Cyclization of 5-Hexenyl Radical:
Thermodynamics vs. Kinetics
Brandon Vittur
University of Houston, Department of Chemistry
Physical Chemistry II
Presented to Dr. Bittner
Spring 2007
Abstract
Computations involving the cyclization of the 5-hexenyl radical to produce
methylcyclopentane (81%), 1-hexene (17%), and cyclohexane (2%) as a result,
proved that the reaction is kinetically rather than thermodynamically controlled.
Specifically the stereoelectronic requirement of the addition of the radical center to
the alkene in the transition state is the underlying factor of the difference in the ratios
of the product and the rate of the reaction because the geometry in cyclized 5-hexenyl
radical resembling methylcyclopentane meets the stereoelectronic requirements more
readily than cyclized 5-hexenyl radical resembling cyclohexane.
Introduction
Gas phase radical processes received
considerable attention for about thirty
years after Moses Gomberg published
a paper in 1900 titled “An Instance of
Trivalent Carbon: Triphenylmethyl.”1
Though free radicals received this
attention the possibility that free
radical intermediates might be
involved in organic reactions was not
seriously considered until W. A.
Waters, D. H. Hey, and M.S. Kharasch
contributed to the development of free
radical
chemistry.1
Free-radical
reactions are now considered useful for
synthesizing aliphatic and alicyclic
systems.1 In particular Kharasch
explored virtually all of the elementary
pathways available to free radicals
which is shown in scheme 1:1
Scheme 1:
A• + B• ↔ A-B
(1)
A• + B-D ↔ A-B + D•
(2)
A• + B=D ↔ A-B-D•
(3)
A• + e ↔ A⎯; A•-e ↔ A+ etc. (4)
Most free radical reactions in use
today can be rationalized by the four
steps in scheme 1 or slight variations
of them.1 Since the findings of these
mechanistic pathways, only one
completely new process has been
found: pericyclic reactions of radicals
and radical-ions.1 Much of the
knowledge acquired about the factors
that influence free radical reactions is
derived from kinetic studies.1 Highly
selective reactions are controlled by
the rapid formation of one product over
other much slower possible products.1
What affects the kinetic rates and ratios
of product formation are the energies
of transition complexes.1 In earlier
studies it was thought that “radical
reactions follow the most exothermic
available pathway” and “radical
reactions afford the most stable
product.”1 This idea is based on the
assumption that activation enthalpies
reflect reaction enthalpy changes and
lead one to conclude that the rates of
related reactions can be estimated from
the bond dissociation energies of the
products formed.1 However, as we now
know, thermodynamics is not the only
driving force for product formation
involving free radicals.1 The other
factors include stereoelectronic, polar,
steric and kinetic effects.1 The outcome
of any particular reaction may involve
one or a combination of these factors.1
Cyclization of 5-Hexynyl radical and
the final products of this reaction are
shown in scheme 2:2
Scheme 2:
Bu3SnH
AIBN
BR
Heat
*
i
17%
ii
*
Rearrangement
iii
81%
iv
2%
vi
*
v
Most chemist will quickly recognize
that six-membered rings are more
stable than five membered rings (based
on combustion data which suggest
cyclohexane has a total ring strain of 0
kJ and cyclopentane has a total ring
strain of 27 kJ) and 2º radicals are
more stable than 1º radicals.3,4 This
assumption
is
based
on
thermodynamics, however as was
mentioned earlier this is not the only
factor to consider when thinking about
reaction pathways. As scheme 2 shows
the overwhelming product formed is
not the expected thermodynamic
product cyclohexane it is however the
less
thermodynamically
favored
product methylcyclopentane. There are
two possible explanations for the
results of scheme 2: The reaction is
thermodynamically controlled and
theories on radical stability need to be
revised or the reaction is kinetically
controlled.2 This paper will attempt to
show, based on computational
chemistry
calculations,
that
methylcyclopentane is indeed the
desired mechanistic pathway for
cyclization of 5-Hexynyl radical and
give insight as to why this is the case.
Experimental
The calculations for all structures
(figures 1-10 introduced in the results
and discussion section) were made in
the following order: Geometry
optimization, molecular energy of the
optimized geometry and finally
(figures 5 & 8 only) transition state
optimization
of
the
optimized
geometry. All calculations were made
by a Gaussian program made available
by Dr. Bittner and made accessible
through the course website at
http://minime.chem.uh.edu/pchem07/index.html
and energy values were given in units
of Hartree.
