Computational Chemistry at GVSU

Predicting the Absorption Peak Wavelength for a Conjugated Dye

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, E_LUMO-HOMO, is relate to the wavelength of the absorption peaks, l_max, 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: E_photon = hn = hc/l.)

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:

• Stereochemistry - Are there stereoisomers of the molecule? Which stereoisomer is needed?

• Conformational Degrees of Freedom - Often we will want to look at the lowest energy conformations, and need to determine if there are there pertinent internal degrees of freedom (e.g., single bond rotation, ring puckers) that would affect the calculation results. Which conformers may reasonably represent low energy structures?

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?

Do steps 1-8 for each dye in turn. Complete the steps for one dye before continuing with the next.

1. Build the dye with the proper stereochemistry. Hint: It helps to "clean" the structure from time to time as you’re building it. This avoids building a "scrunched up" molecule that has twisted dihedrals and hence improper stereochemistry. Have the instructor check your final structure.
   
   
2. Once the dye is built and "cleaned", use AM1 geometry optimization calculations to determine the most stable form. (We will use AM1 since these are rather large structures, and ab initio methods would take too long to complete in one lab period.) You can get to AM1 by choosing the "Quantum 1" menu deck and then "MOPAC" and "Run". Choose "AM1" as your method. (Note: Make sure to set the charge correctly when you run AM1.)
   
   
3. Examine the geometry optimized bond lengths within the conjugated system (use "Geometry" in the top menu bar, and then "Measurements"; select the bonds of interest).

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)?

 

 

 

 

4. Sum the bond distance of the conjugated system and record in your notebook.

    

5. Examine the HOMO. Record its energy.

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?

 

 

 

 

6. Examine the LUMO. Record its energy.

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?

 

 

 

 

 

7. Determine the HOMO-LUMO energy gap of the most stable conformation. Record this in your laboratory notebook.

 

 

 

 

 

8. Predict the absorption wavelength from these energy gaps. Record this in your laboratory notebook.

 

 

 

 

(repeat above for each molecule)

9. Does the energy gap increase or decrease as the conjugated system lengthens?

 

 

10. Is the trend in the energy gap due to increasing/decreasing HOMO energy or increasing/decreasing LUMO energy, or both?

     

     

11. In general, as the relative amount of bonding vs. antibonding character of an orbital increases, the energy of an orbital drops. Does the bonding vs. antibonding nature of the HOMO's or the LUMO's support the trend in energies?

 

 

 

 

12. Discuss how (or if) you could predict an L_effective from the 3-D representation of the HOMO & LUMO.