Prof. Axon's full lecture notes are available in PDF and PPT formats.
The main ideas for today are
You can find this material described in your textbook:
The goal for this week is to understand the spectra of light emitted or absorbed by molecules. We'll take it in two parts: today, we look at the bonds between atoms which create stable molecules. Next time, we'll investigate how multi-atomic structures can change their internal energy and emit or absorb light.
We can describe atomic bonds as falling into several categories:
In real life, molecular bonds are really a mixture of these simple approximations.
Van der Waals
Metallic bond
The weak hydrogen bond is very important in large organic molecules
Another example: potassium and chlorine
Which atoms are most likely to form ionic bonds?
When ions arrange themselves in crystalline solids, one can compute the overall potential energy of a single ion in the crystal using the Madelung constant. See Thornton and Rex, Sect 10.3, or Krane, Sect 11.1.
How can we understand these bonds? It helps to simplify a bit....
Let's focus on the simplest covalent molecule: two protons plus one electron.
Two real Coulomb potentials -- one for each nucleus -- are complicated. We are going to simplify even further by pretending that each nucleus creates a square well potential around it.
Time out!
Do you remember the wave equation for a particle in an infinite square well?
Actually, we should really say that there are two possible solutions to the wave equation.
When there are two square wells, we must remember that the electron may have either solution in each of the wells.
Okay, time in again.
Q: Draw a simple graph showing the probability
of finding the electron as a function of
position for the "even" combination of
wave functions.
Q: Draw a simple graph showing the probability
of finding the electron as a function of
position for the "odd" combination of
wave functions.
The "even" and "odd" states, also called "symmetric" and "antisymmetric" states, can be combined to describe some interesting real states.
Another way to look at the H2+ ion is to think about the electric force between the single electron and the two protons.
In the symmetric case, the electron has a large probability of being between the protons.
In the anti-symmetric case, the electron is unlikely to lie between the protons.
Now, go back to thinking in terms of energy.
Note the crucial difference in the total energy between the symmetric and antisymmetric cases: only the symmetric case yields a local minimum in the potential energy graph.
Sometimes you see the terms bonding and anti-bonding used to describe the two cases.
Hint: In the world of quantum mechanics,
the relationship between a change in
energy and frequency of emitted
radiation is
E = h * (frequency)
See if you can compute the frequency
for this transition, and then use it
to determine a time.
Q: Well .... ?
