Subject: Re: CCL:charges

From: [email-masked] (Ton Rullmann)
Date: Wed, 28 Sep 1994 18:11:59 +0100 (WDT)

Thanks to Wendy Cornell for the instructive mails about the ESP and RESP models
for deriving atomic charges!

I would like to comment on the last paragraph of the second mail:

> useful for modelling biomolecular systems.  The alternatives
> usually involve either (1) models such as Mulliken charges
> which do not necessarily reproduce the molecular electrostatic
> potential or (2) empirically derived charges such as those
> fit to reproduce interaction energies and distances (CHARMM)
> or liquid properties (OPLS).  Because electrostatic potential

and remark that other alternatives exist, based on reproducing not the 
electrostatic potential but the electric multipole moments of a quantum
mechanical calculation. Some references are:
- Sokalski & Sawaryn, "Correlated molecular and cumulative atomic multipole
  moments", J.Chem.Phys. 87, 526 (1987).
- Stone & Alderton, "Distributed multipole analysis", 
  Mol. Phys. 56, 1047 (1985).
- Faerman & Price, "A transferable distributed multipole model for the
  electrostatic interactions of peptides and amides", JACS 112, 4915 (1990).
- Thole & van Duijnen, "A general population analysis preserving the dipole
  moment", Theor. Chim. Acta 63, 209 (1983).
  (applied in: Bellido & Rullmann, "Atomic charge models for polypeptides
  derived from ab initio calculations", J. Comput. Chem. 10, 479 (1989).)

What these methods have in common is that they try to reproduce the quantum
mechanical charge density by a series of local multipoles, using the expectation
values of the one- and two-center contributions to the electric multipole
moments as a starting point. Simplifying, these methods can be seen as an
extension of the Mulliken method, which only preserves the lowest multipole 
(total charge).

It would be interesting to compare the results of these multipole based
methods to those of electrostatic potential fitting. An advantage of the
former methods is that one does not fit to function values at a series of
judiciously chosen points i.e. one does not have to worry about a "proper"
choice of grid points, weighting functions etc.

Finally I would like to comment on the desirability of having charges that
result in dipole moments larger than in the gas phase, as mentioned in one
of the posts. From a practical point of view this makes sense, of course, if
you want to compensate for electronic polarization effects that are neglected
in standard force fields.

On the other hand it means that energy contributions that are rigourously 
separable on the theoretical level become inextricably mixed. E.g. the electric
potential calculated with these charges is not the true molecular potential, 
and it is virtually impossible to retrieve the latter from an "energy fitted" 
charge set because the distance and orientation dependence of energy and 
potential are not the same. One may also encounter problems with the 
transferability of charges: surely the "effective polarization compensation" 
must be different for cases involving neutral, singly ionized, doubly ionized 
and charge-separated (transition states!) species.

By these remarks I don't mean to attack the work described by Wendy Cornell,
but I do want to draw attention to a problem that in my opinion is sometimes
overlooked in discussions of force fields, which is that in almost all cases
the parameters represent "effective", not "true" interactions; the parameters
are not independent of one another and may not be transferable to other
molecules or other systems.

If one decides to use ab initio theory wouldn't it make sense to start from the
perturbation theoretical approach to intermolecular interactions, describing
interactions in terms of true unimolecular properties such as multipoles and 
polarizabilities? And if one chooses to stick with pair-additive two-body
potentials - for solid practical reasons such as limits of computer time, if 
not (wo)man power needed to redesign a force field - would it be feasible
to discriminate between "true charge distributions" derived for isolated
molecules, and the "charge corrections" needed to get a good fit to inter-
molecular energies in cases of interest? Does anyone care to venture opinions
on the issue of using perturbation theory vs. fitting, and on the use of
ab initio data? 
(The case for perturbation theory was argued in: Rullmann & van Duijnen,
Reports in Molecular Theory 1, 1 (1990). This was a rewrite of a chapter of
my PhD thesis. After that I have worked on other things, but I'm very
interested to hear opinions on the current state of affairs).
 
-- 
| Ton Rullmann                                NMR Spectroscopy            |
| Bijvoet Center for Biomolecular Research  | Tel. : int+31.30.533641     |
| Utrecht University, Padualaan 8,          | Fax  : int+31.30.537623     |
| 3584 CH Utrecht, The Netherlands          | Email: [email-masked] |