0 # 10
# 10 # 1
0 # 10
0
@
1
A
0 # 10
# 10 CN
0 CN NN
0
@
1
A (1)
Various modifications of the carbon values have been proposed for heteroatoms
[1]. If we use the suggested valuesCN¼#1 andNN¼#1.5 we have
0 # 10
# 10 # 1
0 # 1 # 1 : 50
@
1
A
which on diagonalization gives the energy levels#2.111, 0.591, 1.202(cf. for the
carbon system A,#1.414, 0, 1.414). Intuitively, we expect the matrix elementNN
to be more negative thanCC(#1.5 cf. 0) because N is more electronegative than C;
hereCNis the same asCC(#1), butCXvalues have usually been taken as being
less negative than#1, reflecting the probably less complete energy-lowering
delocalization of an electron in a CX-type bond compared to a CC-type bond.^2
The hetero atom parameters have been obtained in various ways, for example by
striving for a best correlation of HOMO values with ionization energies, or of
polarographic reduction potentials with LUMO values. The whole subject of SHM
parameters and best heteroatom parameters is now of little practical importance,
since much better quantitative molecular orbital methods are now readily available.
Reference
- (a) A thorough discussion: Streitwieser A Jr (1961) Molecular orbital theory for organic
chemists. Wiley, chapter 5. (b) A short hands-on presentation: Roberts JD (1962) Notes on
molecular orbital calculations. Benjamin, New York, chapter 6
Chapter 4, Harder Questions, Answers
Q5
What is the result of using as a reference system for calculating the resonance
energy of cyclobutadiene, not two ethene molecules, but 1,3-butadiene? What does
this have to do with antiaromaticity? Is there any way to decide if one reference
system is better than another?
(^2) Discussions of heteroatoms in the SHM written in the heyday of that method present the
heteroatom parameters in a slightly more complicated way, in terms of the coulomb and resonance
integralsaandb, rather than as simple numbers.
614 Answers