE MIN DIST ATOMIC VOL
--------------------------------------------------------------------------------
1 0.0000 0.0000 0.0000 2.7351 1.8411 187.1794
2 2.4332 1.4048 0.9934 0.2623 0.9943 15.3488
3 0.0000 2.8096 1.9867 1.9645 1.0086 39.6482
4 0.0000 0.0000 2.9269 0.2062 0.9946 5.2497
5 2.4332 1.4048 4.0284 0.2062 1.0099 5.3808
6 0.0000 2.8096 4.9003 0.2104 1.0105 5.3435
7 0.0000 0.0000 6.0120 0.2040 0.9943 5.2385
8 2.4332 1.4048 7.0976 0.2206 1.0068 6.2166
9 0.0000 2.8096 7.7650 1.1134 0.9969 29.1451
10 0.0000 0.0000 8.9806 2.8773 1.9209 192.1000
11 -2.4332 4.2143 0.0000 2.7351 1.8411 187.1739
12 0.0000 5.6191 0.9934 0.2623 0.9943 15.3488
13 -2.4332 7.0239 1.9867 1.9646 1.0086 39.6487
14 -2.4332 4.2143 2.9269 0.2062 0.9946 5.2497
15 0.0000 5.6191 4.0284 0.2062 1.0099 5.3808
16 -2.4332 7.0239 4.9003 0.2104 1.0105 5.3435
17 -2.4332 4.2143 6.0120 0.2040 0.9943 5.2385
18 0.0000 5.6191 7.0976 0.2206 1.0068 6.2167
19 -2.4332 7.0239 7.7650 1.1133 0.9969 29.1446
20 -2.4332 4.2143 8.9806 2.8773 1.9209 192.0974
21 4.8663 0.0000 0.0000 2.7351 1.8411 187.1788
22 7.2995 1.4048 0.9934 0.2623 0.9943 15.3490
23 4.8663 2.8096 1.9867 1.9644 1.0086 39.6463
24 4.8663 0.0000 2.9269 0.2062 0.9946 5.2497
25 7.2995 1.4048 4.0284 0.2062 1.0099 5.3808
26 4.8663 2.8096 4.9003 0.2104 1.0105 5.3435
27 4.8663 0.0000 6.0120 0.2040 0.9943 5.2385
28 7.2995 1.4048 7.0976 0.2206 1.0068 6.2167
29 4.8663 2.8096 7.7650 1.1134 0.9969 29.1469
30 4.8663 0.0000 8.9806 2.8773 1.9209 192.0702
31 2.4332 4.2143 0.0000 2.7351 1.8411 187.1779
32 4.8663 5.6191 0.9934 0.2623 0.9943 15.3492
33 2.4332 7.0239 1.9867 1.9645 1.0086 39.6467
34 2.4332 4.2143 2.9269 0.2062 0.9946 5.2497
35 4.8663 5.6191 4.0284 0.2062 1.0099 5.3808
36 2.4332 7.0239 4.9003 0.2104 1.0105 5.3435
37 2.4332 4.2143 6.0120 0.2040 0.9943 5.2385
38 4.8663 5.6191 7.0976 0.2206 1.0068 6.2167
39 2.4332 7.0239 7.7650 1.1134 0.9969 29.1461
40 2.4332 4.2143 8.9806 2.8773 1.9209 192.0648
--------------------------------------------------------------------------------
VACUUM CHARGE: 0.0000
VACUUM VOLUME: 0.0000
NUMBER OF ELECTRONS: 40.0000

As shown, there are 40 total electrons in the calculation, 1 for each Li atom. Therefore, taking atom 1 as an example, the net charge is 1-2.7351=-1.7351, which is an unphysical result. I suspect that it may have something to do with the vacuum, but I am not sure. The BCF.dat shows that many charge density maxima are located more than 1 Ang from the nearest atomic centers, which I also found concerning.

I was not able to fix this issue using the weight method for partitioning. However, using the Voronoi population analysis gave reasonable results (the charge attributed to each atom was around 1.0, leading to a neutral net charge). If you could assist me with this issue, I would greatly appreciate it.

Thanks,
Jeff

[graeme]

If you can post the charge density files, I can take a look.

[jefflowe]

I've attached the charge density files. Thanks for your help!

[graeme]

I don't know about the chemistry of metallic Li, but I can see from the charge density (attached) that there is a significant region of charge below the surface atoms which is being associated with the surface atoms in the Bader decomposition.

Screen Shot 2018-10-11 at 4.36.13 PM.png (69.28 KiB) Viewed 27448 times

[graeme]

And here is the valence charge, showing charge below the surface layer.

Screen Shot 2018-10-11 at 4.40.45 PM.png (94.43 KiB) Viewed 27448 times

You might want to double check these calculations using the Li_sv potentials, which should have all three electrons treated as valence.

[jefflowe]

Thank you for the guidance Prof. Henkelman. I found a very similar result for the charge density, and when computing the Bader charges, using the Li_sv potential. I'll have to do some further research on this to determine if this makes sense from a chemistry perspective, but it's good to know that I'm not introducing any errors by improperly performing the Bader analysis.