Results
The following figures give a three
dimensional optimized geometrical
representation
of
the
radicals,
transition states and the final products
involved in the reaction shown in
scheme 1 and the computations carried
out:
Figure 1: 1-hexene (ii)
Figure 2: 5-hexenyl radical (i)
Figure 6: cyclohexane (chair
conformation) (vi)
Figure 3: methylcyclopentane (iv)
Figure 7: cyclohexyl radical (chair
conformation) (v)
Figure 4: methylcyclopentyl radical
(iii)
Figure 8: cyclized 5-hexenyl radical to
resemble cyclohexane (chair
type conformation)
Figure 5: cyclized 5-hexenyl radical to
resemble methylcyclopentane
Figure 9: cyclized 5-hexenyl radical to
resemble methylcyclopentane (bond
angle and nuclear distance changed to
mimic transition state)
The following table summarizes the
transition state energies obtained from
Gaussian computations on figures 5
and 8:
Table 2: Summary of Transition State Energy
Structure
Energy (kJ/mol)
Figure 8
-609817.3982
Figure 5
-609850.2468
The following table gives the
difference in energy for the
calculations with which the proposed
reasons for the results are based for
figures 4, 5, 7, 8, 9, and 10:
Figure 10: cyclized 5-hexenyl radical
to resemble cyclohexane
(bond angle and nuclear
distance changed to mimic
transition state)
Table 3: Structural (fig. 4 & 7 and 9 &10) and Transition
State (fig. 8 & 5)Energy Differences
Structures
Energy (kJ/Mol)
Figures 4 and 7
24.29151
Figures 8 and 5
32.84799
Figures 9 and 10
218.1663
The following table presents various
differences in transition state energies
and their corresponding expected ratio
of major : minor product formation
based on calculations from the
Boltzmann distribution: 2
Table 4: Differences In Transition State Energy and
Expected Ratio Values of Products
∆E (kJ/mol)
The following table summarizes the
structural energy calculations obtained
from Gaussian computations on figures
1-10:
Table 1: Summary of Structural Energy
Structure
Energy (kJ/mol)
Figure 1
-611431.2279
Figure 2
-609775.7153
Figure 3
-611503.3361
Figure 4
-609850.2676
Figure 5
-609850.2647
Figure 6
-611523.7638
Figure 7
-609874.5595
Figure 8
-609874.5591
Figure 9
-609423.3318
Figure 10
-609205.1655
Major : Minor (25˚C)
4
~90:10
8
~95:5
12
~99:1
Discussion
From the data in table 1, the original
thought, based on thermodynamics
about product formation, is justified
because figure 6 is lower in energy
than figure 3 by roughly 20 kJ/mol (see
table 3). Also the 2º radical (figure 7)
is more stable than the 1º radical
(figure 4) by roughly 24 kJ/mol (see
table 3). These results rule out the first
possibility that theories on radical
stability are incorrect and leave only
that the reaction is kinetically
controlled.
Another
expected
thermodynamic outcome is that the
structural energy, according to table 1,
for the transition state structures for
figure 8 is more stable than figure 5.
All of the previous results mentioned
combined suggest that there is
something about how the geometry in
figure 5 is oriented that affects the
transition state in such a way that it
forms the major product after the
transition.
From the data in table 2, the
proposed theory that the reaction is
kinetically controlled is strengthened
significantly because figure 5 is lower
in energy than figure 8. The difference
in transition state energy of the two
products in question is roughly 33
kJ/mol (see table 3). Furthermore
based on calculations made by
previous theoretical chemists (see table
4), the ratio of the products formed
should also not be very surprising.
For figure 8 there are two possible
conformations: chair and boat.
According to Wade4, cyclohexane is
most stable in its chair confirmation
which is why I chose to use this
confirmation instead of the boat.
Cyclopentane takes on only one stable
conformation and that is the so called
slightly
puckered
“envelope”
conformation as shown in figures 3, 4,
and 5.4 These conformations are
formed in order to reduce eclipsing and
lower torsional and angle strain.4
The figures 5 and 8 are both lower in
energy than figure 2. This is most
likely due to hyper conjugation
(stabilization by electron density). It is
possible that as the 1˚ radical moves
closer to the double bond during
cyclization it “feels” the π system in
the chain and takes on a more 2˚
radical role and ultimately moves into
a transition state for rearrangement. It
has also been suggested that the
conversion of a double bond to two
single bonds provides the driving force
for the reaction.3
Now widely accepted is that, the
reason this reaction is kinetically
controlled is due to stereoelectronic
factors which play a dominant role in
regiochemistry.1 In order to rationalize
the results it is assumed that “…the
strain engendered in accommodating
the mandatory disposition of reactive
centres within the transition structure
for 1,6-ring closure outweighs those
steric and thermochemical factors
expected to favour the formation of the
more stable possible product.”1
As noted earlier the total ring strain
energy for cyclohexane is 0 kJ and 27
kJ for cyclopentane. In order for the
transition state of figure 5 to be
favored over figure 8, it must somehow
overcome this energy difference to
become a reasonable product. In fact in
order for the transition to take place the
orbital that the radical resides in must
line up with the π* orbital of one of the
carbon atoms in the double bond
(terminal carbon for cyclohexane
formation
and
α-carbon
for
methylcyclopentane formation).1 For
this to happen the radical based carbon
atom and one of the carbon atoms in
the double bond must have an
internuclear bond length of 2.4Å and
form a bond angle of 106º (see figure
11).1
Figure 11: Transition state
requirements for cyclized
product formation at the
reactive centers (pictorial
reference only)
The bond length in figure 8 is
1.562Ǻ with a bond length of 111º,
therefore figure 8 must open up, which
increases its ring strain, in order to
create this required internuclear
distance. Figure 8 must also change its
conformation in order to achieve the
required bond angle (see figure 10).
