Bond Order
9.3 Bonding in Homonuclear Diatiomic Molecules
homonuclear diatomic molecules.
The 1s orbitals on the lithium atoms are much smaller than the 2s orbitals and therefore do not overlap in space to any appreciable extent (see Fig. 9.31).
Thus the two electrons in each 1s orbital can be assumed to be localized and not to participate in the bonding.
To participate in molecular orbitals, atomic orbitals
Figure 9.31
The relative sizes of the lithium 1s and 2s atomic orbitals.
Only the valence orbitals of the atoms contribute significantly to the molecular orbitals of a particular molecule.
The molecular orbital diagram of the Li2 molecule and the shapes of its bonding and antibonding MOs are
shown in Fig. 9.32.
Figure 9.32
The molecular orbital energy-level diagram for the Li2 molecule.
The electron configuration for Li2 (valence electrons only) is σ2s2, and the bond order is
For the beryllium molecule (Be2) the bonding and antibonding orbitals both contain two electrons.
The bond order is (2 － 2)/2 ＝ 0.
Since the boron atom has a 1s22s22p1 configuration, we describe the B2 molecule by considering how p atomic
orbitals combine to form molecular orbitals.
Recall that p orbitals have two lobes and that they
occur in sets of three mutually perpendicular orbitals [see Fig. 9.33(a)].
When two B atoms approach each other, two pairs of p orbitals can overlap in a parallel fashion [Fig. 9.33(b) and
Figure 9.33
(a) The three mutually perpendicular 2p orbitals on two
adjacent boron atoms. The signs indicate the orbital phases.
Figure 9.33
Two pairs of parallel p orbitals can overlap, as shown in (b) and (c), and the third pair can overlap head-on, as shown in (d).
The molecular orbitals from the head-on overlap, as shown in Fig. 9.34(a).
The p orbitals that overlap in a parallel fashion also produce bonding and antibonding orbitals [Fig. 9.34(b)].
Since the electron probability lies above and below the line between the nuclei, both the orbitals are pi (π)
molecular orbitals.
They are designated as π2p for the bonding MO and π2p* for the antibonding MO.
Figure 9.34
Figure 9.34
(a) The two p orbitals on the boron atoms that overlap head-on combine to form σ bhead-onding and antibhead-onding orbitals. The bonding orbital is formed by reversing the sign of the right orbital so the positive phases of both orbitals match between the nuclei to produce constructive interference. This leads to enhanced electron probability between the nuclei. The
antibonding orbital is formed by the direct combination of the orbitals, which gives destructive interference of the positive phase of one orbital with the negative phase of the second orbital. This produces a node between the nuclei, which gives decreased electron probability.
Figure 9.34
Figure 9.34
(b) When the parallel p orbitals are combined with the positive and negative phases matched, constructive
interference occurs, giving a bonding π orbital. When the orbitals have opposite phases (the signs of one orbital are reversed), destructive interference occurs, resulting in an antibonding π orbital.
Figure 9.35 gives the molecular orbital energy-level diagram expected when the two sets of 2p orbitals on the boron atoms combine to form molecular orbitals.
Note that there are two π bonding orbitals at the same energy (degenerate orbitals) formed from the two pairs of parallel p orbitals, and there are two degenerate π
antibonding orbitals.
Figure 9.35
The expected molecular orbital energy-level diagram resulting from the combination of the 2p orbitals on two
The energy of the π2p orbitals is expected to be higher than that of the σ2p orbital because σ interactions are generally stronger than π interactions.
The total molecular orbital diagram for the B2 molecule, is shown in Fig. 9.36.
Note that B2 has six valence electrons.
Figure 9.36
The expected molecular orbital energy-level
diagram for the B2 molecule.
This diagram predicts the bond order:
Therefore, B2 should be a stable molecule.
Paramagnetism causes the substance to be attracted into the inducing magnetic field.
Diamagnetism causes the substance to be repelled from the inducing magnetic field.
Figure 9.37 illustrates how paramagnetism is measured.
Paramagnetism is associated with unpaired electrons and diamagnetism is associated with paired electrons.
Paramagnetism
Figure 9.37
Diagram of the kind of
apparatus used to measure the paramagnetism of a
sample. A paramagnetic sample will appear heavier when the electromagnet is turned on because the
sample is attracted into the inducing magnetic field.
The expected molecular orbital energy-level diagram for the B2 molecule.
For B2: Calculations show that when the s and p
orbitals are allowed to mix in the same molecular orbital, a different energy-level diagram results (see Fig. 9.38).
The C2 and N2 molecules use the same set of orbitals as for B2 (see Fig. 9.38).
Figure 9.38
The correct molecular orbital energy-level diagram for the B2 molecule. When p—s
mixing is allowed, the
energies of the σ2p and π2p orbitals are reversed. The two electrons from the B 2p
orbitals now occupy separate, degenerate π2p molecular orbitals and this have parallel spins. Therefore, this diagram ecplains the observed
Because the importance of 2s—2p mixing decreases across the period, the σ2p and π2p orbitals revert to the order expected in the absence of 2s—2p mixing for the molecules O2 and F2, as shown in Fig. 9.39.
Figure 9.39
The molecular orbital energy-level diagrams, bond orders, bond
energies, and bond
lengths for the diatomic molecules B2 through F2. Note that for O2 and F2 theσ2p orbital is
lower in energy than the π2p orbitals.
Several significant points arise from the orbital
diagrams, bond strengths, and bond lengths summarized in Fig. 9.39 for the Period 2 diatomics:
1. There are definite correlations between bond order, bond energy, and bond length. As the bond order
predicted by the molecular orbital model increases, the bond energy increases and the bond length decreases.
This is a clear indication that the bond order predicted
strongly supports the reasonableness of the MO model.
2. comparison of the bond energies of the B2 and F2 molecules indicates that bond order cannot
automatically be associated with a particular bond
energy. Although both molecules have a bond order of 1, the bond in B2 appears to be about twice as strong as the bond in F2. As we will see in our later discussion of the halogens, F2 has an unusually weak single bond
(there are 14 valence electrons on the small F2 molecule).
3. Note the very large bond energy associated with the N2 molecule, which the molecular orbital model predicts will have a bond order of 3, a triple bond. The very strong bond in N2 is the principal reason that many nitrogen-containing compounds are used as high
explosives. The reactions involving these explosives
releasing large quantities of energy.
4. The O2 molecule is known to be paramagnetic. This can be very convincingly demonstrated by pouring
liquid oxygen between the poles of a strong magnet, as shown in Fig. 9.40. The oxygen remains there until it evaporates. Significantly, the molecular orbital model correctly predicts oxygen’s paramagnetism, while the localized electron model predicts a diamagnetic
Figure 9.40
When liquid oxygen is poured into the space between the poles of a strong magnet, it remains there until it boils away.
This attraction of liquid oxygen for the magnetic field demonstrates the paramagnetism of the O2 molecule.
For the species O2, O2＋, and O2－, give the electron
configuration and the bond order for each. Which has the strongest bond?
Solution
The O2 molecule has 12 valence electrons (6 ＋ 6); O2＋ has 11 valence electrons (6 ＋ 6 －1); and O2－ has 13 valence electrons (6 ＋ 6 ＋ 1). We will assume that the ions can be treated using the same molecular orbital
diagram as for the neutral diatomic molecule:
Sample Exercise 9.6