[CPMD-list] COMPLETNESS in PROJECT WAVEFUNCTION

[Juerg Hutter]

Hi

> I tried to use projection of wavefunction on atomic pseudized
> wavefunction and found few points which completely confused me.
> I hope somebody can help me.
>
> 1. Let's look on output of sample properties calculation of B2H6 which
> comes with 3.9.1 release.
>
> ------------------
>       ORBITAL      1       2       3       4       5       6
>   COMPLETNESS    0.986   0.972   0.986   0.986   0.972   0.986
>   OCCUPATION     2.000   2.000   2.000   2.000   2.000   2.000
>   1   B  S       0.339   0.146  -0.064  -0.339  -0.146   0.064
>          Px      0.000  -0.201   0.000   0.000  -0.201   0.000
>          Pz      0.192  -0.219   0.060  -0.192   0.219  -0.060
>          Py      0.406   0.000   0.019   0.406   0.000   0.019
>   2   B  S      -0.064   0.146   0.339   0.064  -0.146  -0.339
>          Px      0.000  -0.201   0.000   0.000  -0.201   0.000
>          Pz     -0.060   0.219  -0.192   0.060  -0.219   0.192
>          Py     -0.019   0.000  -0.406  -0.019   0.000  -0.406
>   3   H  S      -0.034   0.513  -0.034   0.034   0.157   0.034
>   4   H  S      -0.034  -0.157  -0.034   0.034  -0.513   0.034
>   5   H  S       0.052  -0.055   0.519   0.023   0.055   0.032
>   6   H  S      -0.023  -0.055  -0.032  -0.052   0.055  -0.519
>   7   H  S       0.519  -0.055   0.052   0.032   0.055   0.023
>   8   H  S      -0.032  -0.055  -0.023  -0.519   0.055  -0.052
> ------------------
>
> Completness values around 0.97-0.99 looks very good (even not
> realistic). But the sums of squares of projection coefficients
> are far from completeness values (for orbital #1 sum of squares is 0.601).
> Could you explain me the meaning of COMPLETENESS value in this
> procedure?

Typical completeness values for occupied states in simple systems
is about 0.95 or better. This is the reason why tight binding works.
Completeness is the amount of an orbital that is described by the
projection basis. However, the localized projection basis is not
orthonormal, therefore you cannot just add up the square of the
coefficients, you have to take the overlap matrix into account.


> Or here is a problem...
>
> 2. CPMD documentation on PROJECT WAVEFUNCTION calculation
> made me even more confused:
>
> citation:
> ------------------
> PROJECT WAVEFUNCTION
> Section: &PROP
> The wavefunctions are projected on atomic orbitals.
> The projected wavefunctions are then used to calculate atomic populations and bond
> orders. The atomic orbitals have to be specified in the file ATWFN, which is found
> in the pseudo-potential library directory.
> ------------------
>

I think this was already explained by Axel.


> Is the last sentence correspond to reality?
> ATWFN is the file which corresponds to all-electron wavefunction in
> Hammann's atomic code and it doesn't actually required for PROJECT
> WAVEFUNCTION jobs... Am I right?
>

No, ATWFN is not the all-electron wfn file from Haman's code.
The names are the same by coincident.


> 3. What is MODIFIED ATOMIC ORBITALS ?
> Could somebody give reference or definition?

Have a look at the references (from the manual)
E. R. Davidson, J. Chem. Phys. 46, 3320 (1967); K. R. Roby, Mol. Phys. 27,
81 (1974); R. Heinzmann and R. Ahlrichs, Theoret. Chim. Acta (Berl.) 42,
33 (1976); C. Ehrhardt and R. Ahlrichs, Theoret. Chim. Acta (Berl.) 68,
231 (1985)

Juerg Hutter


>
>
>
> --
> Best regards,
>  Oleg
>
>
> ______________________________________________________
> Oleg Yazyev
> Institute of Molecular and Biological Chemistry
> Swiss Federal Institute of Technology in Lausanne (EPFL)
> EPFL - BCH
> CH-1015 Lausanne (Switzerland)
> Tel.: +41 21 693 9881
> E-mail: oleg.yazyev at epfl.ch
> WWW: http://icmbcu001.epfl.ch/yazyev/index.html
> _______________________________________________________
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