Kinetics and equilibrium constants for reactions of α-phenyl- substituted cyclopropylcarbinyl radicals

Article abstract of DOI:10.1021/ja991114h

Laser-flash photolysis methods were used to determine Arrhenius functions for cyclizations of the 4,4-diphenyl-3-butenyl (2) and trans-4- phenyl-3-butenyl (5) radicals to the 1,1-diphenylcyclopropylcarbinyl (1) and 1-phenylcyclopropylcarbinyl (4) radicals, respectively. At 20 °C, the cyclization rate constants are 1.7 x 10⁷ and 5.4 x 10⁶ s^-1. Equilibrium constants for the two processes were estimated and evaluated with thermochemical data and via computational methods, and Arrhenius functions for the ring-opening reactions of the cyclopropylcarbinyl radicals were calculated. The cyclization reactions of 2 and 5 are strongly enthalpy controlled. Production of radicals 1 and 2 from the corresponding tert- butylperoxy esters in the presence of Et₃SnH gave diphenylcyclopropylmethane and 1,1-diphenyl-1-butene from H-atom trapping of radicals 1 and 2 and 4- phenyl-1,2-dihydronaphthalene which derives from the product radical formed by addition of the radical moiety in 2 to the cis-phenyl group. Rate constants for the latter cyclization of 2 and for reactions of radicals 1 and 2 with Et₃SnH were obtained from the indirect kinetic studies.

Full text of DOI:10.1021/ja991114h

2988
J. Am. Chem. Soc. 2000, 122, 2988-2994
Kinetics and Equilibrium Constants for Reactions of
R-Phenyl-Substituted Cyclopropylcarbinyl Radicals
Thomas A. Halgren,*,1a John D. Roberts,*,1b John H. Horner,1c Felix N. Martinez,1c
Christopher Tronche,1c and Martin Newcomb*,1c
Contribution from Gates and Crellin Laboratories of Chemistry, California Institute of Technology,
Pasadena, California 91125, Department of Chemistry, Wayne State UniVersity, Detroit, Michigan 48202,
and Molecular Systems Department, Merck Research Laboratories, Rahway, New Jersey 07065
ReceiVed April 8, 1999. ReVised Manuscript ReceiVed February 2, 2000
Abstract: Laser-flash photolysis methods were used to determine Arrhenius functions for cyclizations of the
4,4-diphenyl-3-butenyl (2) and trans-4-phenyl-3-butenyl (5) radicals to the 1,1-diphenylcyclopropylcarbinyl
(1) and 1-phenylcyclopropylcarbinyl (4) radicals, respectively. At 20 °C, the cyclization rate constants are 1.7
× 107 and 5.4 × 106 s-1. Equilibrium constants for the two processes were estimated and evaluated with
thermochemical data and via computational methods, and Arrhenius functions for the ring-opening reactions
of the cyclopropylcarbinyl radicals were calculated. The cyclization reactions of 2 and 5 are strongly enthalpy
controlled. Production of radicals 1 and 2 from the corresponding tert-butylperoxy esters in the presence of
Et3SnH gave diphenylcyclopropylmethane and 1,1-diphenyl-1-butene from H-atom trapping of radicals 1 and
2 and 4-phenyl-1,2-dihydronaphthalene which derives from the product radical formed by addition of the
radical moiety in 2 to the cis-phenyl group. Rate constants for the latter cyclization of 2 and for reactions of
radicals 1 and 2 with Et3SnH were obtained from the indirect kinetic studies.
The 1,1-diphenylcyclopropylcarbinyl radical (1) and its
objectives similar to those originally presented for 1. In a report
focusing on the utility of “benzylic” cyclopropylcarbinyl radicals
as radical clocks in mechanistic studies, Bowry et al. showed
that the equilibrium between 4 and 5 favors the cyclic benzylic
radical 4 and determined a rate constant for cyclization of 5 at
42 °C by an isotopic scrambling approach.4 More recently,
Beckwith and Bowry determined Arrhenius parameters for ring
opening of 4 and cyclization of 5 by competition kinetics
employing nitroxyl radical trapping.5 The extent of resonance
stabilization of a radical by a cyclopropyl group was addressed
experimentally by Walton via low-temperature ESR studies of
methylene rotation in the cyclopropylcarbinyl radical.6 In
addition, high-level calculations of the cyclopropylcarbinyl
radical, made possible by the small number of atoms and the
rigidity of the ring, have been carried out.7,8
acyclic isomer, the 4,4-diphenyl-3-butenyl radical (2), were the
subjects of a report by Halgren et al. three decades ago.2 The
objectives of the work were to determine whether 1 and 2 were
discrete species or resonance forms of a nonclassical radical
and, if discrete species, to evaluate the relative stabilities and
reactivities of 1 and 2. The first point was resolved in favor of
discrete species by analyses of product distributions from
reactions of the radicals with hydrogen-atom transfer agents.
