[CP2K-user] [CP2K:18551] Re: Evaluation of basis functions over a grid and computation of overlap integrals

[Aleksandros Sobczyk]

Update on this:
There appear to be two (maybe more) normalization procedures for orbital 
coefficients:
1) https://github.com/cp2k/cp2k/blob/f26eaef31a9d3f80ca30d8d2f11790a2a072e370/src/aobasis/basis_set_types.F#L1099
2) https://github.com/cp2k/cp2k/blob/f26eaef31a9d3f80ca30d8d2f11790a2a072e370/src/atom_types.F#L2374
The results of 1) seem to be closer to the output of cp2k (for s-orbitals). 
For p-orbitals it starts to diverge.

It would be great if someone can confirm which normalization method is used 
internally for contracted Gaussians.
(what is the goal of the normalization? are the primitive Gaussians 
normalized to integrate to 1? is it something more advanced?)

Best regards,
Aleksandros Sobczyk
On Monday, March 13, 2023 at 11:00:04 AM UTC+1 Aleksandros Sobczyk wrote:

> Dear prof. Hutter and CP2K developers,
>
> The example helped to figure out how to reproduce the overlap matrix for 
> our systems. We had to apply the following two steps:
>
> 1) For the basis sets, we had to use the normalized coefficients that are 
> found inside the output file of CP2K. The un-normalized coefficients from 
> the original BASIS_SET file did not work (as you suggested). For now, we 
> can directly use the CP2K output to derive these normalized coefficients 
> for our experiments, but it would be also helpful to know how to reproduce 
> them (i.e., what is the normalization procedure).
>
> 2) We also had to scale all the exponents of all the basis sets by a 
> factor of (1/0.529)^2 (to convert Angstrom to atomic units). This was an 
> arbitrary guess, but without it the overlaps do not match.
>
> Could you confirm that this is the correct way to compute the orbital 
> overlaps? (and if not, propose the correct way). 
> It would also be helpful if these details can be documented, e.g. in this 
> page: https://www.cp2k.org/basis_sets
>
> Best regards and thank you again for the feedback,
> Aleksandros Sobczyk
>
> On Friday, March 10, 2023 at 6:35:28 PM UTC+1 Aleksandros Sobczyk wrote:
>
>> 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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>>>
>>

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