Page 1097 - Advanced Organic Chemistry Part A - Structure and Mechanisms, 5th ed (2007) - Carey _ Sundberg

1082 coefficients at that wavelength. If we assume that the quantum yield for conversion of
cis→trans is approximately equal to that for trans→cis, the conversion of trans alkene
CHAPTER 12 to cis will occur faster than the converse process when the two isomers are in equal
Photochemistry concentrations. On continued photolysis, a photostationary state will be achieved when
the rate of trans→cis is equal to that of cis→trans. At this point the concentration of the
cis isomer will be greater than that of the trans isomer. The relationship can be expressed
quantitatively for monochromatic light as

trans
c
= c →t (12.3)
cis
t t→c
The cis-trans isomerization of alkenes is believed to take place via an excited
2

state in which the two sp carbons are twisted by about 90 with respect to one another.
This twisted geometry is believed to be the minimum energy geometry for both the
singlet and triplet excited states. The twisted geometry is an energy maximum on the
ground state surface. The twisted geometry for the excited state permits the possibility
of returning to either the cis or trans configuration of the ground state. The return
from the singlet excited state to the ground state involves re-pairing of the electrons
by a nonradiative process. Return from the triplet state requires intersystem crossing.

12.2.1.1. Photoisomerization of Ethene and Styrene We consider the excited states of
ethene and styrene in some detail. These molecules do not exist as cis and trans isomers
unless they are isotopically labeled. However, they are prototypes of isolated and conju-
gated alkenes and have been studied extensively. The excited states of ethene have been
studied both by experiment and computation. The S and T excited states have been
1
1
7
described by MP4(SDTQ)/6-311G ∗∗ computations. At this level of computation the
energy of T is 2.92 eV and S is 5.68 eV. The T state is calculated to have a perpendicular
1
1
1
structure with extension of the C−C bond to 1.455 Å. The S state is also twisted and is
1
very strongly pyramidalized at one carbon. The C−C bond distance is 1.360 Å. This state
is believed to have a large degree of zwitterionic character, with the negative charge at the
pyramidalized carbon. These structures are depicted in Figure 12.5.
The excited state lifetime of ethene is very short ( <10 −13 s). Both the valence
and Rydberg excited states return to the ground state through a conical intersection.
The CIs of the S state have been examined using quantum dynamics calculations. 8 9
1
Return from an excited state to the ground state involves both twisting at the C–C
bond and pyramidalization. Another conical intersection, which is similar in structure
to the carbene ethylidene, occurs at a similar energy. These structures are shown
in Figure 12.6. As we explore alkene photochemistry, we will see that the excited
states and CIs depicted in Figures 12.5 and 12.6 are prototypical of the structures
that are involved in the photochemistry of alkenes. The triplet T state of alkenes
1
can be represented as a twisted triplet diradical. The S state is often referred to as a
1
zwitterionic state and can be thought of as having cationic character at one carbon and
carbanionic character at the other. The S excited state is quite similar to the strongly
1
7
S. El-Taher, P. Hilal, and T. A. Albright, Int. J. Quantum Chem., 82, 242 (2001); V. Molina, M. Merchan,
B. O. Roos, and P.-A. Malmqvist, Phys. Chem. Chem. Phys., 2, 2211 (2000).
8 M. Ben-Nun and T. J. Martinez, Chem. Phys. Lett., 298, 57 (1998); M. Ben-Nun, J. Quenneville, and
T. J. Martinez, J. Chem. Phys. A, 104, 5161 (2000); J. Quenneville, M. Ben-Nun, and T. J. Martinez,
J. Photochem. Photobiol., 144, 229 (2001).
9
M. Ben-Nun and T. J. Martinez, Chem. Phys., 259, 237 (2000).