Number of PAW one-center entries in CHGCAR

[yuansheng_zhao]

Dear Admin and VASP users,

I am trying to interpret the one-center terms in CHGCAR.
These terms should represent Eq.7 of PhysRevB 59, 1758:
rho_ij = sum_n f_n <psi_n|p_i> <p_j|psi_n>
Thus, for element with a total of n lm-decomposed projectors, there should be n(n+1)/2 entries.
However, this is not the case.

For elements with 2s + 2p projectors such as O, n = 2*1 + 2*3 = 8, so I am expecting 8*9/2 = 36 entries while there are only 33 in CHGCAR.
Likely, for elements with 2s + 2p + 1d (such as Mg) or 2s + 2p + 2d (such as Zn), I am expecting 13*14/2 = 91 and 18*19/2 = 171 entries instead of 78 and 138 in CHGCAR, respectively.

The same also goes to augmentation part in POT file.

I am wondering what I am missing. Any help is appreciated.

Best regards,
YZ

[alexey.tal]

Dear Younsheng,

If you would like to understand how the number of augmentation occupanices is calculated you should look at the routine RETRIEVE_RHOLM in paw_base.F
In the essence, we have two projectors for each angular momentum that gives us 2*n*(2*n'+1)/2. Then for each pair of angular momenta l and l' we add all occupancy channels J=2L+1, where L=|l-l'|...l+l'.
And certain elements of this array will be zero due to the sum rule.

[yuansheng_zhao]

Dear Alexey

Thank you for your reply.
Now I have managed to understand the numbers.
They are stored using LM basis instead of ll'mm', and the terms that are identically zero are not written out.

Best regards,
YZ