Subject: Summary: NBO for transition metal

From: Jerry C C Chan <[email-masked]>
Date: Thu, 2 May 1996 09:00:30 +0800 (HKT)

Dear Netters,

        Some days ago I posted a message below:

>       I notice that NBO has already been applied to transition metal 
> containing systems.  Could anybody give me some references which concern 
> the transition metal-ligand interaction using NBO analysis, in addition to
> the work by Maseras and Morokuma CPL 1992.

>       I have tried applying NBO analysis to [Co(NH3)5Cl]2+ and I find 
> some difficulties in interpretating some of the results: 

> if LP ( 1) N 3 / BD*( 1)Co 1-Cl 2, "lone pair electrons of N (donor) /
> antibonding orbital of Co-Cl (acceptor)", is interpreted as an
> indication of the importance of the resonance N-Co <-> N(+)-Co Cl(-), how
> should one interprete BD ( 1)Co 1-Cl 2 / RY*(16)Co 1 ?

        I would like to express my gratitude to all who response to my
query.  Special thanks are due to Profs. Frank Weinhold, Jay Badenhoop,
Martin Kaupp and Eric Glendening.  I wish my summary would contribute to
the popularity of NBO analysis. 

*************

> 1.  Is it justified if NBO scheme is used to analyze the SCF density 
> obtained by dft method?

While not developed for DFT wavefunctions, NBO analyzes the 1st order
density matrix, and therefore should be more compatible with density-
based methods than methods which analyze the wavefunction to determine
bond order.  We have had much success (and yes, some surprising results
which were found later to be consistent with experimental results)
>from NBO analysis of coordination complexes.

> 2.  Is there any physical meaning associated with the energy of the 
> natural bonding orbital?  I don't understand the physical picture of 
> "Population inversion found on atom ..." although there is an 
> operational explanation in the NBO manual.

The natural bond orbitals are calculated as the 1- and 2-center set
of orthogonal orbitals which takes account of the greatest amount of
the electron density in a maximum-occupancy sense.  Each orbital
has an energy or eigenvalue associated with it, just as the atomic 
orbitals and molecular orbitals do.  However, sometimes one or more 
orbitals will be higher in occupancy, but also higher in energy than 
one or more other orbitals.  Therefore the ordering from highest to 
lowest occupancy and the ordering from lowest to highest energy will 
not be the same.  Often this occurs if you have a large number of 
orbitals which are fairly close in energy and population, which is 
common in these coordination complexes.  This warning message about 
"population inversion" just alerts you to this different ordering of 
the orbitals, and does not indicate the orbitals are of inferior 
quality or are mislabeled in any way.

> 3.  How can the NBO result be considered as valid?  NHO procedure 
> fail in CO2 (JACS, 1980) because of the miscount of the total number 
> of orbitals.  However, if the total number of orbitals is counted 
> correctly but some of the BD and *BD occupancy are < 1.7 and > 0.4, 
> respectively, can we still accept the NBO result?

First, the NBO procedure has been modified to handle a wider variety of
cases than in 1980.  I do not believe that the CO2 case fails with the
latest version of NBO. ... However, you must not just consider the NBO's
listed in the table.  This is the "best"  localized set of orbitals, but
low-occupancy bonding orbitals (BD or LP) or high-occupancy anti-bonds
(BD*) indicates a highly delocalized molecule.  You must also consider the
list of second order perturbative estimates of the donor-acceptor
interactions.  This list indicates the most important delocalizations from
bonding to antibonding orbitals. You will find both Co --> ligand and
backbonding ligand --> Co interactions. 

 ...

In addition, our group has developed a quantitative NBO-based resonance
theory, which calculates a set of localized resonance structures and
associated resonance weights which best describe the full density,
then calculates not only a bond order but also partitions the bond
into covalent and ionic contributions to this bond order based on
the bond polarization coefficients.  This bond order is more comparable
to Bader's bond order than a measure of bond order only based on the
"best" localized NBO structure (resonance structure of highest "weight")
only.  Unfortunately, the method has been developed for organic 
molecules, and cannot handle transition metal complexes without further 
development.

