Hi
You want to normalize a contracted Gaussian function (cgf) basis set, which is performed in two steps: (1) normalization of the primitive Cartesian Gaussian functions and thereafter (2) normalization of the contracted Gaussian functions as indicated in line 1075. This is all in Cartesian representation. For the spherical orbital representation, you will need a further Cartesian to spherical orbital transformation step. CP2K calculates integrals internally in the Cartesian representation, but the default printout, e.g. for the overlap integral matrix, is in spherical orbitals.
Firstly, I would try to reproduce the normalization for an uncontracted basis set (one primitive function per l only). In the next step, you can try two primitive functions. Normalization is required to keep for instance the electron count (trace of PS).
HTH
Matthias
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Hi Aleksandros
The basis set output in the top of the CP2K output is in Cartesian representation (i.e. not spherical coordinates) which you can easily recognize as soon as you have basis functions with l > 1 (d, f …), because there are 6 Cartesian d orbitals printed. I just wanted to note that the default output for integral matrices like the overlap matrix S, however, is in the spherical orbital representation (5 d orbitals d(-2) … d(+2)). Maybe, I confused you in that respect, since you are still trying to reproduce the initial basis set normalization.
I suggest to start exercising with a primitive basis set and a single He atom, e.g.
He
1 0 2 1 1 1 1
1.2 0.5 0.4 0.3
and then try a contracted basis set with two primitive Gaussian functions per l value
He
1 0 2 2 1 1 1
1.2 0.5 0.4 0.3
0.8 0.4 0.2 0.1
Here, I just selected exponents and coefficients randomly without testing or calculating anything in an exemplary manner.
Note, that Cartesian and spherical Gaussian functions have different normalization factors.
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