[CP2K-user] [CP2K:18530] Re: Evaluation of basis functions over a grid and computation of overlap integrals

Aleksandros Sobczyk sobczykalek at gmail.com
Fri Mar 10 13:26:42 UTC 2023

Update: I have also calculated several overlap integrals analytically (for 
s-orbitals which are simpler), they still don't match the values of the S 
Any feedback would be greatly appreciated.

On Wednesday, March 8, 2023 at 12:57:02 PM UTC+1 Aleksandros Sobczyk wrote:

> 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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