Jay Badenhoop
Department of Chemistry
Southern Illinois University at Carbondale

*******************

>        In the Second Order Perturbative Analysis of Co(NH3)5H2O, I get
>  BD*( 1)Co 1- N 4     /299. BD*( 1)Co 1- N 5      2168.13    0.01    0.249

> I really do not understand the physical picture implied by these large >
interactions. 

The BD*-BD* 2nd-order energies should be ignored, since the BD* is
not even approximately "doubly occupied" and the PT picture is no longer
valid.  (NBO prints out these entries for convenience in analyzing
excited states, which may have significant population in BD* orbitals.)
Only the donor(LP,BD)-acceptor(BD*,RY*) entries have physical significance
in this case.  FW

*******************

> 	I notice that NBO has already been applied to transition metal 
> containing systems.  Could anybody give me some references which concern 
> the transition metal-ligand interaction using NBO analysis, in addition 
> to the work by Maseras and Morokuma CPL 1992.
> 
We frequently use the NPA, and to a lesser extent the NBO analysis for
TM compounds. Some references are: Inorg. Chem. 1994,33,2122; Chem.Eur.J.
1996,2,348; J.Am.Chem.Soc. 1996,118,3018.

> 	I have tried applying NBO analysis to [Co(NH3)5Cl]2+ and I find 
> some difficulties in interpretating some of the results:
> 

One principle problem with the NBO part is that for many TM compounds the
program fails to find _one_ Lewis structure. Thus, you should be very
careful in examining the Lewis structure you get. Does it make any
chemical sense? How large are, e.g., the energy terms in the second-order
perturbation theory analysis (values larger than, say, 30-50 kcal/Mol
clearly tell you that your Lewis structure does not describe the density
matrix well) ? Of course there are other criteria one may look at, such as
the percentage of the density matrix described by the Lewis structure. 

To get around these problems, Weinhold and coworkers have meanwhile
developed an extension they call 'natural resonance theory' which expands
the density matrix in several NBO Lewis structures. While the theory is,
as far as I know, at the moment just available as an internal report of
the University of Wisconsin, some interesting applications (to main group
species) may be found in: J. Chem. Educ. 1995, 72, 583. I expect this to
give a much improved analysis for TM systems as well and hope it will be
available soon (it's now part of the NBO 4.0 program). 

Of course the NPA is no problem, so charges and NAO populations may be used
safely even with the present version.

One point regards the use of NBO/NPA with DFT (Kohn-Sham) calculations: In
principle the Kohn-Sham orbitals only describe a wavefunction for the
so-called 'noninteracting reference system' and thus can not be
interpreted as the wavefunction for the real system. In practice, however,
this does not create any problems. Comparisons with HF, MP2, etc....
density matrices show that the KS orbitals give the expected
characteristics (e.g. showing effects of electron correlation) and we have
found them to provide a useful basis for qualitative interpretations, in
particular for TM systems. 

Hope this helps a bit.
Regards, Martin Kaupp

------------------------------------------------------------------
| Dr. Martin Kaupp                                               |
| Max-Planck-Institut fuer Festkoerperforschung,                 |
| Heisenbergstrasse 1, D-70569 Stuttgart, Germany,               |
| Tel.: country-code+711/689-1532                                |
| Fax.: country-code+711/689-1562                                |
| email: [email-masked]                       |
|                                                                |
| and Institut fuer Theoretische Chemie, Universitaet Stuttgart, |
| Pfaffenwaldring 55, D-70569 Stuttgart, Germany                 |
| Tel.: country-code+711/685-4399                                |
| Fax.: country-code+711/685-4442                                |
| http://www.theochem.uni-stuttgart.de/~kaupp/                   |
------------------------------------------------------------------

************************

The Co-Cl bond that NBO calculates is probably highly polarized
toward Cl and might alternatively be described as a Cl lone pair
with fairly strong charge transfer interaction with Co.  The 
interaction is apparently strong enough that NBO calculates a 
bond between these two atoms.  Co-Cl --> RY*(16) is then a 
separate charge transfer interaction between the Cl lone pair 
and a different hybrid on Co (presumably one of the 3d orbitals?).

