Energetics of the allyl group

Article abstract of DOI:10.1021/jo701397r

(Figure Presented) Aiming to improve our understanding of the stability of radicals containing the allylic moiety, carbon-hydrogen bond dissociation enthalpies (BDEs) in propene, isobutene, 1-butene, (E)-2-butene, 3-metylbut-1-ene, (E)-2-pentene, (E)-1,3-pentadiene, 1,4-pentadiene, cyclohexene, 1,3-cyclohexadiene, and 1,4-cyclohexadiene have been determined by quantum chemistry calculations. The BDEs in cyclohexene, 1,3-cyclohexadiene, and 1,4-cyclohexadiene have also been obtained by time-resolved photoacoustic calorimetry. The theoretical study involved a DFT method as well as ab initio complete basis-set approaches, including the composite CBS-Q and CBS-QB3 procedures, and basis-set extrapolated coupled-cluster calculations (CCSD(T)). By taking the C(sp³)-H BDE in propene as a reference, we have concluded that one methyl group bonded to C3 in propene (i.e., 1-butene) leads to a decrease of 12 kJ mol^-1 and that a second methyl group bonded to C3 (3-methylbut-1-ene) further decreases the BDE by 8 kJ mol^-1. When the methyl group is bonded to C2 in propene (isobutene), an increase of 7 kJ mol^-1 is observed. Finally, a methyl group bonded to C1 in propene (2-butene) has essentially no effect (-1 kJ mol^-1). While this trend can be rationalized in terms of stabilization of the corresponding radical (through hyperconjugation and π-delocalization), the BDE values observed for the dienes can only be understood by considering the thermodynamic stabilities of the parent compounds.

Full text of DOI:10.1021/jo701397r

Energetics of the Allyl Group
Filipe Agapito,†,‡ Paulo M. Nunes,† Benedito J. Costa Cabral,†,‡
Rui M. Borges dos Santos,§ and Jose´ A. Martinho Simo˜es*,†
Departamento 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, and Institute for Biotechnology and Bioengineering, Centro de Biomedicina
Molecular e Estrutural, UniVersidade do AlgarVe, Campus de Gambelas, 8005-139 Faro, Portugal
jams@fc.ul.pt
ReceiVed June 27, 2007
Aiming to improve our understanding of the stability of radicals containing the allylic moiety,
carbon-hydrogen bond dissociation enthalpies (BDEs) in propene, isobutene, 1-butene, (E)-2-butene,
3-metylbut-1-ene, (E)-2-pentene, (E)-1,3-pentadiene, 1,4-pentadiene, cyclohexene, 1,3-cyclohexadiene,
and 1,4-cyclohexadiene have been determined by quantum chemistry calculations. The BDEs in
cyclohexene, 1,3-cyclohexadiene, and 1,4-cyclohexadiene have also been obtained by time-
resolved photoacoustic calorimetry. The theoretical study involved a DFT method as well as ab initio
complete basis-set approaches, including the composite CBS-Q and CBS-QB3 procedures, and basis-
set extrapolated coupled-cluster calculations (CCSD(T)). By taking the C(sp3)-H BDE in propene
as a reference, we have concluded that one methyl group bonded to C3 in propene (i.e., 1-butene) leads
to a decrease of 12 kJ mol-1 and that a second methyl group bonded to C3 (3-methylbut-1-ene) further
decreases the BDE by 8 kJ mol-1. When the methyl group is bonded to C2 in propene (isobutene), an
increase of 7 kJ mol-1 is observed. Finally, a methyl group bonded to C1 in propene (2-butene) has
essentially no effect (-1 kJ mol-1). While this trend can be rationalized in terms of stabilization of
the corresponding radical (through hyperconjugation and π-delocalization), the BDE values observed
for the dienes can only be understood by considering the thermodynamic stabilities of the parent
compounds.
Introduction
oxidant effects of this latter compound at higher concentrations.2
The initial step of the proposed terpene peroxidation mechanism
involves hydrogen abstraction by a hydroperoxyl radical.2 The
efficiency of this step will increase with the exothermicity of
the abstraction, which in turn corresponds to a decrease of the
C-H BDE in the terpene. Therefore, the knowledge of the C-H
BDEs in terpenes and other structurally related compounds is
of great interest to understand which structural factors influence
the antioxidant properties of these compounds.
Bond dissociation enthalpies (BDEs) are fundamental
to discuss molecular structure-reactivity relationships. For
instance, it has been shown that the antioxidant properties
of terpinolene (1), R-terpinene (2), and γ-terpinene (3)
are comparable to those of R-tocoferol,1 without the pro-
* Address correspondence to this author. Phone: 351-217500005, Fax: 351-
217500088.
† Faculdade de Cieˆncias, Universidade de Lisboa.
‡ Grupo de F´ısica Matema´tica da Universidade de Lisboa.
§ Universidade do Algarve.
(2) Foti, M. C.; Ingold, K. U. J. Agric. Food Chem. 2003, 51, 2758-
2765.
(1) Ruberto, G.; Baratta, M. T. Food Chem. 2000, 69, 167-174.
10.1021/jo701397r CCC: $37.00 © 2007 American Chemical Society
Published on Web 10/09/2007
8770
J. Org. Chem. 2007, 72, 8770-8779

Energetics of the Allyl Group
in 3-methyl-1-butene span almost 30 kJ mol-1. These uncertain-
ties hinder our understanding of structural effects on C-H BDEs
and therefore affect our ability to predict new data.
In this work we report our determinations of C-H BDEs for
a series of hydrocarbons containing structural features of terpene
molecules. We started our study with the terpenes body,
cyclohexene, 1,3-cyclohexadiene, and 1,4-cyclohexadiene, using
time-resolved photoacoustic calorimetry (TR-PAC)12 and quan-
tum chemistry methods. PAC (and hence TR-PAC) is a very
reliable method to determine BDEs.13 However, unlike the
experimental methods referred to above, it is a solution
technique (i.e., all the species in reaction 2 are in solution),
affording solution-phase BDEs. To derive the gas-phase BDEs,
one needs to consider the solvation enthalpies of all the species
in reaction 2. For some types of radicals (e.g., oxygen-centered
radicals), these data are still a matter of some debate.14,15 In
the case of carbon-centered radicals, there is evidence that the
solvation enthalpies of R• and RH are identical and therefore
the solution- and gas-phase BDEs differ only by the solvation
enthalpy of the hydrogen atom.16 An additional advantage of
TR-PAC is that it allows discrimination between competitive
reactions, provided that these occur at different rates.
The TR-PAC experimental results were then complemented
by quantum chemistry calculations, aiming to understand the
effects of the carbon-carbon double bonds and alkyl groups
on the C-H BDE. The computational study included the
following molecules: propene, isobutene, 1- and (E)-2-butene,
3-methylbut-1-ene, (E)-2-pentene, (E)-1,3- and 1,4-pentadiene,
and 1,3- and 1,4-cyclohexadiene. As remarked above, we have
found that the accuracy of the literature data for such simple
molecules was not sufficient to draw useful conclusions about
structural effects on C-H BDEs. On the other hand, a
quantitative discussion of the stabilization of the corresponding
radical requires only relatiVe BDEs. Computational chemistry
is a particularly suitable source of these relative data. Their
accuracy can in some cases be assessed by using thermochemical
cycles that involve well-established enthalpies of formation of
parent molecules (RH in reaction 2).
The C-H BDE in an organic molecule RH, DH°(C-H), is
closely related to the thermodynamic stability of the corre-
sponding carbon-centered radical R•, as measured by its standard
enthalpy of formation ∆fH°(R•,g). The relation is illustrated by
eq 1, the definition of BDE, which corresponds to the enthalpy
of reaction 2. Note that all the molecules are in the ideal gas
phase (isolated).
