Subject: Re: CCL:Development of new Force Fields

From: [email-masked] (Joerg Hill)
Date: Sun, 1 May 1994 15:48:26 -0700

Frank Jensen wrote:

> 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.

The functional form above is mathematically equivalent to a Morse potential
if you express c as a function of a and b (sorry, I don't have the full
expression at hand), so it is not qualitatively wrong at long bond
lengths. But there is a more practical problem with Morse potentials in
geometry optimizations. The Morse potential has a very shallow slope at
long bond lengths, i.e. the forces in this range are very small. This
results in problems with the convergence of geometry optimizations if
the start geometry is very poor.

> 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?

You can easily apply boundary conditions to a 4th order Taylor series
expansion which give you the desired shape of the potential (b and
c are in this case determined from the boundary conditions and only
a is fitted). This is done in the Biosym CFF force field.

>       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?

That is simple a question of how to determine the non-bond para-
meters. If you would have parameters for each pair of interaction,
you need a large number of data to fit them. Unfortunately, experi-
mental information is sparse and the use of ab initio calculations
requires methods which include electron correlation to get the
dispersion (i.e. at least MP2). For the derivation of force fields
this is still to demanding for the computers currently available.
Maybe the density functional theory can provide some improvement here.
An other point is the transferability of the force field. Force
fields break down interactions to bonds, angles, torsions etc. and
assume that these ones are transferable. Bond lenghts or angles
are (at least in organic chemistry) comparatively constant so that
this approach works. The non-bond interactions have a much larger
range of possible distances (in solids in principle to infinite).
So these interactions can not easily be based on pairwise parameters.
Besides, non-bond parameters are a real problem in all force fields
which still needs a lot of research.

Joerg-R. Hill