I gather that you're using the NBO perturbative analysis to
judge the degree of delocalization between the ligands and Co. 
If so, you should probably force NBO to treat the ligands 
consistently.  That is, if NBO doesn't calculate any bonds
between Co and NH3, then prevent the program for calculating a
Co-Cl bond.  This is accomplished with NBO $CHOOSE keylist,
which is described in the NBO manual.  $CHOOSE allows the user
to stipulate the pattern of bonds (the Lewis structure) that 
NBO will calculate.  For your complex, only ask for NH bonds;
no bonds would then be calculated between Co and N or Cl.

If you don't have an NBO manual and would like to try $CHOOSE,
send me a copy of your input deck.  I'll add the $CHOOSE keylist
to it (it's fairly simple) and return the file to you.

Eric Glendening
Department of Chemistry
Indiana State University
Terre Haute, IN  47809
[email-masked]

**************************

The rule of thumb that I use is to neglect any interaction that
is an order of magnitude weaker than the strongest appearing in
NBO's perturbative analysis.  This works well whenever one is 
looking for a qualitative description of the delocalization
patterns in a molecule (or complex, as in your case).  So I'd
ignore the RY* interaction.

 ...

It is certainly reasonable to judge the degree of covalent character
>from the presence or absence of a bonding NBO.  If NBO calculates a
bond, then the polarization coefficients give a quantitative measure
of covalent character; if NBO calculates a lone pair, then covalency
can be judged from the strength of the orbital interactions.  You won't
however be able to compare the covalency of two interactions when NBO
assigns one a bond and the other a lone pair.  While it is likely that
the interaction with the bonding NBO should have higher covalent 
character, this may not always be the case.  I really recommend
$CHOOSE as it will allow a consistent comparison of all interactions
based on lone pair delocalizations.

Eric Glendening

************************

[Co(NH3)5Cl]2+

 CO   0.00000     0.00000     0.00000
 CL  -1.72778    -0.00000    -1.47168
 N    1.47849     0.00000     1.27277
 N    1.25572    -0.00000    -1.50461
 N   -0.03050    -1.96150    -0.01613
 N   -0.03050     1.96150    -0.01613
 N   -1.27561     0.00000     1.51536
 H    1.15559     0.00000     2.23183
 H    2.07308     0.81190     1.16605 ...

Here's the CHOOSE input for your Co complex:

 $nbo  $end
 $choose
    lone  1 3  2 4  3 1  4 1  5 1  6 1  7 1  end
    bond  s 3  8   s 3  9   s 3 10
          s 4 11   s 4 12   s 4 13
          s 5 14   s 5 15   s 5 16
          s 6 17   s 6 18   s 6 19
          s 7 20   s 7 21   s 7 22  end
 $end

Note that the "resonance" keyword is not needed when the Lewis
structure is specified in $choose.  $choose is free-format and
reads as follows:

First the lone pairs (lone ... end); atom 1 (Co) has 3, atom 2
(Cl) has 4, etc.

Then the bonds (bond ... end); a single bond between atoms 3 and
8, a single bond between atoms 3 and 9, etc.

Attach the $choose...$end input to the end of your input deck and
run; no need to modify your input deck in any other way.  NBO always
searches the input deck for $choose and uses it if available.  
Otherwise, NBO defaults to its standard search for a Lewis structure.

Also, $choose input will in no way affect the population analysis.
Just run NBO once; you'll get the atomic charges and $choose Lewis
structure in one calculation.

Eric

*************************

From [email-masked] May  2 08:35:05 1996
Date: Mon, 29 Apr 96 11:44 CST
From: [email-masked]
To: jerry@dft
Subject: Re: NBO

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