[CP2K-user] dimension inconsistency of the overlap and MO coefficients

Xiaoming Wang wxia... at gmail.com
Fri Oct 12 14:53:59 CEST 2018


Hi Vladimir,

I'm sorry I made a mistake. I mean could the overlap matrix be transformed 
to cartesian coordinates? Because I only have the MO of LUMO printed in 
cartesian coordinates.

Best,
Xiaoming 

On Friday, October 12, 2018 at 8:48:45 AM UTC-4, Vladimir Rybkin wrote:
>
> Hi Xiaoming,
>
> overlap matrix is already in spherical Gaussians. The overlap is taken 
> between basis functions (AO), not between MO(s). It is calculated before 
> any MOs are obtained.
>
> Yours,
>
> Vladimir
>
> пятница, 12 октября 2018 г., 14:34:43 UTC+2 пользователь Xiaoming Wang 
> написал:
>>
>> Hi Vladimir,
>>
>> Thanks for your confirmation. Yes, with Cartesian off, the dimensions are 
>> consistent now. If cp2k does not print MO of vacant state, then is it 
>> possible to transform the overlap matrix to spherical coordinates?
>>
>> Best,
>> Xiaoming
>>
>> On Friday, October 12, 2018 at 8:18:30 AM UTC-4, Vladimir Rybkin wrote:
>>>
>>> Dear Xiaoming,
>>>
>>> thank you for the data. I don't see any inconsistency now. You get 52 
>>> with Cartesian off and 54 with Cartesian on. Turning Cartesian off you can 
>>> now multiply your C with your S. Isn't that what you want? Unfortunately, I 
>>> can't comment on why orbital #5 is not printed. Perhaps, that is due to the 
>>> fact that it is vacant.
>>>
>>> Yours,
>>>
>>> Vladimir
>>>
>>> пятница, 12 октября 2018 г., 13:47:35 UTC+2 пользователь Xiaoming Wang 
>>> написал:
>>>>
>>>> Hi Vladimir,
>>>>
>>>> Thanks for you reply.
>>>>
>>>> My input of the print part is:
>>>>
>>>> ------------
>>>>
>>>>     &MO
>>>>
>>>>       EIGENVALUES
>>>>
>>>>       EIGENVECTORS
>>>>
>>>>       CARTESIAN
>>>>
>>>>       FILENAME mos
>>>>
>>>>       MO_INDEX_RANGE 4 5
>>>>
>>>>       OCCUPATION_NUMBERS
>>>>
>>>>       &EACH
>>>>
>>>>        QS_SCF 0
>>>>
>>>>       &END EACH
>>>>
>>>>      &END MO
>>>>
>>>> --------------
>>>>
>>>>
>>>> With CARTESIAN on, I get
>>>>
>>>>
>>>> ----------------
>>>>
>>>>  MO EIGENVALUES, MO OCCUPATION NUMBERS, AND CARTESIAN MO EIGENVECTORS
>>>>
>>>>
>>>>                               4            5
>>>>
>>>>                           -0.260963    -0.034173
>>>>
>>>>
>>>>                            2.000000     0.000000
>>>>
>>>>
>>>>      1     1  O  2s        0.000000     0.236782
>>>>
>>>>      2     1  O  3s        0.000000    -0.090781
>>>>
>>>>      3     1  O  4s        0.000000    -0.240258
>>>>
>>>>      4     1  O  3px      -0.917807    -0.000000
>>>>
>>>>      5     1  O  3py      -0.000000    -0.000000
>>>>
>>>>      6     1  O  3pz       0.000000    -0.238095
>>>>
>>>>      7     1  O  4px       0.020934    -0.000000
>>>>
>>>>      8     1  O  4py       0.000000    -0.000000
>>>>
>>>>      9     1  O  4pz      -0.000000     0.013849
>>>>
>>>>     10     1  O  5px      -0.003042     0.000000
>>>>
>>>>     11     1  O  5py       0.000000     0.000000
