[CP2K-user] MO coefficients not normalized?

[Xiaoming Wang]

Hi Matt,

It seems that the dimensions of the C and S are not consistent. For 
example, for my H2O moculue, the C is 54*1, but the overlap S is 52*52. Why 
is that?

Best,
Xiaoming

On Wednesday, May 9, 2018 at 4:21:37 PM UTC-4, Matt W wrote:
>
> Dear Daniel,
>
> the Gaussian basis set is not orthonormal, so the overlap matrix is 
> required to provide a metric that converts to an orthonormal basis. Due to 
> symmetry the pz orbital is orthogonal to the others in your example, so in 
> that case every thing is easy.
>
> In general, the relation is C^T S C = I, where C is the matrix of MO 
> coefficients, S is the overlap matrix and I is the identity matrix. You can 
> print of the S matrix and check this. It is somewhere in the AO_MATRICES 
> section of DFT % PRINT.
>
> See, for instance, Szabo and Ostlund, Modern Quantum Chemistry, 
> Introduction to Advanced Electronic Structure Theory - exercise 3.10 in my 
> version.
>
> Matt
>
> On Wednesday, May 9, 2018 at 8:20:13 PM UTC+1, Dan_M wrote:
>>
>> Dear all,
>>
>> After requesting the printing out of the MO coefficients, I have observed 
>> that the coefficients do not seem to be normalized. For instance, here are 
>> the MOs for 1 water molecule with a SZV basis (after a single point 
>> calculation on the "real" geometry, with diagonalization algorithm 
>> standard):
>>
>>  MO EIGENVALUES, MO OCCUPATION NUMBERS, AND SPHERICAL MO EIGENVECTORS
>>
>>                               1              2                3         
>>        4
>>                            -0.952554    -0.496599    -0.304175    
>> -0.250528
>>
>>                             2.000000     2.000000     2.000000     
>> 2.000000
>>
>>      1     1  O  2s        0.807460    -0.000000     0.542312     0.000000
>>      2     1  O  3py      -0.246487    -0.000000     0.810927     0.000000
>>      3     1  O  3pz      -0.000000     0.000000    -0.000000     1.000000
>>      4     1  O  3px       0.000000    -0.661844    -0.000000    -0.000000
>>
>>      5     2  H  1s        0.125677    -0.390214    -0.194623    -0.000000
>>
>>      6     3  H  1s        0.125677     0.390214    -0.194623    -0.000000
>>
>> So only the MO 4 is trivially normalized, but the others are not. Am I 
>> missing something (some correction factor, etc) or is this just the way it 
>> is?
>>
>> Thanks and best
>> Daniel
>>
>>
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