Biomedical Engineering Reference
In-Depth Information
where
R
is the distance between a pair of atoms, ε are characteristic distances and
a
,
b
,
c
and
d
are parameters.
4.8.7 Unified Force Field (UFF)
I have discussed so far a number of force fields of increasing degrees of special-
ity and application. Let me finish this chapter by drawing your attention to the UFF; in
the words of the authors Rappé
et al.
(1992), 'a Full Periodic Table Force Field for Molecu-
lar Mechanics and Molecular Dynamics Simulations'. Molecular dynamics is the subject
of a later chapter in this topic. I commend this article to you as a model of logic and lucidity
and it illustrates beautifully all the principles I have discussed so far. Here is the abstract
(Rappé
et al.
1992):
A new molecular mechanics force field, the universal force field (UFF), is described wherein
the force field parameters are estimated using general rules based only on the element, its
hybridization and its connectivity. The force field functional form, parameters, and generating
formulas for the full periodic table are presented.
In particular, the parameters used to generate the UFF include a set of hybridization-
dependent atomic bond radii, a set of hybridization angles, van der Waals parameters,
torsional and inversion barriers and a set of effective nuclear charges.
Thus, the force field is represented by Equation (4.20); there is a slight clash of notation,
for my 'out-of-plane' read 'inversion'. If I focus on the bond stretch, UFF allows both the
simple harmonic and Morse pair potentials. Both involve an 'equilibrium' value for the
bond length, and this is one of the 'parameters' that has to be fixed. The authors took this
to be the sum of atom type specific single bond data, plus a bond order correction, plus an
electronegativity correction.
The authors describe many simple and more difficult organics, together with a good
number of metal-containing molecules, and conclude that their predicted bond lengths are
good to 10 pm, and bond angles to about 7
◦
.
References
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