Question

Are inner shells involved in molecular orbital theory

Answer 1

In molecular orbital theory, the total charge density is given by the sum of the orbital charge density. The total force exerted on the nuclei by the electronic charge distribution is thus equal to the sum of the forces exerted by the charge density in each of the molecular orbitals.

An idealized inner shell molecular orbital has a charge equivalent of unity, similar to the separated atom value. An inner shell orbital in non binding. A non binding orbital has a charge equivalent equal unity. The orbital charge density plays the same role in the molecules as in separated atoms. For instance, $1s_g$ and $1s_u$ molecular orbitals of $Li_2$ to $F_2$ are inner shell orbitals.

The charge equivalents of the $1s_g$  and $1s_u$ orbital densities for $Li_2$ are significantly less than unity. While these orbitals are not as contracted around the nuclei in $Li_2$ as they are in $O_2$