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I have been reading Molecular Orbitals and Organic Chemical Reactions (Student Edition) by Ian Fleming. On Pg 5, Fleming mentions that the diatomic helium molecule cannot exists because there is an overall energy increase from populating both the bonding and antibonding molecular orbitals equally (i.e. putting 2 electrons into each). However, why should there be a larger absolute energy difference between the antibonding MO and the atomic orbitals compared to the energy difference between the bonding MO and atomic oritals? Fleming explains this by saying that this is due to the presence of inter-electronic repulsion in the MOs as there are two electrons present in each MO. This may seem to make sense.

However, in most MO diagrams, the energy levels of the bonding and antibonding MOs are drawn equidistant away from the energy level of the atomic orbitals. Does there seem to be a contradiction?

It is not a duplicate as I am proposing a new explanation of "inter-electronic repulsion upon population of the MOs", which has never been discussed before.

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  • $\begingroup$ To my understanding, the discrepancy is caused by most MO diagrams being drawn qualitatively, leaving off a spectroscopically determine energy scale. When you are just drawing an MO diagram from scratch, it makes sense to draw the bonding and anti bonding as equidistant from the atomic orbitals, because the difference is subtle unless you have experimentally determined orbital energy values to scale the difference. $\endgroup$ – Tyberius May 31 '17 at 14:59
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    $\begingroup$ @TanYongBoon No, the population of the orbitals is not the reason for the energy levels of the MOs not being equidistant from the AOs. It is rather the fact that the AOs overlap and are thus not orthogonal. If they were, the levels would be equidistant. The process of forming bonding and antibonding MOs, which are required to be orthogonal (due to the Pauli exclusion principle), leads to an overlap-dependent energy-raising term in the expressions for the energy levels of both the bonding and antibonding MOs. See this answer for the equations. $\endgroup$ – Philipp May 31 '17 at 19:44
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    $\begingroup$ @TanYongBoon The problem with inter-electronic repulsion is that it is not the whole story when it comes to "occupation phenomena". You have for example also exchange energy contributions, so I'm not sure if the energy of an orbital necessarily rises when you fill it with electrons. This is rather complex. But more importantly it is simply not the reason why the energy levels of the MOs are not being equidistant from the AOs. This is a result you get from the perturbational treatment of the problem of interacting orbitals which does not deal with different occupations. $\endgroup$ – Philipp Jun 2 '17 at 19:18
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    $\begingroup$ @TanYongBoon If you only need MO theory for understanding reactivities on a "pictorial level" especially in the context of organic chemistry then I'd recommend Molecular Orbitals and Organic Chemical Reactions by Fleming. This should give you most of what you will need to get a good understanding for orbitals in organic reactions. $\endgroup$ – Philipp Jun 2 '17 at 19:25
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    $\begingroup$ @TanYongBoon Another good and short read which gives you a glimpse of orbitals in the context of solids - and is easy on the math while doing so - is Solids and surfaces: A chemist's view of bonding in extended structures by Roald Hoffman. It is really remarkable how much it explains in so little pages. $\endgroup$ – Philipp Jun 2 '17 at 19:28