[CP2K-user] [CP2K:18526] Evaluation of basis functions over a grid and computation of overlap integrals

[Aleksandros Sobczyk]

Hello,

I have a set of atoms in real-space and the corresponding SZV basis sets.
I want to evaluate each basis function over a grid of points in the cell.
E.g., I have a grid of 3d points [r1, r2, ..., rk] and I want to evaluate 
each 
Φj(r1), Φj(r2), ... Φj(rk)
As a test, I tried to numerically integrate Φj * conj(Φj) over the grid 
that it was evaluated, and compare the result with the corresponding entry 
S[j, j] of the overlap matrix that
is returned by CP2K.
Unfortunately my integral differs substantially from the element S[j, j], 
so I am doing something wrong.

Can we find somewhere more detailed documentation on  the precise 
mathematical formulation of the basis sets, and also on the specific 
algorithms that are used by CP2K to compute the overlap integrals?
(So far I have followed as precisely as possible the following 
page: https://www.cp2k.org/basis_sets
but it is still missing information, e.g. are the coefficients normalized? 
do we assume that the spherical harmonics include the phase factor? etc.)

Thanks a lot in advance!
Aleksandros

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