Do 1s & 2s orbitals overlap of different atoms while forming sigma bond? I think they should overlap as there will not be enough energy difference between them.
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$\begingroup$ Not a bad question but I can't think of any compounds that contain a $\sigma$ bond between $1s$ and $2s$. $\ce{LiH}$ e.g. is ionic, not covalent. $\endgroup$– GertNov 26, 2017 at 17:56
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1$\begingroup$ @Gert that's awfully narrow minded. The covalent component obviously needs these combinations. In any case where a hydrogen binds to anything other, there will always be overlap between its 1s and the other elements higher s orbital. (Obviously in the confinement of molecular orbital theory.) $\endgroup$– Martin - マーチン ♦Nov 26, 2017 at 18:19
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$\begingroup$ "there will always be overlap between its 1s and the other elements higher s orbital" Really? Do you know the MO structure of say $\ce{NH3}$ or $\ce{CH4}$? Most sigma bonds do not involve two s-orbitals. Sigma bonds form between AO where most of the electron density is on the axis connecting both bonding orbitals. It's not so easy to find examples that involve only s-orbitals. $\endgroup$– GertNov 26, 2017 at 18:30
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$\begingroup$ Lithium hydride in the gas phase maybe? $\endgroup$– Oscar LanziNov 26, 2017 at 20:48
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2$\begingroup$ @OscarLanzi Ok I searched it, LiH is only 26% ionic, so now we have a example with 1s & 2s orbitals overlap. $\endgroup$– TontyTonNov 27, 2017 at 14:25
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Orbital combinations involving inner shell electrons can indeed interact with outer-shell counterparts having the same symmetry. But, the inner shell orbitals are so deeply buried inside their respective atoms that the amount of overlap, and therefore the effect on bond/orbital energies, is very small. We find that in general, molecules are well modeled, without unneeded complexity, by including only outer shell orbitals. Moreover, any overlap involving inner shells, or even with outer shells, usually does not involve just $s$ orbitals. There can be $p$ orbital combinations and even $d$ orbital combinations having the same symmetry as the $s$ orbital ones, so the higher angular momentum orbitals also mix in. Only hydrogen and helium atoms with just $1s$ electrons can avoid that.
It isn't just our description of chemical bonding that exploits this property of inner shell electrons. We sometimes identify elements in a sample by hitting the samples with X rays that knock out inner shell electrons, and measuring the spectrum of absorbed energies. The energy required to knock out inner shell electrons from an atom is a characteristic of that element, and lack of strong overlap with other atoms makes that energy essentially invariant.
answered Nov 26, 2017 at 20:28
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1$\begingroup$ To cut to the chase: do you have any examples of MOs that are of the $\sigma_{ss}$ type, other than the $\sigma$ bond in $\ce{H2}$? $\endgroup$– GertNov 26, 2017 at 20:50
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$\begingroup$ Added more to 1st paragraph. We do not have use $s$ orbital interactions in commonly encountered molecules except hydrogen (helium atoms do not generally combine with anything). $\endgroup$ Nov 26, 2017 at 21:04
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1$\begingroup$ I was thinking. Maybe plumbane would satisfy this criteria. The electronegativities of lead and hydrogen are quite similar and thus, interaction between lead's 6s and 6p orbitals and hydrogen's 1s orbital may be significant $\endgroup$ Nov 27, 2017 at 2:43
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$\begingroup$ In fact, in methane, we should also see overlap between 1s of H and 2s of C. Since hybrid orbitals can be used to describe the bonding in CH4, of course there should be some overlap between the s orbitals of the two atoms. $\endgroup$ Nov 27, 2017 at 2:50
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$\begingroup$ @Gert The asker isn't specifying that it must be a pure s-s overlap. He/She only asked if they is overlap (even a very slight overlap). $\endgroup$ Nov 27, 2017 at 2:52