The bond length for figure 5 is 1.551Ǻ
with a bond angle of 114˚. Figure 5
must also open up and change its
conformation resulting in increased
ring strain. Although both molecules
have to change their confirmation to
match that of the transition state if you
look at figures 9 and 10 and compare
them with figures 5 and 8 you will
notice that figure 8 must undergo more
drastic changes than figure 5. Based on
the visual geometry changes alone one
would conclude that the transition state
of figure 5 is significantly lower than
figure 8. Based on calculations this is
indeed the case and figure 8 is higher
in energy by roughly 218 kJ/mol (see
table 3). This was also the conclusion
of Beckwith1, who found that the
energy difference was 11kJ/mol greater
for figure 8 than for figure 5. This
difference is so great that cyclization of
5-hexynyl radical to figure 5 forms the
major product which has an 81% yield
compared with figure 8 which forms
the minor product with only a 2% yield.
An interesting point to make is that
table 4 suggests that an energy
difference of only 12kJ/mol will give a
product ratio of 99:1. The energy
difference for the reaction in scheme 2
is roughly 33 kJ/mol and yet
cyclohexane makes up 2% of the total
yield. This yield seems too high and
further research on this reaction
concerning this result must be
conducted in order to find out why this
is indeed the case. Possible reasons
why may be factors or a combination
of
factors
mentioned
earlier:
stereoelectronic, polar and steric
effects, different conformations of the
molecules or the actual temperature
with which the reactions are
experimentally carried out.
Conclusion
The ratio of products shown in
scheme 1 give an interesting view into
kinetic controlled reactions and help
give insight into the actual mechanistic
pathways involved in reactions in
general. The cyclization of 5-hexynyl
radical has become such an important
kinetic reaction that it is used as a
“Free-Radical Clock” for determining
the rates of other reactions.5,6,7
Through free radical reactions chemist
have
learned
that
though
thermodynamics is a powerful driving
force for reactions it is not always the
most powerful nor is it the only one
worth considering. In addition to the
thermodynamics of the system, one
needs to consider the possible kinetic,
stereoelectronic, polar, and steric
effects on the system before making a
conclusion about the final products.
Notes
Scheme 2 was made using ChemDraw
Ultra 8.0. All tables were made using
Microsoft Excel and the original units
were converted to kJ/mol by
multiplying the value in Hartree by
627.518 in order to convert to kcal/mol
then dividing by 0.239019 in order to
convert to kJ/mol. All figures were
imported from the Gaussian results
summary using Microsoft Paint.
References
1
2
3
Beckwith, A. L. J. Chem. Soc.
Rev. 1993, 22, 143.
Ebgal, T. Quantum Chemistry
& Spectroscopy 2006, Pearson
Education Inc.
Carroll, F.A. Perspectives On
Structure and Mechanism In
Organic Chemistry 1998
Brooks/Cole Publishing
Company
4
5
6
7
8
9
Wade, L.G. Jr. Organic
Chemistry 2003, 5th ed. Pearson
Education Inc.
Newcomb, M. Tetrahedron
1993, 49, 1151.
Griller, D.; Ingold, K.U. Acc.
Chem. Res. 1980, 13, 317.
Lal, D.; Griller, D.; Mendenhall
G. D.; Van Hoof W.; Ingold,
K.U. 1974 J. Amer. Chem. Soc.,
in press.
Van Der Heide, P. 2007
Chemistry 4272: Physical
Chemistry Laboratory II.
Garland, C. W.; Nibler, J. W.;
Shoemaker, D. P. Experiments
In Physical Chemistry 2003, 7th
ed. McGraw-Hill Higher
Education.
Acknowledgements
I would like to thank Dr. Bittner for the
unlimited use of his Gaussian program,
his help and advice throughout my
project.
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728 C6H11(5) cGeometry Optimizationbmvittur
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