>>>>
>>>>     12     1  O  5pz      -0.000000     0.099980
>>>>
>>>>     13     1  O  3dx2     -0.000000     0.000099
>>>>
>>>>     14     1  O  3dxy     -0.000000    -0.000000
>>>>
>>>>     15     1  O  3dxz     -0.005256    -0.000000
>>>>
>>>>     16     1  O  3dy2     -0.000000     0.000744
>>>>
>>>>     17     1  O  3dyz      0.000000    -0.000000
>>>>
>>>>     18     1  O  3dz2      0.000000    -0.000844
>>>>
>>>>     19     1  O  4dx2     -0.000000     0.000357
>>>>
>>>>     20     1  O  4dxy      0.000000    -0.000000
>>>>
>>>>     21     1  O  4dxz     -0.022359     0.000000
>>>>
>>>>     22     1  O  4dy2      0.000000     0.004105
>>>>
>>>>     23     1  O  4dyz     -0.000000     0.000000
>>>>
>>>>     24     1  O  4dz2      0.000000    -0.004463
>>>>
>>>>     25     1  O  5s       -0.000000    -0.011663
>>>>
>>>>     26     1  O  5px       0.024750    -0.000000
>>>>
>>>>     27     1  O  5py      -0.000000     0.000000
>>>>
>>>>     28     1  O  5pz       0.000000    -0.077018
>>>>
>>>>
>>>>     29     2  H  1s        0.000000    -0.116793
>>>>
>>>>     30     2  H  2s        0.000000    -0.003374
>>>>
>>>>     31     2  H  3s       -0.000000     0.197029
>>>>
>>>>     32     2  H  2px       0.011575    -0.000000
>>>>
>>>>     33     2  H  2py       0.000000     0.008716
>>>>
>>>>     34     2  H  2pz      -0.000000    -0.004748
>>>>
>>>>     35     2  H  3px       0.028901    -0.000000
>>>>
>>>>     36     2  H  3py       0.000000     0.013894
>>>>
>>>>     37     2  H  3pz      -0.000000    -0.010138
>>>>
>>>>     38     2  H  4s       -0.000000     0.421270
>>>>
>>>>     39     2  H  4px       0.026994     0.000000
>>>>
>>>>     40     2  H  4py       0.000000     0.041403
>>>>
>>>>     41     2  H  4pz      -0.000000    -0.044975
>>>>
>>>>
>>>>     42     3  H  1s        0.000000    -0.116793
>>>>
>>>>     43     3  H  2s       -0.000000    -0.003374
>>>>
>>>>     44     3  H  3s        0.000000     0.197029
>>>>
>>>>     45     3  H  2px       0.011575    -0.000000
>>>>
>>>>     46     3  H  2py       0.000000    -0.008716
>>>>
>>>>     47     3  H  2pz      -0.000000    -0.004748
>>>>
>>>>     48     3  H  3px       0.028901    -0.000000
>>>>
>>>>     49     3  H  3py      -0.000000    -0.013894
>>>>
>>>>     50     3  H  3pz      -0.000000    -0.010138
>>>>
>>>>     51     3  H  4s        0.000000     0.421270
>>>>
>>>>     52     3  H  4px       0.026994     0.000000
>>>>
>>>>     53     3  H  4py       0.000000    -0.041403
>>>>
>>>>     54     3  H  4pz       0.000000    -0.044975
>>>>
>>>>
>>>>
>>>>   Fermi energy:                -0.260963
>>>>
>>>>
>>>>   HOMO-LUMO gap:                0.226790 =   6.17 eV
>>>> ---------------------------------------
>>>>
>>>> However, with CARTESIAN OFF, I get only the orbital #4:
>>>>
>>>> ----------------------------------------
>>>>
>>>>  MO EIGENVALUES, MO OCCUPATION NUMBERS, AND SPHERICAL MO EIGENVECTORS
>>>>
>>>>
>>>>                               4
>>>>