Kinetic models involving rapid equilibration of 1 and 2 with
relatively slow and irreversible cyclization of radical 2 to radical
3 were consistent with the product ratios, but the model of
reactions from a nonclassical radical required implausible kinetic
and thermodynamic values.3 The second objective was ac-
complished by deriving Arrhenius parameters for absolute and
relative kinetic quantities of interest from a detailed mechanistic
analysis,3 but the absolute rate constants and the equilibrium
constant for equilibration of 1 and 2 were rendered uncertain
by the need to apply thermochemical assumptions that could
not be independently validated.
Despite recent related work, the equilibrium between radicals
1 and 2 and the rates of the reactions have not been addressed
since the early studies.2,3 We report here a combination of laser-
flash photolysis (LFP) kinetic measurements, computations, and
thermochemical analysis that provides this information. The
kinetics and equilibrium between radicals 4 and 5 were also
(4) Bowry, V. W.; Lusztyk, J.; Ingold, K. U. J. Chem. Soc., Chem.
Commun. 1990, 923-925.
Cyclopropylcarbinyl radicals have been the focus of numerous
studies in the intervening years, some of which have had
(5) Beckwith, A. L. J.; Bowry, V. W. J. Am. Chem. Soc. 1994, 116,
2710-2716.
(1) (a) Merck & Co., Inc. Current address: Schrodinger, Inc., One
Exchange Place, Suite 604, Jersey City, NJ 07302. (b) California Institute
of Technology. (c) Wayne State University.
(2) Halgren, T. A.; Howden, M. E. H.; Medof, M. E.; Roberts, J. D. J.
Am. Chem. Soc. 1967, 89, 3051-3052.
(3) Halgren, T. A. Ph.D. Thesis, California Institute of Technology, 1968.
(6) Walton, J. C. Magn. Reson. Chem. 1987, 25, 998-1000.
(7) Martinez, F. N.; Schlegel, H. B.; Newcomb, M. J. Org. Chem. 1996,
61, 8547-8550. Martinez, F. N.; Schlegel, H. B.; Newcomb, M. J. Org.
Chem. 1998, 63, 3618-3623.
(8) Smith, D. M.; Nicolaides, A.; Golding, B. T.; Radom, L. J. Am. Chem.
Soc. 1998, 120, 10223-10233.
10.1021/ja991114h CCC: $19.00 © 2000 American Chemical Society
Published on Web 03/21/2000

R-Phenyl-Substituted Cyclopropylcarbinyl Radicals
J. Am. Chem. Soc., Vol. 122, No. 13, 2000 2989
Figure 1. Time-resolved spectra showing formation of 4 and 1
following irradiation of 7 and 6, respectively. (A) Traces from
irradiation of 7 at 60, 100, 180, and 500 ns with data at 20 ns subtracted
to give a baseline. (B) Traces from irradiation of 6 at 34, 54, 74, 94,
and 134 ns with data at 14 ns subtracted to give a baseline. The symbols
in the late-time spectra show the monitoring wavelengths.
Figure 2. Rate constants for cyclization of radicals 2 (squares) and 5
(circles). The lines are the Arrhenius functions in Table 1.
Table 1. Temperature Dependent Functions for Cyclizations, Ring
Openings, and Equilibria
b
reaction temp dependent functiona k(20) or K(20)
source
addressed by the same approach in order to place the values
obtained for the diphenyl-substituted system in context.
2 f 1
(10.67 ( 0.38) -
(4.59 ( 0.52)/θ
12.3 - 12.4/θ
1.7 × 107 s-1 this work, LFP
1 f 2
2 a 1
5 f 4
1.1 × 103 s-1 this work, derived
Results
-1.6 + 7.8/θ
1.7 × 104
ref 3
(11.41 ( 0.19) -
(6.26 ( 0.26)/θ
13.3 - 11.4/θ
-1.9 + 5.1/θ
12.1 - 11.1/θ
(13.04 ( 0.10) -
(6.99 ( 0.09)/θ
-0.94 - 4.11/θ
5.4 × 106 s-1 this work, LFP
Direct Kinetic Studies. Direct studies of the cyclizations of
radicals 2 and 5 were measured by conventional LFP methods
employing the PTOC ester9,10 radical precursors 6 and 7, both
of which were prepared from the corresponding known car-
boxylic acids, from reaction of the acid chlorides with the
sodium salt of N-hydroxypyridine-2-thione.10 Because PTOC
esters are thermally unstable and sensitive to UV light,
compounds 6 and 7 were characterized only by NMR spectros-
copy. PTOC esters are excellent radical sources for LFP studies
because they have a strong long-wavelength absorbance at λmax
about 360 nm and are efficiently cleaved by 355 nm light from
a Nd:YAG laser.11 These features require dilute solutions of
precursors in LFP studies and the use of a flow-cell assembly.
