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318 9MOLECULAR STRUCTURE
I9.4 �e lower the energy of the vacant orbital, the lower the energy cost of transfer-
ring an electron into that orbital. Hence the tendency of the species to accept
electrons is greater, and so the standard reduction potential of the given species
is also greater.�erefore lower LUMO energy leads to greater standard reduc-
tion potential.
I9.6 (a) �e table below lists the energy of the HOMO and the LUMO of the
relevant molecules calculated using the PM3 method. �e energy gap
∆E between the HOMO and LUMO is given in eV, as well as the corre-
sponding wavenumber of the transition.
molecule ELUMO EHOMO ∆E (∆E/hc) ν̃obs
/eV /eV /eV /(104 cm−1) /cm−1
C2H4 1.23 −10.6 11.8 9.52 61500
C4H6 0.263 −9.47 9.73 7.85 46080
C6H8 −0.249 −8.90 8.65 6.98 39750
C8H10 −0.557 −8.58 8.02 6.47 32900
C10H12 −0.756 −8.38 7.62 6.15
3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5
6
7
8
9
10
ν̃obs/(104 cm−1)
(∆
E/
hc
)/
(1
04
cm
−1
)
Figure 9.9
(b) A plot of the predicted frequency of the transitions against the observed
frequencies is shown in Fig. 9.9. �e data points are of a good �t to a
straight line.�e equation of the best �t line is
(∆E/hc)/(104 cm−1) = 1.09 ν̃obs/(104 cm−1) + 2.78
(c) �e HOMO–LUMO energy gap for decapentaene calculated using the
PM3 method corresponds (∆E/hc)/(104 cm−1) = 6.15, therefore the
predicted wavenumber of the transition is given by
ν̃obs/(104 cm−1) = 6.15 − 2.78
1.09
= 3.09
hence the transition is predicted to be at 3.09 × 104 cm−1 .