The su orbitals are therefore classified as antibonding. It is evident from the form of density distribution for the 1su orbital that the charge density in this orbital pulls the nuclei apart rather than drawing them together. Generally, the occupation of an equal number of sg and su orbitals results in an unstable molecule. The attractive force exerted on the nuclei by the charge density in the sg orbitals is not sufficient to balance both the nuclear force of repulsion and the antibinding force exerted by the density in the su orbitals. Thus molecular orbital theory ascribes the instability of He2 to the equal occupation of bonding and antibonding orbitals. Notice that the Pauli exclusion principle is still the basic cause of the instability. If it were not for the Pauli principle, all four electrons could occupy a sg-type orbital and concentrate their charge density in the region of low potential energy between the nuclei. It is the Pauli principle, and not a question of energetics, which forces the occupation of the 1su antibonding orbital.
The total molecular charge distribution is obtained by summing the individual molecular orbital densities for single or double occupation numbers as determined by the electronic configuration of the molecule. Thus the total charge distribution for He2 (Fig. 8-6) is given by the sum of the 1sg and 1su orbital densities for double occupation of both orbitals. The adverse effect which the nodal property of the 1su orbital has on the stability of He2 is very evident in the total charge distribution. Very little charge density is accumulated in the central portion of the binding region. The value of the charge density at the mid-point of the bond in He2 is only 0.164 au compared to a value of 0.268 au for H2.
We should reconsider in the light of molecular orbital theory the stability of He2+ and the instability of the hydrogen molecule with parallel spins, cases discussed previously in terms of valence bond theory. He2+ will have the configuration 1sg2 1su1. Since the 1su orbital is only singly occupied in He2+, less charge density is accumulated in the antibinding regions than is accumulated in these same regions in the neutral molecule. Thus the binding forces of the doubly-occupied 1sg density predominate and He2 is stable. The electron configuration of H2 is 1sg1()1su1() when the electronic spins are parallel. The electrons must occupy separate orbitals because of the Pauli exclusion principle. With equal occupation of bonding and antibonding orbitals, the H2 ()species is predicted to be unstable.
Lithium. The Li2 molecule with the configuration 1sg21su22sg2 marks the beginning of what can be called the second quantum shell in analogy with the atomic case. Since the 1su antibonding orbital approximately cancels the binding obtained from the 1sg bonding orbital, the bonding in Li2 can be described as arising from the single pair of electrons in the 2sg orbital. Valence bond theory, or a Lewis model for Li2, also describes the bonding in Li2 as resulting from a single electron pair bond. This is a general result. The number of bonds predicted in a simple Lewis structure is often found to equal the difference between the number of occupied bonding and antibonding orbitals of molecular orbital theory.
The forms of the orbital density distributions for Li2 (Fig. 8-7) bear out the prediction that a single electron pair bond is responsible for the binding in this molecule.