Subject: Population analysis

From: [email-masked] (Dominic Ryan)
Date: Fri, 3 Dec 93 14:57:43 -0500

As was pointed out, population analysis is not unique.  There are a host 
of methods available for partitioning density between sites.  One must 
ask what the charges will be used for. 

In a force field context an atomic charge is simply one more fudge factor
available in the system for tuning to get the 'right' answer.  Early days
of force field development concentrated on intramolecular energies, in
vacuo at that.  After you make pretty good guesses at bond stretching and
angle bending components (and cross terms when part of your flavor of
force field) you are left with torsion terms, VDW terms and charges.

Early work derived VDW terms from rare gas data in part and from crystal
packing (making allowances for the differences one sees there in x-ray,
electron and neutron diffraction).  One is generally left then with
torsions and charges (VDW terms are also modified and combining rules are
modified in Tom Halgren's work).  You try to assign chemically sensible
charges and tweak the torsion terms until conformational energies
reproduce your reference states (quantum mechanical, and experimental).

More recently there has been greater emphasis on intermolecular energies
(lets ignore solvation for now).  These are dominated by electrostatic
forces.  Now one needs to worry more about getting both chemically
sensible charges and charges that will give the 'correct' interaction
energy which must be taken from high level QM where one needs to worry
about basis set effects etc.

A relatively recent method of defining atomic charges calculates the
molecular electrostatic potential around a molecule and constrains the
charges to reproduce this distribution as much as possible.  This has the
advantage of in principle reproducing the bulk of the interaction energy
between two molecules, including the anisotropy.  In practice there are
limitations here as well, and in small molecules particularly (H2O) a set
of atom-centered charges in not sufficient to adequately describe the
potential.  One advantage of using 'fitted' charges is that the dipole
(and higher order molecular multipoles) are well reproduced.  There is a
*lot* of literature on this approch now.  Check out Reviews in
Computational Chemistry, vol. 2 for a recent review.

Bader's method of partitioning charge is consistent but leads to a
different picture of atomic charge from the fitted methods.  Neither one
is *wrong* but they look at different things. 
___________________________________________________________________________
M. Dominic Ryan       (215)-270-6529     SmithKline Beecham Pharmaceuticals 
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