Energetic differences between the five- and six-membered ring hydrocarbons: Strain energies in the parent and radical molecules

Article abstract of DOI:10.1021/jo800690m

(Chemical Equation Presented) The C-H bond dissociation enthalpies (BDEs) for the five- and six-membered ring alkanes, alkenes, and dienes were investigated and discussed in terms of conventional strain energies (SEs). New determinations are reported for

Full text of DOI:10.1021/jo800690m

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Energetic Differences between the Five- and Six-Membered Ring
Hydrocarbons: Strain Energies in the Parent and Radical Molecules
Filipe Agapito,†,‡ Paulo M. Nunes,† Benedito J. Costa Cabral,‡ Rui M. Borges dos
Santos,*,†,§,| and Jose´ A. Martinho Simo˜es†,§
Centro de Qu´ımica e Bioqu´ımica, Faculdade de Cieˆncias, UniVersidade de Lisboa, 1749-016 Lisboa, Portugal,
Grupo de F´ısica Matema´tica da UniVersidade de Lisboa, AV. Professor Gama Pinto 2, 1649-003 Lisboa,
Portugal, Instituto de Tecnologia Qu´ımica e Biolo´gica, UniVersidade NoVa de Lisboa, AV. da Repu´blica,
2780-157 Oeiras, Portugal, and Institute for Biotechnology and Bioengineering Centro de Biomedicina
Molecular e Estrutural, UniVersidade do AlgarVe, Campus de Gambelas, 8005-139 Faro, Portugal
rmsantos@fc.ul.pt
ReceiVed March 27, 2008
The C-H bond dissociation enthalpies (BDEs) for the five- and six-membered ring alkanes, alkenes, and
dienes were investigated and discussed in terms of conventional strain energies (SEs). New determinations
are reported for cyclopentane and cyclohexane by time-resolved photoacoustic calorimetry and quantum
chemistry methods. The C-H BDEs for the alkenes yielding the alkyl radicals cyclopenten-4-yl and cyclohexen-
4-yl and the R-C-H BDE in cyclopentene were also calculated. The s-homodesmotic model was used to
determine SEs for both the parent molecules and the radicals. When the appropriate s-homodesmotic model
is chosen, the obtained SEs are in good agreement with the ones derived from group additivity schemes. The
different BDEs in the title molecules are explained by the calculated SEs in the parent molecules and their
radicals: (1) BDEs leading to alkyl radicals are ca. 10 kJ mol-1 lower in cyclopentane and cyclopentene than
in cyclohexane and cyclohexene, due to a smaller eclipsing strain in the five-membered radicals relative to
the parent molecules (six-membered hydrocarbons and their radicals are essentially strain free). (2) C-H
BDEs in cyclopentene and cyclohexene leading to the allyl radicals are similar because cyclopenten-3-yl has
almost as much strain as its parent molecule, due to a synperiplanar configuration. (3) The C-H BDE in
1,3-cyclopentadiene is 27 kJ mol-1 higher than in 1,4-cyclohexadiene due to the stabilizing effect of the
conjugated double bond in 1,3-cyclopentadiene and not to a destabilization of the cyclopentadienyl radical.
The chemical insight afforded by group additivity methods in choosing the correct model for SE estimation
is highlighted.
Introduction
latter compound at higher concentrations.2 Because this property
is linked with the C-H BDE in the terpene, knowledge of the
C-H BDEs in terpenes and other structurally related molecules
is of great interest to understand which structural factors
influence the antioxidant properties of these compounds.
Some terpenes exhibit antioxidant properties comparable to
those of R-tocoferol,1 without the pro-oxidant effects of this
† Faculdade de Cieˆncias, Universidade de Lisboa.
‡ Grupo de F´ısica Matema´tica da Universidade de Lisboa.
§ Universidade Nova de Lisboa.
The C-H BDE in an organic molecule RH, DH°(C-H),
corresponds to the enthalpy of reaction 1, where all of the
| Universidade do Algarve.
