Chemistry Reference
In-Depth Information
Table 11.1
Energies and coefficients of the atomic orbitals contributions to the molecular orbitals
of ethene and butadiene
Hydrocarbon
K
ε
c
1
c
2
c
3
c
4
1
√
2
1
√
2
C
2
H
4
−
1.0000
ε
1
= ε
HOMO
= α + β
-
-
1
√
2
1
√
2
1.0000
ε
2
= ε
LUMO
= α − β
−
-
-
C
4
H
6
−
1.6180
ε
1
= α +
1.6180
β
0.3717
0.6015
0.6015
0.3717
−
0.6180
ε
2
= ε
HOMO
= α +
0.6180
β
0.6015
0.3717
−
0.3717
−
0.6015
0.6180
ε
= ε
= α −
0.6180
β
0.6015
−
0.3717
−
0.3717
0.6015
3
LUMO
1.6180
ε
4
= α −
1.6180
β
0.3717
−
0.6015
0.6015
−
0.3717
Fig. 11.1
Energetic diagrams for ethene (
a
) and butadiene (
b
)
Table 11.2
Absolute bonding energies in kcal/mol (
18 kcal/mol) for the Hückel orbital
HOMO- like levels for molecules of Table
11.1
, along the related bondonic radii of action, mass
ratio respecting the electronic unit, and the bondonic gravitational ratio respecting the universal
gravitational unit, according with Eqs. (
11.37a
,
11.37b
,
11.37c
), respectively
Hydrocarbon
α =
0,
β =−
10
6
10
−
53
E
bond
(
kcal/mol
)
X
B
(Å)
ς
m
×
ς
G
×
C
2
H
4
ε
1
= ε
HOMO
=−
18
201.174
120.607
246.591
C
4
H
6
ε
1
=−
29.124
124.335
195.142
94.1932
ε
2
= ε
HOMO
=−
11.124
325.525
74.5352
645.654
The bondonic radii and gravitational actions are parallel increasing, while some-
how anti-parallel with the bondonic mass variation as the bonding energy
decreases from more to less bonding nature, i.e. from inner molecular orbital
to the frontier HOMO;
For larger system the HOMO level is less bound so having less bondonic mass
and higher radius of action that determine also a higher gravitational influence (in
order to keep the bond to a longer range of action).