The initial homolysis of 6 or 7 gives an acyloxyl radical, which
decarboxylates rapidly on the nanosecond time scale,12 and the
2-pyridinethiyl radical (8). Radical 8 has a long wavelength
absorbance with λmax at 490 nm13 but does not absorb strongly
between 310 and 350 nm, the region where the di- and
monophenyl benzylic radicals 1 and 4 were expected to absorb.14
4 f 5
5 a 4
10 f 9
9 f 10
6.1 × 104 s-1 this work, derived
80
ref 5
6.5 × 103 s-1 see text
6.6 × 107 s-1 ref 29
10 a 9
1.0 × 10-4
this work, derived
a Log k for rate constants or log K for equilibria. Stated errors are
2σ. θ ) 2.3RT kcal/mol. b Rate or equilibrium constant at 20 °C.
previously described for radical 4 formed “instantly” from
photolysis of a benzene solution of di-tert-butyl peroxide and
benzylcyclopropane.4
Kinetics of the cyclizations were studied over a temperature
range of 4-48 °C. The results are listed in the Supporting
Information and shown graphically in Figure 2. Both cyclizations
are reversible, but the cyclic products are strongly favored at
equilibrium, and cyclization of radical 2 to give radical 3 is
about 2 orders of magnitude slower than cyclization of 2 to 1
(see below). Therefore, the observed kinetics are only those for
the cyclization reactions. Arrhenius parameters for the cycliza-
tions are collected in Table 1 along with other rate constants
and equilibrium constants discussed later. At 20 °C, the ring-
closure rate constants are 1.7 × 107 s-1 for 2 and 5.4 × 106 s-1
for 5.
Following 355 nm laser irradiation of the PTOC esters 6 and
7, the expected UV signals for radicals 1 and 4, produced by
3-exo cyclizations of 2 and 5, grew in smoothly. Benzylic radical
4 had maxima at 312 and 322 nm, and dibenzylic radical 1 had
λmax at 334 nm. Time-resolved spectra are shown in Figure 1.
The spectrum in Figure 1A is in good agreement with that
With the precise LFP-determined rate constants for cyclization
of radicals 2 and 5 to radicals 1 and 4, respectively, rate
constants for the corresponding ring-opening reactions can be
calculated from temperature-dependent functions for the equi-
librium constants. Such a function for equilibration of radicals
1 and 2, derived in the original study of this system,3 is listed
in Table 1. A function for the equilibration of radicals 4 and 5
can be computed from the results of Beckwith and Bowry, who
determined rate constants for both reactions by nitroxyl radical
trapping,5 and this is also listed. Table 1 also contains the
temperature-dependent functions for the parent radical system
(9 and 10). The Arrhenius function for ring opening of radical
9 was recently modified to incorporate refined values for the
kinetics of H-atom transfer from reactive trapping agents.15 The
Arrhenius function for cyclization of 10 derives from competi-
(9) The acronym PTOC is derived from pyridine-2-thioneoxycarbonyl.
(10) Barton, D. H. R.; Crich, D.; Motherwell, W. B. Tetrahedron 1985,
41, 3901-3924.
(11) For early LFP applications of PTOC esters in kinetic studies, see:
Bohne, C.; Boch, R.; Scaiano, J. C. J. Org. Chem. 1990, 55, 5414-5418.
Ha, C.; Horner, J. H.; Newcomb, M.; Varick, T. R.; Arnold, B. R.; Lusztyk,
J. J. Org. Chem. 1993, 58, 1194-1198.
(12) Falvey, D. E.; Schuster, G. B. J. Am. Chem. Soc. 1986, 108, 7419-
7420. Hilborn, J. W.; Pincock, J. A. J. Am. Chem. Soc. 1991, 113, 2683-
2686. Bockman, T. M.; Hubig, S. M.; Kochi, J. K. J. Am. Chem. Soc. 1996,
118, 4502-4503.
(13) Alam, M. M.; Watanabe, A.; Ito, O. J. Org. Chem. 1995, 60, 3440-
3444.
(14) Chatgilialoglu, C. In Handbook of Organic Photochemistry; Scaiano,
J. C., Ed.; CRC Press: Boca Raton, FL, 1989; Vol. 2, pp 3-11.
(15) Newcomb, M.; Choi, S. Y.; Horner, J. H. J. Org. Chem. 1999, 64,
1225-1231.

2990 J. Am. Chem. Soc., Vol. 122, No. 13, 2000
Halgren et al.
tive deuterium scrambling studies of the homoallyl radical16 and
has been corrected for the now accepted values for Bu3SnH
trapping of primary alkyl radicals.17
kcal/mol in comparison to the unsubstituted radicals. Because
the homoallyl radical (10) is favored by 4.1 kcal/mol over the
cyclopropylcarbinyl radical (9) (Table 1), the enthalpic prefer-
ence for cyclic radical 5 over radical 4 should be about 6 kcal/
mol, in good agreement with the value of 6.3 kcal/mol in Table
1.
