Biomedical Engineering Reference
In-Depth Information
4.4.4 Out-of-Plane Angle Potential (Inversion)
Next we consider the out-of-plane potential terms. Imagine molecule ABCD in Figure 4.4
to be ammonia, a molecule with a very low barrier to inversion; as ψ changes from positive
to negative, the molecule inverts. We can write the inversion potential either in terms of
the angle indicated (ψ) or in terms of the height (
h
) of atom D above the plane of atoms A,
B and C. Four examples are as follows:
k
1
2 sin
2
ψ
e
cos ψ
e
)
2
U
=
(cos ψ
−
U
=
k
2
h
2
(4.16)
U
=
k
3
(1
+
k
4
cos(
n
ψ))
U
=
k
5
(1
+
cos(
n
ψ
−
k
6
))
where
n
is a periodicity parameter, the
k
's are constants that have to be fixed against
experiment and ψ
e
is the equilibrium value.
D
C
Ψ
B
A
Figure 4.4
Out-of-plane (inversion) potential
4.4.5 Nonbonded Interactions
I mentioned earlier that molecular mechanics force fields have to be transferable from
molecule to molecule, and explained the necessity for nonbonded interactions. These are
usually taken to be Lennard-Jones 12-6 type, and they are included between all nonbonded
pairs of atoms:
C
12
R
12
C
6
R
6
U
L
−
J
=
−
The Born-Mayer-Huggins potential
C
8
R
8
is sometimes used when dealing with polar species.
B
is a parameter determined by the
size and 'softness' of an ion,
C
6
(not the same as
C
6
in
U
L
−
J
) has to do with dipole-dipole
interactions whilst
C
8
is determined by dipole-quadrupole interactions.
Some force fields make special provision for hydrogen-bonded atoms; they treat them
as nonbonded interactions but soften the Lennard-Jones 12-6 potential for A-H ...Btoa
12-10 version:
C
6
R
6
U
BMH
=
A
exp (
−
BR
)
−
−