DH°(C-H) ) ∆fH°(R•,g) + ∆fH°(H•,g) - ∆fH°(RH,g) (1)
RH (g) f R• (g) + H• (g)
(2)
The stability of a large number of long-lived organic
molecules is well established.3,4 This standard enthalpy of
formation database has been very important for the assessment
of quantum chemistry methods5 and has fostered the develop-
ment of reliable empirical schemes to predict new values.5-7
The present knowledge on the stability of organic free radicals
(as measured by their standard enthalpies of formation or by
the corresponding C-H BDEs in their parent molecules, eq 1)
is far less satisfactory than that for stable molecules. This is
due to the fact that traditional experimental techniques, such as
combustion calorimetry, are not suitable to probe the thermo-
chemistry of species whose lifetime is less than ca. 1 µs. Most
of the “best” BDEs known for organic compounds have been
obtained in the gas phase from kinetics studies, ion cycles, and
photoionization mass spectrometry.8,9 Although these methods
may afford chemically accurate results (i.e., with an error smaller
than ca. 4 kJ mol-1) this accuracy has only been achieved for
a relatively small number of compounds.8,10 On the other hand,
there are abundant examples of large disagreements in literature
data for BDEs in many basic compounds.9,11 For instance, the
literature values of R-C-H BDEs in 1,4-cyclohexadiene and
Experimental Section
Materials. Benzene (HPLC grade, 99.9+%) was used without
further purification. Cyclohexene (initial purity 99%) was chro-
matographed in a column of activated alumina grade I under
nitrogen and stored in a refrigerator under inert atmosphere. 1,3-
Cyclohexadiene (initial purity 97%) was dried over CaCl2, distilled
from NaBH4 under nitrogen, stored under inert atmosphere, and
refrigerated. 1,4-Cyclohexadiene (initial purity 97%) was dried over
CaCl2, distilled under nitrogen, stored in an inert atmosphere, and
refrigerated. All three substrates were passed through a column of
activated alumina under nitrogen prior to use. Di-tert-butyl peroxide
was purified according to a literature procedure.17 o-Hydroxyben-
zophenone was recrystallized twice from an ethanol-water mixture.
(3) Linstrom, P. J.; Mallard, W. G. NIST Chemistry WebBook; NIST
Standard Reference Database No. 69 (http://webbook.nist.gov); National
Institute of Standards and Technology: Gaithersburg, MD, 2005.
(4) Pedley, J. B. Thermochemical Data and Structures of Organic
Compounds; Thermodynamics Research Center: College Station, TX, 1994;
Vol. I.
(5) Irikura, K. K.; Frurip, D. J., Eds. Computational Thermochemistry.
Prediction and Estimation of Molecular Thermodynamics; ACS Symp. Ser.
No. 677: Washington, DC, 1998.
(6) Cox, J. D.; Pilcher, G. Thermochemistry of Organic and Organo-
metallic Compounds; Academic Press: New York, 1970.
(7) Benson, S. W. Thermochemical Kinetics, 2nd ed.; Wiley: New York,
1976.
(8) Blanksby, S. J.; Ellison, G. B. Acc. Chem. Res. 2003, 36, 255-263.
(9) Luo, Y.-R. Handbook of Bond Dissociation Energies in Organic
Compounds; CRC Press: Boca Raton, FL, 2003.
(10) Ruscic, B.; Boggs, J. E.; Burcat, A.; Csaszar, 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.; Berces, T. J. Phys. Chem.
Ref. Data 2005, 34, 573-656.
(11) McMillen, D. F.; Golden, D. M. Annu. ReV. Phys. Chem. 1982, 33,
493-532.
(12) Peters, K. S. Angew. Chem., Int. Ed. Engl. 1994, 33, 294-302.
(13) Laarhoven, L. J. J.; Mulder, P.; Wayner, D. D. M. Acc. Chem. Res.
1999, 32, 342-349.
(14) 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.
(15) Guedes, R. C.; Coutinho, K.; Cabral, B. J. C.; Canuto, S.; Correia,
C. F.; Borges dos Santos, R. M.; Martinho Simo˜es, J. A. J. Phys. Chem. A
2003, 107, 9197-9207.
(16) Muralha, V. S.; Borges dos Santos, R. M.; Martinho Simo˜es, J. A.
J. Phys. Chem. A 2004, 108, 936-942.
(17) Diogo, H. P.; Minas da Piedade, M. E.; Martinho Simo˜es, J. A.;
Nagano, Y. J. Chem. Thermodyn. 1995, 27, 597-604.
J. Org. Chem, Vol. 72, No. 23, 2007 8771

Agapito et al.
Photoacoustic Calorimetry. The basis of photoacoustic calo-
rimetry,12,18 our photoacoustic calorimeter setup,19,20 and the
experimental technique are described in detail elsewhere.21,22
Briefly, argon-purged solutions in benzene of ca. 0.4 M di-tert-
butyl peroxide and an adequate concentration (see Analysis of
Thermochemical Data) of each organic molecule studied (cyclo-
hexene, 1,3-cyclohexadiene, and 1,4-cyclohexadiene) were flowed
through a quartz flow cell and photolyzed with pulses from a
nitrogen laser (337.1 nm, pulse width 800 ps). To check for
multiphoton effects, the incident laser energy was varied by using
neutral density filters (ca. 5-30 µJ/pulse at the cell, flux <40 J
m-2). Each pulse produced photolysis of di-tert-butyl peroxide (t-
BuOOBu-t), generating tert-butoxyl radicals (reaction 3), which in
turn abstracted an allylic hydrogen from the organic molecule RH,
reaction 4.
R-C-H bond, were determined by using density functional theory
(DFT).25 In this approach the energy of a system, E[F], is given by
eq 6, where VNN is the nucleus-nucleus repulsion energy, Hcore is
the one-electron kinetic and electron-nuclei potential energy
contribution to the total energy, and Vee is the Coulombic electron-
electron repulsion energy.
E[F] ) VNN + Hcore + Vee + Ex[F] + Ec[F]
(6)
The terms Ex[F] and Ec[F] are respectively the exchange and
correlation functionals of the electronic density, F. The optimized
geometry for a molecule is found by determining the set of nuclear
coordinates that minimizes the energy given by eq 6. In this work
the geometry optimizations were carried out with Becke’s three-
parameter hybrid method26 with the correlation functional of Lee,
Yang, and Parr (B3LYP).27 The accuracy of the energy also depends
on the completeness of the basis set in which the molecular orbitals
are expanded. For these geometry optimizations Dunning’s triple-ú
correlation consistent basis set (cc-pVTZ) was used.28 Vibrational
analysis was performed for all optimized geometries to ensure that
they represented minima of the energy surfaces. The choice of
B3LYP/cc-pVTZ geometries for the structural analysis was dictated
by its cost-effectiveness and the fact that several works indicate
that the molecular geometries thus obtained are in good agreement
with experimental data.29-31 Nevertheless, it is well-known that DFT
methods systematically underestimate bond dissociation enthalp-
ies.32,33 Therefore, in addition to B3LYP, BDEs were also computed
by using two composite theoretical procedures, namely CBS-Q and
CBS-QB3.34-36 These were specifically devised to allow an accurate
determination of thermochemical properties for large systems, by
resorting to extrapolation to the complete basis set limit. We note,
however, that the geometry optimizations of CBS-Q and CBS-QB3
are performed respectively with MP2(FC)/6-31G† (frozen-core
Møller-Plesset second-order perturbation theory,37 in which the
electrons from inner shells are excluded from the calculation of
the correlation energy) and B3LYP/6-31G†, and therefore are
slightly less accurate than B3LYP/cc-pVTZ geometries.29,31
Complete basis set extrapolated coupled cluster calculations with
single and double excitations and perturbative inclusion of triple
excitations (CCSD(T)),38 using B3LYP/cc-pVTZ geometries, are
also reported. Extrapolation of CCSD(T) energies to complete basis
set was carried out through a dual (2)cc-pVDZ,3)cc-pVTZ)
scheme proposed by Truhlar for both the Hartree-Fock and
correlation energies.39 This procedure has proven to be very reliable
for the determination of BDEs,40,41 although computationally more
demanding than any of the aforementioned methods.
