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.

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:

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

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, Ha & Hb together, the two 1s orbitals should give us two molecular orbitals, MO1 and MO2:

MO1 = 1sa + 1sb

MO2 = 1sa - 1sb

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.

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.

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?

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.

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.

H atom

HF molecule

F atom

E
   sigma*  

1s
   
     
     
     
     
    2p
     sigma  

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


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