10.1021/jo800690m CCC: $40.75
Published on Web 07/24/2008
2008 American Chemical Society
J. Org. Chem. 2008, 73, 6213–6223 6213

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Agapito et al.
molecules are in the ideal gas phase (isolated). It is related to
the thermodynamic stability of the corresponding carbon-
centered radical R•, as measured by its standard enthalpy of
formation ∆fH°(R•,g), through eq 2.
free reference molecule, regardless of the cause. To relate
BDEs to strain we need to consider it both in the parent
molecule and in its radical. However, evaluating strain in
the radicals is considerably more complex that in the parent
molecules. An important part of this work was therefore the
selection of a method that allows quantifying the strain in
the radicals studied.
RH(g) f R•(g) + H•(g)
(1)
DH°(C-H) ) ∆fH°(R•,g) + ∆fH°(H•,g) - ∆fH°(RH, g) (2)
Results
Most well-known BDEs for organic compounds have
been obtained in the gas phase from kinetics studies, ion cycles,
and photoionization mass spectrometry, but chemical accuracy
(i.e., values with errors smaller than ca. 4 kJ mol-1) was
achieved for only relatively few data.3–5 As the literature values
for the C-H BDEs in many small hydrocarbons have uncertain-
ties well above chemical accuracy, we investigated a number
of those molecules using a combined approach of theoretical
chemistry methods and time-resolved photoacoustic calorimetry
(TR-PAC).6,7
The strategy used to obtain BDEs from photoacoustic
calorimetry was based on the photochemical process below: di-
tert-butylperoxide (t-BuOOBu-t) is photolyzed, generating tert-
butoxyl radicals (reaction 3), each abstracting an hydrogen atom
from the organic molecule RH, reaction 4.
t-BuOOBu-t(sln)
9
hν8 2t-BuO•(sln)
(3)
2RH(sln) + 2t-BuO•(sln) f 2R•(sln) + 2t-BuOH(sln)
(4)
In a previous study we determined the C-H BDEs in a series
of open-chain hydrocarbons containing the allyl group.8We then
used the results to select the “best” values for the C-H BDEs
in these molecules, which allowed a quantitative discussion
of the factors that determine the stability of the corresponding
radicals, namely, hyperconjugation and resonance. Having
dealt with all relevant molecules from the simplest propene
to cyclohexadiene (viz., propane, propene, isobutene, 1-butene,
2-butene, 3-methyl-1-butene, 2-pentene, 1,3- and 1,4-penta-
diene, cyclohexene, and 1,3- and 1,4-cyclohexadiene), we
now turned our attention to the effect of ring strain on the
C-H BDEs. To this end we need to compare the five-
membered rings cyclopentane, cyclopentene, and 1,3-cyclo-
pentadiene, with the six-membered ones, cyclohexane, cy-
clohexene, and 1,4-cyclohexadiene, respectively. In this work
we report the TR-PAC determinations of C-H BDEs in
cyclopentane and cyclohexane. The TR-PAC experimental
results were complemented by quantum chemistry calcula-
tions for the same molecules and the corresponding radicals
(cyclopentyl and cyclohexyl), plus cyclopentene, cyclopenten-
3-yl, cyclopenten-4-yl, cyclohexen-4-yl, propane, and iso-
propyl. These and the previous results for the remaining
cyclic hydrocarbons, together with the simpler molecules
propene, 1-butene, (E)-2-pentene, 1,3- and 1,4-pentadiene,8
werethenusedtosystematicallyinvestigatethestructure-energetics
relationship in the five- and six-membered ring hydrocarbons
(see Supporting Information for the complete list of molecules
investigated).
