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Why Doesn't Molecular Oxygen Have a Simple Rotational Spectrum?
If you have not done any molecular spectroscopy for awhile, as I haven't,
or even if you have, you might have forgotten the reasons why the spectrum
of molecular oxygen (O2) looks so different from CO, which has
a simple rotational spectrum depending only on the quantum number J. You
might also have trouble trying to answer the related question of why O2
is paramagnetic and CO is not. The following comments are intended to remind
you of the answers to these questions by bringing back fond memories of
your first courses in physical chemistry and molecular spectroscopy.
The electronic configuration of atomic oxygen is easily arrived at by
applying the Aufbau (or building up) Principle to the Atomic Orbital (AO)
theory of hydrogen. In its simplest form the aufbau principle states that
the successsive electrons of a multi-electron atom should be added by placing
them in the orbitals of decreasing stability while taking into account
the Pauli Exclusion Principle. Furthermore, if two atomic orbitals have
the same energy and only two electrons are to occupy them, then Hund's
Rule is applied to place them in separate orbitals with the same spin.,
rather than the same orbital with opposite spin. Applying these rules to
atomic oxygen, we arrive at the familiar electronic configuration: (1s2)
(2s2) (2p4), where the leading number in each of these terms is the principle
quantum number (n), the middle letter represents the orbital angular momentum
(l, with s for l=0, p for l=1, d for l=2, etc.) and the superscript is
the total number of electrons occupying the orbital. The p-orbital contains
three degenerate states corresponding to the (2l+1) possible values of
the projection of the orbital angular momentum (ml) about some
preferred direction. Therefore, one of the three p-orbitals contains 2
electrons with opposite spin (by the Exclusion Principal) and the other
two each contain one electron (by Hund's Rule).
This is all very circuitous, but it leads us to where we want to be,
namely a description of the electronic configuration of molecular oxygen.
One might guess that O2 can be described simply by pairing up
the two unpaired electrons in each oxygen atom. Based on this simple idea,
molecular oxygen would have no unpaired electrons and would therefore not
be paramagnetic., which we know it to be. Atomic Orbital theory breaks
down for molecules; what is needed is a Molecular Orbital theory, which
in its simplest form is a Linear Combination of Atomic Orbitals (LCAO),
or a hybrid orbital theory. The basic idea here is that simple AO theory
does not work because once bonding begins the orbitals begin interacting
with one another so that each state of the bonding molecule is in fact
a superposition of all possible states. The electronic configuration of
O2 might be either (
1)2
(1*)2
(2)2
(
)4
(*)2
or (1)2
(1*)2
()4
(2)2
(*)2
. Either way, the bond order is predicted to be two and two unpaired electrons
are expected. Both these predictions are in good agreement with experiment,
the experimental bond energy being 118 kcal/mole. It is also interesting
to note that the addition of electrons to O2 causes the bond
length to increase [d(0 e)= 1.21 A, d(1 e)= 1.26 A, and d(2 e)= 1.49 A],
while the loss of an electron decrease the bond length to d(-1 e)= 1.12
A. Bond length varies inversely with bond strength. These values are in
excellent agreement with the MO electron configuration, since the orbital
to and from which the electrons are added or removed is an antibonding
one. Hence, contrary to the usual situation, removal of an electron strengthens
the bond, while addition weakens it.