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Why is the HOMO-LUMO gap in $\ce{N2}$ and $\ce{CO}$ different even though they have the same number of valence electrons?

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    $\begingroup$ So what if they have the same number of valence electrons? See, CH4 and H2O have the same number of valence electrons; does that mean they are similar in any other way? $\endgroup$ – Ivan Neretin Feb 6 at 6:28
  • $\begingroup$ @IvanNeretin Maybe the OP wanted to say that N2 and CO are isoelectronic, have the same symmetry, and their atomic orbitals are at similar energy because they are neighbors in the periodic table. $\endgroup$ – Karsten Theis Feb 7 at 2:04
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As correctly noted in the question, $\ce{CO}$ and $\ce{N2}$ are iso-electronic, so they should be comparable. But a difference remains: $\ce{CO}$ is hetero-nuclear, $\ce{N2}$ is homo-nuclear. The latter case typically means that there is better overlap between the orbitals (because they are of similar extent/energy). This translates into a greater gap between the bonding and the anti-bonding combination of the orbitals. This will definitely change the HOMO-LUMO gap. However, without performing a detailed quantum chemical calculation, it is not clear to me whether the HOMO-LUMO gap should be bigger or smaller for the homo-nuclear case, because one has to take the entire molecular orbital diagram into account.

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