Subject: RE: summary on population analysis

From: Andrzej Sokalski <[email-masked]>
Date: Mon, 13 Dec 1993 08:13:41 +0100 (CET)

Let me add my 2c to the problem how to define atomic charge.
> Patrick Bultinck writes: My question is :
> What is the use of the S^nPS^(1-n) derived population analysis ?

 It is very useful to demonstrate the arbitrariness of popular definitions
of atomic charge. I always recomend it to beginning students to realize
that there is entire universe of population analyses besides Mulliken.
  Unfortunately, other known definitions (like Potential Derived, zero
Charge Flux, etc.) are not much less arbitrary. Sooner or later someone
demonstrates in the literature their arbitrariness or complains on their
basis set dependence.

            How to correct this problem in general way ?
  Perhaps the easiest way out is substituting atomic charges by higher atomic
multipole moments. As it has been already pointed out here by Anthony Stone
numerous procedures developed since early 70's are known in literature.
 For example if someone insists to start multipole expansion from  particular
atomic charge definition one can use our Cumulative Atomic Multipole Moments
(CAMM), (Chem.Phys.Lett.98,86(1983), which can be derived starting from any
possible atomic charge definition (Theochem, 256,91(1992), J.Comp.Chem.,13,883
(1992)). It may be Mulliken, Lowdin, any arbitrary n value in general
S^nPS^(1-n) charge definition, GATP, Potential Derived, assumed ZERO charge
on each atom (or even your telephone number if you have such desire) !
   The use od CAMM procedure to correct Mulliken and Lowdin charge definitions
(also at short distances !) has been demonstrated recently by Koster, Koelle
and Jug  (J.Chem.Phys. 99,1224(1993). However, the most practical choice will
be using definition maximizing monopole contribution, so the multipole expansion
will quickly converge. Although it may depend on the case, PD charges
recommended by Don Williams seem to be quite good in this respect. This
topics is covered in  Rev.Comp.Chem,2,219-271(1991). However, the higher
multipole corrections to PD charges remain still significant, although
better balanced than within Mulliken or Lowdin definitions.
     What is also important for those dealing with large molecules is
that CAMM procedure does not involve expensive and arbitrary fitting process.
 For those who prefer dealing with point charges instead of multipoles, one
may analytically decompose each atomic multipole into set of off-atom charges
(see Comp.Phys. Comm.,52,397(1989) or Theor. Chim. Acta, 85,209(1993).
Again this procedure does not involve arbitrary fitting and even works at short
distances allowing to monitor intramolecular electrostatic interactions !
   So in conclusion - we all are probably condemned to use arbitrary atomic
charge definitions in building simple models of molecular charge distribution,
but there are several ways to correct their deficiencies or estimate
corresponding  errors  "a posteriori".
                W. Andrzej Sokalski
          Institute of Physical and Theoretical Chemistry, Wroclaw, Poland