t-BuOOBu-t (sln)
9
hν8 2 t-BuO• (sln)
(3)
2RH (sln) + 2 t-BuO• (sln) f 2R• (sln) + 2 t-BuOH (sln) (4)
Each laser pulse induced a sudden volume change in solution,
which generated an acoustic wave, detected by a piezoelectric
transducer (0.5 MHz) in contact with the bottom of the cell. The
signals were amplified and measured by a digital oscilloscope. The
signal-to-noise ratio was improved by averaging 32 acquisitions
for each data point obtained at a given laser energy. The apparatus
was calibrated by carrying out a photoacoustic run with an optically
matched solution of o-hydroxybenzophenone (in the same mixtures
but without the peroxide), which dissipates all of the absorbed
energy as heat.18 For each run (experiment or calibration), four data
points were collected corresponding to four different laser intensities
obtained with the neutral density filters. The resulting waveforms
from each data point were recorded for subsequent mathematical
analysis, affording two waveforms for each point: sample and
calibration. The analysis involved, for each laser energy, first the
normalization of both waveforms and then their deconvolution,
using the software Sound Analysis.23 This analysis first allowed
the confirmation of the reaction scheme indicated above (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.24 The enthalpy of the hydrogen abstraction reaction
was derived from eq 5,
-∆obsH2
∆rH2 )
(5)
Φr
(25) Zhou, Z.; Parr, R. G. J. Am. Chem. Soc. 1989, 111, 7371-7379.
(26) Becke, A. D. J. Chem. Phys. 1993, 98, 5648.
(27) Lucas, C. R.; Gabe, E. J.; Lee, F. L. Can. J. Chem. 1988, 66, 429-
434.
where ∆obsH2 corresponds to the observed enthalpy change and is
calculated by multiplying Em ) NAhν (the molar photon energy)
by φobs,2 (the observed heat fraction associated with reaction 2).
Φr is the reaction quantum yield for the photolysis of di-tert-butyl
peroxide. All experiments were performed at 293 ( 0.5 K.
Theoretical Calculations. The structures of propene, isobutene,
1- and (E)-2-butene, 3-methylbut-1-ene, (E)-2-pentene, (E)-1,3- and
1,4-pentadiene, cyclohexene, and 1,3- and 1,4-cyclohexadiene, as
well as the respective radicals resulting from homolysis of an
(28) Dunning, T. H., Jr. J. Chem. Phys. 1989, 90, 1007.
(29) Byrd, E. F. C.; Sherrill, C. D.; Head-Gordon, M. J. Phys. Chem. A
2001, 105, 9736-9747.
(30) Agapito, F.; Cabral, B. J. C.; Martinho Simo˜es, J. A. THEOCHEM
2005, 719, 109-114.
(31) Wang, J. T.; Feng, Y.; Liu, L.; Li, X.-S.; Guo, Q.-X. Chin. J. Chem.
2004, 22, 642-648.
(32) Cabral do Couto, P.; Guedes, R. C.; Cabral, B. J. C.; Martinho
Simo˜es, J. A. Int. J. Quantum Chem. 2002, 86, 297-304.
(33) Kern, R. D.; Zhang, Q.; Yao, J.; Jursic, R. S.; Tranter, R. S.; Greybill,
M. A.; Kiefer, J. H. Proc. Combust. Inst. 1998, 102, 143-150.
(34) Ochterski, J. W.; Petersson, G. A.; Montgomery, J. A. J. Chem.
Phys. 1996, 104, 2598-2619.
(18) Braslavsky, S. E.; Heibel, G. E. Chem. ReV. 1992, 92, 1381-1410.
(19) Borges dos Santos, R. M.; Lagoa, A. L. C.; Martinho Simo˜es, J. A.
J. Chem. Thermodyn. 1999, 31, 1483-1510.
(20) Nunes, P. M.; Correia, C. F.; Dos Santos, R. M. B.; Simoes, J. A.
M. Int. J. Chem. Kinet. 2006, 38, 357-363.
(21) Correia, C. F.; Nunes, P. M.; Borges, dos Santos, R. M.; Martinho
Simo˜es, J. A. Thermochim. Acta 2004, 420, 3-11.
(22) 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.
(23) Sound Analysis, version 1.50D; Quantum Northwest: Spokane, WA,
1999.
(35) Montgomery, J. A.; Frisch, M. J.; Ochterski, J. W.; Petersson, G.
A. J. Chem. Phys. 1999, 110, 2822-2827.
(36) Montgomery, J. A.; Frisch, M. J.; Ochterski, J. W.; Petersson, G.
A. J. Chem. Phys. 2000, 112, 6532-6542.
(37) Møller, C.; Plesset, M. S. Phys. ReV. 1934, 46, 618.
(38) Raghavachari, K.; Trucks, G. W.; Pople, J. A.; Headgordon, M.
Chem. Phys. Lett. 1989, 157, 479-483.
(24) Nunes, P. M.; Correia, C. F.; Borges dos Santos, R. M.; Martinho
Simo˜es, J. A. Int. J. Chem. Kinet. 2006, 38, 357-363.
(39) Truhlar, D. G. Chem. Phys. Lett. 1998, 294, 45-48.
8772 J. Org. Chem., Vol. 72, No. 23, 2007

Energetics of the Allyl Group
TABLE 1. C-H Bond Dissociation Enthalpies (in kJ mol-1) from the Literature and Determined by Using Theoretical Methods, at 298.15 K
molecule
radical
lit.a
CBS-Qb
CBS-QB3b
B3LYPb,c
CCSD(T)d
propene
isobutene
1-butene
(E)-2-butene
3-methylbut-1-ene
(E)-2-pentene
(E)-1,3-pentadiene
1,4-pentadiene
cyclohexene
allyl
2-methylallyl
1-methylallyl
1-methylallyl
3-methyl-1-buten-3-yl
2-penten-4-yl
pentadienyl
371.5 ( 1.7e
361.3f
364.9f
352.2
371.5f
378.2
359.6
370.8
351.7
360.0
352.5
325.0
357.9
325.3
326.3
360.7 ( 4.2; 372.8
341.0 ( 6.3; 350.6
366.9 [377.1]
347.8 [358.1]
360.4 [370.7]
340.1 [350.3]
344.9 [355.2]
333.5 [343.7]
301.9 [312.1]
347.2 [357.5]
305.8 [316.1]
307.8 [318.0]
371.3 [377.9]
351.9 [358.5]
363.1 [369.7]
343.8 [350.4]
351.7 [358.3]
338.3 [344.9]
310.5 [317.2]
349.5 [356.1]
311.3 [317.9]
311.0 [317.6]
359.2 [378.6]
334.9 [354.2]
349.4 [368.7]
322.8 [342.1]
334.0 [353.3]
326.9 [346.2]
291.9 [311.2]
333.8 [353.2]
296.4 [315.7]
297.0 [316.4]
322.1 ( 6.3;g 347.7
333.5 ( 4.2; 347.3 ( 12.6
319.7; 332.6 ( 7.1
343 ( 10h
pentadienyl
cyclohexen-3-yl
cyclohexadienyl
cyclohexadienyl
1,3-cyclohexadiene
1,4-cyclohexadiene
292.9; 322.2
a Interval of available experimental values quoted from ref 9 (see text), unless noted otherwise. The TR-PAC values determined in the present work are
given in the text. b Results from the direct homolysis (reaction 2) and from the isodesmic and isogyric reaction (reaction 9 with R′ ) allyl and using the
experimental C(sp3)-H BDE in propene, 371.5 kJ mol-1). The later values are bracketed. c Calculations performed with Dunning’s cc-pVTZ basis set.
d Complete basis set extrapolated results based on the dual (2,3) scheme proposed by Truhlar (see text). 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. e Selected experimental value, from ref 8. f From ref 41. g From
ref 48. h The uncertainty was estimated.
