Subject: Development of new Force Fields

From: Frank Jensen <[email-masked]>
Date: 1 May 94 12:48 +0200

Hi netters

	I have a couple of questions regarding development of new
force fields that I would like to have some oppinions on.
	
	Any force field contains diagonal terms like Estreth, Ebend
etc. In developing a new force field, one first have to choose 
how many coupling terms to include, then select a given functional 
form for each term, and finally parameterize against experimental
and/or other computational results. The early "Class I" force fields
like MM2 and AMBER have very few (or none at all) coupling terms,
and the diagonal terms are typically just a second order Taylor
expansion for Estretch and Ebend. The new "Class II" force fields
that are being developed, contain many coupling terms, and
employ functions with more parameters for each term. That way
one can avoid special parameters for small rings etc. and 
also obtain reasonable vibrational frequencies. 

	Now the essense of my question is: 
why is it that people insist on just extending
the Taylor expansion instead of selecting a functional form
which is fundamentally more correct? For example, in the MM3 and
the CFF93 force field from Biosym, the stretch energy is
written as a fourth order Taylor expansion:

	Estr = a(r-r0)^2 + b(r-r0)^3 + c(r-r0)^4

This is better than just the second order term, but still become
qualitatively wrong at long bond lengths as it does not go towards
the dissociation energy. Why not simply select say, a Morse potential
instead? The Taylor expression contains four parameter 
(r0 and a,b,c), the Morse only three. In my oppinion, the Morse 
potential will be as good as the fourth order expansion near
r0, and much improved at long bond length (yes I know it takes
longer to evaluate an exp function than a simple multiply, but for
any reasonably sized molecule the non-bonded energy dominates
the computational time anyway). The same holds for
Ebend. MM3 and CFF93 just expand the Taylor to 6th or 4th order.
This may be fine for say the CCC bend in propane, but fundamentally
wrong for the COC bend in dimethyl ether (or any divalent central
atom). The latter has a maximum at 180 degrees which the polynomia
only accidentally will have. Why not select a functional form 
which from the start has a maximum at 180 degees?
	Another question along the same lines: why do people
insist that the non-bonded energy parameters _must_ be broken
down to atomic parameters? The non-bonded energy depends on 
two atoms, just as the strecth energy. Why then assign atomic
non-bonded parameters but stretch parameters which depends
on both atoms? Maybe one could get much better non-bonded 
energies if accepting the parameters as two atom dependent,
and thereby also avoiding the sometimes rather complicated rules
for combining the atomic non-bonded parameters to the actual
energy expression. Yes, that would give more parameters to fit, but
it would be no worse than the stretch energy, and still much
less than the torsional parameters.

	Frank