Biomedical Engineering Reference
In-Depth Information
10
Molecular Dynamics
Molecular mechanics (MM) tends these days to be concerned only with prediction of local
minima on molecular potential energy surfaces. QSAR properties are often calculated
in order to assist high-volume screening studies in pharmaceuticals applications. Should
we want to study the motions of the molecule, all that would be needed would be to
investigate the normal modes of vibration (which can be obtained from the Hessian). MM
does not take account of zero-point vibrations and the calculations refer to a molecule at
0 K, when it is completely at rest. Workers in the modelling field often refer to MM as
energy minimization
.
As we saw in Chapter 9, Monte Carlo modelling tends to be concerned with thermody-
namic properties. It is now time to consider molecular dynamics which gives a direct way
to study time evolution.
I have stressed in previous chapters the intermolecular potential energy, which I chose
to write as Φ in Chapter 9. Assuming pair wise additivity, Φ can be found by summing
over all distinct pairs of particles
N
−
1
N
Φ
=
U
ij
(10.1)
i
=
1
j
=
i
+
1
If the assumption of pair wise additivity is not valid, then one way forward is to include all
possible triples and so on
N
−
1
N
N
−
2
N
−
1
N
Φ
=
U
ij
+
U
ijk
+···
(10.2)
i
=
1
j
=
i
+
1
i
=
1
j
=
i
+
1
k
=
j
+
1
