# Molecular Orbitals of Li₂ to F₂

Skills to Develop

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

The molecular orbital theory (MO) has been introduced for the diatomic hydrogen molecules. The same method can be applied to other diatomic molecules, but involving more than the 1s atomic orbitals. For the second period elements, the 2s and 2p orbitals are important for MO considerations. 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

Atomic energy levels E in kJ mol-1
of second group elements
Element E2s E2p E2p-E2s
$$\ce{Li}$$ -521
$$\ce{Be}$$ -897
$$\ce{B}$$ -1350 -801 549
$$\ce{C}$$ -1871 -1022 849
$$\ce{N}$$ -2470 -1274 1196
$$\ce{O}$$ -3116 -1524 1592
$$\ce{F}$$ -3879 -1795 2084
$$\ce{Ne}$$ -4680 -2084 2596

In the discussion of electronic configurations of many-electron atoms, the variation of energy levels of the atomic orbitals was given. All the corresponding levels become more negative as the atomic number increases. The energy levels E2s and E2p of the second period are given in the table on the right.

The energy level E2s ranges from -521 to -4680 kJ mol-1 for these elements. The E2p energy levels also become more negative, but the decrease (because they are negative) is not as rapid as that of the E2s levels. Thus, the differences E2p - E2s 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
$$\ce{H}$$
_2s_ _ _2p

_ 1s
$$\ce{Li}$$

_ _ _ 2p
_ 2s

_ 1s
$$\ce{Be}$$

_ _ _ 2p

_ 2s

_ 1s
$$\ce{B}$$

_ _ _ 2p

_ 2s

_ 1s
$$\ce{C}$$

_ _ _ 2p

_ 2s

_ 1s
$$\ce{N}$$

_ _ _ 2p

_ 2s

_ 1s
$$\ce{O}$$

_ _ _ 2p

_ 2s

_ 1s
$$\ce{F}$$

_ _ _ 2p

_ 2s

_ 1s

### Relative Energy Levels of Molecular Orbitals of O2 and F2

The 2s and 2p energy levels of $$\ce{O}$$ and $$\ce{F}$$ are very far apart. The combination of the 2s orbitals from the two atoms form a sigma bonding and sigma antibonding orbitals in a way very similar to the case of the hydrogen molecules, because the 2p orbitals have little to do with the 2s orbitals.

On the other hand, the three 2p orbitals of each $$\ce{O}$$ (or $$\ce{F}$$) 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 $$\ce{O2}$$ and $$\ce{F2}$$ has the following arrangement:

Relative energy levels of $$\ce{O2}$$ and $$\ce{F2}$$ molecules

_ _ _
2p

_
2s

Atomic
orbital

__ s*2p
__ __ p*2p

__ __p2p
__ s2p

__ s*2s

__ s2s

Molecular orbitals

_ _ _
2p

_
2s

Atomic
orbital

The electronic configuration for $$\ce{O2}$$ is:

s2s2 s*2s2 s2p2 p2p4 p*2p2

This electronic configuration indicates a bond order of 2, and the bond can be represented by $$\ce{O=O}$$. There is no net bonding from the s2s orbitals, because the number of bonding electrons equals the number of antibonding electrons. The two electons in p*2p2 cancel two of the 6 bonding electrons (s2p2 p2p4). Therefore, there are 4 total bonding electrons. The two electrons in the p*2p2 orbitals have the same spin, and they are responsible for the paramagnetism of oxygen.

As an exercise, please fill electrons in the molecular orbitals of a relative energy level diagram to derive and confirm the above conclusion as well as the conclusion regarding the $$\ce{F2}$$ molecule.

The electronic configuration for $$\ce{F2}$$ is:

s2s2 s*2s2 s2p2 p2p4 p*2p4

Bond length (pm) and bond
energy (kJ mol-1) of $$\ce{O2}$$ and $$\ce{F2}$$
Bond length Bond energy
$$\ce{O=O}$$ 121 494
$$\ce{F-F}$$ 142 155

This electronic configuration shows a single $$\ce{F-F}$$ bond in the molecule for the reasons given for the $$\ce{O2}$$ molecule. The bond lengths and bond energies of $$\ce{O2}$$ and $$\ce{F2}$$ (shown on the right) correspond to $$\ce{O=O}$$ and $$\ce{F-F}$$ respectively. The bond energy is higher for $$\ce{O=O}$$ than for $$\ce{F-F}$$ due to the double $$\ce{O=O}$$ bond, and its $$\ce{O=O}$$ bond length is shorter than that of $$\ce{F-F}$$.

### Relative Energy Levels of Molecular Orbitals for Li2 to N2

Recently, the study of the energies of electrons in molecules revealed that the relative energy levels of molecular orbitals of $$\ce{Li2}$$ to $$\ce{N2}$$ are different from those of $$\ce{O2}$$ and $$\ce{F2}$$. The explanation for the difference comes from the consideration of hybrid atomic orbitals. Because the 2s energy levels and 2p energy levels for $$\ce{Li}$$ to $$\ce{N}$$ are relatively close, the 2s orbitals are influenced by the 2p orbitals. This influence makes the bonding orbitals stronger than, and the antibonding orbitals weaker than, those formed by pure 2s orbitals. This process is called s p mixing.

Due to s p mixing, the s2p orbital is weakened, and the s*2p2 is also affected. These effects cause the relative order to change, and the typical relative energy levels for $$\ce{Li2}$$, $$\ce{Be2}$$, $$\ce{B2}$$, $$\ce{C2}$$ and $$\ce{N2}$$ to have the following diagram:

Relative energy levels of $$\ce{Li2}$$ to $$\ce{N2}$$ molecules

_ _ _
2p

_
2s

Atomic
orbital

__ s*2p
__ __ p*2p

__ s2p
__ __p2p

__ s*2s

__ s2s

Molecular orbitals

_ _ _
2p

_
2s

Atomic
orbital

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

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