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

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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

The molecular orbital theory (MO) has been introduced for the diatomic hydrogen molecules. The same method can be applied to for 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
Li -521
Be -897
B -1350 -801 549
C -1871 -1022 849
N -2470 -1274 1196
O -3116 -1524 1592
F -3879 -1795 2084
Ne   -4680   -2084   2596
In the discusion of electronic configurations of many-electron atoms, the variation of energy levels of the atomic orbitals was given. The all corresponding levels become more negative as the atomic number increases. The energy levels E2s and E2p of the second period is given in the table on the right.

The energy level E2s range 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
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.

The 2s and 2p energy levels of O and 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 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:

s2s2 s*2s2 s2p2 p2p4 p*2p2 This electronic configuration indicates a bond order of 2, and the bond can be represented by 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 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:

s2s2 s*2s2 s2p2 p2p4 p*2p4
Bondlength (pm) and bond
energy (kJ mol-1) of O2 and F2
Bondlength Bond energy
O=O 121 494
F-F 142 155
This electronic configuration shows a single F-F bond in the molecule for the reasons given for the O2 molecule. The bondlengths and bond energies of O2 and F2 shown on the right, correspond to O=O and F-F respectively. The bond energy is higher for O=O than for F-F due to the double O=O bond, and its O=O bondlength is shorter than that of F-F.

Relative energy levels of molecular orbitals for Li2 to N2.

Recently, the study of the energies of electrons in molecules revealled that the relative energy levels of molecular orbitals of Li2 to N2 are different from those of O2 and F2. The explanation for the difference comes from the consideration of hybrid atomic orbitals. Because the 2s energy levels and 2p energy levels for Li to 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 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.

©cchieh@uwaterloo.ca