| Colleagues,
I think this
is of enough general interest to allow for a CCL wide reply. Negative Fukui
functions have been a main focus in my work and there is a lot of nonsense being
written on it too. Let me summarize the following
points.
1. Fukui functions through space (not atom
condensed) - Fukui functions can be negative and probably always are
in some parts of space. There is nothing strange there and I have proven it both
through observation and through a closed analytical mathematical proof. There is
nothing fancy there. If you extend the function to a matrix form and diagonalize
that, you see that negative eigenvalues MUST exist. If they would at some point
not be there at Hartree-Fock or DFT level, your calculation is simply wrong.
Whether you will actually see it in a plot is another matter and depends on the
eigenvectors (or rather their mutual shape). - Same thing: do not use
a frontier MO approximation. You miss the physics of the business if you want to
get into the details of negative Fukui functions. There is, however, a simple
explanation why FMO theory works if you want to see only a big
picture.
Take a look at:
Bultinck,
P.; Clarisse, D.; Ayers, P.W., Carbo-Dorca, R. The Fukui matrix: a simple
approach
to the analysis of the Fukui function and its positive character. Phys. Chem.
Chem. Phys., 2011, 13, 6110–6115.
Bultinck,
P.; Van Neck, D.; Acke, G.; Ayers, P.W. Influence of electron correlation on
the Fukui matrix and extension of frontier molecular orbital theory to
correlated quantum chemical methods. Phys.
Chem. Chem. Phys., 2012, 14, 2408 -
2416.
2.
Atom condensed Fukui functions -
There are two ways to compute atom condensed Fukui functions that both can be
argumented for. There is a way in which you do not take into account the change
in atomic weights upon the change in number of electrons and there is the way
you do allow for it. This has been discussed in detail
in Bultinck,
P.; Van Alsenoy, C.; Ayers, P.W.; Carbó-Dorca, R. A critical analysis of
the
Hirshfeld atom in a molecule. J.
Chem.
Phys., 2007, 126, 144111.
- In general, I am reluctant to use the scheme that you
say that the atom condensed Fukui function is a difference in atomic charges.
You need to do the integral numerically (most often) yourself! Read the original
work of Yang and Mortier on atom condensed Fukui functions and you will see that
they say something like "provided atom condensing and taking the derivative
commute, ...". This is usually not the case, so you should carefully consider
what you do! I tend to be very wary of charge difference based atom condensing.
Actually; Mulliken is probably the only scheme where this IS allowed!!! I agree
with the late Richard Bader that for atom condensing you need to condens the
molecular response and not compute the response of an atom in the molecule.
Check the above reference for details. - There have been lots of claims that stockholder/Hirshfeld atom condensed
Fukui functions would be "best" because they give fewest negative values. This
is wrong and a consequence of the fact that the Hirshfeld method is arbitrary.
You should use a Hirshfeld-I model which is much closer in philosophy to the
Bader scheme. If then you use the right method (not difference in charges); you
will get different results. See Bultinck,
P.; Van Alsenoy, C.; Ayers, P.W.; Carbó-Dorca, R. A critical analysis of
the
Hirshfeld atom in a molecule. J. Chem.
Phys., 2007, 126, 144111.
3. Your calculations - It is hard to say anything on your results
if you do not give a basis set. Mulliken MAY be problematic but not necessarily.
Too many people just repeat what they read and never personally checked the
properties of the overlap matrix of their basis functions. - You may
have found a very interesting case of oxidation of an atom under global
reduction. They ARE known to exist (check work by Melin and
Ayers)!!! - Your Fukui functions sum to minus 1 instead of 1, so try
to sort that out. There may be another error somewhere if you were a bit too
careless with checking whether your data fulfill the requirements for Fukui
functions.
Feel free to contact me for more information
personally.
Patrick Bultinck On
11 Sep 2012, at 18:39, AMBRISH KUMAR SRIVASTAVA ambrishphysics]^[gmail.com
wrote: |