Do 1s & 2s orbitals overlap of different atoms while forming sigma bond? I

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.

• 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. – Gert Nov 26 '17 at 17:56
• @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.) – Martin - マーチン Nov 26 '17 at 18:19
• "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. – Gert Nov 26 '17 at 18:30
• Lithium hydride in the gas phase maybe? – Oscar Lanzi Nov 26 '17 at 20:48
• @OscarLanzi Ok I searched it, LiH is only 26% ionic, so now we have a example with 1s & 2s orbitals overlap. – TontyTon Nov 27 '17 at 14:25

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.
• 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 $\ce{H2}$? – Gert Nov 26 '17 at 20:50
• 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). – Oscar Lanzi Nov 26 '17 at 21:04