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

Jürg Hutter hutter at chem.uzh.ch
Fri Mar 10 14:18:21 UTC 2023

```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: cp2k at googlegroups.com <cp2k at googlegroups.com> on behalf of Aleksandros Sobczyk <sobczykalek 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.)

Aleksandros

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