Deconvolution of the resulting waveform (see Experimental
Section) first made it possible to confirm the reaction scheme
(reactions 3 and 4) and then afforded the observed fraction of
photon energy released as heat, φobs,i, for each process, and the
lifetime of the second, τ2. An estimate of the rate constant can
be obtained from this lifetime.10 The enthalpy of the hydrogen
abstraction reaction was derived from eq 5, where ∆obsH2
corresponds to the observed enthalpy change and is calculated
by multiplying φobs,2 (the observed heat fraction associated with
reaction 2) by Em ) NAhν (the molar photon energy). Φr is the
reaction quantum yield for the photolysis of di-tert-butylper-
oxide.11
-∆obsH2
∆rH2 )
(5)
Φr
As the enthalpy of reaction 4 is simply twice the difference
between the solution BDEs of the hydrocarbon C-H and tert-
butyl alcohol O-H, DH°sln(C-H) can be derived from eq 6,
where the subscript “sln” indicates that both BDEs are solution
values.
∆rH2
DH°sln(C-H) )
+ DH°sln(t-BuO-H)
(6)
2
In a previous work we determined DHosln(t-BuO-H) ) 455.2
( 5.2 kJ mol-1 in benzene.12 To derive the gas-phase value
DH°(C-H), the solvation terms illustrated in eq 7 must be
considered.13
Strain is the central concept in this discussion, used in the
conventional sense of Cox and Pilcher,9 i.e., including all
the stabilizing and destabilizing effects in relation to a strain-
DH°(C-H) ) DHs°ln(C-H) + ∆slnH°(RH,g) -
∆slnH°(R•,g) - ∆slnH°(H•,g) (7)
(1) Ruberto, G.; Baratta, M. T. Food Chem. 2000, 69, 167–174.
(2) Foti, M. C.; Ingold, K. U. J. Agric. Food Chem. 2003, 51, 2758–2765.
(3) Blanksby, S. J.; Ellison, G. B. Acc. Chem. Res. 2003, 36, 255–263.
(4) Ruscic, B.; Boggs, J. E.; Burcat, A.; Csa´sza´r, A. G.; Demaison, J.;
Janoschek, R.; Martin, J. M. L.; Morton, M. L.; Rossi, M. J.; Stanton, J. F.;
Szalay, P. G.; Westmoreland, P. R.; Zabel, F.; Be´rces, T. J. Phys. Chem. Ref.
Data 2005, 34, 573–656.
The solvation of the hydrogen atom was estimated as
∆slnH°(H•,g) ) 5 ( 1 kJ mol-1 for organic solvents.13 On the
other hand, for carbon-centered radicals ∆slnH°(RH,g) ≈
∆slnH°(R•,g),12 so the difference between solution and gas-phase
(5) Luo, Y.-R. Handbook of Bond Dissociation Energies in Organic
Compounds; CRC Press: Boca Raton, 2003.
(10) Nunes, P. M.; Correia, C. F.; Borges dos Santos, R. M.; Martinho
Simo˜es, J. A. Int. J. Chem. Kinet. 2006, 38, 357–363.
(6) Peters, K. S. Angew. Chem., Int. Ed. Engl. 1994, 33, 294–302.
(7) Laarhoven, L. J. J.; Mulder, P.; Wayner, D. D. M. Acc. Chem. Res. 1999,
32, 342–349.
(11) Wayner, D. D. M.; Lusztyk, E.; Page´, D.; Ingold, K. U.; Mulder, P.;
Laarhoven, L. J. J.; Aldrich, H. S. J. Am. Chem. Soc. 1995, 117, 8737–8744.
(12) Muralha, V. S. F.; Borges dos Santos, R. M.; Martinho Simo˜es, J. A. J.
Phys. Chem. A 2004, 108, 936–942.
(8) Agapito, F.; Nunes, P. M.; Costa Cabral, B. J.; Borges dos Santos, R. M.;
Martinho Simo˜es, J. A. J. Org. Chem. 2007, 72, 8770–8779.
(9) Cox, J. D.; Pilcher, G. Thermochemistry of Organic and Organometallic
Compounds; Academic Press: London, New York, 1970.
