Subject: Summary: NBO vs AIM

From: "Dale A. Braden" <[email-masked]>
Date: Mon, 20 Dec 1999 17:46:06 -0800 (PST)

Dear CCL,

A while ago I asked for people to tell me their opinions and experiences
with the NBO and AIM methods of population analysis.  There were many
responses, and I am grateful to all who responded.  Summarizing will be
difficult, but here goes:

I think we all agree that there is no right answer, in the sense that one
method should not be used at all, as was implied by the comments of a
reviewer.  A number of respondents said that they use both methods: NBO
when orbitals must be discussed, and AIM otherwise.  The methods are so
fundamentally different that, I think, a proper comparison should involve
many calculations on many different kinds of molecules before the
different tendencies of each method are really clear.  I have a feeling
that too much use has been made of a paper claiming that AIM exaggerates
the charge associated with an electronegative atom [Perrin, JACS 113
(1991) 2865], even though there were two subsequent papers refuting it
[Laidig, JACS 114 (1992) 7912; Gatti and Fantucci, J. Phys. Chem. 97
(1993) 11677].  In my opinion, the papers I've seen which compare both
methods AND try to conclude that one or the other is faulty aren't really
based on enough evidence to be convincing.  The fact that one method or
the other doesn't agree with intuition doesn't strike me as a sound
argument-- maybe "intuition" needs to be updated.

Interestingly, some people found that NBO is more basis set dependent than
AIM, and others found exactly the reverse-- another reason why many, many
molecules need to be examined before the tendencies of each method are
clearly revealed!

Some emphasized the fact that AIM is based on an observable electron
density while NBO is based on unobservable orbitals.  Others said, "So
what?", and still others suggested that maybe orbitals are in fact
observable after all, witness things like certain STM images and the d_z2
orbital of CuO which made C&E News recently.  Um, I'm not going to go
there....... 

That AIM or NBO atomic charges don't by themselves give a "full picture"
of electronic structure isn't really a problem.  In what is called "NBO
analysis", one can also look at hybridizations, bond orders, bond
polarizabilities, atomic orbital populations, and energy changes as a
function of removing one or more NBOs from the basis.  In the AIM method,
one can look at the Laplacian and the kinetic and potential energy
densities to answer questions about bond orders, bond polarizations,
ionicity/covalency, and so forth.  Both methods are quite complete.

One thing that always bothered me was using NBO results for one resonance
structure when I knew that the molecule I was dealing with had at least
two very good resonance structures.  But with NBO version 4.0 there is
included Natural Resonance Theory (NRT) which allows, for example, the
calculation of bond orders using the full range of resonance structures
for a molecule.  It also reports the weights of the different resonance
structures.  What I still don't understand is why atomic charges are not
also re-adjusted.  Are they? 

The one demonstrable shortcoming in this whole business is with the AIM
method: sometimes the integrations over the atomic basins won't converge,
and then you get no atomic properties at all.  A comparison of speed
between NBO and AIM isn't that much of an issue, as Cioslowski's AIM
methods in the Gaussian program are much faster than those in PROAIM, but
not as robust as PROMEGA.  On the other hand, PROMEGA is so incredibly
slow that it's almost not worth it.  AIM definitely could do with some
improvements in implementation! 

A few references for those interested (a Science Citation Index search on
these will bring out a lot more, but these are a good starting place):

Reed, Curtiss, Weinhold, Chem. Rev. 88 (1988) 899.

Bader, Chem. Rev. 91 (1991) 893. (Also Bader's book Atoms in Molecules,
Oxford, 1990).

Bachrach, Reviews in Computational Chemistry, vol. 5, Chapter 3 (Lipkowitz
and Boyd, eds.) VCH, New York, 1994.

Macchi, Proserpio, Sironi, JACS, 120 (1998) 13429.

Arnold, Organometallics, 18 (1999) 4800.

van Alem, Sudho:lter, Zuilhof, J. Phys. Chem. A, 102 (1998) 10860.

Levy, Struct. Chem. 10 (1999) 121.

Slee, MacDougall, Can. J. Chem. 66 (1988) 2961.

Merry Christmas to All and Happy Y2K,

Dale

Dale Braden
Department of Chemistry
University of Oregon
Eugene, OR 97403-1253
[email-masked]