Biomedical Engineering Reference
In-Depth Information
and the final atom of the MM region is attached to this quantum mechanical atom by a
harmonic MM potential.
24.2
IMOMM
When faced with the theoretical study of a system involving very large molecules, there are
two possible approaches. One is to model the real system as a simpler one and proceed with
(for example) an
ab initio
treatment of the simpler system. Thus for example, transition
metal complexes often contain bulky ligands with large organic susbtituents; those far away
from the metal atom are usually replaced by hydrogen atoms. This approach works well
because the metal-ligand interaction remains well described. The only problem arises when
the bulky ligands give rise to steric interactions.
Molecular mechanics methods have found favour in biochemical applications where
very large molecules are involved, or areas such as MD where a large number of different
calculations are required.
One possible way to overcome the shortcomings of both approaches is to mix quantum
mechanics and MM in different parts of the same molecule. The
integrated ab initio
+
molecularmechanics (IMOMM)
schemewas introduced byMaseras andMorokuma (1995).
As usual, I will give the abstract.
A new computational scheme integrating
ab initio
and molecular mechanics descriptions in
different parts of the same molecule is presented. In contrast with previous approaches, this
method is especially designed to allow the introduction of molecular mechanics corrections
in full geometry optimizations concerning problems usually studied through
ab initio
calcu-
lations on model systems. The scheme proposed in this article intends to solve some of the
systematic error associated with modelling through the use of molecular mechanics calcula-
tions. This method, which does not require any new parameter, evaluates explicitly the energy
derivatives with respect to geometrical parameters and therefore has a straightforward applica-
tion to geometry optimization. Examples of its performance on two simple cases are provided:
the equilibrium geometry of cyclopropane and the energy barriers on S
N
2 reactions of alkyl
chloride systems. Results are in satisfactory agreement with those of full
ab initio
calculations
in both cases.
Twenty years is a long time in molecular modelling, and it is interesting to note both the
change of emphasis for hybrid models and the increased level of sophistication. Geometry
optimization is
de rigueur
, and transition states are fair game for scrutiny.
To fix our ideas, I will discuss the (hypothetical) 'real' system M(P(CH
3
)
3
)
2
used by the
authors quoted above. Here M is a transition metal such as platinum. Our 'model' system
for the
ab initio
study is M(PH
3
)
2
where we have replaced the methyl groups by hydrogen.
In Figure 24.2 we divide the atoms in both the real (MM, lower molecule) and model (
ab
initio
, upper molecule) systems into four different sets, each of them with corresponding
coordinates.
•
Set 1 atoms are present in both.
•
Set 2 atoms are present in the
ab initio
system but not in the MM.
•
Set 3 atoms are present in the MM calculation, but each atom is replaced by a simpler
one in the
ab initio
calculation (these are of course the 'link atoms' discussed earlier).
•
Set 4 atoms are present only in the MM calculation.