(13) Borges dos Santos, R. M.; Costa Cabral, B. J.; Martinho Simo˜es, J. A.
Pure Appl. Chem. 2007, 79, 1369–1382.
6214 J. Org. Chem. Vol. 73, No. 16, 2008

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Energetic Differences between 5- and 6-Membered Ring Hydrocarbons
TABLE 1. Theoretical and Experimental C-H Bond Dissociation Enthalpies (in kJ mol-1) at 298.15 K
molecule
propenec
radical
B3LYP-TZa
CBS-Qa
CBS-QB3a
CCSD(T)a
371.5
exptlb
allyl
352.2
361.3
364.9
371.5 ( 1.7d
412.5 ( 1.7e
401.8 ( 5.8
propane
cyclopentane
cyclopentene
isopropyl
cyclopentyl
397.5
410.9
413.9
416.3
388.4 [403.3]f
390.5 [405.5]f
335.5 [354.9]g
333.4 [352.7]g
399.4 [414.3]f
398.1 [413.1]f
333.8 [353.2]g
297.0 [316.4]g
404.1 [405.7]f
406.6 [408.2]f
347.3 [357.5]g
346.1 [356.4]g
417.8 [419.4]f
418.3 [419.9]f
347.2 [357.5]g
307.8 [318.0]g
403.7 [402.3]f
406.1 [404.7]f
350.5 [357.1]g
345.9 [352.5]g
416.1 [414.7]f
415.1 [413.7]f
349.5 [356.1]g
311.0 [317.6]g
406.8 [403.0]f
408.7 [404.8]f
358.7h
cyclopenten-4-yl
cyclopenten-3-yl
cyclopentadienyl
cyclohexyl
cyclohexen-4-yl
cyclohexen-3-ylf
cyclohexadienyl
i
344.3 ( 4.2
357.8 ( 7.1
419.8 ( 6.0
1,3-cyclopentadienej
cyclohexane
cyclohexene
353.4h
j
418.5 [414.6]f
417.7 [413.9]f
357.9h
350.0 ( 5.6
312.8 ( 6.1
c
c
1,4-cyclohexadiene
326.3h
a Results from the direct homolysis reaction 1 and, in brackets, from the isodesmic and isogyric reaction 9. This work unless noted otherwise.
b TR-PAC results from this work, unless noted otherwise. The error is twice the standard deviation of the mean for 5-6 independent experiments.
f
c From ref 8. d From ref 3. e From ref 4. Using the literature value for the C2-H BDE in propane as the anchor (412.5 ( 1.7 kJ mol-1). g Using the
literature value for the C(sp3)-H BDE in propene as the anchor (371.5 ( 1.7 kJ mol-1). h In this case there is no need to derive the BDEs from
reaction 9 since the computed C(sp3)-H BDE in propene matches the experimental result. i From ref 16. j From ref 17.
C-H BDEs is equal to the solvation enthalpy of the hydrogen
atom indicated above.14
Regarding the theoretical results, bond dissociation enthalpies
were computed from eq 8, equivalent to eq 2 but with the
standard enthalpies of formation replaced by the theoretically
obtained entalpies H.
then the structural features in reaction 9 would be matched to
a lesser extent, since R′• would be a primary radical, whereas
the product is a secondary radical. When the C2-H BDE in
propane is used, both radicals are secondary.
As expected, Table 1 shows that the BDEs computed from
reaction 1 have larger discrepancies than the bracketed values
obtained with reaction 9. A closer analysis reveals that when
alkyl radicals are involved, this difference is only important for
the DFT calculations, but when allylic radicals are formed, the
discrepancy is also noticeable for the complete basis set
methods. These results also follow our previous observation8
that the discrepancies are smaller for CBS-QB3 than for CBS-
Q, indicating that the former is the most accurate of these two
methods for the systems under study. We will however favor
the results of the CCSD(T) calculations, which are expected to
be the most reliable. It is also observed that the CBS-QB3 and
CCSD(T) results are in excellent agreement, with the previously
noted exception of the BDE for 1,4-cyclohexadiene (and the
remaining dienes, (E)-1,3- and 1,4-pentadiene, and 1,3-cyclo-
DH°(C-H) ) H(R•) + H(H•) - H(RH)
(8)
The C-H BDEs for the molecules investigated in this work
are presented in Table 1. The touchstone for discussing the
energetics of the allyl radicals is the C(sp3)-H BDE in propene,
which is well established as 371.5 ( 1.7 kJ mol-1.3 Similarly,
the basis for discussing the energetics of the alkyl radicals in
this work is the also well-known C2-H BDE in propane that
corresponds to the formation of the isopropyl radical (412.5 (
1.7 kJ mol-1).4 These BDEs were used as the anchors to derive
more accurate computational results in Table 1. Indeed, C-H
BDEs calculated from eq 8, which relies on reaction 1, are
usually low limits of the exact values. This problem can be
avoided by using a particular type of reaction, eq 9, in which
the structural features of reactants and products (such as the
number of electron pairs, the number of carbon atoms in a given
state of hybridization, etc.) are matched to some degree (for a
more complete description see Calculating the Strain Energy).
hexadiene), but even then the discrepancy is smaller than 8 kJ
8
mol-1
.
The BDEs corresponding to the C-H bond cleavages yielding
the cyclopentadienyl, cyclohexen-3-yl, and cyclohexadienyl
radicals (Table 1) were also the subject of previous studies by
our group and the corresponding selected values were 355,17
8
357.9, and 326.3 kJ mol-1
,
respectively. The first value
RH + R′• f R• + R′H
(9)
corresponds to a rounded average of the CCSD(T) calculation
with the TR-PAC result, while the remaining values are simply
the CCSD(T) results (which are in good agreement with the
experimental TR-PAC values). For the sake of consistency, in
the present study we will also use the CCSD(T) result for the
C-H BDE in cyclopentadienyl, 353.4 kJ mol-1. To compare
the new results with the literature data we followed our previous
strategy and relied mainly on the compilation by Luo,5
complemented with a brief analysis of the data collected by
this author.
The experimental results for the C-H BDE in cyclopentane
vary in a narrow range, 397 ( 4 to 400 ( 4 kJ mol-1.5 The
latter value, selected by Luo, is based on the EPR determination
of the equilibrium constant for the exchange reaction between
methyl radical and cyclopentyl iodide.18 It should be revised
The differences DH°(R-H) - DH°(R′-H), which are equal
to the enthalpies of reaction 9, are largely method-independent
and usually more accurate than the BDEs obtained from eq 8,
because reaction 9 takes advantage of error cancelation.15
Moreover, these differences may yield absolute BDE values by
using a reliable value for the anchor, DH°(R′-H). The bracketed
values in Table 1 were obtained from reaction 9 with R′ )
isopropyl and using the experimental C2-H BDE for propane,
412.5 kJ mol-1, whenever alkyl radicals are formed, and with
R′ ) allyl and using the experimental C(sp3)-H BDE for
propene, 371.5 kJ mol-1, when allylic radicals are involved.
Note that the accurately known C-H BDE in methane could
in principle be used instead of the C2-H BDE in propane, but
(14) The final uncertainty of the TR-PAC determination of DH°(C-H) (eq
7) is equal to the uncertainty of DH°sln(C-H) (eq 6), since the error in ∆slnH°(H•,g)
cancels out and the error in ∆slnH°(RH,g)-∆slnH°(R•,g) is negligible, see e.g.,
ref 12.
(15) Computational Thermochemistry. Prediction and Estimation of Molec-
ular Thermodynamics; Irikura, K. K., Frurip, D. J., Eds.; ACS Symposium Series
No. 677; American Chemical Society: Washington, DC, 1998.
(16) Furuyama, S.; Golden, D. M.; Benson, S. W. Int. J. Chem. Kinet. 1970,
2, 93–99.
(17) Nunes, P. M.; Agapito, F.; Costa Cabral, B. J.; Borges dos Santos, R. M.;
Martinho Simo˜es, J. A. J. Phys. Chem. A 2006, 110, 5130–5134.
(18) Castelhano, A. L.; Griller, D. J. Am. Chem. Soc. 1982, 104, 3655–3659.
J. Org. Chem. Vol. 73, No. 16, 2008 6215

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Agapito et al.
TABLE 2. Selected Values for the Relative [∆DH°(C-H)] and
taking into account the most recently auxiliary data, namely,
Absolute [DH°(C-H)] C-H BDEs (in kJ mol-1), and Recommended
the enthalpy of formation of the methyl radical (146.7 ( 0.3 kJ
Enthalpies of Formation for the Corresponding Radicalsa
mol-1).4 The revision is however small, yielding 402.9 kJ mol-1
.
∆DH°
DH°
∆fH°
Both our calculated and experimental values are in conformity
with this result, and we selected 403.0 kJ mol-1 (CCSD(T)), in
excellent agreement with our TR-PAC result of 401.8 ( 5.8 kJ
mol-1. The TR-PAC experiments were performed with cyclo-
pentane concentrations of 4.0 and 10.1 M (this latter concentra-
tion referring to neat cyclopentane plus the peroxide). From the
lifetime obtained for reaction 4, τ2, we estimate 7 × 105 M-1
s-1 for the rate constant of hydrogen abstraction from cyclo-
pentane (k2), in good agreement with the reported laser flash
molecule
propane
radical
isopropyl
cyclopentyl
cyclopenten-4-yl
cyclohexyl
cyclohexen-4-yl
allyl
1-methylallyl
2-penten-4-yl
pentadienyl
pentadienyl
cyclopenten-3-yl
cyclohexen-3-yl
(C-H) (C-H) (R•,g)b
0.0
-9.5
-7.7
2.1
1.4
0.0
-11.9
-11.5
-19.0
-46.5
-12.8
-13.6
412.5
403.0
404.8
414.6
413.9
371.5
359.6
360.0
352.5
325.0
358.7
357.9
353.4
326.3
89.8
108.6
220.8
73.3
cyclopentane
cyclopentene
cyclohexane
cyclohexene
propene
191.0
173.5
141.7
110.1
210.6
212.7
174.7
135.0
269.7
213.1e
1-butenec
(E)-2-pentenec
(E)-1,3-pentadienec
1,4-pentadienec
cyclopentene
cyclohexenec
photolysis values, e.g., 8.51 × 105 M-1 s-1
.
19 The value of the
C-H BDE in cyclopentane is very close to the calculated
ꢀ-C-H BDE in cyclopentene yielding the alkyl radical cyclo-
penten-4-yl, 404.8 kJ mol-1 (CCSD(T)).
1,3-cyclopentadiened cyclopentadienyl -18.1
1,4-cyclohexadienec
cyclohexadienyl
-45.2
For the R-C-H BDE in cyclopentene, which leads to the
allylic radical cyclopenten-3-yl, the results reported by Luo are
again very close, 344 ( 4 and 343 ( 8 kJ mol-1.5 However,
all of our calculations point to a higher BDE, varying in a narrow
range, viz., 355 (B3LYP-TZ) to 359 kJ mol-1 (CCSD(T)), in
keeping with previous high-level calculations of 352.3 (G3),20,21
353.1 (G3B3),22 and 355.6 kJ mol-1 (W1).21 We select the result
a Estimated uncertainty of ca. ( 4 kJ mol-1 b Calculated using
∆fH°(H•,g) ) 217.998 ( 0.006 kJ mol-1 (ref 24) and ∆fH°(RH,g) from
ref 25. c From ref 8. d From ref 17. e ∆fH°(RH,g) from ref 26.
Discussion
The above data analysis led to the set of recommended values
collected in Table 2. They are all based on the values derived
from CCSD(T), with exception of the anchor molecules propane
and propene, for which the recommended literature values are
given. The top part of the table lists the alkyl radicals. The allyl
radicals presented next include mostly earlier results8,17 that are
relevant for the present discussion.
of the CCSD(T) method for this BDE, 359 kJ mol-1
.
The reported values for the C-H BDE in cyclohexane range
from 403 to 416 kJ mol-1, the latter selected by Luo.5 The data
presented by this author includes a non-time-resolved PAC result
of 410 kJ mol-1 23 Since reaction 4 is too slow for PAC without
.
deconvolution analysis, the experiment involved two competing
reactions, namely, reaction 4 with cyclohexane and with 1,4-
cyclohexadiene. Using this strategy, the derivation of the desired
BDE for cyclohexane depends on the knowledge of both rate
constants and the C-H BDE in the latter compound. TR-PAC
directly affords the BDE in cyclohexane and also the rate
constant for reaction 4. Our experiments led to 419.8 ( 6.0 kJ
mol-1, in good agreement with Luo’s selection, and were
performed with cyclohexane concentrations ranging from 2.2
to 9.0 M (neat cyclohexane plus the peroxide). From the lifetime
obtained for reaction 4, τ2, we derived 8 × 105 M-1 s-1 for the
rate constant of hydrogen abstraction from cyclohexane (k2),
In our previous work dealing with simple (and unstrained)
alkanes, alkenes, and dienes, we explained the differences in
C-H BDEs using the concepts of hyperconjugation and
resonance. These effects are reflected by the structural changes
that accompany radical formation. For instance, hyperconjuga-
tion can be measured by the shortening of the C-C bond(s)
adjacent to the radical center; resonance in an allyl group is
characterized by two carbon-carbon bonds of identical length,
which were a single and a double bond in the parent molecule.
Both factors are accompanied by a decrease in spin density at
the carbon atom where abstraction occurs, which correlates
rather well with the C-H BDEs in the alkanes and alkenes
studied. This supports the view that those BDEs are mainly
determined by alkyl and allyl radical stabilization through spin
delocalization. In the case of the dienes we have also to consider
the thermodynamic stabilities of the parent compounds, namely,
the possibility of a strongly stabilizing conjugated double bond.8
In the present study, deviations from the above behavior will
be attributed to strain and assessed by comparing the title
molecules with a suitable reference. This reference should
obviously be a strain-free compound but having stabilization
effects that are identical to those in the molecule under study.
Suitable references that will be used throughout this discussion
are displayed in Figure 1.
which matches a recent laser flash photolysis result (8.13 ×
19
105 M-1 s-1
)
and is in fair agreement with the value used in
the PAC study indicated above (5.5 × 105 M-1 s-1).23 Our
calculations are also in good agreement with Luo’s recom-
mendation, and we selected 414.6 kJ mol-1 (CCSD(T)). The
value of this BDE is very close to the calculated ꢀ-C-H BDE
in cyclohexene that leads to the alkyl radical cyclohexen-4-yl,
413.9 kJ mol-1 (CCSD(T)).
(19) Finn, M.; Friedline, R.; Suleman, N. K.; Wohl, C. J.; Tanko, J. M. J. Am.
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To rationalize the effect of strain on the BDEs, we will start
by inspecting the geometries of the parent molecules and radicals
for “anomalous” (with regard to the references) C-C bond
lengths (Figure 2) and C-C-C angles (Figure 3).
Cyclohexane versus Cyclopentane. The C-H BDE in
propane leading to isopropyl (412.5 kJ mol-1) is similar to the
C-H BDE in cyclohexane (414.6 kJ mol-1). This is consistent
with the known fact that cyclohexane and its radical have little
or no strain. However, the C-H BDE in cyclopentane is some
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6216 J. Org. Chem. Vol. 73, No. 16, 2008