

Greetings Miquel:

	You asked about link between the properties of (3,-1) critical
points and the character of bonding; specifically about the sign of the
Laplacian and the 'ionic character' of bonding in LiF and CO.  While its
true that the character of chemical bonding can be summarized by the
properties at the 'bond critical point' (BCP), I think its unwise to treat
the values as magic numbers which tells all about the nature of
interaction between two atoms.  One must take stock of the entire set of 
data to get the correct results from these characterizing properties.

	The rule of thumb is that a low amount of charge AND a positive 
Laplacian signify an ionic interaction.  In the case of LiF vs. CO, the 
magnitude of the Laplacian at the BCP of CO is more positive, but there 
is a good deal more electronic charge than typically found in 'ionic 
bonds' (see Bader and Essen, JCP, 1984).  LiF has the small amount of 
charge typically found in the interatomic region of ionic interactions.

 LITHIUM FLUORIDE HF/6-311++G**      CARBON MONOXIDE HF/6-311++G**

 RHO        7.0078622807E-02         RHO        5.1842212832E-01
 DEL2       7.2110756059E-01         DEL2       1.0834101333E+00

	So, the bonding in CO is not the same as that in LiF, 'ionic'.

---Further ramblings---

	In fact, the case of CO is particularly interesting as the
Laplacian makes clear the seeming contradiction of the different
electronegativities of C & O and the small dipole moment for this system. 
The small dipole moment of CO would lead you to believe that the atoms
were roughly electroneutral, based upon the simple idea that the dipole 
moments is the result of separation of charge.  But then how does one 
reconcile this with the large expected electronegatvities of the two atoms?

	There is a large transfer of charge from C --> O.  But there is
also a large opposing polarization of the remaining charge on the carbon
atom (unlike what one would expect for spherical ions).  It is this large
opposing polarization which produces a large dampening of the dipole
moments, canceling the contribution from charge transfer, and making the
overall dipole nearly zero.  This can be seem in the Laplacian map of CO
in which the valence shell of carbon is polarized away from the direction
of charge transfer, producing a large, relatively diffuse region of charge
concentration (see the cover of Bader's paperback to see the Laplacian of
CO (blue)).  This is why the carbon of CO is so reactive.  

	In addition, the polarization of the carbon valence shell away
from oxygen is the reason that the Laplacian is positive at the bond
critical point.  The Laplacian map of CO shows that the valence shell of O
reaches almost to the interatomic surface and that the valence shell of
carbon is polarized away from the interatomic surface.  So, it is this 
polarization of C away from O that gives rise to the relatively large 
value of rho at BCP (a 'sort-of' shared interaction) and the larger, 
positive magnitude of the Laplacian.

	Anyway, I think its all pretty interesting...

	Keith

   ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
     Keith E. Laidig 
     Department of Medicinal Chemistry, BG-20,
     University of Washington, Seattle, WA 98195 
     E-Mail: [email-masked]
     Phone: (206) 616-2780 or 685-1000          FAX #: (206) 685-3252
   ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++