Biomedical Engineering Reference
In-Depth Information
MINDO/3 uses an s, p minimal basis set of STOs and the elements of the HF-LCAO
matrix are
P
ij
γ
ij
−
2
P
ij
λ
ij
1
h
ii
=
U
ii
+
+
(
P
BB
−
Z
B
)γ
AB
j
on A
B
=
A
1
2
P
ij
λ
ij
if χ
i
and χ
j
on A
(18.13)
h
ij
=−
1
2
P
ij
γ
AB
otherwise
h
ij
=
h
core
ij
−
I have written the atomic Coulomb and exchange integrals
e
2
4πε
0
1
r
12
χ
j
(
r
2
) χ
j
(
r
2
) dτ
1
dτ
2
γ
ij
=
χ
i
(
r
1
)χ
i
(
r
1
)
e
2
4πε
0
χ
i
(
r
1
)χ
j
(
r
1
)
1
r
12
χ
i
(
r
2
) χ
j
(
r
2
) dτ
1
dτ
2
for simplicity of notation. The parameters for MINDO/3 were obtained in an entirely dif-
ferent way from the CNDO/INDO/NDDO family; many quantities like the STO exponents
were allowed to vary during the fitting procedure. The bonding parameter β
AB
was allowed
to vary, and experimental data such as enthalpies of formation and accurate molecular
geometries were also used to get the best fit.
An interesting feature was the treatment of core-core repulsions (the core in this
case being identified with the nucleus plus any inner-shell atomic electrons). The simple
Coulomb term
λ
ij
=
Z
A
Z
B
R
AB
(where
Z
A
and
Z
B
are the 'effective' nuclear charges) was modified for various complicated
reasons to make it a function of the electron repulsion integrals:
e
2
4πε
0
U
AB
=
Z
A
Z
B
γ
AB
+
e
2
4πε
0
γ
AB
exp
1
R
AB
−
α
AB
R
AB
m
U
AB
=
−
(18.14)
Here α
AB
is a dimensionless constant and it depends on the natures of the atoms A and B.
For O-H and N-H bonds a slightly different scheme was adopted:
Z
A
Z
H
γ
AH
+
e
2
4πε
0
γ
AB
α
AH
exp
1
R
AH
−
R
AH
m
U
AH
=
−
(18.15)
18.13 MNDO
MINDO/3 proved very successful but it had a number of limitations; enthalpies of formation
of conjugated molecules were generally too positive, bond angles were not well predicted,
and so on. Dewar and Thiel (1977) introduced the modified neglect of differential overlap
(MNDO) model, which they based on NDDOwhilst retaining the philosophy of MINDO/3.