C6H5CH2CH3 + H2CdCH2 f
CH3CH3 + C6H5CHdCH2 (1)
Thermochemical Analysis. A thermochemical analysis of
the unsubstituted, monophenyl-substituted, and diphenyl-
substituted radical systems was performed to evaluate the
consistency of the temperature-dependent functions for the
equilibrium constants in Table 1. From the bond dissociation
energies (BDEs) of methane, ethane, toluene, phenylethane,
diphenylmethane, and 1,1-diphenylethane,18 phenyl group sub-
stitution results in a radical stabilization of 15-16 kcal/mol,
and substitution of a second phenyl group provides an additional
4-7 kcal/mol stabilization (Table S15 in the Supporting
Information). Some inconsistency is apparent in the measured
values; we employ BDE values of 101 kcal/mol for ethane, 88.5
kcal/mol for toluene, 86 kcal/mol for phenylethane, 82 kcal/
mol for diphenylmethane, and 80 kcal/mol for diphenylethane
for our analysis.
In comparison to a methyl group, a cyclopropyl group also
stabilizes a radical center. In the cyclopropylcarbinyl radical,
this stabilization is about 3 kcal/mol as determined from both
measured (Table S15)18 and high-level G219 computed BDE
values for ethane and methylcyclopropane; the G2 results are
100.8 and 98.0 kcal/mol, respectively.20 The physical basis for
this stabilization is provided by low-temperature ESR studies
of the rotational barrier in 9 (2.7 kcal/mol)6 and by three
reasonably sophisticated calculations of that barrier (3.3-3.5
kcal/mol).8 In the case of radicals 1 and 4, the well-known effect
of “saturation” will attenuate the cyclopropyl group stabilization.
In addition, our B3LYP/6-31G* calculations indicate that the
minimum-energy conformation of 1 has the ring twisted about
47° from the bisected structure,21 unlike radicals 9 and 4 which
have “bisected” minima. Overall, we assume a 3 kcal/mol
stabilization by the cyclopropyl group in 9, a 2 kcal/mol
stabilization in 4 and a 1 kcal/mol stabilization in 1. This gives
net stabilizations of the phenyl groups of 14 kcal/mol for 9 f
4 and 5 kcal/mol for 4 f 1.
C6H5CH2CH3 + C6H5CHdCH2 f
CH3CH3 + (C6H5)2CdCH2 (2)
The effect of the second phenyl ring on the stability of the
double bond in the acyclic radical 2 should be smaller.
Unfortunately, consistent thermochemical data for the isodesmic
reaction in eq 2 are not available.23,24 We estimated the
incremental stabilization of the second phenyl group by comput-
ing the relative energies for the processes in eqs 1 and 2. Results
are given in the Supporting Information. The calculations
consistently overestimated the effect of monophenyl substitution,
but B3LYP/6-31G* calculations, B3LYP/cc-pVTZ(-f) calcula-
tions, and high-quality localized MP2/cc-pVTZ(-f)25 calculations
showed a much smaller role for the second substitution.
Assuming that the differential stabilization of the second phenyl
group in the alkenes is 2 kcal/mol, 1 should be stabilized relative
to 2 by 3 kcal/mol more than is 4 relative to 5, in good
agreement with the enthalpic difference of 2.7 kcal/mol between
the corresponding temperature-dependent functions for the
equilibria in Table 1.
Indirect Kinetic Studies. Radicals 1 and 2 were produced
from their respective tert-butylperoxy esters 11 and 12 in the
presence of trapping agents, and both “in-cage” and “out-of-
cage” radical-derived products were characterized3 (see the
scheme in the Supporting Information). Scheme 1 shows the
reactions and products from diffusively free radicals. Peroxy
ester 12 had a half-life of 150 min at 110 °C, whereas 11 had
a half-life of about 100 min at 25 °C; therefore, studies from
the two radical sources at a common temperature were not
possible. Complex mixtures were obtained with the relatively
poor hydrogen atom donor, 1,4-cyclohexadiene, apparently
because of production of high concentrations of labile 1,4-
cyclohexadienyl radicals that reacted by recombination and
disproportionation with radicals produced in the peroxy ester
fragmentation. Nonetheless, the product ratios could be ac-
counted for computationally with reasonable assumptions.3
Details of the product studies are given in the Supporting
Information.
The effect of phenyl substitution on the stability of ring-
opened radical 5 was evaluated with the isodesmic reaction in
eq 1. From heats of formation,22 the phenyl group stabilizes
the double bond by 4.4 kcal/mol. Offsetting this quantity against
the estimated radical-center stabilization of 14 kcal/mol in
radical 4 results in the estimate that the net effect of phenyl-
substitution should be to favor radical 4 over radical 5 by 10
(23) Thermochemical estimates vary considerably. For example, Fischer
and co-workers used measured and assumed values for BDEs and heats of
formation to estimate the exothermicities of methyl radical additions to
alkenes. Comparisons between (i) additions to ethene and styrene and (ii)
additions to styrene and 1,1-diphenylethene are germane to the thermo-
chemistry we are attempting to address. Differences of 10.7 and 2.5 kcal/
mol for processes i and ii, respectively, were reported in 1995 (Wu, J. Q.;
Fischer, H. Int. J. Chem. Kinet. 1995, 27, 167-179), in good agreement
with the thermochemical differences we discuss. In ref 24, however, the
same differences were listed as 11.7 and 7.9 kcal/mol, respectively. The
latter value appears to be out of line; it can be traced mainly to a difference
of about 6 kcal/mol in the estimated values for the heat of formation of
1,1-diphenylethene used in the two works.
