[Sasquatch]

If anyone can help with these problems I would greatly appreciate it!

Thanks for the help, and enjoy the challenging problems.

See attached picture.

[billnotgatez]

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[Sasquatch]

Thanks for pointing that out to me, I am new to this site.  I have worked out what I believe to be a solution to the first one. But, I would appreciate if someone could explain to me how we get the 4 MOs in butadiene, or could point me in the right direction. When butadiene reacts with a free electron to generate a [C4H6]- anion is steric hinderance the thing that limits reasonable resonance contributors?

[Babcock_Hall]

Molecular orbitals are linear combinations of atomic orbitals.  http://www.chemtube3d.com/orbitalsbutadiene.htm  Now about your answer...

[Sasquatch]

Thanks for link, that helped to better explain the theory of MO.  Could someone please help to explain how you figure out where to place the nodes in the higher energy levels in MO theory?

For problem #5 in order to begin a synthesis with the Diels Alder reaction to get the 6 membered ring backbone wouldn't one of the starting molecules need to be s-cis, or can I freely rotate molecule #2 from s-trans to s-cis? 

[clarkstill]

See page 6.7 for how to work out nodal positions in polyenes:

http://www.chem.qmul.ac.uk/software/download/mo/6.pdf

And yes, you can freely rotate the dienes as long as they are acyclic, the reactive conformation won't be a ground state but that doesn't matter.