Normally the pi bonding orbitals are of higher energy because pi orbitals experience less direct overlap than sigma orbitals however in a few species this is not the case and I could not find any websites directly addressing this topic.
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The molecule $\ce{C2}$ is extremely instable. To my knowledge, it only exists in the famous blue cone to be seen in the Bunsen flame. Its lifetime should probably be less than one millisecond. I would be pleased to know how and who somebody has decided that the first pi level is lower than the first sigma level. Is it not a mistake ? – Maurice Oct 27 '23 at 18:27
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I should note that dicarbon is in fact very unstable but this pehnomenon is observed in a few other species such as N2 as well. – werymash Oct 27 '23 at 19:32
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How to justify that the first pi level is lower than the sigma bond made with 2p orbitals ? – Maurice Oct 27 '23 at 20:38
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C2 is a very weird molecule. I don't think all theoreticians agree how does it really bond. – Mithoron Oct 27 '23 at 20:59
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https://chemistry.stackexchange.com/questions/594/bonding-in-diatomic-c2-a-carbon-carbon-quadruple-bond – Mithoron Oct 27 '23 at 21:02
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https://chemistry.stackexchange.com/questions/85223/in-c2-molecule-both-bonds-of-the-double-bond-are-pi-bonds-but-isnt-the-rule-t https://chemistry.stackexchange.com/a/32552/9961 – Mithoron Oct 27 '23 at 21:03