[CP2K-user] MO coefficients not normalized?
Xiaoming Wang
wxia... at gmail.com
Wed Oct 10 12:55:57 UTC 2018
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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