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

[Aleksandros Sobczyk]

Dear Prof. Hutter,

Thank you very much for your reply and for the example.
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
>
> ________________________________________
> From: cp... at googlegroups.com <cp... at googlegroups.com> on behalf of 
> 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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