Subject: Bader Atomic Charges

From: "Richard Bone" <[email-masked]>
Date: 2 Oct 1994 15:38:22 -0800

Subject:      Bader Atomic Charges

John Sichel wrote:

> Some quantum chemists use the method proposed by Richard Bader 
                                                                                
              (McMaster
> University, Canada) which is based on analysis of the charge density. If
> this method is accepted, it does provide a unique partition of the 
> electronic charge appropriate for Hartree-Fock quality wavefunctions. 

To be a little pedantic, in response:

The Bader atomic definitions arise from the quantum mechanics of a 
subsystem, applicable when a subspace is defined to be one with a 
'zero-flux' boundary condition.  Bader partitions the charge-density in
this way.  It is a little facile to refer to the origin of such "atoms in
molecules" as deriving from an analysis of the 'charge density'.  

Because the definition is based on the charge density it is not restricted
to wavefunctions of 'Hartree Fock quality'.  Given a charge density from
any source, it is possible to split it up in this way.

This atomic partitioning has been shown, by way of a number of examples, to
retain certain desirable 'chemical' features, particularly
loose 'transferability' of properties of a number of types.  As an 
example, the contributions of -CH2- groups to the heats of formation of
a homologous series of alkanes are well-replicated.  One would argue
that the success of this definition of a chemically bound atom in descr-
ibing measurable properties augers well for the associated atomic 
charges (and higher multipoles) that result.  I add, however, that the
charges themselves often have magnitudes which are much larger than
those typically employed in molecular modelling.  This has given rise
to a little skepticism of this approach.  The atomic charge, per se, is
rather an ambitious parameter with which to expect to replicate MEP's
very well, except when using some fitting procedure.  The Bader 
approach lends itself to the use of a self-consistent set of atomic 
multipole moments, i.e., not just charge, but dipole, quadrupole, etc.  
I am not aware of any study which has demonstrated the success (or
otherwise) of Bader atomic properties in modelling the MEP of some
'relevant' molecule, though small-molecule studies have appeared in the past and
there is by now a large body of literature on the charges them-
selves.  Recent papers by K. E. Laidig have addressed the issue of how to
build up a molecular moment (of any order) from atomic contributions.

Much of the theory behind atomic properties and subspace partitioning 
 is covered in Bader's book ["Atoms in Molecules, A Quantum Theory"  
-OUP, now available in paperback.]

This message is a comment, not a 'flame', and I am not seeking to open
a sub-debate on the "Theory of Atoms in Molecules".  I merely feel these
aspects have some relevance to the current discussion of atomic charges,
particularly today's posting.

Richard Bone

__________________________________________________________
 
 Richard G. A. Bone, PhD.
 Computational Chemist
 Terrapin Technologies, Inc.
 South San Francisco
 USA
 
 E-mail  [email-masked]