Computational Chemistry

Chapter 3, Harder Questions, Answers

Q10

How many parameters do you think a reasonable forcefield would need to minimize
the geometry of 1,2-dichloroethane?

CC

H

H

H

H

Cl

Cl

Look at the structure of the molecule:
At a bare minimum, we would need parameters for these seven contributors to
the energy (here C is theatom typesp^3 C):

(1) Estretch(C–C)
(2) Estretch(C–H)
(3) Estretch(C–Cl)
(4) Ebend(HCC)
(5) Ebend(ClCC)
(6) Ebend(HCCl)
(7) Etorsion(ClCH 2 –CH 2 Cl)

For each of the three Estretch(X–Y) terms, kstretch(X–Y) and leq(X–Y) are needed,
for a total of 6 parameters. For each of the three Ebend(XYZ) terms, kbend(XYZ) and
aeq(XYZ) are needed, for a total of 6 parameters. The torsional curve likely requires
at least 5 parameters (see chapter 3, section3.2.2) for reasonable accuracy. This
makes a total of 6þ 6 þ 5 ¼17 parameters. But this would be a very stunted
forcefield; it has no parameters for nonbonded interactions and so is not suitable for
molecules with bulky groups, and it is parameterized only for the atom types sp^3 C,
H, and Cl. It cannot handle other kinds of carbon and other elements, and it has no
special parameters for electrostatic interactions.
A reasonable forcefield would be of more general applicability: it should be able
to handle the eight common elements C(sp^3 , sp^2 , sp), H, O(sp^3 , sp^2 ), N(sp^3 , sp^2 , sp),
F, Cl, Br, I; we are focussing for convenience on an organic chemistry forcefield.
Yet this would have only 13 atom types, compared to the typical organic forcefield
with 50–75 [1]. Similar considerations applied to the stretching of C–H, C–O, C–N,
C–F, ..., H–O, H–N, etc. bonds, to the bending of various C–C–C, CO–C, etc.
angles, to rotation about single bonds, and to nonbonded interactions, reveals that
we need hundreds of parameters. The popular Merck Molecular Force Field
MMFF94 is said to have about 9,000 parameters [2].

Answers 609