Subject: NBO

From: Maija Lahtela <[email-masked]>
Date: Tue, 23 Feb 1999 07:25:10 +0200

Dear CCLers,

Approximately a week ago I send an inquire about NBO (Natural Bond
Orbital) analysis within Gaussian98 having warning messages. 
 
WARNING:  1 low occupancy (<1.9990e) core orbital  found on  P 3
           1 low occupancy (<1.9990e) core orbital  found on  C 5

 WARNING:  Population inversion found on atom  P 3
           Population inversion found on atom  O 4
           Population inversion found on atom  C 5
           Population inversion found on atom  C 6
           Population inversion found on atom  C 7
           Population inversion found on atom  C 8
           Population inversion found on atom  C 9
           Population inversion found on atom  C10
           Population inversion found on atom  O11
           Population inversion found on atom  S13

Thank you all for you help.

I was asked to summarize this so here all all the answers that I got from
you.

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Hi!

        I cannot say much about the warnings you get from G98 in the
output.
But if it's not normal, it might be caused by the bug in NBO link (l607)
which was confirmed to us by Doug Fox three months ago.  Unusually, the
bug
appeared only under Linux.  If your G98 works under Linux, and if you
purcha-
sed G98 more than 3 months ago, you should consider this possibility too.

        If you have an access to G98 (or G94) on different platforms and
if 
you get the same output everywhere, it's probably not related to the bug. 
Otherwise, let me know and I'll send you the copy of my correspondence
with
Doug Fox which also includes the fix for the bug.

                Sincerely,

                   Darko Babic
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Those WARNINGs are quiet usual. When NBO program prints Natural Atomic
Orbitals
(1s, 2s, 3s etc. ),it does on the basis of the energy order or on the
basis of occupancy. The
WARNING message "Population inversion" comes when, the orbital occupancies
and energy ordering don't match or don't coincide. suppose, for example
when one of 3d orbital lies below in energy, but it's population
(occupancy) is lower than 4s or any of 4p orbitals, then population
inversion occurs and should print warning massage.

For core (NAO treated as unhybridized single center core NBO) orbitals,
which in formal Lewis sense should be filled by 2 electrons. Sometimes due to
unphysical mixing of core and valence lone pairs, the core occupancy goes
below the threshold <1.9990e) and should print worning massage

However, your NBO analysis should be ok.

Cheers.

Jamal

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I'm quite new to this area but as i heard, an occupancy
above 1.99 should refer to a core orbital. Your ones are
probably  a bit lower than the usual ones (i have no 
experience in it) but i think they might be correct.
     However, if you calculate those occupancies to
determine which orbitals to use in a multi-reference
calculation, they might not be reliable: that is what the 
warning is for (in the non-dynamic correlation, those
determinants/configurations will dominate that have
orbitals with low occupancies, thus the outer ones).
     I have no idea about the warning "population
inversion"... 
     Since i'm a beginner to this topic, i'd like to ask 
you to summarize to the list.

Best regards,
Tamas Karpati

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Such warnings can usually be ignored.

> WARNING:  1 low occupancy (<1.9990e) core orbital  found on  P 3
>           1 low occupancy (<1.9990e) core orbital  found on  C 5

In the first case NBO has calculated a couple core orbitals with
occupancies slightly lower than threshold.  The occupancies reflect
delocalizing interactions of the two core orbitals with nearby acceptor
functions.  But the strengths of these interactions are likely so weak
that they can be neglected.

Examine the perturbative analysis for interactions involving the two
orbitals in question.  You'll probably find that the interactions are
weaker than a kcal/mol or two and can thus be ignored when developing a
qualitative description of the calculated wavefunction.

> WARNING:  Population inversion found on atom  P 3
>           Population inversion found on atom  O 4
>           Population inversion found on atom  C 5
>           Population inversion found on atom  C 6
>           Population inversion found on atom  C 7
>           Population inversion found on atom  C 8
>           Population inversion found on atom  C 9
>           Population inversion found on atom  C10
>           Population inversion found on atom  O11
>           Population inversion found on atom  S13

In the second case NBO has encountered a high energy NAO that has an
occupancy somewhat greater than a lower energy NAO.  This is a fairly
common occurence for  extended basis sets for which there are a
considerable number of Rydberg orbitals identified by NAO.  Examine the
output for P3, for example.  You might find a 6s NAO with slightly higher
occupancy than the 5s, or something similar. However, the occupancies of
these orbitals are probably small enough that they can neglected anyway.

Eric Glendening

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the warning about 'Low Occupancy Core Orbitals' is nothing more than a 
warning with cautious thresholds: just have a look at the occupancies 
to confirm that they are close to 2 electrons.

I also found the 'Population Inversion' warning in some of my outputs 
and just ignore it if the inversion is between the occupancies of 
lowly occupied orbitals (that is lower than maybe .02 electrons). 
The warning is more common with extended basis sets because then there 
are more unoccupied basis functions and consequently more NAOs with 
near zero occupancies.

The warning about 'Population Inversion' needs a little background:
The Natural Population Analysis (NPA) is conducted in the basis of 
Natural Atomic Orbitals (NAOs). They are created by orthogonalizing 
the (atom centered) basis set used in GAUSSIAN under the constraint of 
changing highly populated basis functions as little as possible. On the 
other hand, lowly occupied basis functions may change much more. During 
this process the orbitals of the 'Natural Minimal Basis' (consisting of 
the orbital types that are occupied in the ground state of the atoms, 
e.g. 1s,2s and _all_ 2p orbitals in the case of boron) and the orbitals 
of the 'Natural Rhydberg Basis' (the rest) are treated differently. 
(This has led to some discussion on NPA and transition metals, because 
their np orbitals are treated as Rhydberg Orbitals by the NPA although 
they are sometimes populated, e.g. in complexes of late transition 
metals.) I think that the test for 'Population Inversion' checks if 
the NAO occupancies are decreasing with increasing NAO energy. 

Stefan

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Yours,

Maija Lahtela-Kakkkonen

***************************************
Maija Lahtela-Kakkonen
Researcher
CSC-Center for Scientific Computing
P.O.Box 405
FIN-02101 ESPOO FINLAND
TEL 358-9-4572079
FAX 358-9-4572302
E-MAIL [email-masked]
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