The ground state enthalpies of each parent molecule and radical
were calculated from eq 7,
Analysis of Thermochemical Data
We have not attempted to make a comprehensive critical
analysis of carbon-hydrogen bond dissociation enthalpies for
the molecules investigated in the present study. Instead we have
relied mainly on the compilation by Luo,9 although we have
examined in some detail the data collected by this author. This
option is enough to provide a clear picture of the available
experimental BDE data and to assess their quality.
Table 1 collects literature C-H BDEs for the molecules
studied (displayed in Figure 1) and summarizes the values
obtained in this work by theoretical methods. Relative BDEs,
which provide a clearer picture of BDE trends and are
particularly important in discussing the computational data, are
presented in Table 2.
H ) U + kBT ) Eelec + Ethermal + kBT
(7)
where U is the internal energy, Eelec is the computed electronic
energy, Ethermal is the thermal correction to the internal energy at T
) 298.15 K (which is calculated from the partition function for
each species and includes the zero-point energy correction), and
kB is the Boltzmann constant. For a C-H bond homolysis reaction
(eq 2) the reaction enthalpy ∆rH°, identified with the R-H bond
dissociation enthalpy, was computed from eq 8.
∆rH° ) H(R•) + H(H•) - H(RH)
(8)
The B3LYP/cc-pVTZ calculations were also used to determine
the Mulliken atomic spin densities42-45 for the radical species under
study. It is well-known that this population analysis can prove to
be unreliable and is, by definition, basis set-dependent. Nonetheless,
B3LYP/6-311G** Mulliken spin densities have been successfully
used in the study of heterosubstituded allyl radicals.46 Another factor
that led to the choice of this population analysis is the fact that,
due to its formal simplicity, it is widely used.
Accuracy of Computational Results. As noted in the case
of the allyl radical (Table 1), the R-C-H BDEs calculated from
eq 8, which relies on reaction 2, are usually low limits of the
true values. This problem can be avoided by using isodesmic
and isogyric reactions such as
RH + R′• f R• + R′H
(9)
All calculations were carried out with the Gaussian-03 program.47
In these reactions the number and type of chemical bonds, the
number of carbon atoms in a given state of hybridization, and
the number of electron pairs are equal on both sides of the
reaction, and therefore advantage is taken from error cancella-
tion.5 It is also important to ensure that the number of hydrogen
atoms bonded to each carbon atom in a given state of
hybridization is conserved.22 If these criteria are met, the
differences DH°(R-H) - DH°(R′-H), which are equal to the
enthalpy of reaction 9, are largely method-independent and
usually more accurate than the BDEs obtained from eq 8.
Moreover, these differences can then be used to derive absolute
BDE values by using a highly reliable value for the anchor,
DH°(R′-H).
The bracketed values in Table 1 were obtained from reaction
9 with R′ ) allyl and using the experimental C(sp3)-H BDE
for propene, 371.5 kJ mol-1. In the case of the 2-methylallyl
radical, it is noted that while the BDEs computed from reaction
2 range from 359 to 371 kJ mol-1, the results from reaction 9
agree within 2 kJ mol-1. A similar pattern is observed for the
remaining theoretical results in Table 1: the BDEs derived from
reaction 9 are much less dependent on the theoretical method
than those obtained from the direct homolysis. Analysis of the
(40) Cabral, B. J. C.; Canuto, S. Chem. Phys. Lett. 2005, 406, 300-
305.
(41) Nunes, P. M.; Agapito, F.; Cabral, B. J. C.; dos Santos, R. M. B.;
Simoes, J. A. M. J. Phys. Chem. A 2006, 110, 5130-5134.
(42) Mulliken, R. S. J. Chem. Phys. 1955, 23, 2338-2342.
(43) Mulliken, R. S. J. Chem. Phys. 1955, 23, 2343-2346.
(44) Mulliken, R. S. J. Chem. Phys. 1955, 23, 1833-1840.
(45) Mulliken, R. S. J. Chem. Phys. 1955, 23, 1841-1846.
(46) Wiberg, K. B.; Cheeseman, J. R.; Ochterski, J. W.; Frisch, M. J. J.
Am. Chem. Soc. 1995, 117, 6535-6543.
(47) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb,
M. A.; Cheeseman, J. R.; Montgomery, J. A., Jr.; Vreven, T.; Kudin, K.
N.; Burant, J. C.; Millam, J. M.; Iyengar, S. S.; Tomasi, J.; Barone, V.;
Mennucci, B.; Cossi, M.; Scalmani, G.; Rega, N.; Petersson, G. A.;
Nakatsuji, H.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.;
Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Klene, M.; Li,
X.; Knox, J. E.; Hratchian, H. P.; Cross, J. B.; Bakken, V.; Adamo, C.;
Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.;
Cammi, R.; Pomelli, C.; Ochterski, J. W.; Ayala, P. Y.; Morokuma, K.;
Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Zakrzewski, V. G.; Dapprich,
S.; Daniels, A. D.; Strain, M. C.; Farkas, O.; Malick, D. K.; Rabuck, A.
D.; Raghavachari, K.; Foresman, J. B.; Ortiz, J. V.; Cui, Q.; Baboul, A.
G.; Clifford, S.; Cioslowski, J.; Stefanov, B. B.; Liu, G.; Liashenko, A.;
Piskorz, P.; Komaromi, I.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham,
M. A.; Peng, C. Y.; Nanayakkara, A.; Challacombe, M.; Gill, P. M. W.;
Johnson, B.; Chen, W.; Wong, M. W.; Gonzalez, C.; Pople, J. A. Gaussian-
03; Gaussian, Inc.: Wallingford, CT, 2004.
J. Org. Chem, Vol. 72, No. 23, 2007 8773

Agapito et al.
the discrepancy is smaller than 8 kJ mol-1. In the following
discussion we will use the results from these two methods.
(a) Allyl. The enthalpy of formation of the allyl radical seems
well established as 173.5 ( 1.8 kJ mol-1, which corresponds
to 371.5 ( 1.7 kJ mol-1 for the C(sp3)-H BDE in propene.8
The CBS-Q and CBS-QB3 results derived from the direct
homolysis of the same C-H bond are 361.3 and 364.9 kJ mol-1
,
.
respectively. The B3LYP result is even lower, 352.2 kJ mol-1
A CCSD(T) calculation (371.5 kJ mol-1) is in excellent
agreement with experiment.41
(b) 2-Methylallyl. There are three experimental results for
the C(sp3)-H BDE in isobutene quoted in Luo’s compilation,9
viz. 361 ( 4,49 363 ( 3,50 and 373 kJ mol-1 51
The first was
.
derived from a pyrolysis study of 2-methyl-1-butene and was
in close agreement with the result from a previous shock tube
study.52 Yet, the latter value was recently re-evaluated by its
author as 373 kJ mol-1 51
. The second result quoted above (363
( 3 kJ mol-1) was obtained from a gas-phase kinetic study,50
which also reported the enthalpy of formation of the allyl radical
as 167 ( 3 kJ mol-1, i.e., some 7 kJ mol-1 lower than the
presently accepted value (see above). This suggests that the best
experimental value must be the one recommended by Tsang,
373 kJ mol-1, rather than the one selected by Luo (363 kJ
mol-1).9 Indeed, Tsang’s value is closer to the bracketed data
in Table 1 and to the result derived from CCSD(T), 378.2 kJ
mol-1
.
(c) 1-Methylallyl. There are several experimental values for
the R-C-H BDE in 1-butene quoted in Luo’s compillation,9
ranging from 341 ( 6 to 351 kJ mol-1. The CBS-QB3 result is
358.5 kJ mol-1 (Table 1), in excellent agreement with the one
obtained from CCSD(T) (359.6 kJ mol-1), suggesting that the
experimental values are low limits.
The C(sp3)-H BDE in (E)-2-butene also leads to the enthalpy
of formation of the 1-methylallyl radical. Unfortunately, no
experimental values are available. The BDEs derived from CBS-
QB3 and CCSD(T) are 369.7 and 370.8 kJ mol-1, respectively
(Table 1).
