Current Topics in Chemistry - Bruice

Dr. Glaser's "Chemistry is in the News"
To Accompany Bruice, Organic Chemistry, 3/e.
Chapter 12. Mass Spectroscopy, Infrared Spectroscopy, and Ultraviolet/Visible Spectroscopy.

For each of the following questions, please refer to the following article:

WHAT WOULD IT BE LIKE WITHOUT AN OZONE LAYER?
by Usha Lee McFarling (The Boston Globe, January 27, 1998)

Editorial Comments

The discussion of the HOMO-LUMO gaps of ethene, butadiene, hexatriene, and octatetraene and so on is a central part of the section on UV/Vis spectroscopy in pretty much every text. You can find this discussion in the text by Bruice in Chapter 12. It makes a lot of sense: The longer the conjugated system, the higher is the HOMO energy, the lower is the LUMO energy, and, hence, the HOMO-LUMO gap is reduced. As a result, the absorption shifts to longer wavelengths with the number of double bonds n in the polyene, H-(HC=CH)_n-H.

A rather similar relation exists between the optical spectra of the normal oxygen molecule (dioxygen) and ozone (trioxygen). Yet, this similarity frequently is not recognized (even by many graduate students). The addition of the third O-atom does extend the pi-system of dioxygen and that is all that is required to lower the HOMO-LUMO gap. Consequently, the HOMO-LUMO gap of dioxygen is higher than in ozone. Dioxygen absorbs light with a wavelength of less than 240 nm (UV-C) and this energy is enough to split the molecule into atoms. These O-atoms then form ozone. So, all of the really high energy UV-C is used up in the process of making ozone. Once the ozone is made, it will absorb UV light at longer wavelength (lower energy). Photons with wavelengths below 320 nm will be absorbed by ozone and lead to ozone destruction (regeneration of dioxygen). So, that is where the problem lies: If there is something eating up the ozone, then we are not protected well enough against the UV light with wavelengths between 240 and 320 nm.

If you are interested in atmospheric chemistry, do take a look at the Nobel lectures by Crutzen, Molina and Rowland in Angew. Chem. Int. Ed. Engl. 1996, 35, 1758ff.

Pertinent Text References
Chapter 8.9. Radicals and Stratospheric Ozone.
Chapter 12. Mass Spectrsocopy, Infrared Spectroscopy and Ultraviolet/Visible Spectroscopy.
Chapter 12. Box on "Ultraviolet Light and Sunscreen".

Questions

Question 1: What are the wavelength ranges of UV-A, UV-B, and UV-C radiation?

Answer 1: HIGH ENERGY END || UV-C: 180-290 nm; UV-B: 290-315 nm; UV-C: 315-400 nm. || LOW ENERGY END - Visible light starts at 400 nm.

Question 2: Which "window" of the UV radiation is absorbed by ozone? Is the author of the Globe article correct?

Answer 2: Everything between 240 and 320 nm; whatever is left unabsorbed by dioxygen and all of the UV-B range. The author of the Globe article only talks about UV-B; the article is lacking in accuracy as far as this point is concerned.

Question 3: Suppose you made it into the year 2040 (and you are about to retire) and the thinning of the ozone layer has progressed even beyond the worst case scenarios predicted by even the most advanced models of the late 20th century (yes, that is today). (There goes the golfing you were looking forward to all your life.) How would the UV-B damage your skin? [Reflect on the fact that a mole of 300 nm photons carries 95.4 kcal/mol of energy.]

Answer 3: 95.4 kcal/mol is enough energy to crack C-C bonds - including your C-C bonds. You will literally be "dissociated". Scary, is it not?

Question 4: Let's look some more at the effects of pi-extension on electronic excitation energies. Draw the HOMO and the LUMO of ethene by positive and negative linear combination of the C-atom's p-AOs. In a similar way, draw the HOMOs and LUMOs of butadiene, hextriene and octatetraene. Indicate the number of nodes in every MO nd comment as to whether each MO is bonding, non-bonding or anti-bonding.

Answer 4: See text and "Chemistry Online Exploratorium".

Chemistry Online Exploratory.
Take a look at the visualization center of Chapter 12 on Ultravilot/Visible Spectroscopy and note the links "Eigenvalues". Follow these links to find the results of theoretical calculations of the electronic properties of the molecules. The energies of the molecular orbitals are called "eigenvalues". Take a look at the ethene file. This is the output of an "optimization", that is, a calculation that determined the best structures, the structure with the lowest energy. We want to look at the eigenvalues of that optimized structures. Open the file and find the following block of data:

 **********************************************************************

            Population analysis using the SCF density.

 **********************************************************************

 Alpha  occ. eigenvalues --  -11.22955 -11.22790  -1.02661  -0.78798  -0.63612
 Alpha  occ. eigenvalues --   -0.58215  -0.50234  -0.37043
 Alpha virt. eigenvalues --    0.17945   0.26456   0.29139   0.30709   0.39074
 Alpha virt. eigenvalues --    0.49125   0.66796   0.76655   0.77577   0.85256
 Alpha virt. eigenvalues --    0.89019   0.95315   1.10904   1.15631   1.20170
 Alpha virt. eigenvalues --    1.21084   1.33244   1.47359   1.74074   1.82154
 Alpha virt. eigenvalues --    2.13038   2.19866   2.32076   2.40156   2.61836
 Alpha virt. eigenvalues --    2.71212   3.05400   3.06643   4.51973   4.66997

The energy of the HOMO is -0.37 eV and the energy of the LUMO is 0.17 eV. So, the energy of the HOMO-LUMO gap is 0.54 eV. Now find the respective data for butadiene, hexatriene and octatetraene. What trends can you observe for the HOMO energies, the LUMO energies and the band gaps as a function of the number of conjugated double bonds?