# [CP2K-user] [CP2K:18534] Re: Evaluation of basis functions over a grid and computation of overlap integrals

Aleksandros Sobczyk sobczykalek at gmail.com
Fri Mar 10 17:35:27 UTC 2023

Dear Prof. Hutter,

Let us investigate it with my colleagues and see if we can resolve our
problem.

Best regards,
Aleksandros

On Friday, March 10, 2023 at 3:18:28 PM UTC+1 Jürg Hutter wrote:

> Hi
>
> are you assuming normalized or un-normalized Gaussians?
> The basis set input in CP2K uses (like all QC codes) normalized Gaussians.
> Internally, CP2K works with un-normalized Cartesian Gaussians, i.e. the
> coefficients are adapted at the beginning of the calculation.
>
> I have attached a simple example where you can play with the basis set
> in the input and the overlap matrix is printed.
>
> regards
> JH
>
> ________________________________________
> Aleksandros Sobczyk <sobcz... at gmail.com>
> Sent: Friday, March 10, 2023 2:26 PM
> To: cp2k
> Subject: [CP2K:18530] Re: Evaluation of basis functions over a grid and
> computation of overlap integrals
>
> 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
> matrix.
> 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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