FIGURE 1. Bond lengths (pm) for the radicals and their parent
molecules (in parentheses), calculated with B3LYP/cc-pVTZ.
It is very important to note that the computed BDEs for 1-
and (E)-2-butene are thermodynamically consistent. This can
be demonstrated by taking the enthalpies of formation of the
respective parent molecules, as shown in Figure 2. The quantity
∆ can be calculated as 11.2 kJ mol-1 (CBS-QB3 and CCSD-
(T)) from the difference BDE2 - BDE1. This is in remarkable
agreement with 11.3 kJ mol-1, the result obtained from the
difference between the experimental enthalpies of formation of
1-butene (-0.1 ( 0.9 kJ mol-1) and (E)-2-butene (-11.4 (
1.0 kJ mol-1).4
FIGURE 2. Thermochemical cycle relating the C-H bond dissociation
enthalpies of 1- and (E)-2-butene with their gas-phase standard
enthalpies of formation.
(d) 3-Methyl-1-buten-3-yl. The available experimental values
for the R-C-H BDE in 3-methylbut-1-ene range from 322 to
348 kJ mol-1 9,48,53,54
The CBS-QB3 and CCSD(T) results are
.
DFT and CBS data in Table 1 reveals that the discrepancies
between the BDEs obtained from reactions 2 and 9 are smaller
for CBS-QB3, which is a strong indication that this is the most
accurate of those methods for the systems under study, closely
followed by CBS-Q. It is also noted that, apart from CCSD(T)
calculations, CBS-QB3 is the one that yields the best value for
the C(sp3)-H BDE in propene.
(48) Trenwith, A. B. Trans. Faraday Soc. 1970, 66, 2805-2811.
(49) Trenwith, A. B.; Wrigley, S. P. J. Chem. Soc., Faraday Trans. I
1977, 73, 817-822.
(50) Roth, W. R.; Bauer, F.; Beitat, A.; Ebbrecht, T.; Wu¨stefeld, M.
Chem. Ber. 1991, 124, 1453-1460.
(51) Tsang, W. In Shock WaVes in Chemistry; Lifshitz, A., Ed.; Marcel
Dekker: New York, 1981; pp 59-129.
(52) Tsang, W. Int. J. Chem. Kinet. 1973, 5, 929-946.
(53) Trenwith, A. B. J. Chem. Soc., Faraday Trans. I 1982, 78, 3131-
3136.
The CBS-QB3 bracketed values and the data derived from
CCSD(T) calculations are in excellent agreement, with the
exception of the BDEs for (E)-1,3- and 1,4-pentadiene, and 1,3-
and 1,4-cyclohexadiene (Table 1). However, even in these cases
(54) Luo incorrectly quotes a lower value of 319.7 kJ mol-1, which in
fact corresponds to the C(sp3)-H BDE in 1,4-pentadiene determined by
Trenwith (ref 53). The value for 3-methylbut-1-ene was determined in a
previous work by the same author (ref 48).
8774 J. Org. Chem., Vol. 72, No. 23, 2007

Energetics of the Allyl Group
TABLE 2. Computed r-C-H Bond Dissociation Enthalpies (in kJ mol-1) RelatiWe to the C(sp3)-H BDE in Propene Using the Data
Corresponding to the Direct Homolysis Reaction from Table 1
molecule
propene
radical
CBS-Q
CBS-QB3
B3LYP
CCSD(T)
allyl
0.0
5.6
0.0
6.4
0.0
7.0
0.0
6.7
isobutene
2-methylallyl
1-butene
(E)-2-butene
1-methylallyl
1-methylallyl
-13.5
-0.9
-13.0
-1.8
-17.3
-2.8
-11.9
-0.7
3-methylbut-1-ene
(E)-2-pentene
(E)-1,3-pentadiene
1,4-pentadiene
cyclohexene
3-methyl-1-buten-3-yl
2-penten-4-yl
pentadienyl
-21.2
-16.3
-27.8
-59.4
-14.0
-55.5
-53.5
-21.1
-13.2
-26.6
-54.4
-15.4
-53.6
-53.9
-29.4
-18.2
-25.3
-60.3
-18.4
-55.8
-55.2
-19.8
-11.5
-19.0
-46.5
-13.6
-46.2
-45.2
pentadienyl
cyclohexen-3-yl
cyclohexadienyl
cyclohexadienyl
1,3-cyclohexadiene
1,4-cyclohexadiene
350.4 and 351.7 kJ mol-1, respectively (Table 1), i.e., some 18
kJ mol-1 higher than the selection by Luo.9 However, they are
close to the value recommended by Brocks et al., 348 kJ
From the lifetime obtained for reaction 4, τ2, we derived 5 ×
106 M-1 s-1 for the rate constant of hydrogen abstraction from
cyclohexene (k2), which is in good agreement with a reported
mol-1 55
.
laser flash photolysis value, 5.8 × 106 M-1 s-1 59
.
(e) 2-Penten-4-yl. The R-C-H BDE in (E)-2-pentene,
obtained by CBS-QB3, is 358.3 kJ mol-1. To our knowledge
there are no experimental values for this BDE.
Both the TR-PAC result and the BDE computed from CBS-
QB3 (356.1 kJ mol-1) are higher than the electrochemical value
but in keeping with the complete basis set extrapolated CCSD-
(f) Pentadienyl. The C(sp3)-H BDE in (E)-1,3-pentadiene
ranges from 334 to 347 kJ mol-1.9 The upper limit, selected by
Luo, was recommended in McMillen and Golden’s review,11
and is in good agreement with the CBS-QB3 result, 344.9 kJ
mol-1. However, in this case the result derived from CCSD(T)
(352.5 kJ mol-1) is some 8 kJ mol-1 higher than the CBS-QB3
value (Table 1).
(T) result, 357.9 kJ mol-1
.
(h) Cyclohexadienyl. The literature values for C(sp3)-H
BDE in 1,3-cyclohexadiene vary in a narrow range, viz., 305
to 311 kJ mol-1.9 However, contrary to the information provided
by Luo, none of these is a direct experimental result.
It is noted that the CBS-QB3 result (317.9 kJ mol-1) differs
by 7 kJ mol-1 from the CCSD(T) result (325.3 kJ mol-1).
However, the latter is quite close to our TR-PAC value (329.3
( 5.5 kJ mol-1). In the photoacoustic experiments we used 1,3-
cyclohexadiene concentrations ranging from 0.030 to 0.043 M.
The lifetime obtained for reaction 4, τ2, led to a rate constant
for the hydrogen abstraction from 1,3-cyclohexadiene of k2 )
4 × 107 M-1 s-1. This value is in agreement with a reported
The same radical is also produced by cleaving the C(sp3)-H
bond in 1,4-pentadiene. The corresponding BDE ranges from
320 to 333 kJ mol-1 9,56 Luo’s selection, 321 kJ mol-1, is close
.
to the CBS-QB3 value, 317.2 kJ mol-1. As for the 1,3 isomer,
the result derived from CCSD(T) (325.0 kJ mol-1) is 8 kJ mol-1
higher than the CBS-QB3 value (Table 1).57
As in the case of 1-methylallyl, the thermodynamic consis-
tency of the BDEs for (E)-1,3- and 1,4-pentadiene can be
assessed by using the experimental enthalpies of formation of
the respective parent molecules (Figure 3). The quantity ∆ can
be calculated as 27.7 (CBS-QB3) or 27.5 kJ mol-1 (CCSD(T))
from the difference BDE2 - BDE1. This is in good agreement
with the ∆ value of 29.6 kJ mol-1computed from the difference
between the enthalpies of formation of 1,4-pentadiene (105.7
( 1.1 kJ mol-1) and (E)-1,3-pentadiene (76.1 ( 0.8 kJ mol-1).4
(g) Cyclohexen-3-yl. The only experimental result for
R-C-H BDE available in the literature and quoted by Luo is
343 kJ mol-1. This value was determined through an electro-
chemical cycle by Bordwell and co-workers and its uncertainty
laser flash photolysis result, 4.2 × 107 M-1 s-1 60
.
