Biomedical Engineering Reference
In-Depth Information
The core-core repulsions were further modified:
Z
A
Z
B
e
2
4πε
0
s
A
(
r
1
)
s
A
(
r
1
)
1
r
12
U
AB
=
s
B
(
r
2
)
s
B
(
r
2
)
dτ
1
dτ
2
(18.16)
1
exp
exp
α
A
R
AB
m
α
B
R
AB
m
+
−
+
−
with a different formula for OH and NH bonds.
18.14 Austin Model 1 (AM1)
Next came AM1, due to Dewar
et al.
(1985). AM1 was designed to eliminate the problems
from MNDO caused by a tendency to overestimate repulsions between atoms separated
by the sum of their van der Waals radii. The strategy adopted was to modify the core-
core terms by multiplication of the Coulomb term with sums of Gaussian functions. In
the original AM1 paper, there are four terms in the Gaussian expansion. Each Gaussian
is characterized by its position along the A-B vector and by its width. This significantly
increased the number of parameters for each atom.
18.15 PM3
PM3 is the third parameterization of MNDO, and the PM3 model contains essentially all
the same terms asAM1. The parameters for PM3 were derived by Stewart (1989) in a more
systematic way than those for AM1, many of which were derived by 'chemical intuition'.
As a consequence, some of the parameters are quite different from those of MNDO but the
two models seem to predict physical properties to the same degree of accuracy.
18.16 SAM1
The final 1993 offering in Michael Dewar's name was semi-ab-initio model 1 (SAM1)
(Dewar
et al.
1993). In SAM1, two-electron integrals are calculated using a standard STO-
3G basis set (and hence the appearance of
ab initio
in the title). The resulting integrals were
then scaled, and the Gaussian terms in the core-core repulsions were retained in order to
fine-tune the calculations.
18.17 ZINDO/1 and ZINDO/S
Michael Zerner and co-workers developed these models for transition metal compounds
(Zerner 1991). ZINDO/1 is a variant of INDO and ZINDO/S is an INDO-like method used
to calculate electronic spectroscopic properties of molecules.
