[CP2K-user] [CP2K:18552] Re: Evaluation of basis functions over a grid and computation of overlap integrals

[Aleksandros Sobczyk]

Below is the precise example we are using.
These un-normalized orbitals:








*Sr SZV-MOLOPT-SR-GTH SZV-MOLOPT-SR-GTH-q1012 0 1 6 2 1     7.290111894735 
 0.069364270475 -0.016182746349  0.035659445929     2.536776771327 
-0.571246927373  0.158928639982 -0.195822349727     1.283099546928 
 0.167836311459 -0.041157757852  0.260320252229     0.532449841650 
 0.904733330629 -0.431882417196  0.555386362294     0.211628059408 
 0.250907816117 -0.073959284415  0.267635587013     0.050841303698 
 0.007135721199  0.825600560103  0.001214128781*

after the normalization (cp2k output) become as follows:








*Sr SZV-MOLOPT-SR-GTH SZV-MOLOPT-SR-GTH-q1012 0 1 6 2 1 7.290111894735     
  0.221325      -0.071449       0.684627 2.536776771327      -0.825808     
  0.317914      -1.004793 1.283099546928       0.145521      -0.049379     
  0.569764 0.532449841650       0.405577      -0.267899       
0.404860 0.211628059408       0.056304      -0.022965       
0.061570 0.050841303698       0.000549       0.087969       0.000047*

None of the two aforementioned normalization procedures can reproduce this.

On Friday, March 17, 2023 at 4:54:28 PM UTC+1 Aleksandros Sobczyk wrote:

> 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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