The cyclohexadienyl radical can also be obtained from 1,4-
cyclohexadiene. The literature values for C(sp3)-H BDE range
from 293 to 322 kJ mol-1 9,61-63
Luo’s selection, 318 ( 5 kJ
.
mol-1, relies on a gas-phase kinetic study by Tsang64 and is in
excellent agreement with the CBS-QB3 result, 317.6 kJ mol-1
.
A BDE value of 312.8 ( 6.1 kJ mol-1 was obtained in our
laboratory from TR-PAC experiments, which were carried out
with 1,4-cyclohexadiene concentrations ranging from 0.032 to
0.036 M. The lifetime calculated for reaction 4, τ2, led to k2 )
5 × 107 M-1 s-1 for the rate constant of hydrogen abstraction
from 1,4-cyclohexadiene, in agreement with a reported laser
flash photolysis value, 5.4 × 107 M-1 s-1 60
.
is no less than 10 kJ mol-1 58
.
In this case, Truhlar’s extrapolation of CCSD(T) energies led
to 326.3 kJ mol-1, 13 kJ mol-1 higher than the experimental
TR-PAC value and some 9 kJ mol-1 higher than the CBS-QB3
result.
TR-PAC experiments in our laboratory led to 349.8 ( 5.6
kJ mol-1 for the same BDE. These experiments were performed
with cyclohexene concentrations ranging from 0.25 to 0.56 M.
(55) Brocks, J. J.; Beckhaus, H.-D.; Beckwith, A. L. J.; Ru¨chardt, C. J.
Org. Chem. 1998, 63, 1935-1943.
(59) Encinas, M. V.; Scaiano, J. C. J. Am. Chem. Soc. 1981, 103, 6393-
6397.
(60) Effio, A.; Griller, D.; Ingold, K. U.; Scaiano, J. C.; Sheng, S. J. J.
Am. Chem. Soc. 1980, 102, 6063-6068.
(61) Griller, D.; Wayner, D. D. M. Pure Appl. Chem. 1989, 61, 717-
724.
(62) Ciriano, M. V.; Korth, H. G.; van Scheppingen, W. B.; Mulder, P.
J. Am. Chem. Soc. 1999, 121, 6375-6381.
(63) It should be pointed out that, as in the case of 1,4-pentadiene (see
ref 57), the older PAC result (ref 61) quoted by Luo was latter reappraised
by Laarhoven et al. (ref 13) and coincides with the most recent PAC value
reported in the literature, 322.2 kJ mol-1 (ref 62).
(64) Tsang, W. J. Phys. Chem. 1986, 90, 1152-1155.
(56) Clark, K. B.; Culshaw, P. N.; Griller, D.; Lossing, F. P.; Martinho
Simo˜es, J. A.; Walton, J. C. J. Org. Chem. 1991, 56, 5535-5539.
(57) It should be noted that Luo’s selection is based on an early PAC
result (ref 56) that depended on wrong assumptions and was latter
reappraised by Laarhoven et al. (ref 13) as 343.0 kJ mol-1. Although the
older value was similar to those obtained through other techniques (namely
from appearance energy measurements reported in the same work),
Laarhoven et al. considered that the PAC experiment cannot be used to
determine this BDE since it is beset by errors resulting from competing
reactions.
(58) Bordwell, F. G.; Cheng, J.-P.; Harrelson, J. A., Jr. J. Am. Chem.
Soc. 1988, 110, 1229-1231.
J. Org. Chem, Vol. 72, No. 23, 2007 8775

Agapito et al.
predict the enthalpies of formation of the isomers66 leads to ∆
) -16.4 kJ mol-1, matching the TR-PAC result.
Hyperconjugation and Resonance Effects
The previous data analysis led to the set of recommended
values collected in Table 3. They are all based on the values
derived from complete basis set extrapolated CCSD(T) calcula-
tions, which in most cases are similar to the CBS-QB3 results.
Those values will now be used to discuss the stability of the
carbon-centered radicals.
Table 4 displays selected C-H BDEs in methane, ethane,
propane, and 2-methylpropane. The BDE trend can be rational-
ized by using different models. One of these models centers
the discussion on the stability of the parent molecules (RH),
rather than on the stability of the radicals (R•), and claims that
the trend is due to a variation of 1,3-repulsive steric interactions
(geminal repulsion).67 This model is able to predict the trend in
Table 4 by using an additive scheme and a set of empirical
parameters calculated from the enthalpies of formation of the
alkanes. Another way to predict the trend in Table 4 is using
the electronegativity concept. For instance, Zavitsas’ group
demonstrated that, in the absence of steric effects, Pauling’s
equation relating electronegativity to bond dissociation enthal-
pies yields accurate BDE values.68 A third model that is often
used to explain the trend in Table 4 is focused on the stability
of the alkyl radicals, discussed in terms of hyperconjugation.
Hyperconjugation can be described as the radical stabilization
due to the overlap between the single-occupied orbital at the
carbon atom where the bond dissociation occurred and a
neighbor C-H bond σ-orbital. This effect leads to an increase
of the electronic density between the two carbon atoms and
therefore to a shorter C-C bond.30 For instance, in the case of
the ethyl radical the C-C bond is 4 pm shorter than the
corresponding bond in ethane.30 In the case of the isopropyl
radical, our calculations revealed that both C-C bonds are also
4 pm shorter than the C-C bonds in propane, indicating that
the radical is stabilized by “double” hyperconjugation.
To discuss the BDE trend in Table 3, we begin by noting
that the resonance stabilization of the allyl radical is evaluated
as 68 kJ mol-1 by comparing the C(sp3)-H BDE in propene,
371.5 kJ mol-1, with the C-H BDE in methane (Table 4).69
This resonance effect is reflected by a decrease of the spin
density in the carbon atom where the bond dissociation occurred
(see below).
The BDE in the allyl radical has been used as the reference
for all the remaining BDEs included in Table 3. Therefore,
negative values of relative BDEs mean that the corresponding
BDE is smaller than the C(sp3)-H BDE in propene and vice
versa. As will be shown below, most of the trends can be
understood on the basis of hyperconjugation and resonance. For
this purpose, Figure 1 and Table 5 will be used. Figure 1
contains C-C bond lengths in the radicals and their parent
molecules, and Table 5 shows Mulliken spin densities in the
allylic moiety of each radical. We note that the atomic spin
densities for the allyl radical are in good agreement with the
experimental and theoretical data reported by Wiberg et al.46
(a) 2-Methylallyl. Interestingly, the C(sp3)-H BDE in
isobutene is 7 kJ mol-1 higher than the C(sp3)-H BDE in
FIGURE 3. Thermochemical cycle relating the C-H bond dissociation
enthalpies of (E)-1,3- and 1,4-pentadiene with their gas-phase standard
enthalpies of formation.
FIGURE 4. Thermochemical cycle relating the C-H bond dissociation
enthalpies of 1,3- and 1,4-cyclohexadiene with their gas-phase standard
enthalpies of formation.
As discussed for 1-methylallyl and pentadienyl radicals, it is
possible to assess the above BDEs through the enthalpies of
formation of 1,3- and 1,4-cyclohexadiene (Figure 4). However,
this exercise is not as simple as in the previous two cases
because there are several discrepant literature values for those
enthalpies of formation. Pedley’s compillation recommends
106.3 ( 0.9 and 100.4 ( 3.1 kJ mol-1 for 1,3- and 1,4-
cyclohexadiene, respectively.4 However, more recent experi-
ments by Steele et al. led to 104.6 ( 0.6 and 104.8 ( 0.6 kJ
mol-1 65
( 3.2 and -0.2 ( 0.8 kJ mol-1, respectively. The TR-PAC
results lead to ∆ ) BDE2 - BDE1 ) -16.5 ( 4.4 kJ mol-1
. These two pairs of experimental data lead to ∆ ) 5.9
,
whereas the theoretical methods imply ∆ ) -0.3 (CBS-QB3)
and 1.0 kJ mol-1 (CCSD(T)).
