• Explain how the energy levels of atomic orbitals vary for H, Li, Be, B, C, N, and O.
• Draw relative energy levels diagrams for homonuclear diatomic molecules of period 2 elements.
• Explain why the relative energy levels diagrams for Li₂, Be₂, B₂, C₂, N₂ are different from those of O₂ and F₂.
• Point out relevant data to support the energy level diagrams of diatomic molecules of period 2 elements.

Underconstruction - Red Alert:
This page is made up on Dec. 5, 1999, yet to be proof read....
The molecular orbital theory of Li₂ to F₂ gives a graphical explanation. The following is more verbal.

Molecular orbitals of Li₂, Be₂, ... to F₂

A linear combination of properly oriented atomic orbitals for the formation of sigma s and pi p bonds. The formation of bonds from the linear combination of atomic orbitals is the same as that of the valence bond theory. For simplicity, we are not going into the details of the theory, but simply show you how to construct the MO energy level diagram.

Relative energy levels of atomic orbitals from hydrogen to fluorine

The energy level E_2s range from -521 to -4680 kJ mol^-1 for these elements. The E_2p energy levels also become more negative, but the decrease (because they are negative) is not as rapid as that of the E_2s levels. Thus, the differences E_2p - E_2s increase as the atomic numbers increase.

A qualitative diagram showing the changes of energy levels of atomic orbitals is given below:

Variation of energy levels for atomic orbitals of some elements
H _2s_ _ _2p _ 1s	Li _ _ _ 2p _ 2s _ 1s	Be _ _ _ 2p _ 2s _ 1s	B _ _ _ 2p _ 2s _ 1s	C _ _ _ 2p _ 2s _ 1s	N _ _ _ 2p _ 2s _ 1s	O _ _ _ 2p _ 2s _ 1s	F _ _ _ 2p _ 2s _ 1s

Relative energy levels of molecular orbitals of O₂ and F₂.

On the other hand, the three 2p orbitals of each O (or F) atom can form one sigma and two pi bonds and their corresponding antibonding molecular orbitals. The interaction of the 2p orbitals for the sigma bond is stronger, and the levels of sigma and anti sigma bonds are farther apart than those of pi and anti pi bonds. Thus, the relative energy level diagram of O₂ and F₂ has the following arrangement:

Relative energy levels of O2 and F2 molecules
_ _ _ 2p _ 2s Atomic orbital	__ s*2p __ __ p*2p __ __p2p __ s2p __ s*2s __ s2s Molecular orbitals	_ _ _ 2p _ 2s Atomic orbital

The electronic configuration for O₂ is:

As an exercise, please fill electrons in the molecular orbitals of relative energy levels diagram to derive and confirm the above conclusion as well as the conclusion regarding the F₂ molecule.

The electronic configuration for F₂ is:

Relative energy levels of molecular orbitals for Li₂ to N₂.

Due to s p mixing, the s_2p orbital is weakened, and the s*_2p² is also affected. These effects cause the relative order to change, and a typical relative energy levels for Li₂, Be₂, B₂, C₂ and N₂ to have the following diagram:

Relative energy levels of Li2 to N2 molecules
_ _ _ 2p _ 2s Atomic orbital	__ s*2p __ __ p*2p __ s2p __ __p2p __ s*2s __ s2s Molecular orbitals	_ _ _ 2p _ 2s Atomic orbital

The electronic configurations agrees with the experimental bondlengths, and bond energies of homonuclear diatomic molecules of second-period elements. They are given in a table below. The argument regarding bondlengths, bond orders, and bond energies given for O₂ and F₂ above applies to all these molecules. Note also that B₂ and O₂ are paramagnetic due to the unpaired electrons in the molecular orbitals. Other molecules in this group are diamagnetic.

Electronic configuration, bondlength (pm) and bond energy (kJ mol-1 of Li2 to F2
	Electronic configuration	Bondlength	Bond energy
Li-Li	s2s2	267	110
Be..Be	s2s2 s*2s2	exist?	exist?
B-B	s2s2 s*2s2 p2p2	159	290
C=C	s2s2 s*2s2 p2p4	124	602
NºN	s2s2 s*2s2 p2p4 s2p2	110	942
O=O	s2s2 s*2s2 s2p2 p2p4 p*2p2	121	494
F-F	s2s2 s*2s2 s2p2 p2p4 p*2p4	142	155

The molecular orbital theory of Li₂ to F₂ has given a diagramatic explanation of s p mixing leading to the difference in relative orbital energy levels. This link is from the University of Florida.