(24) Zytowski, T.; Fischer, H. J. Am. Chem. Soc. 1997, 119, 12869-
12878.
(25) Friesner, R. A.; Murphy, R. B.; Beachy, M. D.; Ringnalda, M. N.;
Pollard, W. T.; Dunietz, B. D.; Cao, Y. J. Phys. Chem. A 1999, 103, 1913-
1928. Beachy, M. D. Ph.D. Thesis, Columbia University, 1998. Murphy,
R. B.; Pollard, W. T.; Friesner, R. A. J. Chem. Phys. 1997, 106, 5073-
5084.
(16) Effio, A.; Griller, D.; Ingold, K. U.; Beckwith, A. L. J.; Serelis, A.
K. J. Am. Chem. Soc. 1980, 102, 1734-1736.
(17) Chatgilialoglu, C.; Ingold, K. U.; Scaiano, J. C. J. Am. Chem. Soc.
1981, 103, 7739-7742.
(18) (a) Berkowitz, J.; Ellison, G. B.; Gutman, D. J. Phys. Chem. 1994,
98, 2744-2765. (b) McMillen, D. F.; Golden, D. M. Annu. ReV. Phys. Chem.
1982, 33, 493-532. (c) Rossi, M.; McMillen, D. F.; Golden, D. M. J. Phys.
Chem. 1984, 88, 5031-5039.
(19) The G2 (Gaussian-2) method was found to give a mean absolute
error of only 1.3 kcal/mol for a test set of 125 well-characterized energy
differences; see: Curtiss, L. A.; Raghavachari, K.; Trucks, G. W.; Pople J.
A. J. Phys. Chem. 1990, 94, 7221-7230.
(20) Schlegel, H. B. Private communication of unpublished results. We
are grateful to Prof. Schlegel for providing us with this information.
(21) The structure of 1 was originally computed by Prof. K. N. Houk
and D. Sawicka to whom we are grateful: Houk, K. N.; private com-
munication to JDR 1998.
(22) CRC Handbook of Chemistry and Physics, 79th ed.; Lide, D. R.,
Ed.; CRC Press: Boca Raton, 1998; pp 5-5 to 5-60.

R-Phenyl-Substituted Cyclopropylcarbinyl Radicals
J. Am. Chem. Soc., Vol. 122, No. 13, 2000 2991
Scheme 1
3.26 In practice, the data from decomposition of peroxy ester
12 are not useful, however. The ratio of products 14 to 13
decreased as the tin hydride concentration increased (Figure 3A);
this is not possible unless alkene 14 was consumed in a
secondary reaction. We assume that hydrostannation occurred
at the elevated temperatures, resulting in loss of 14.
At the lower temperatures involved in the thermolyses of
peroxy ester 11, product destruction in secondary reactions
apparently was not a problem. The ratio of products (13/14)
increased smoothly as a function of tin hydride concentration
(Figure 3B). Equation 3 describes the kinetics where the rate
SnH
(13/14) ) (kT1 k /kr kT2SnH) + (kT1SnH/kr)[Et3SnH]m (3)
c1
constants listed are those in Scheme 1 and [Et3SnH]m is the
average concentration of tin hydride.26 Using the slopes of the
(13/14) ratios at 35 and 10 °C (Table S11 in the Supporting
Information) gives the Arrhenius function for Et3SnH trapping
of radical 1 relative to ring opening shown in eq 4. Division of
log((kT1SnH/kr)/ M-1) ) -4.62 + 4.61/θ
(4)
the intercepts by the slopes at each temperature gives the
Arrhenius function for Et3SnH trapping of radical 2 relative to
cyclization shown in eq 5. Combining the relative Arrhenius
log((kT2SnH/kc1)/M-1) ) -1.80 + 1.68/θ
(5)
functions in eqs 4 and 5 and the absolute Arrhenius functions
for ring opening of radical 1 and cyclization of 2, respectively,
one computes the absolute Arrhenius functions for reactions of
Et3SnH with the two radicals that are given in eqs 6 and 7. The
values for reaction of radical 2 with Et3SnH are similar to those
for reactions of alkyl radicals with Bu3SnH,17 indicating that
the results are reliable. The rate constant for reaction of Et3-
SnH with radical 1 at 20 °C is 70 M-1 s-1
.
Et3SnH reaction with 1:
log(kT1/M-1 s-1) ) 7.65 - 7.8/θ (6)
log(kT2/M-1 s-1) ) 8.9 - 2.9/θ (7)
Et3SnH reaction with 2:
Figure 3. (A, top) Product yields from reaction of peroxyester 12 at
110 °C in the presence of Et3SnH; the solid circles are the ratios for
[14]/[13] (right axis), and the thick line is the regression fit for this
ratio. (B, bottom) Product yields from the reaction of peroxyester 11
at 35 °C in the presence of Et3SnH; the solid circles are the ratios for
[13]/[14] (right axis), and the thick line is the regression fit for this
ratio.