The enthalpies of formation derived by Steele et al. are
probably more accurate than the values listed by Pedley. These
values imply that 1,3- and 1,4-cyclohexadiene have similar
stabilities, which is consistent with both the results from CBS-
QB3 and complete basis set extrapolated CCSD(T). We feel
therefore inclined to consider that the TR-PAC value is a lower
limit. Nevertheless, a reasonable doubt remains: a simple
exercise using the extended Laidler terms tabulated by Leal to
(66) Leal, J. P. J. Phys. Chem. Ref. Data 2006, 35, 55-76.
(67) Gronert, S. J. Org. Chem. 2006, 71, 1209-1219.
(68) Matsunaga, N.; Rogers, D. W.; Zavitsas, A. A. J. Org. Chem. 2003,
68, 3158-3172.
(69) The comparison should not be made with the C-H BDE in ethane,
because the ethyl radical is stabilized by hyperconjugation.
(65) Afeefy, H. Y.; Liebman, J. F.; Stein, S. E. In NIST Chemistry
WebBook; NIST Standard Reference Database No. 69 (http://webbook.nist-
.gov); Linstrom, P. J., Mallard, W. G., Eds.; National Institute of Standards
and Technology: Gaithersburg, MD, 2005.
8776 J. Org. Chem., Vol. 72, No. 23, 2007

Energetics of the Allyl Group
TABLE 3. Selected Values for the Relative, ∆DH°(C-H), and Absolute, DH°(C-H), r-C-H BDEs (in kJ mol-1), and Recommended
Enthalpies of Formation for the Corresponding Radicalsa
molecule
propene
isobutene
1-butene
radical
∆DH°(C-H)
DH°(C-H)
∆fH°(R•,g)b
allyl
0.0
7
-12
-1
-20
-12
-19
-47
-14
-46
-45
371.5
378
360
371
352
360
353
325
358
325
326
173.5
143
142
141
106
110
211
213
135
212c
213c
2-methylallyl
1-methylallyl
1-methylallyl
3-methyl-1-buten-3-yl
2-penten-4-yl
pentadienyl
(E)-2-butene
3-methylbut-1-ene
(E)-2-pentene
(E)-1,3-pentadiene
1,4-pentadiene
cyclohexene
pentadienyl
cyclohexen-3-yl
cyclohexadienyl
cyclohexadienyl
1,3-cyclohexadiene
1,4-cyclohexadiene
a Estimated uncertainty of ca. (4 kJ mol-1 b Calculated by using ∆fH°(H•,g) ) 217.998 ( 0.006 kJ mol-1 (Cox, J. D.; Wagman, D. D.; Medvedev, V.
.
A. Codata Key Values for Thermodynamics; Hemisphere: New York, 1989) and ∆fH°(RH,g) from ref 4, unless noted otherwise. c ∆fH°(RH,g) from ref 65.
TABLE 4. Absolute, DH°(C-H), and Relative, ∆DH°(C-H),
than producing it from (E)-2-butene. The difference, discussed
above, stems from the fact that (E)-2-butene is 11 kJ mol-1
more stable than 1-butene (see Figure 2) and can be rationa-
lized by using the Laidler scheme.6 Consider the two types of
C-C single bonds in 1- and (E)-2-butene, by decreasing
order of strength (as indicated by bond length data in Figure
1): two C(sp2)-C(sp3) bonds in (E)-2-butene and one in
1-butene; and one C(sp3)-C(sp3) bond in 1-butene. The higher
stability of (E)-2-butene essentially reflects the dif-
ference between the C(sp2)-C(sp3) and the C(sp3)-C(sp3) bond
strengths.
BDEs (in kJ mol-1) in Selected Alkanes
molecule
methane
ethane
propane
radical
DH°(C-H)a
∆DH°(C-H)
methyl
ethyl
isopropyl
tert-butyl
439.1 ( 0.5
423.0 ( 1.7
412.5 ( 1.7
403.8 ( 1.7
0.0
-16.1
-26.6
-35.3
2-methylpropane
a Data from ref 8, except for methane, which is from ref 10.
TABLE 5. Spin Densities at the Carbon Atoms That Define the
Allyl Backbone in the Radicalsa
There is an alternative way to explain the 11 kJ mol-1
difference between the C-H BDEs in 1-butene and (E)-2-
butene (see Figure 1). By cleaving a secondary C-H bond in
1-butene the resulting (unrelaxed) fragment is then stabil-
ized by both hyperconjugation and resonance, whereas the
fragment formed from (E)-2-butene (by cleaving a primary C-H
bond) is only stabilized by resonance. In other words,
when the C-H bonds in 1-butene and (E)-2-butene are cleaved
the resulting fragments relax to the ground state of the
1-methylallyl radical, but this relaxation is more exothermic
for the fragment formed from 1-butene than that from (E)-2-
butene.
molecule
propene
isobutene
1-butene
(E)-2-butene
3-methylbut-1-ene
(E)-2-pentene
(E)-1,3-pentadiene
1,4-pentadiene
cyclohexene
radical
C1
C2
C3
allyl
0.643 -0.210 0.643
0.669 -0.201 0.617
0.597 -0.202 0.637
0.637 -0.202 0.597
2-methylallyl
1-methylallyl
1-methylallyl
3-methyl-1-buten-3-yl 0.575 -0.203 0.624
2-penten-4-yl
pentadienyl
0.593 -0.195 0.593
0.466 -0.177 0.487
0.487 -0.177 0.466
0.605 -0.197 0.605
0.392 -0.160 0.520
0.520 -0.160 0.392
pentadienyl
cyclohexen-3-yl
1,3-cyclohexadiene cyclohexadienyl
1,4-cyclohexadiene cyclohexadienyl
a C1 is the carbon atom where the bond was cleaved. See Figure 1.
(c) 3-Methyl-1-buten-3-yl. The R-C-H BDE in 3-methylbut-
1-ene is 20 kJ mol-1 lower than the C(sp3)-H BDE in propene.
Table 5 indicates a higher degree of delocalization than in the
case of allyl. On the other hand, Figure 1 shows that the C1-
Me and C1-Me′ in the radical are 3-4 pm shorter than the
corresponding bonds in the parent molecule, suggesting “double”
hyperconjugation.
(d) 2-Penten-4-yl. The R-C-H BDE in (E)-2-pentene is 12
kJ mol-1 lower than the C(sp3)-H BDE in propene. The data
in Figure 1 show a shortening of 4 pm in the C1-Me bond
(relative to the corresponding bond in the parent molecule),
indicating hyperconjugation. Yet, no significant shortening is
observed in the C1-C2 bond in (E)-2-pentene.
It is interesting to note that the relative C-H BDEs in
1-butene and (E)-2-pentene are similar (-12 kJ mol-1). In both
cases we have used hyperconjugation to explain this variation.
Recall that hyperconjugation was also invoked to justify the
C-H BDE in ethane (-16 kJ mol-1), relative to the C-H BDE
in methane.
A second comparison is provided by the “double” hypercon-
jugated 3-methyl-1-buten-3-yl and isopropyl radicals. The
relative C-H BDE in 3-methylbut-1-ene (-20 kJ mol-1) can
be regarded as the combination of two hyperconjugations, the
propene. This is in keeping with the data in Table 5: the spin
density in the carbon atom where dissociation occurred (C1) is
higher than in the case of allyl, indicating a lower electron
delocalization. This is probably related to an anisotropy in the
electronic distribution induced by the methyl group, which
impairs delocalization. Evidence of the anisotropy is provided
by the fact that the allylic C-C bond lengths are not equal
(Figure 1). It is also suggested by the observation that the shorter
allylic C-C bond is coplanar with a C-H bond of the methyl
group.