>>>>                           -0.260963
>>>>
>>>>
>>>>                            2.000000
>>>>
>>>>
>>>>      1     1  O  2s        0.000000
>>>>
>>>>      2     1  O  3s        0.000000
>>>>
>>>>      3     1  O  4s        0.000000
>>>>
>>>>      4     1  O  3py      -0.000000
>>>>
>>>>      5     1  O  3pz       0.000000
>>>>
>>>>      6     1  O  3px      -0.917807
>>>>
>>>>      7     1  O  4py       0.000000
>>>>
>>>>      8     1  O  4pz      -0.000000
>>>>
>>>>      9     1  O  4px       0.020934
>>>>
>>>>     10     1  O  5py       0.000000
>>>>
>>>>     11     1  O  5pz      -0.000000
>>>>
>>>>     12     1  O  5px      -0.003042
>>>>
>>>>     13     1  O  3d-2     -0.000000
>>>>
>>>>     14     1  O  3d-1      0.000000
>>>>
>>>>     15     1  O  3d0       0.000000
>>>>
>>>>     16     1  O  3d+1     -0.005256
>>>>
>>>>     17     1  O  3d+2     -0.000000
>>>>
>>>>     18     1  O  4d-2      0.000000
>>>>
>>>>     19     1  O  4d-1     -0.000000
>>>>
>>>>     20     1  O  4d0       0.000000
>>>>
>>>>     21     1  O  4d+1     -0.022359
>>>>
>>>>     22     1  O  4d+2     -0.000000
>>>>
>>>>     23     1  O  5s       -0.000000
>>>>
>>>>     24     1  O  5py      -0.000000
>>>>
>>>>     25     1  O  5pz       0.000000
>>>>
>>>>     26     1  O  5px       0.024750
>>>>
>>>>
>>>>     27     2  H  1s        0.000000
>>>>
>>>>     28     2  H  2s        0.000000
>>>>
>>>>     29     2  H  3s       -0.000000
>>>>
>>>>     30     2  H  2py       0.000000
>>>>
>>>>     31     2  H  2pz      -0.000000
>>>>
>>>>     32     2  H  2px       0.011575
>>>>
>>>>     33     2  H  3py       0.000000
>>>>
>>>>     34     2  H  3pz      -0.000000
>>>>
>>>>     35     2  H  3px       0.028901
>>>>
>>>>     36     2  H  4s       -0.000000
>>>>
>>>>     37     2  H  4py       0.000000
>>>>
>>>>     38     2  H  4pz      -0.000000
>>>>
>>>>     39     2  H  4px       0.026994
>>>>
>>>>
>>>>     40     3  H  1s        0.000000
>>>>
>>>>     41     3  H  2s       -0.000000
>>>>
>>>>     42     3  H  3s        0.000000
>>>>
>>>>     43     3  H  2py       0.000000
>>>>
>>>>     44     3  H  2pz      -0.000000
>>>>
>>>>     45     3  H  2px       0.011575
>>>>
>>>>     46     3  H  3py      -0.000000
>>>>
>>>>     47     3  H  3pz      -0.000000
>>>>
>>>>     48     3  H  3px       0.028901
>>>>
>>>>     49     3  H  4s        0.000000
>>>>
>>>>     50     3  H  4py       0.000000
>>>>
>>>>     51     3  H  4pz       0.000000
>>>>
>>>>     52     3  H  4px       0.026994
>>>>
>>>>
>>>>
>>>>   Fermi energy:                -0.260963
>>>>
>>>> -----------------------------
>>>>
>>>>
>>>> Why the MO #5 is not printed in spherical coordinate?
>>>>
>>>>
>>>> Best,
>>>>
>>>> Xiaoming
>>>>
>>>> On Friday, October 12, 2018 at 5:51:08 AM UTC-4, Vladimir Rybkin wrote:
>>>>>
>>>>> Hi Xiaoming,
>>>>>
>>>>> it is. I mean that by default it is not printed, only the basis is. 
>>>>> So, please attach your input/output: this will help to stay on equal 
>>>>> footing.
