Molecular Bond Theory

Outline

• Electrons Among Atoms
  • Delocalized electrons
  • MO Principles
  • Diatomic molecules
  • Resonance molecules
• Practice with Concepts
• Discussion Questions
• Optional Website Reading

Electrons Among Atoms

So far, we've been focussed on two atoms sharing a pair of electrons to form a covalent bond. But the close proximity of multiple nuclei in a molecule creates superimposed fields that affect the electrons of the atoms. Sometimes the concept of a pair of electrons shared between only two atoms can't account for all the phenomena we observe, and another theory is necessary.

Delocalized Electrons

The molecular orbital theory is the brain child of Robert S. Milliken (the "oil-drop" man to you physicists). While the VSEPR theory gives us a good general picture of molecules (particularly those with many atoms), the MO theory is used when we want a more detailed, quantified view, especially if we have electrons in excited states.

We do the same kind of theory application when we use both an analog and digital watch to figure the difference between 12:15pm and 12:30pm. The analog watch (with long and short hands) gives us a graphical, qualitative "picture-sense" of the relationship between two times as the "second" or lower-right quarter of a circle. The digital watch requires us to do some arithmetic to figure the difference as 15 minutes, which is more precise numerically.

In most cases, both theories account for the same phenomenon with the same results. In the case of some molecules (especially those involving oxygen with one other atom), MO provides an adequate explanation while VSEPR cannot.

One of the results of MO theory is that some electrons will be in orbitals that do not lie between the bonding atoms. These orbitals are called anti-bonding orbitals.

MO Principles

1. The number of molecular orbitals is the sum of the atomic orbitals contributed by the individual atoms.

   In an H₂ molecule, there are two 1s orbitals shared by the two H atoms. The first rule of MO theory means there must be two molecular orbitals. To determine the orbitals, we can think of the mathematical equivalent of the Venn diagram for the union and difference of sets. One orbital is the sum of the two areas of the individual 1s orbitals; the other orbital is the difference of the two areas of the individual 1s orbitals. The difference, of course, leaves the common space of the 1s orbitals blank — no electron will be found in this region, which lies between the nuclei. Since no electrons exist in this orbital to shield the positive nuclei from each other, the result is repulsion between the nuclei — in other words, a force working against bonding the two nuclei together. So the second orbital is an anti-bonding orbital, and the first a bonding orbital.

2. The molecular bonding orbital is LOWER than the original atomic orbital, and the molecular anti-bonding orbital is HIGHER in energy than the original.

   This makes sense: the system will move to the lower energy level if at all possible. Anything working against this and requiring an input of energy will work against the bonding tendency.

   Each orbital can carry two electrons. The H atoms each contribute one electron, for a total of two, so both will be in the lower-energy molecular orbital, the bonding orbital. In this molecule, the 1s sigma anti-bonding orbital is empty.

   By contrast, He atoms each contribute two electrons, for a total of four electrons. Two go into the bonding orbital, and two into the anti-bonding orbital. The two configurations cancel the bonding tendency, hence He atoms tend not to form molecules!

   We can also determine bond order from the MO theory as one half of the difference given by subtracting the number of electrons in anti-bonding orbitals from the number of electrons in bonding orbitals. For H₂, we have 2 electrons in the bonding orbital and none in the anti-bonding orbital, so

   bond order H₂ = 1/2 (2 - 0) = 1

   For He₂, we would get

   bond order He₂ = 1/2 (2 - 2) = 0

   If there is an odd number of electrons in bonding and anti-bonding orbitals, the bond order will be fractional.

3. Electrons are assigned to orbitals of successively higher energy, starting with the lowest one and working up until the molecule runs out of shared electrons.

   Memorize this sequence of orbitals:

   1. 1s sigma
   2. 1s sigma anti-bonding
   3. 2s sigma
   4. 2s sigma antin-bonding
   5. 2p pi (2)
   6. 2p sigma
   7. 2p pi anti-bonding (2)
   8. 2p sigma anti-bonding

   Electrons fill the orbitals from lowest to highest levels for ground-state electrons.

4. Molecular orbitals are best formed when the electrons are at the same energy level.

This means we don't add and subtract orbitals at different levels; we add and subtract first level orbitals separately from second level orbitals, and so on. In general, for any full energy level below the valence level, the orbitals cancel anyway and don't contribute to the bonding effect, which is what we would expect.

Diatomic molecules

Homonuclear molecules are formed when atoms in the molecule have identical nuclei, such as O₂ and N₂. For these molecules, bond energy and bond order are directly related, and bond distance is inversely related. As bond energy goes up, so does bond order: the higher the order, the more difficult it is to break the bond, and the shorter the distance between nuclei.

Heteronuclear molecules are formed when atoms in the molecule have different nuclei, such as NO or CO. We can estimate the behavior of these molecules by following the same rules as for homonuclear molecules.

Resonance molecules

In the MO theory, resonance occurs when there is a half-order pi bond. Such a bond indicates that a bonding pair is spread across two bonds; that is, the electrons randomly "jump" back and forth between the bond areas, since there is no preference for which area they should occupy. This creates a double bond over one of the sigma bonds for some finite period; the electron shifts and the pi bond then extends over the other sigma bond.

Practice with the Concepts

Bond configuration

What is the bond configuration for Li₂?

Discussion Questions

• What do we mean by orbital overlap? How does such overlap create a bond between atoms?
• What is the difference in orientation between sigma and pi bonds? Why can there only be one sigma bond between two atoms?

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