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### Topic: Perturbation theory (qualitative question)  (Read 2699 times)

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#### LogicX

• Regular Member
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• Mole Snacks: +0/-0 ##### Perturbation theory (qualitative question)
« on: May 04, 2012, 05:46:23 PM »
1. Question:

How does the energy change (negative, positive or no change) in the HOMO-LUMO transition of a conjugated polyene where there are 5 double bonds when a nitrogen is substituted in the center of the chain? The substitution lowers the potential energy in the center of the box (everywhere else V(x)=0 for particle in a box).

When there are 6 double bonds, the opposite change happens. Why?

2. Relevant equations

E1=<ψ(0)|H1ψ(0)>

E(perturbed)= E(0) + E(1)λ

3. My attempt

Ok, so if you look at the particle in a box ψ*ψ for n=5 and for n=6, the center of the n=5 is at the top of a peak, while for n=6 it is at a node (i.e. where the probability=0). I'm not sure how to use this info to say how the excitation energy would change.

I think it means that for n=6 there is no change because there is no probability of an electron being there so the substitution does not change the excitation energy. And for n=5 there is a decrease in potential energy so E1 is more negative and the gap would be larger? (or would a decrease in V(x) mean that the gap is smaller?)

Does any of that make sense? Again, I just need a qualitative answer, and it basically boils down to how E1 changes with the substitution.

#### al77

• Very New Member
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• Mole Snacks: +0/-0 ##### Re: Perturbation theory (qualitative question)
« Reply #1 on: May 07, 2012, 12:28:06 PM »
i was googling the similar question earlier, hoping that i would find some information on this topic (perturbation), and i found post, i suppose you are taking CHE320 and this is one of the questions in practice problem right?

have you figured out the answer or an explanation for this? for n=6 i kinda agree with your explanation (wavefunction is at a node, probability=0), but the question says the wavelength is opposite to n=5..

and for n=5, the center is at the top of a peak, i guess we are wondering the same question, would the decrease in potential energy increase or decrease the gap...?