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two variables to specify their orientation. Here, only five vibrations
are eliminated, leaving 3N-5.
Calculated vibrational frequencies will not exactly match measured
frequencies (they are typically too large by about 12%). For example, a
measured frequency of 1700 cm1 would correspond to a calculated frequency
of around 1900 cm1.
wavenumber (cm '*)
Chapter 19 Spectroscopy 257
Spectral Identification of Short-Lived Molecules
Energy minima have all real frequencies, while molecules with one or more
imaginary frequencies are not minima.
Short-lived molecules may often be identified by their infrared spectra
measured at extremely low temperatures. In most cases, the experimental
spectrum will be incomplete, although a few "characteristic" lines or
bands are often sufficient to decide among alternative structures.
The infrared spectrum of a C4H4 isomer shows strong absorptions at 215,
854, 1608, 2994 and 3080 cm4. "Reasonable" C4H4 structures include but-l-
yne-3-ene, butatriene, singlet and triplet cyclobutadiene, methylene-
cyclopropene and tetrahedrane. Examine the vibrational frequencies of
each. Are all of these structures actually energy minima, or can you
eliminate one or more? Which structure best fits the experimental
infrared spectrum? (Recall that calculated frequencies are typically 12%
larger than measured frequencies.) Is it the lowest-energy QH4 isomer?
Assign the vibrational frequencies in the experimental spectrum using the
data from the structure you selected.
258 Chapter 19 Spectroscopy
Electronic Spectra of Conjugated Alkenes
Alkenes absorb ultraviolet (UV) light and use the absorbed energy to
excite an electron from the HOMO (highest-occupied molecular orbital) to
the LUMO (lowest-unoccupied molecular orbital).
HOMO • ground state
Absorption maxima (A,max) data (see table at right) show the effects of
conjugation. Assuming that excitation energies, related to A,max by
equation (1), parallel HOMO-LUMO energy gaps, which molecule would you
expect to have the smallest HOMO-LUMO gap? The largest gap? What effect
does conjugation have on the HOMO-LUMO energy gap?
Another way to look at the effect of conjugation is to examine the shape
of the HOMO and LUMO. First, examine the HOMO of ethene. Is it bonding or
antibonding? Next, examine the HOMO of 1,3-butadiene,
1,3,5-hexatriene and beta-carotene. For each, count the number of bonding
interactions and the number of antibonding interactions. Which HOMO (if
any) are "pure" bonding orbitals? Which HOMO (if any) are nonbonding
(equal number of bonding and antibonding interactions)? Order the HOMO by
energy (assume that HOMO energy falls as net bonding character
increases). What effect does conjugation have on HOMO shape and energy?
Repeat your analysis for the LUMO of ethene,
1,3-butadiene, 1,3,5-hexatriene and P-carotene, except now focus on each
orbital's net antibonding character. (Assume that LUMO energy rises as
net antibonding character increases.) What effect does conjugation have
on LUMO shape and energy? Are your predictions for the HOMO-LUMO energy
gap consistent with the experimental data?
Alkene Xniax (nm)
E = 45.6/A(tm)ax
E is the
excitation energy (in au)
Kmi", is the excitation wavelength (in nm)
and LUMO of 1,3,5-hexatriene show origin and destination of excited
Chapter 19 Spectroscopy 259
Solvent Effects on Electronic Spectra
HOMO (top) and LUMO (bottom) of acetone change occupancy upon absorption
Electrostatic potential map for the ground state of acetone shows
negatively-charged regions (in red) and positively-charged regions (in
E = 45.6/Xmax (1)
E is the excitation energy (in au)
Xmax is the excitation wavelength (in nm)
The lowest-energy electronic excitation in acetone is n->K*, and is
usually described as promotion of a nonbonding electron on oxygen to a e
antibonding orbital involving the carbonyl bond. This excitation is
triggered by UV radiation, and causes a significant change in molecular
Examine and describe both the highest-occupied and lowest-occupied
molecular orbitals (HOMO and LUMO, respectively) of ground state acetone.
On which atom(s) is the HOMO primarily concentrated? Is it in the i
system or in the n system? Repeat your analysis for the LUMO.