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298 9MOLECULAR STRUCTURE
−4 −2 0 2 4 6 8 10
R = 2a0
R = 3a0
R = 5a0
z/a0
Figure 9.4
9C Molecularorbitaltheory: homonucleardiatomicmolecules
Answer to discussion questions
D9C.2 �e building-up principle for homonuclear diatomic molecules is essentially
the same as for atoms, but the diatomic molecular orbitals used in the former
are di�erent in name and in nature than the atomic orbitals used in the latter.
A diagram of energy levels (orbitals) and degeneracies is needed. For diatomic
molecules, these energy levels are either nondegenerate (for σ bonds) or doubly
degenerate (for all others). �e orbitals are populated with electrons, placing
each successive electron in the lowest-energy orbital available, no more than
two electrons per orbital. Hund’s rule indicates that di�erent degenerate or-
bitals should be populated �rst, with electrons that have parallel spins, before
pairing two electrons in the same degenerate orbital.
D9C.4 �e bond strength is related to the extent towhich the occupied bondingmolec-
ular orbitals are lowered in energy compared to the constituent atomic orbitals.
As described in Topic 9B for the case of H2+, this lowering in energy depends
on the size of the term k, [9B.5c–353], which is a measure of the interaction
between a nucleus and the excess electron density in the internuclear region
arising from overlap.
�e overlap integral, S, is a di�erent quantity than k, but its behaviour with
(for example) internuclear distance is quite similar. �us the overlap integral
is o�en taken as a proxy for k, not least as it much easier to imagine how
the overlap varies when the orbital or the internuclear distance is varied. It is
therefore common to speak of a bond being strong when ‘there is good overlap’.
�e fact that there is a correlation between overlap and bond strength may,
however, simply be fortuitous as the theory does not indicate such a connection.
Solutions to exercises
E9C.1(b) �e molecular orbital diagram for O22− and F2− is shown in Fig. 9C.11 on page
361, and that of N2 is shown in Fig. 9C.12 on page 361. According to the Pauli
principle, up to two valence electrons can be placed in each of the molecular