orthogonality of wave functions - PAW

[myronk]

Hello,

Recently, I perform numerical calculations in graphene using VASP.
I use a 2 atom unit cell and the PAW potentials.

In order to assess the accuracy of my calculations I examine the orthonormality
of the electronic wave function by calculating products of the form
<\phi_N| \phi_M> for various bands N and M.

Firstly, I constructed the wfs using only the plane wave expansion, neglecting the projected part.

In this case I notice that the wfs are not always orthogonal. For some bands the product
is about 0.1E-1, instead of a small number, while for N=M I usually get numbers
like 1.05 or 0.090.
That happens for a small number of band, about 10% of the total NBANDS=120.

Assuming that, the plane wave expansion is not enough for a very accurate description of the electronic wf
I desided to use the full PAW wfs, by modifying VASP in order to add the projected part. For that I have used
the analysis presented in PHYSICAL REVIEW B, VOLUME 63, 125108 by B. Adolph (see attached file).

However, the problem remains the same.
The products that were non-zero previously don't become zero now, although they are slightly lower.
In every case the new contribution, introduced by the 2nd term of Eq (4), is 1 order of magnitude lower that the 1st.
More particularly, if the 1st term of the overlap operation (4) gives in (3) a number C then the 2nd term gives something like -C/10.
So, if this number was 1 order of magnitude higher then I will get satisfying numerical results.

My questions are the following.

1) Is is possible that the wfs that VASP calculates are not orthogonal?.
What is the expected numerical accuracy of the calculation I describe before?

2)In formula (1) of the attached paper, how the atomic AE and PS wfs are normalized?
Is there any need for unit restoration when this formula is applied?

Has anyone come across with such a problem?
Any suggestions?

Thanks
Myron

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