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Chemists often discuss sigma and pi bonds. To a physicist, it's not easy to figure out what these actually are, as discussions tend to be full of lots of chemistry jargon about "antibonding", "backbonding", "aromaticity", "ligands", "reactivity", etc. - terms which most physicists aren't familiar with. I suspect (although I'm not sure) that sigma and pi bonds are probably fairly easy to define precisely in terms of fundamental quantum-mechanical principles like wavefunctions, spherical harmonics, and symmetry groups that a physicist is more likely to be familiar with, and that the difficulty is mostly a language issue rather than a conceptual issue.

Is there a definition of sigma and pi bonds that uses a minimum of chemistry jargon (but as much physics jargon as necessary :-) )? Please state any assumptions explicitly - for example, chemists talk about "orbitals" a lot in a multi-electron context, so I assume they're pretty much always working in the Hartree-Fock approximation and neglecting inter-electron entanglement (but please correct me if I'm wrong).

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  • $\begingroup$ Guess: sigma bonds are bonds between $s$ ($\ell=0$) orbitals, and pi bonds are between $p$ ($\ell=1$) orbitals. This would be supported if they also have delta bonds between $d$ ($\ell = 2$) orbitals, though I think bonds between $d$ orbital valence electrons tend to be metallic, so the electron isn't so much localized to the bond. No idea how the describe mixed orbital bonds (are those ionic?). $\endgroup$ – Sean E. Lake Jan 14 '18 at 21:12
  • $\begingroup$ All the chemistry texts I have seen that discuss these actually show which orbitals are included in the bonding in a picture, and they go hand in hand with the above comment $\endgroup$ – Triatticus Jan 14 '18 at 21:16
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    $\begingroup$ @SeanE.Lake Yeah, there are also delta bonds from d orbitals and even phi bonds from f orbitals. $\endgroup$ – Mithoron Jan 14 '18 at 21:21
  • $\begingroup$ @SeanE.Lake What exactly is a "bond between [specific] orbitals"? $\endgroup$ – tparker Jan 14 '18 at 21:24
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    $\begingroup$ @SeanE.Lake: Considering $2p$ atomic orbitals in the oxygen molecule, there is a sigma bonding orbital with two electrons. Then there are two bonding pi-orbitals, with two electrons each. Then there are two antibonding pi-orbitals, each with a single electron (parallel spin). $\endgroup$ – Pieter Jan 14 '18 at 21:44
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It is about the symmetry: sigma orbitals do not have a nodal plane containing the molecular axis, pi bonds have one such plane, delta have two.

So two p-atomic orbitals can form a sigma bond if they are parallel with the bond. See this image: enter image description here

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