Biomedical Engineering Reference
In-Depth Information
Table 18.3
Extended Hückel treatment of
ClO
4
−
(tetrahedral, R
Cl−O
=
148
pm)
Orbital
Energy/
E
h
4t
2
0.5234
3a
1
0.4938
3t
2
−
0.5340
1t
1
−
0.5361
1e
−
0.5487
2t
2
−
0.5890
2a
1
−
0.7312
1t
2
−
1.2324
1a
1
−
1.3718
Some transitions are allowed (and possibly strong) and some are forbidden (but often are
present as weak bands).Without going into the details and the group theory, my prediction is
that absorption bands for ClO
4
−
should be seen at about 1 hartree (1 hartree = 27.2114 eV),
which is much too large compared to the experimental value of 6 eV. Perhaps you can see
now why Wolfsberg and Helmholtz had to fiddle around so much in order to get decent
agreement with experiment. ClO
4
−
is of course colourless, so at least the prediction is on
the right side of credibility.
18.2.2 Roald Hoffmann
Credit for extending the Hückel ideas to organic molecules belongs to Roald Hoffmann
(Nobel prizewinner in 1981). The synopsis of his 1963 paper says it all (Hoffmann 1963).
The Hückel theory, with an extended basis set consisting of 2s and 2p carbon and 1s hydrogen
orbitals, with inclusion of overlap and all interactions, yields a good qualitative solution of
most hydrocarbon conformational problems. Calculations have been performed within the
same parameterization for nearly all simple saturated and unsaturated compounds, testing a
variety of geometries for each. Barriers to internal rotation, ring conformations, and geometrical
isomerism are among the topics treated. Consistent σ and π charge distributions and overlap
populations are obtained for aromatics and their relative roles discussed. For alkanes and
alkenes charge distributions are also presented. Failures include overemphasis on steric factors,
which leads to some incorrect isomerization energies; also the failure to predict strain energies.
It is stressed that the geometry of a molecule appears to be its most predictable property.
Valence shell orbitals are used, and the same key formula (Equation (18.1)) is used to
find the Hamiltonian.
18.3 Pariser, Parr and Pople
The next advances came in the 1950s, with amore systematic treatment of electron repulsion
in π -electron molecules. These two keynote papers due to Rudolf Pariser and Robert Parr
and to John Pople are so important that I will give the abstracts (almost) in full. Pople
(1953) wrote:
