how cp2k calculates PDOS

[Artem Fediai]

Dear all,

What is the theoretical framework for calculating PDOS in cp2k?
If we have orthogonal basis, we can calculate PDOS straightforwardly by 
using expansion coefficient or MO by AO, and the sum of PDOS will be equal 
to the total DOS, as it should be.
In our case the atomic basis is not orthogonal and this rule doesn't work, 
thus we need  to 'separate' atomic orbitals somehow from each other, in 
other words make the basis orthogonal.
How this procedure has been realized in cp2k?
How to obtain PDOS on the specific orbital manually, having in hand 
expansion of MO by AO (and overlap matrix)?

Thanks for your answers and comments,
Artem
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