(b) 1-Methylallyl. The R-C-H BDE in 1-butene is 12 kJ
mol-1 lower than the C(sp3)-H BDE in propene. Indeed, Table
5 shows that the spin density in C1 is lower than that in allyl,
indicating a higher electron delocalization. In addition, it is noted
in Figure 1 that the C1-Me bond length in 1-methylallyl is 4
pm shorter than the corresponding bond in 1-butene, suggesting
that hyperconjugation is involved.
The 1-methylallyl radical is also formed by cleaving
the C(sp3)-H bond in (E)-2-butene. However, as shown in
Table 3, the enthalpy of this process is only 1 kJ mol-1 lower
than the C(sp3)-H BDE in propene. In other words, producing
the 1-methylallyl radical from 1-butene costs 11 kJ mol-1 less
J. Org. Chem, Vol. 72, No. 23, 2007 8777

Agapito et al.
first of which contributes with -12 kJ mol-1 and the second
with -8 kJ mol-1. In the case of propane, the relative C-H
BDE in propene is -27 kJ mol-1 and the individual contribu-
tions are -16 and -11 kJ mol-1
.
In summary, the hyperconjugation contributions to the
stability of alkyl and allyl derivatives are similar. However, they
are not equal. The hyperconjugation effect is more important
for alkyl radicals than for allyl radicals because in the latter the
electron is delocalized and therefore less available to hyper-
conjugate.
(e) Pentadienyl. The C(sp3)-H BDE in (E)-1,3-pentadiene
is 19 kJ mol-1 lower than the BDE for the corresponding bond
in propene. In both cases the radicals are resonance-stabilized
but, as expected, the stabilization is higher in the five-carbon-
atom system. This is in keeping with the data in Table 5: the
spin density in the carbon atom where dissociation occurred
(C1) is lower than that in the case of allyl, indicating a higher
electron delocalization.
FIGURE 5. C-H bond dissociation enthalpies, (DH°(C-H)) vs
Mulliken atomic spin densities (FM) at the radical center for selected
radicals: DH°(C-H)) 163.4FM + 206.3 (r ) 0.967).
served (Figure 5). This supports the view that the BDEs are
mainly determined by the radical stabilization through electron
delocalization. Similar correlations have been reported, for
instance, by Brocks et al.,55 and involved plots of either radical
stabilization energies or BDEs against esr-derived hyperfine
coupling constants (which can be related to the spin density at
the radical center, provided that the radical is planar). An
advantage of the correlation in Figure 5 is that spin densities
can be directly computed for any radical, regardless of its
geometry.
The pentadienyl radical can also be produced by cleaving
the C(sp3)-H BDE in 1,4-pentadiene, which costs 28 kJ mol-1
less than when using the 1,3 isomer as the starting point.
As noted in Figure 3, the difference results from the relative
stabilities of the isomers, i.e., (E)-1,3-pentadiene is about 30
kJ mol-1 more stable than 1,4-pentadiene. The existence
of conjugated double bonds in the 1,3 isomer, involving a
C(sp2)-C(sp2) bond, may be responsible for its relative stability,
as suggested by the application of a recent set of extended
Laidler (bond enthalpy) terms that includes a term for conju-
gated double bonds.66 This is consistent with the fact that the
conjugated C2-C3 bond in (E)-1,3-pentadiene is 6 pm
shorter than the C2-C3 or C3-C4 bonds of 1,4-pentadiene (see
Figure 1).
The plot in Figure 5 (correlation coefficient of 0.967) includes
the BDE data in Tables 3 and 4. The correlation fits quite well
the values for the alkyl and allyl radicals but not the values for
the dienes.
(f) Cyclohexen-3-yl. The R-C-H BDE in cyclohexene is 14
kJ mol-1 lower than the C(sp3)-H BDE in propene. This value
is similar to the results computed for 1-butene and (E)-2-pentene,
suggesting that the cyclohexen-3-yl radical is stabilized by
hyperconjugation and resonance. The bond length variations in
Figure 1 and the spin densities in Table 5, which are comparable
to those observed for the 2-penten-4-yl radical, support this
conclusion.
(g) Cyclohexadienyl. The R-C-H BDEs in 1,3- and 1,4-
cyclohexadiene are about 46 kJ mol-1 lower than the C(sp3)-H
BDE in propene. This value could be expected having in mind
that the stabilization of pentadienyl and cyclohexadienyl radicals
should be similar. The only difference is that (E)-1,3-pentadiene
is 30 kJ mol-1 more stable than the 1,4 isomer, whereas the
enthalpies of formation of 1,3- and 1,4-cyclohexadiene are
identical.
Conclusions
By using quantum chemistry calculations and time-resolved
photoacoustic calorimetry, we have attempted to determine
carbon-hydrogen bond dissociation enthalpies of selected
alkenes within chemical accuracy (ca. 4 kJ mol-1), aiming to
improve our understanding of the stability of allylic radicals.
By taking the C(sp3)-H BDE in propene as a reference, we
have concluded that one methyl group bonded to C3 in propene
(i.e., 1-butene) leads to a decrease of 12 kJ mol-1 and that a
second methyl group bonded to C3 (3-methylbut-1-ene) further
decreases the BDE by 8 kJ mol-1. Interestingly, however, when
the methyl group is bonded to C2 in propene (isobutene), an
increase of 7 kJ mol-1 is observed. Finally, a methyl group
bonded to C1 in propene (2-butene) has essentially no effect
(-1 kJ mol-1).
Understanding the different stabilities of the cyclohexadiene
isomers is slightly more complex than in the case of the
pentadienes. Consider the three types of C-C single bonds in
1,3- and 1,4-cyclohexadiene, by decreasing order of strength
(as indicated by bond length data in Figure 1): one conjugated
C(sp2)-C(sp2) bond in 1,3-cyclohexadiene; two C(sp2)-C(sp3)
bonds in 1,3-cyclohexadiene and four in 1,4-cyclohexadiene;
and one C(sp3)-C(sp3) bond in 1,3-cyclohexadiene. Therefore,
the stabilizing effect of the conjugated C(sp2)-C(sp2) bond in
the 1,3 isomer is apparently offset by a much weaker C(sp3)-
C(sp3) bond.
The previous conclusions were used to rationalize other
relative C-H BDEs. For instance, the R-C-H BDEs in (E)-
2-pentene and cyclohexene (one alkyl group bonded to C1 and
one to C3 in both cases) can be estimated as -13 kJ mol-1, in
keeping with the computed results, -12 and -14 kJ mol-1
,
respectively.
The above values can be rationalized by assuming that the
BDE changes are solely due to the stabilization of the corre-
sponding radicals (relative to the stabilization of the allyl
radical). In other words, to explain those BDEs (and therefore
to predict new data), one does not need to consider the
thermodynamic stabilities of the parent compounds. Indeed the
relative stabilization of the simple alkenes involved in the
present study correlates well with the spin density distribution,
Correlation between BDEs and Spin Densities. By plot-
ting the BDEs in Table 3 against the Mulliken atomic spin
density at C1 of each radical, a linear correlation is ob-
8778 J. Org. Chem., Vol. 72, No. 23, 2007

Energetics of the Allyl Group
indicating that hyperconjugation and π-delocatization can be
invoked to understand the BDE trend.
Acknowledgment. P.M.N. and F.A. thank Fundac¸a˜o para a
Cieˆncia e a Tecnologia, Portugal, for a postdoctoral (SFRH/
BPD/26677/2005) and a Ph.D. (SFRH/BD/22854/2005) grant,
respectively.
For the dienes, however, the radical-based justification of the
BDE trends does not hold, in keeping with the fact that these
data do not correlate with the spin density at the radical center
(with the probably fortuitous exception of 1,3-cyclohexadiene).
The BDE values can only be understood by considering the
thermodynamic stabilities of the parent compounds.
Supporting Information Available: Tables containing com-
puted optimized geometries and total energies for radicals and parent
compounds. This material is available free of charge via the Internet
at http://pubs.acs.org.
JO701397R
J. Org. Chem, Vol. 72, No. 23, 2007 8779