Biomedical Engineering Reference
In-Depth Information
where the
h
X
and the
k
XY
have to be determined by appeal to experiment. For example,
the nitrogen atom in pyridine ought to carry a larger negative charge because nitrogen is
more electronegative than carbon and a direct calculation shows that
h
N
should be positive.
Also, the values are different for the N atom in pyridine (where the N atom formally
donates one electron to the π system) and pyrrole (where the N atom donates two electrons)
(Figure 18.2). Typical values are shown inTable 18.2. Notice that CH
3
is treated as a π group.
H
N
pyridine
pyrrole
Figure 18.2
Pyridine and pyrrole
Table 18.2
Typical h and k parameters
Atom X
h
X
k
CX
C
0
1
N (one
π
-electron)
0.5
0.8
N (two
π
-electrons)
1.5
1.0
B
−
1.0
0.7
O (two
π
-electrons)
1.0
0.8
CH
3
2.0
0.7
Thus for pyridine with the N atom labelled 1, the secular equations are
⎛
⎞
⎛
⎞
⎛
⎞
0.50.80000.8
0.8 0100 0
0 1010 0
0 0101 0
0 0010 1
0.8 0001 0
c
1
c
2
c
3
c
4
c
5
c
6
c
1
c
2
c
3
c
4
c
5
c
6
⎝
⎠
⎝
⎠
⎝
⎠
=
x
18.2 Extended Hückel Theory
Hückel's calculations on planar conjugated systems were welcomed by the scientific com-
munity of the 1930s and were heavily exploited for many years. You might like to glance
at the classic text
Molecular Orbital Theory for Organic Chemists
(Streitwieser 1962) to
get the flavour of those early days.
Despite these successes, the natives were restless. Theoreticians were unhappy because of
the arbitrary division of electrons into 'core' and 'valence' or 'π -electron'with no apparent
justification other than it worked; how did the π -electrons know the core electrons were
there, if they were not formally included in the calculation? Organic chemists were unhappy
