In this exercise, we will determine the energy gap between the Highest Occupied Molecular Orbital (HOMO) and the Lowest Unoccupied Molecular Orbital (LUMO) for the dye molecules in Figure 1. This energy gap, ELUMO-HOMO, is relate to the wavelength of the absorption peaks, lmax, for these molecules.
Q 1. Why would the photon wavelength that gives the peak absorbance be related to the HOMO-LUMO energy gap? Discuss with others and record your answer below. (Hint: Ephoton = hn = hc/l.)
Figure 1: Structures of a Series of Conjugated Dyes |
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1,1-diethyl-2-2-cyanine |
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1,1-diethyl-2-2-carbocyanine |
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1,1-diethyl-2-2-dicarbocyanine |
We will determine the HOMO and LUMO orbital energy of the most stable conformation of the molecules above. In building any structure, we first need to consider:
(In our case, the correct stereoisomer is that shown in Figure 1.)
Q 2. What are possible low energy conformers for the molecules in Figure 1?
We will be looking at the extent of conjugation in the dyes above. Draw possible resonance structures of these dyes. Over what atoms do you expect the delocalization of the conjugated system to extend?
Calculations:
Do steps 1-8 for each dye in turn. Complete the steps for one dye before continuing with the next.
Q 3. Do the bond lengths support that this is a conjugated system? How does the average bond length compare to that for benzene (1.39Å)?
Q 4. Is the HOMO s or p in nature? Is it delocalized as you would expect? Are there other orbitals degenerate with the HOMO, as might be expected if more than one pair of equivalent electrons is in the conjugated system?
Q 5. You will find in the "wet" lab that this system is fairly well modeled by the one-dimensional particle-in-a-box model. Is there any hint of this in the HOMO shape? The HOMO is a wavefunction, of course. Does it look like the highest energy ground state electron would experience a flat potential energy function that quickly rises at the ends? How long, in Å, would the "box" length be?
Q 6. Is the LUMO s or p in nature? Is it delocalized also?
Q 7. Does the LUMO have a similar extent as the HOMO, giving about the same size box length? How long, in Å, would the "box" length be? Does it look like the lowest excited state wavefunction for the 1-D particle-in-the-box?
(repeat above for each molecule)