# MO coefficients not normalized?

Matt W mattwa... at gmail.com
Wed May 9 20:21:36 UTC 2018

```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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