Chemistry Reference
In-Depth Information
Table 11.7
The parameters
values considered for the
conjugated systems by
Hückel molecular orbital
(HMO method); the number
of points indicates the
δ
r
η
rs
δ
|
−
=
0
.
0
η
C
−
O
−
−
=
0
.
8
C
−
δ
|
−
=
0
.
5
η
C
−
N
<
=
0
.
8
N
−
π
electrons/atom. (Putz et al.
2010
)
η
C
...
δ
C(N
|
<
)
=
0
.
5
=
1
.
0
−
C
η
C
...
δ
CH
3
=
1
.
1
=
1
.
0
N
|
CH
3
−
N
−
−
δ
−
H
=
1
.
5
-
−
N
H
δ
−
−
=
2
.
0
-
O
−
item in lowering the degree of the secular determinant which is obtained following
the Hückel molecular orbital (HMO) method (Hückel
1930
,
1931
; Mandado et al.
2007
) in joint using the data from Table
11.7
.
In this computational framework several parameter were calculated: the Hückel
matrices, the eigenvectors, the
π
levels
o
f energy, the total ground state energy (
E
π
),
the delocalization energy/
π
electrons (
π
), the charge densities (
ρ
r
), the bond orders
(
p
rs
) and the free valence
F
r
=
−
p
rs
.
On the other side, the present-based molecular computations employ for the DFT
computational framework, the exchange sum and the correlation contributions in the
mixed functional of Eq. (
11.52
)
1
.
732
E
XC
[
ρ
]
=
EXCHANGE
+
K[
ρ
]
E
c
[
ρ
]
CORRELATION
(11.55)
under the for of hybrid B3-LYP functional proposed by Becke through empirical
comparisons made against very accurate experimental results, containing the ex-
change contribution (20 % Hartree Fock
+
8 % Slater
+
81 % Becke88) which was
added to the correlation energy (81 % Lee-Yang-Parr
19 % Vosko-Wilk-Nusair).
Nevertheless, the Becke's functional
via
the so-called semiempirical (SE) modified
(
β
,
γ
)-parameterized gradient-corrected functional (Becke
1986
) was use for the
considered 81 % contribution in the
exchange
term:
+
β
σ
x
σ
(r)
K
SE
ρ
4
/
3
σ
=
K
0
−
γ
x
σ
(r)
d
r
,
1
+
3
4
π
1
/
3
3
2
(11.56)
ρ
4
/
3
(
r
)d
r
,
K
0
=−
=
|∇
ρ
σ
(
r
)
|
x
σ
(
r
)
,
ρ
4
/
3
(
r
)
σ