Relative rate constants for cyclization of radical 2 to radical
3 in competition with trapping of 2 were obtained as follows.
Plots of 15/14 versus the inverse of the concentration of trapping
agent give the ratio (kc2/kT2)26 if radical 3 gives product 15
exclusively. From the studies with peroxy ester 11 reacting in
the presence of Et3SnH (Table S11 in the Supporting Informa-
tion), the slopes are (0.019 ( 0.004) and (0.016 ( 0.001) M at
10 and 35 °C. Assuming a value of 0.018 M at 20 °C and
combining this with eq 5, one calculates relative rate constants
for the two cyclization reactions of radical 2 of (kc1/kc2) ) 200
at 20 °C or kc2 ) 0.9 × 105 s-1 at 20 °C. Radical 3, however,
also yields additional products that appear to include 1-phen-
yltetrahydronaphthalenes. If we include trapping studies with
1,4-cyclohexadiene and estimated conversion efficiencies of ca.
35% for both reactions (see the Supporting Information), we
calculate an Arrhenius function for cyclization of 2 to 3 that
gives kc2 ) 1.4 × 105 s-1 at 20 °C (eq S11 in the Supporting
Information).
Results of trapping studies with the reactive trapping agent
Et3SnH were more readily analyzed. Good to high yields of
products 13-15 were obtained in the presence of the tin hydride
(Tables S10 and S11 in the Supporting Information). As shown
in Scheme 1, these are the ultimate products from reactions of
diffusively free radicals. In the plots in Figure 3, the linear ratios
of products 13 and 14 as a function of tin hydride concentration
with nonzero intercepts suggest that the equilibration reactions
between radicals 1 and 2 were competitive with tin hydride
trapping. That the yield of product 15 rapidly decreased as the
concentrations of tin hydride increased indicates that cyclization
of radical 2 to radical 3 is considerably slower than cyclization
of 2 to 1.
Quantum Chemical Calculations. Table 2 lists calculated
energies and enthalpies for the cyclizations of radicals 2 and 5
In principle, the relative rate constants from an equilibrating
radical system such as 1 and 2 with trapping of both components
can be obtained from the product distributions shown in Figure
(26) Newcomb, M. Tetrahedron 1993, 49, 1151-1176.

2992 J. Am. Chem. Soc., Vol. 122, No. 13, 2000
Halgren et al.
Table 3. Calculated Energy Components for Isomerization of
Table 2. Calculated Relative Energies and Entropies of
Interconversion at B3LYP/6-31G* Geometries
Radical 10 to Radical 9
relative energy (kcal/mol)
B3LYP/ B3LYP/
conversion 6-31G* cc-pVTZ(-f) Table 1 6-31G* Table 1
rel entropy (eu)
B3LYP/
calculation
E(10) - E(9)a
∆PMP2/cc-pVTZ(-f)a
1.61
-0.38
2.18
0.72
-0.36
4.53
∆PMP2/6-31G*a
∆PMP4(SDQT)/6-31G*a
∆ZPE(B3LYP/6-31G*)b
∆Hvib(B3LYP/6-31G*)b
total ∆Hc
10 a 9
5 a 4
2 a 1
2.26
-5.79
-8.24
4.05
-4.18
-6.15
4.1
-5.1
-7.8
-3.18
-4.44
-5.41
-4.3
-8.7
-7.3
a Computed using Gaussian 94 at Jaguar B3LYP/6-31G*-optimized
geometries. b Computed using Jaguar v3.5 at restricted-open-shell
B3LYP-optimized geometries. c PMP2/cc-pVTZ(-f) + (PMP4(SDQT)/
6-31G* - PMP2/6-31G*) + ZPE + ∆Hvib; see text.
and the parent radical, 3-butenyl (10). The B3LYP/6-31G*
results are not definitive, but such calculations perform reason-
ably well for the unsubstituted system in comparison to ones
carried out at much higher levels of theory.8 Comparison of
the B3LYP/6-31G* value for cyclization of 10 with the
experimentally determined enthalpic preference of 4.1 kcal/mol
shows that the calculation overestimates the stability of the
cyclopropylcarbinyl radical by 1.8 kcal/mol. If the same
“overstabilization” is assumed for the mono- and diphenyl
systems, the adjusted predictions for the enthalpies of 4 relative
to 5 and of 1 relative to 2 become -4.0 and -6.4 kcal/mol,
respectively, in qualitative agreement with the experimental
values in Table 1. The larger-basis B3LYP/cc-pVTZ(-f) calcula-
tions gave a similar level of agreement more directly. Each set
of calculations predicts a large change in reaction enthalpy for
monophenyl substitution followed by a much smaller change
for substitution of the second phenyl group.
we were unable to address the larger systems by this approach
because we could not obtain a full set of converged UHF wave
functions with either Gaussian 94 or Gaussian 98.
