[ktaber]

Okay, so I have a few problems that I'm just going to lump into one post.  I have attempted these problems, but once P.chem hit quantum, I got really lost really quickly.  I think what I mostly need is a push in the right direction.

1.  Write the slater determinant for the ground state of the carbon atom.
So I know that the determinant needs to be set up so the columns aren't identical, because that'll screw things up.  So I have to have an x, y, and a z coordinate.  So since C is 1s^2 2s^2 2p^2, that gives the p orbital having an x and a y line. 

So I just have a lot of problems setting up determinants.  My professor really didn't explain it well (he just gave us a handout from a different book... which gives me two books that don't explain it well), and never did any original examples in class.  So any help in setting up the determinant would really help.


2. Show that a variation theory treatment of H using (phi)=e^-kr as an unnormalized trial function yields the correct minimum-energy solution for the hydrogen atom when the specific expression for k is determined.

So I know that the unnormalized wavefunction is generally given the equation ∫φ*Ĥφdτ/(∫φ*φ)

But when I plug in the equation and the value for the operator H, the answer I'm getting is making absolutely no sense to me.  (the integral is just the function/function... which would be one.  And I'm really not thinking that's right). 


3. Do a Huckel calculation on cyclobutadiene.
     a) draw an energy level diagram
     b) is the ground electronic state a singlet or a triplet?

In this problem, we were given a handout in class, and I really can't even figure out how to start it from the handout.  My professor flew through the handout, and I kind of just sat there with a blank stare on my face.  If I could just get a push in the right direction, that would be really helpful.



I know it doesn't seem like I did a lot, but I've been staring at this crap for like 3 days now, and I just can't make any progress.  So any help would be really appreciated.  Thanks a bunch.

[jbaldwin]

I am not familiar with questions 1 and 2, but I can help you with 3.

To begin you must consider that all four carbon atoms are sp2 hybridized, thus all of the Pi electrons are oriented in the z-direction whilst all of the other orbitals are perpendicular to the Pi electrons.  There are two Pi-bonds and therefore, four Pi-electrons.  You must build the molecular orbital based on their symmetry properties.  For instance, the first level, psi[1], will have all of the bonding orbitals pointing in one direction.  This molecular orbital has two Pi-electrons.  So you have two left and they must go in the next highest molecular orbital.  This orbital is called the highest occupied molecular orbital HOMO.  So you see that this orbital is filled because of the Exclusion principle.  The HOMO is the ground state.  There is only one orbital at this energy level (as there is in all Pi-electron systems).  Thus, it is a singlet.