Humboldt State University ® Department of Chemistry

Richard A. Paselk

Chem 110	General Chemistry	Summer 2006
Lecture Notes::Lec 15_20 June	© R. Paselk 2006
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Hybrid Atomic Orbitals, cont.

Remember, that with Hybrid Orbital Theory we are looking at individual atoms, not molecules. All of our calculations and predictions are for the atoms. We make molecules by overlapping the new hybrid orbitals with other hybrid orbitals or with atomic orbitals of other atoms to make a molecule.

Let's look now at the examples and illustrations in your text , noting single and multiple bonds etc.

• Tetrahedral Electronic Geometry = sp³. Four orbitals (s + 3 p's) combined. (Note the sum of "exponents" = number of orbitals) [overhead]
  • Methane (CH₄) - tetrahedral molecule. [overhead]
  • Ammonia (NH₃) - trigonal bipyramidal molecule. [overhead]
• Trigonal Planar Electronic Geometry = sp². Three orbitals (s + 2 p's) combined, one p orbital left as is. [overhead]
  • Ethylene (H₂CCH₂) - each carbon has trigonal planar geometry. [overheads]
• Linear Electronic Geometry = sp¹, or sp. Two orbitals (s + p) combined, two p orbitals left as is. [overhead]

Note we get two basic bond types when we overlap orbitals:

1. Sigma (sigma) bonds: These are cylindrically symmetrical around the axis connecting the bonded atoms. Single bonds are always sigma bonds, and in a multiply bonded system the "first" or "central" bond is a sigma bond. [overhead]
2. Pi (pi) bonds: these are made up of two lobes with planar symmetry round a plane though the nuclei of the two bonded atoms. The "second" and "third" bond of multiply bonded atoms are pi bonds. For systems with two pi bonds the bond panes are perpendicular to each other. [overhead]

To reiterate, the hybrid atomic orbital model is a localized electron model - the quantum calculations are looking at the atoms individually. The hybrid orbital model is particularly useful to us at this time because it gives nice pictures of two aspects of bonding:

• Molecular shape - look at sp, sp², sp³, dsp³, and d²sp³ (overhead, text figure)
• Multiple bond formation - sigma and pi bonds.

However, the localized electron, hybrid orbital theory does not do well in other areas:

• Since the electrons are assumed to be localized, resonance must be invoked to explain partial bonds etc.
• It gives no direct information about bond energies since it is not calculating the way electrons are shared.
• It doesn't work well for unpaired electrons in molecules.

In the hybrid orbital model described we look at the atoms individually in creating the orbitals, then we allow them to overlap to give bonds. Of course in a real molecule nature does not distinguish between atoms and orbitals in this way, in fact when atoms form a bond new orbitals are formed based on the entire molecule. Now I want to introduce some of the concepts involved in this molecular orbital. picture.

Molecular Orbitals

Molecular Orbital Model of Bonding: As with atoms, we will begin with the simplest system, in this case the dihydrogen molecule, H₂. (Strictly speaking, the simplest molecule is the dihydrogen molecular ion, H₂⁺, with a single electron.)

As I noted in the beginning of our discussion of modern bonding, orbitals are conserved, so if we add two hydrogen atoms, H_a & H_b together, the two 1s orbitals should give us two molecular orbitals, MO₁ and MO₂:

Note that one orbital will have a lower energy and the second a higher energy as expected from the approximate conservation of orbital energies we noted earlier. And when we add and subtract the two atomic orbitals they give molecular orbitals of quite different shapes. (overhead, text figure)

The molecular orbitals resulting from this combination are symmetrical along the atomic axis between the bonded atoms, and as before are referred to as sigma (sigma) molecular orbitals. The two orbitals, however have much different properties.

• The ground level (lower energy orbital) is a bonding orbital and called simply a sigma orbital. The electron density for this orbital is largely distributed between the atoms.
• The high energy orbital actually has most of the electron density not between the nuclei, so the nuclei and electrons will repel each other, and no bond is formed. This orbital is referred to as an antibonding orbital and given the designation sigma star (sigma*).
• Note that if electrons occupy both the bonding and antibonding orbitals there will be no net bond formed!

Bond Order = (#bonding electrons - # antibonding electrons)/2. Divide by two to get "classical" two electron bond. Bond order gives a measure of bond strength in units of an electron-pair bond.

• If we look at hydrogen, H₂, both electrons go into the ground state (lowest energy) MO, giving a bond order of one, so H₂ has a single bond.
• If we look at the next possible homonuclear diatomic molecule, He₂, the four electrons will first fill the lowest energy MO, but the next two go into the higher energy, antibonding MO. The bond order is then 0, and theory predicts no bonding and no He₂ molecule.