Discussion
The LFP results provide precise, directly measured rate
constants for cyclizations of radicals 2 and 5. These values
should also be quite accurate because they are much faster than
diffusion-controlled radical-radical couplings and reactions of
radicals with residual oxygen yet slow enough that convolution
of the instrument response cannot be a factor. The major source
of error most likely results from temperature fluctuations during
the kinetic measurements.
The entropy differences obtained from the B3LYP/6-31G*
vibrational analysis, a level of theory found suitable for assessing
vibrational corrections,27 also parallel those inferred experi-
mentally, though the calculations do not support the large
experimental value for the 5 f 4 conversion. The consistent
underestimation of the entropy differences by the theoretical
calculations may be due, at least in part, to the failure of the
standard formulas to recognize the large contribution to the
entropy from the nearly free rotation of the terminal methylene
group in the ring-opened radicals.28
Higher-order calculations on radicals 9 and 10 at their
B3LYP/6-31G* geometries were performed using Gaussian 94
in an attempt to characterize the thermochemistry further. As
would be done in an additive scheme such as G2,19 we estimated
the enthalpy of interconversion for 10 f 9 as shown in eq 8
Kinetic data for the cyclization of radical 5 were previously
reported in two studies. Bowry, Lusztyk, and Ingold determined
a rate constant for cyclization from the isotopic scrambling
observed when 16 was generated in the presence of n-Bu3SnH.4
Using the known rate constant for reaction of the tin hydride
with a primary alkyl radical and assuming no isotope effect on
the kinetics, they established a rate constant of 1.2 × 107 s-1
for cyclization of 16 (and thus of 5) at 42 °C. Beckwith and
Bowry reported the results of nitroxyl radical trapping studies
conducted at temperatures between 42 and 80 °C; their results
give rate constants for cyclization of 5 of 3.2 × 106 s-1 at 20
°C and 0.8 × 107 s-1 at 42 °C.5 The LFP results from this work
give rate constants of 5.4 × 106 s-1 at 20 °C and 1.15 × 107
s-1 at 42 °C. The agreement between the LFP and tin hydride
values is excellent; the factor of 1.4 difference between these
values and the nitroxyl trapping results might reflect the
necessity of assuming that the rate constants for reaction of
radical 5 with the nitroxyl radical are equal to those for a model
radical.5
∆E )
∆E(large-basis MP2) + ∆E(small-basis MP3 +
MP4 corrections) + ∆E(ZPE) + ∆Hvib (8)
where the last term is the thermal enthalpy associated with
populating vibrational energy levels above the ground state
(Table 3). This approach gave a computed enthalpy of inter-
conversion (4.53 kcal/mol) in reasonable agreement with the
experimental value of 4.1 kcal/mol. Despite the agreement, the
calculation was sobering because it contained major contribu-
tions from relatively costly third-order (1.83 kcal/mol) and
fourth-order (0.73 kcal/mol) perturbative corrections. Moreover,
the spin-projected MP2 contribution was a poor estimate and
even had the wrong sign for the small 6-31G* basis. The
vibrational corrections for the parent system were small, but
they would be larger for the monophenyl (∆E(ZPE) ) 1.57
kcal/mol, ∆Hvib ) -0.64 kcal/mol) and diphenyl (∆E(ZPE) )
1.98 kcal/mol, ∆Hvib ) -0.69 kcal/mol) systems. Unfortunately,
The accuracy of the rate constants for ring openings of
radicals 1 and 4 depends on the quality of the calculated
equilibrium constants for these systems. The thermochemical
analysis supports the values in Table 1, although not definitively,
and the quantum calculations are in qualitative agreement.
Further support for the accuracy of the derived equilibrium
constants is found in the consistency of the derived entropic
terms for the ring-opening reactions; the log A values are quite
similar, as they should be because of the rigidity of these
radicals.
(27) Wong, M. W.; Radom, L. J. Phys. Chem. A 1998, 102, 2237-
2245.
(28) We thank Prof. H. B. Schlegel, Wayne State University, for pointing
out this factor.

R-Phenyl-Substituted Cyclopropylcarbinyl Radicals
J. Am. Chem. Soc., Vol. 122, No. 13, 2000 2993
The computed values for ring opening of 4 in Table 1 can
be compared to those measured by nitroxyl trapping. Our
derived rate constant for ring opening at 20 °C (6 × 104 s-1) is
smaller by a factor of 1.7 than that found by Beckwith and
Bowry,5 about the same level of difference as found for the
cyclization of 5 but in the opposite direction. An LFP study of
another benzylic cyclopropylcarbinyl radical ring opening, that
of radical 17, appears to support our derived results. Radical
17 employs a “reporter-group”29 for UV detection, and the
reporter group is known to accelerate ring openings of cyclo-
propylcarbinyl radicals.30 To gauge the extent of the acceleration
in the endothermic ring opening of radical 17, one can consider
the effect of the same reporter group moiety in the endothermic
cyclizations of radicals (E)- and (Z)-18 which are 7-10 times
faster at 20 °C than cyclization of the parent 3-butenyl radical.31
Assuming a similar acceleration for 17 and using the LFP value
for ring opening of 17 at 20 °C of 4.6 × 105 s-1, one estimates
a rate constant of 5-6 × 104 s-1 for ring opening of 4 at 20
°C, in agreement with the value in Table 1.
