If we adopt the molecular orbital model for diatomic molecules, molecular oxygen is certainly, in a general chemistry course, one of the most interesting examples of electron distributions over degenerate levels. This model predicts the existence of three forms of molecular oxygen and explains the paramagnetic character of the ground state, a triplet state, where the two electrons occupying the π-antibonding orbitals have parallel spins in accordance to Hund’s first rule requiring maximum multiplicity. There is spectroscopic and theoretical evidence (3) that in the first excited singlet state ¹Δ_g, the outer electrons are orbiting in the same sense and are paired in the same orbital. In the second excited singlet state, on the contrary, ¹Σ⁺_g, these electrons are orbiting in opposite directions and each π-antibonding orbital remains singly occupied (4).

Unfortunately, these relative energies of the two singlet states cannot be deduced from a simple and intuitive argument (2). The energy order of these two states is indeed surprising and opposed to the common sense: on electrostatic grounds, the mutual repulsion of two electrons on different orbitals of the same energy should be lower than if they occupy the same one (5).

Our difficulty to give an explanation lies in the description of the atomic and molecular states in terms of orbitals, which is a crude approximation that ignores the electron correlation due to the mutual coulombic repulsion between all pairs of electrons. As a matter of fact, the repulsion energy of an electron is not a function of the averaged positions of others as evaluated in the orbital model but should take into account the fact that, at any time, all the electrons tend to synchronize their motion in such a way to keep apart as much as possible. The interested reader could refer to Shriver and Atkins (6).

For other states than the ground state, we may rely on Hund’s second rule which provides some empirical guidance about the energy order (5). This rule is not always reliable but it predicts the correct energy order in the case of molecular oxygen.

Literature Cited

1. Nyasulu, F.; Macklin, J.; Cusworth, W. III. J. Chem. Educ. 2002, 79, 356–359.
2. Laing, M. J. Chem. Educ. 1989, 66, 453–455.
3. Schaefer, H. F.; Harris, F. E. J. Chem. Phys. 1968, 48, 4946. Herzberg, G. Molecular Spectra and Molecular Structure, Vol. 1, Spectra of Diatomic Molecules; VanNostrand Company: New York, 1950, p 345.
4. Atkins, P. W. Physical Chemistry, 4th ed.; Oxford University Press: New York, 1990; p 401.
5. Ebbing, D. D. General Chemistry, 2nd ed.; Houghton Mifflin Company: Boston, 1987; p 226.
6. Shriver, D. F.; Atkins, P. W.; Langford, C. H. Inorganic Chemistry; Oxford University Press: New York, 1990; p 439.