Chem 22
Homework set 12
1. Naphthalene is colorless, tetracene is orange, and azulene is blue.
naphthalene
tetracene
azulene
(a) Based on the colors observed for tetracene and azulene, what color or light does each
compound absorb?
(b) About what wavelength ranges do these colors correspond to?
(c) Naphthalene has a conjugated π-system, so we know it must absorb somewhere in the UVvis region of the EM spectrum. Where does it absorb?
(d) What types of transitions are responsible for the absorptions?
(e) Based on the absorption wavelengths, which cmpd has the smallest HOMO-LUMO gap?
(f) How do you account for the difference in absorption λs of naphthalene vs tetracene?
(g) Thinking about the factors that affect the absorption wavelengths, why does azulene not seem
to follow the trend seen with the first two hydrocarbons?
(h) Use the Rauk Hückelator (www.chem.ucalgary.ca/SHMO/) to determine the HOMO-LUMO
gaps of each compound in β units. The use of this program will be demonstrated during
Monday's class.
2. (a) What are the Hückel HOMO-LUMO gaps (in units of β) for the following molecules?
Remember that we need to focus just on the π-systems. Use the Rauk Hückelator.
(b) Use the Rauk Hückelator to draw some conjugated polyenes — linear as well as branched.
Look at the HOMO. What is the correlation between the phases (ignore the sizes) of the porbitals that make up the HOMO and the positions of the double- and single-bonds in the Lewis
structure? What is the relationship between the phases of p-orbitals of the LUMO to those of the
HOMO?
(c) Use your answer from part b and the pairing theorem to sketch the HOMO and LUMO of
the polyenes below (again, just the phases — don't worry about the relative sizes of the porbitals). Being able to do this on your own is important, so do it, then check with the program.
Chem 22
Spring 2010
Name _________________________________________
HW set 12
25 points; due Wed, April 28 at the beginning of class.
1. s-cis-1,3-Butadiene has λmax = 250 nm, o-xylylene (A) has λmax = 400 nm, and 2,3naphthoquinodimethane (B) has λmax = 540 nm for its longest-wavelength (HOMO-LUMO)
absorption. The absorption spectrum of C has not been reported.
B
A
C
(a) Based on the absorption wavelengths (and keeping in mind that absorptions are generally not
sharp peaks like we see in NMR, but relatively broad) what color is each compound?
Butadiene:___________
A: ___________
B: ___________
(b) What are the energies (in kcal/mol) that correspond to the absorption wavelengths? (Recall
that the conversion factor is 2.86 x 104 nm•kcal/mol.)
Butadiene:___________
A: ___________
B: ___________
(c) Based on the trend you see in part b, estimate the absorption energy of cmpd C. Do not plot
the data and try to do an analytical fit a line or curve — just eye-ball it, please. What wavelength
of light does this correspond to?
(d) If this HOMO-LUMO transition were the only one possible, what color would you expect for
cmpd C?
(e) Why would we not expect compounds like C to display only one electronic transition? If
you're not sure, use the Rauk Hückelator to determine the π-MO energies.
2. (a) Use the Rauk Hückelator to determine the HOMO-LUMO gap (in units of β) of each
compound below.
Ph
(b) Sketch the LUMO of the cation above.
3. (a) Calculate the amount of charge on each C in each of the following ions. Remember that
the calculated charge is the square of the p-orbital coefficient on each C in the NBMO. You can
get the NBMO coefficients from the Rauk Hückelator by checking the "verbose" box and
selecting the orbital. You may have to rotate the orbital array to see all the numbers.
(b) Pentadienyl anion, of course, has three roughly equivalent resonance structures — is the
amount of negative charge you calculated consistent with the resonance prediction? If your
answer is no, go back and figure out what went wrong.
(c) How well do the charges calculated for the two cations correspond with the simple resonance
description of these species? Explain.
(d) Calculate the resonance energy of allyl cation (relative to a localized π-bond and an empty
p-orbital), and of benzyl cation (relative to benzene and an empty p-orbital)
(e) Based on your answer to part d, which should do a faster SN1 reaction, allyl bromide or
benzyl bromide? Would you expect the rates to be very different?