

You should read the section(s) in Richard Bader's book (at least) on this
matter.

I do not believe that there is any correlation, per se, between the mag-
nitude of the Laplacian and any chemical notion of 'covalency/ionicity'.

The Laplacian is simply the trace of the Hessian of Rho; at the bond-
critical point, you look at it as the sum of the 3 eigenvalues (of that
Hessian) and conclude: is the sum of the transverse curvatures greater in 
magnitude than the longitudinal curvature?

You should note, as follows, there are two 'extremes' of behaviour of the
charge density in 'interatomic' regions:  "shared" interactions (typically
between covalently bound atoms) in which the Laplacian is _usually_ negative; 
"closed shell" interactions (like noble-gas vdW dimers and
'ionic' systems) in which it is _invariably_ positive.

In between there are so-called "intermediate" cases, like CO (in fact most
C=O and C=S bonds) in which the interaction is "shared" but the Laplacian
is +ve.  You have to also look at the magnitude of  Rho itself which is 
usually around 10^-1 a.u. for "shared" interactions.  The reason for the 
sign of the Laplacian in these intermediate cases is that the location of 
the 'bond critical point' is close to the "VSCC" (Valence shell charge
concentration) of one of the atoms - see Bader's book.

The point is that you have to look at the _whole_ picture; in the Theory
of Atoms in Molecules, it is often not useful to draw drastic conclusions
from single numbers.  Many people are guilty of that and misinter-
pretations are legion.

Another paper you should look at is Bader and Essen, J. Chem. Phys., 1984.

I also have to ask you: although your numbers look OK to me, you should
check that those values of Del^2 do in fact correspond to the sum of
eigenvalues, if you are using the program "SADD2R" (or "EXTD2R").  E-mail 
me if you think this is a problem.

Richard Bone

__________________________________________________________

Richard G. A. Bone, PhD.
Computational Chemist
Terrapin Technologies, Inc.
South San Francisco
USA

E-mail  [email-masked]