Biomedical Engineering Reference
In-Depth Information
Set 2
H
H
Set 1
PMP
H
H
H
H
Set 2
Set 4
H
H
H
H
H
H
Set 3
C
C
Set 1
PH
M
HP
H
3
C
CH
3
CH
3
H
3
C
Figure 24.2
The (upper) model system is for ab initio study; the (lower) real system for MM
study
The coordinates of atoms in set 3 are a function of those of atoms in sets 1 and 2, and the
authors show how to write equations for the energies and gradients for the combined
ab
initio
and MM descriptions. Care has to be taken to eliminate double counting of energy
terms. The algorithm is as follows.
•
Input coordinates for the set 1, set 2 and set 4 atoms.
•
Use the
ab initio
procedure to calculate the energy and the gradients with respect to the
coordinates of set 1, and of set 2.
•
Carry out a MM optimization for the set 4 atoms keeping set 1 and set 3 frozen.
•
Add the energies and gradients and test for self consistency.
24.3
IMOMO
The next step, integrated molecular orbital
MO, came in 1996 and once again I will let
the originators (Humbel
et al.
1996) spell out the good news.
+
A new theoretical method, called IMOMO (integrated MO (molecular orbital)
MO), for
integration of two different levels of MO approximation is presented. Only the active or more
difficult part of a molecule is treated at a higher level of approximation and the rest of the
molecule at a lower level of approximation. The integrated total energy and energy derivatives
are defined from three different calculations, and the structure of transition state as well as the
equilibrium structure can be optimized using the integrated energy. Any combination of any
molecular orbital approximations (
ab initio
, density functional to semi-empirical) can be used.
Test calculations in the IMOMO method have been performed and compared with normal MO
calculations for the conformation energy of ethane and
n
-butane and the S
N
2 reaction of ethyl,
propyl, isobutyl and neopentyl chloride with Cl
−
. The results indicate that these methods have
a tremendous potential for theoretical study of larger molecules, in particular for transition
states.
+
