[Rutherford]

In a molecule like O₂, what happens with the 1s AOs? Do they undergo LCAO, or are they considered as non-bonding orbitals? Couldn't find non-valence orbitals in any MO diagram, that's why the question.

[magician4]

in MO theory, they will form two MO's 1 s sigma and 1 s sigma*, which, by energy, will cancel each other out exactly, in theory, and hence are left away in most diagrams


an example with these MO's shown anyway would look like this:


(from: link)

regards

Ingo

[Corribus]

We generally regard non-valence orbitals as "non-bonding".  This is because they have small overlap, Coulomb and exchange integrals - which is to say, they do not interact to a large extent.  The degree of bonding interaction of two atomic orbitals, in an MO framework, is dependent on their symmetry class or cardinal direction, their energy difference, and the distance between their atomic centers.  This is also why we can neglect interactions between the 1s and 2s orbitals (large energy difference) and the interaction between the 2p_x/2p_y and 2s orbtials (different symmetry).  In the latter case, the interaction is truly zero.  Note that the 2p_z orbital (z-axis = bond axis) does have appropriate symmetry to interact with a 2s.  The functional dependence on orbital overlap with internuclear distance (R) is complicated and depends on the orbital wavefunctions, but generally speaking it includes an e^-R (exponential) drop-off.

In Li₂, for example, the interaction between the 1s orbitals is predicted to be very small compared to the interaction between the 2s orbitals, because most of the electron density in the 1s orbital of the lithium atom does not overlap with the electron density in the 1s orbtial of the other lithium atom.  So for simplicity we neglect this interaction.  Do note that, strictly speaking, the probability distribution of a 1s atomic orbital extends to infinity, so the interaction between the two 1s orbitals is not zero.  It's just so small that the vast majority of the energy stabilization of the bond comes from the valence electrons, so we make a first approximation that the non-valence orbitals is "non-bonding".

[Rutherford]

Thank you very much for the nice explanation!