>>>>>
>>>>> Yours,
>>>>>
>>>>> Vladimir
>>>>>
>>>>> четверг, 11 октября 2018 г., 16:26:57 UTC+2 пользователь Xiaoming Wang 
>>>>> написал:
>>>>>>
>>>>>> Hi Vladimir,
>>>>>>
>>>>>> Are you saying the option of printing MOs with eigenvector on is not 
>>>>>> printing the MO coefficients?
>>>>>>
>>>>>> Best,
>>>>>> Xiaoming
>>>>>>
>>>>>> On Thursday, October 11, 2018 at 9:36:49 AM UTC-4, Vladimir Rybkin 
>>>>>> wrote:
>>>>>>>
>>>>>>> Dear Xiaoming,
>>>>>>>
>>>>>>> by default CP2K does not print MO coefficients. It prints the basis, 
>>>>>>> which is Cartesian (e.i. 6 d orbitals instead of 5). So, input/output would 
>>>>>>> be helpful.
>>>>>>>
>>>>>>> Yours,
>>>>>>>
>>>>>>> Vladimir
>>>>>>>
>>>>>>> четверг, 11 октября 2018 г., 15:24:16 UTC+2 пользователь Xiaoming 
>>>>>>> Wang написал:
>>>>>>>>
>>>>>>>> Hi,
>>>>>>>>
>>>>>>>> I just missed one thing. The MOs could also be printed with 
>>>>>>>> spherical coordinates. Then, it should be consistent.
>>>>>>>>
>>>>>>>> Best,
>>>>>>>> Xiaoming
>>>>>>>>
>>>>>>>> On Thursday, October 11, 2018 at 9:21:56 AM UTC-4, Xiaoming Wang 
>>>>>>>> wrote:
>>>>>>>>>
>>>>>>>>> Hi Vladimir,
>>>>>>>>>
>>>>>>>>> Thanks for your reply. I'm wondering why the eigenvectors and 
>>>>>>>>> overlap are not using the same basis (or with same basis but different 
>>>>>>>>> coordinates).
>>>>>>>>>
>>>>>>>>> Best,
>>>>>>>>> Xiaoming
>>>>>>>>>
>>>>>>>>> On Thursday, October 11, 2018 at 4:28:32 AM UTC-4, Vladimir Rybkin 
>>>>>>>>> wrote:
>>>>>>>>>>
>>>>>>>>>> Dear Xiaoming,
>>>>>>>>>>
>>>>>>>>>> the 6 d orbitals correspond to the six components in the 
>>>>>>>>>> Cartesian coordinates, whereas 5 d orbitals are the same expressed is 
>>>>>>>>>> spherical coordinates. The coordinate transformation is involved in 
>>>>>>>>>> between. 
>>>>>>>>>>
>>>>>>>>>> Yours,
>>>>>>>>>>
>>>>>>>>>> Vladimir
>>>>>>>>>>
>>>>>>>>>> среда, 10 октября 2018 г., 16:16:56 UTC+2 пользователь Xiaoming 
>>>>>>>>>> Wang написал:
>>>>>>>>>>>
>>>>>>>>>>> Hello,
>>>>>>>>>>>
>>>>>>>>>>> I'd like to check the equation C^T S C = 1, where C is MO 
>>>>>>>>>>> coefficient and S the overlap matrix. 
>>>>>>>>>>> However, for my test calculation, C is 54*1 while S is 52*52. I 
>>>>>>>>>>> checked the basis details, for the
>>>>>>>>>>> MO coefficient, there are 6 d orbitals 
>>>>>>>>>>> (dx2,dxy,dxz,dy2,dyz,dz2), while for the overlap matrix,
>>>>>>>>>>> only 5 d orbitals (d-2,d-1,d0,d+1,d+2) are printed. Why is like 
>>>>>>>>>>> that? Am I missing something?
>>>>>>>>>>>
>>>>>>>>>>> Best,
>>>>>>>>>>> Xiaoming 
>>>>>>>>>>>
>>>>>>>>>>
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