Biomedical Engineering Reference
In-Depth Information
but one then goes down the undesirable path where all difficult cases have their own set of
parameters.
Allinger and others introduced a variety of 'mixed' terms into the standardMMpotential;
for example, a bond length-bond angle term and a torsion-bend interaction.
Figure 4.6 shows typical bicyclic and related hydrocarbons described inAllinger (1976).
4.8.3 MM2 (Improved Hydrocarbon Force Field)
Allinger (1977) subsequently introduced MM2. At the time there was a deal of discussion
in the literature about how different force fields should represent hydrogen atoms: as 'hard'
or 'soft' atoms. A hard atom was said to be one whose plot of force versus distance (in the
diatom) showed a steep slope. Asoft atomwas one where the slope was gentler. It all boiled
down to the repulsive part of the nonbonded interactions but eventually Allinger decided
to retain his exp-6 intermolecular potential.
MM2 differs from MM1 in three main respects.
1. The dihedral term was extended to
U
1
2
U
2
2
U
3
2
U
=
(1
+
cos ω)
+
(1
+
cos 2ω)
+
(1
+
cos 3ω)
(4.21)
where each of the
U
's was found by calibration against experiment.
2. The bending term was extended to
2
k
ABC
θ
ABC
−
θ
e,ABC
2
2
k
ABC
θ
ABC
−
θ
e,ABC
6
1
1
U
ABC
=
+
(4.22)
3. All mention of cross terms between bond stretches and bends were finally dropped.
Agreat deal of importance was attached to the calculation of enthalpies of formation, and
42 hydrocarbons were treated. The author claimed that his enthalpy results were comparable
to experiment in terms of experimental error.
4.8.4 AMBER
AMBER (an acronym for assisted model building and energy refinement; Weiner
et
al.
1984) is a force field for the simulation of nucleic acids and proteins. It was
calibrated against experimental bond lengths and angles obtained from microwave,
neutron diffraction and accurate quantum chemical studies. The parameters were then
refined with MM studies on model compounds such as tetrahydrofuran, deoxyaden-
osine, dimethyl phosphate, 9-methyladenine-1-methylthymine hydrogen bonded complex
and others.
The model differs from our standard expression (Equation (4.19)) in four ways.
1. Hydrogen bonds were included explicitly with a 12-10 potential
C
12
R
12
C
10
R
10
U
H-bonds
=
−
H-bonds