So far we've looked only at atoms with s-electrons and s-orbitals. What happens when we have p-electrons? The first element with p-electrons is boron, with a valence electronic configuration of 2s²2p¹. So what happens if we combine two boron atoms and calculate the new energy levels for the potential molecule?

• First let's look at a simple calculation assuming the s and p orbitals do not interact with each other.
  • Because the s and p orbitals are of significantly different energies we'll get two distinct sets of MO's. (text figure 9.36)
  • As expected the 2s orbitals will combine to give sigma MO's with a splitting just like we saw for hydrogen.
  • The p-orbitals will be a bit more complex. (overhead, figures 9.33 and 9.34)
    • One set, call them the p_x orbitals will overlap with cylindrical symmetry about the axis connecting the nuclei giving a set of sigma orbitals.
    • The other two sets have planar symmetry and give pi orbitals.
  • With this calculation the energy diagram shows, starting at the lowest energy, a sigma_2s, a sigma_2s*, a sigma_2p, two pi orbitals of equal energy (y, and z), two pi* orbitals of equal energy, and a sigma_2p* orbital.
  • Filling from the bottom with the six electrons of the two boron atoms we should see two bonds and one antibond giving a total of one bond, which is what we observe. However, diboron is paramagnetic, which is not at all expected from our filling diagram. What's wrong? Our model is too simple.
• Recall from our earlier discussion that when we look at a molecule the electrons of that molecule are now just that - they belong to the molecule. In our first calculation above we assumed we could treat the electron energy levels the same as we did for the atoms. But when we put the two atoms together as a molecule we shouldn't be surprised that the energy levels are more complex - the valence s and p orbitals of the atoms are all considered together and a whole new set is calculated. Your author refers to this as "mixing" the s and p orbitals, but really there are no s or p valence orbitals in the molecule.)
  • So when we calculate the orbitals fresh, assuming the molecule we of course still get the same number of orbitals, and even the same types, but the energy levels differ. (text figure 9.38)
    • The sigma_2s, and sigma_2s* orbitals remain separate from the other orbitals, but sigma_2s* energy is lowered.
    • The order of the sigma_2p and pi_2p orbitals is reversed, with the two pi_2p at a lower energy. The order of the excited (*) orbitals remains the same.
    • As a result, filling from the lowest energy, we see a sigma_2p bond, a sigma_2p* antibond, and a pi_2p bond made up of two unpaired electrons in different pi_2p orbitals. Thus the diboron molecule is predicted to be paramagnetic, as observed.

Bond Order = (#bonding electrons - # antibonding electrons)/2. Divide by two to get "classical" two electron bond. Bond order gives a measure of bond strength in units of an electron-pair bond.

• If we look at hydrogen, H₂, both electrons go into the ground state (lowest energy) MO, giving a bond order of one, so H₂ has a single bond.
• If we look at the next possible homonuclear diatomic molecule, He₂, the four electrons will first fill the lowest energy MO, but the next two go into the higher energy, antibonding MO. The bond order is then 0, and theory predicts no bonding and no He₂ molecule.

Lets now go back and and look at the bond orders and bonding of the homonuclear diatomic molecules of the second period. (overhead, text figure 9.39) As we can see in each case the bonding is as predicted from molecular orbital theory.

Molecular Orbital Energy Levels and Bonding in Diatomic Homonuclear Molecules, Li₂-Ne₂

	Li2	Be2	B2	C2	N2		O2	F2	Ne2
sigma2p*						sigma2p*
pi2p*						pi2p*
sigma2p						pi2p
pi2p						sigma2p
sigma2s*						sigma2s*
sigma2s						sigma2s
Bonds	1	0	1	2	3		2	1	0

Heteronuclear Molecules: We've looked at homonuclear molecules where the initial orbital energies are identical, what about the more complex situation where two different atoms combine?

The classic example, because of its extremity is HF.

• To simplify our modeling we can assume that we use a single orbital from fluorine, the outermost p-orbital.
  • Again, to simplify our thought processes, let's assume localized electrons for the s and the two filled p orbitals on F.
  • We will then form a sigma orbital between the half-filled p orbital of F and the 1s orbital of H.
    • Keep in mind that Hydrogen has no p orbitals, no pi orbitals will be formed, the sigma bond is the only one that makes sense - a similar rationale will also work for atoms such as Li and Be.
• To form the orbital we next need to think about the energy levels of the two participating orbitals.
  • From electronegativities we recall that fluorine has a greater attraction for electrons than hydrogen, so we get the diagram seen below. (p 439 in your text)

H atom HF molecule F atom E    sigma*   1s                                 2p      sigma

• An example with close energies is NO. Note the correct prediction of paramagnetism and bonding, while the hybrid orbital theory fails in these predictions.

Molecular Orbital Energy Levels in NO sigma2p*   pi2p* sigma2p pi2p sigma2s* sigma2s Bonds  2.5

© R A Paselk

Last modified 2 July 2006