Grade12 AP Chemistry

Tuesday Feb. 22, 2007 (and probably Feb 23 as well)

Bonding and Orbitals
Any theory of bonding should be able to describe why shared pairs of electrons hold two atoms 
together.  It also should be able to predict the bond energy and the bond length.  The potential
energy in a molecule decreases as the distance between the nuclei decreases and the attraction
of each nucleus to the shared pair of electrons increases.  When the two atoms reach some critical
distance, the repulsion that the two nuclei have for each other begins to outweigh the attraction
to the shared pair of electrons and the potential energy starts to increase again.  The distance
at which the potential energy is at a minimum defines the bond length.  The atoms are held together
because if the distance increases or decreases, the potential energy of the molecule increases.


The Valence bond theory is the next step after Lewis diagrams and VSEPR to explain and predict 
bonding.  It is different in that it involves the use of orbitals.

The valence bond theory subsumes Lewis diagrams in that the orbitals that are involved in bonding
are the s and p orbitals of the highest occupied priniciple quantum number (n).  The maximum number
of electrons in these orbitals is 8 (for most elements) which matches the stable octet of Lewis
diagrams.  

Why are these orbitals the ones that interact with other atoms?
As the electron charge density graphs below show, the distance that orbitals extend away from the 
nucleus and the distance of maximum charge density increases as the value of "n" increases.  Also, 
the distance of maximum charge density decreases as the quantum number "l" increases.  So, the
"s" and "p" orbitals of the highest principle quantum number are the orbitals that "stick out the 
farthest from the nucleus."


The number of dots in a Lewis diagram matches the number of electrons in the highest "s" and "p" 
orbitals (see page 226 in the text book), but they way in which they are paired up does not. 
However, as we will see, this is not as big a problem as it seems at first.

Atomic Orbitals
These are the orbitals defined by the Schrodinger equations using the first three quantum numbers 
that describe the regions in which there is a high probability of finding an electron in 
individual atoms.  The surface of the orbital, as drawn, defines the volume in which there is a 90%
chance of finding an electron with a certain quantum state.  Their shapes are s, p, d, f, ect.

What happens when atoms bond together to form molecules?  This is still a topic of ongoing research.
However, there have been a series of theories that have described what happens when atoms share 
electrons in covalent bonds.

Valence Bond Theory
This theory states that as two atoms come together to form a covalent bond, one half-filled orbital
in each atom overlap to form a bonding orbital with two electrons of opposite spin.  This shared 
bonding orbital holds the two atoms together.



How does this work?  
Why does the existance of this shared bonding orbital make the molecule more stable than the two 
atoms are on their own? 
The explanation is that the wave functions of the two atomic orbitals are in phase with each other
when they overlap and, thus, constructively interfere with each other (just as two water waves can 
constructively interfere to make one larger wave).  This constructive interference produces a much 
more "intense" electron wave function.  This corresponds to a much greater electron charge density
between the two atoms.  This is more effective at holding the two nuclei together than the two 
atomic orbitals would be on their own.  But, the atomic orbitals must overlap in order for this 
to happen.

Bond Angles
Look at the diagrams on page 232 in the textbook.  We can see that the angle between two bonds on a
central atom depends on the angle between the two atomic orbitals that went into the two bonds.



The predicted bond angles based on the atomic orbitals involved is 90o.  The problem is
that while this matches the bond angles is H2S, it does not match the tetrahedral family
arrangements of bonds in H2O (109o).

So, we have a problem!

Hybrid Orbitals
The solution to this problem is as follows: when bonding, atoms can lower their potential energy by
hybridizing their atomic orbitals: in a sense, combining their single "s" orbital and their 3 "p" 
orbital and getting 4 identical orbitals which have characteristics of both "s" and "p" orbitals. 
In the case where the "s" and all three "p" orbitals are involved, the four hybrid orbitals that 
result are 75% "p" in terms of their shape and 25% "s."

Since 1 "s" orbital and 3 "p" orbitals go into their make-up, they are called sp3 atomic orbitals.

Since there are four of them and they are all the same, they are oriented tetrahederally around 
the atom: 109.5o apart, so as to attain the maximum separation between orbitals.  This
is interesting, because non-hybridized orbitals seem to be perfectly stable while overlapping in 
space.