Conclusion
The relative rate constants for interconversion of radicals 1
and 2 estimated more than three decades ago from product
analyses have been placed on an absolute kinetic scale. The
temperature-dependent functions for kinetics and equilibria in
Table 1 provide quantitative evaluation of the extent of phenyl
group stabilization of a radical center and the resulting kinetic
effects for both mono- and diphenyl-substituted cases. The
results should serve as a useful standard for future computational
studies that address the effects of phenyl substituents. Because
the parent system radicals 9 and 10 are relatively small and
well-characterized, one will be able to focus mainly on the effect
of added substituents on derived species such as 1, 2, 4, and 5.
Our investigations of these species were hindered because we
found that converged spin-unrestricted wave functions for the
R-phenyl-substituted radicals could not be reliably obtained
using one of the most sophisticated computational approaches
currently available.
The kinetic effect of the phenyl substitution on the homoallyl
radical cyclization is obviously enthalpy driven as one would
expect, but the magnitude of the effect is noteworthy. The
activation energies for addition of methyl radical to a large set
of alkenes, reactions that are primarily enthalpy controlled,
depend on the enthalpy of the reactions (hr) with a proportional-
ity constant of 0.20.24 Considering only the additions of methyl
radical to ethene, styrene, and 1,1-diphenylethene,24 the depen-
dence of Ea on hr would be 0.24 to 0.29; the value is affected
by the thermochemistry of the addition to diphenylethene.23 For
radicals 2, 5, and 10, however, a plot of Ea versus hr has a slope
of 0.54, indicating that about half of the product stabilizations
are manifested in the transition states. It would appear that the
forming three-membered ring is an important feature because
the rate constants for 5-exo cyclizations of radicals 19 (rate
constants at 20 °C in units of s-1 are listed)15,26,32 show a
dependence on relative enthalpy similar to that found in addition
reactions of the methyl radical.24
Experimental Section
General Procedure for Preparation of PTOC Esters. The acid
chloride was prepared by adding oxalyl chloride (1.5 equiv) to a solution
of the carboxylic acid in benzene (0.05 to 0.1 M) containing a catalytic
amount of DMF. After 1-2 h, the solvent and excess oxalyl chloride
were removed under reduced pressure. The resulting acid chloride was
taken up in benzene, and the solution was added to a stirred suspension
of N-hydroxypyridine-2-thione sodium salt34 in benzene containing a
catalytic amount of DMAP. From this point on the reaction mixture
was protected from light. After being stirred for 1-2 h, the reaction
mixture was diluted with benzene, and the mixture was washed with
10% aqueous KHSO4 solution, saturated aqueous NaHCO3 solution,
and brine. The benzene solution was dried over MgSO4, and the solvent
was removed under reduced pressure. The residue was purified by silica
gel chromatography to give the PTOC esters in about 65% yield.
5,5-Diphenyl-4-pentenoic Acid 2-Thioxo-2H-pyridin-1-yl Ester
(6). By use of the general procedure, 5,5-diphenyl-4-pentenoic acid35
1
(0.267 g, 0.0106 mol) gave 6. H (300 MHz): δ 2.63 (q, J ) 7.0 Hz,
2 H), 2.84 (t, J ) 7.2 Hz, 2 H), 6.15 (t, J ) 7.3 Hz, 1 H), 6.61 (td, J
) 7.5, 2.0 Hz, 1 H), 7.18, 7.42 (m, 11 H), 7.50 (d, J ) 5.7 Hz, 1 H),
7.68 (dd, J ) 8.7, 1.7 Hz, 1 H).
trans-5-Phenyl-4-pentenoic Acid 2-Thioxo-2H-pyridin-1-yl Ester
(7). By use of the general procedure, trans-5-phenyl-4-pentenoic acid36
(0.11 g, 0.0068 mol) gave 7. 1H NMR (300 MHz): δ 2.73 (q, J ) 7.2
Hz, 2 H), 2.91 (t, J ) 7.2 Hz, 2 H), 6.28 (dt, J ) 15.9, 6.6 Hz, 1 H),
6.52 (d, J ) 15.9 Hz, 1 H), 6.61 (td, J ) 6.9, 2.0 Hz, 1 H), 7.18-7.38
(m, 6 H), 7.54 (d, J ) 5.4 Hz, 1 H), 7.69 (dd, J ) 9.3, 1.8 Hz, 1 H).
tert-Butyl diphenylcyclopropylperoxyacetate (11) was synthesized
by adding 0.87 g of (100% excess) of powdered sodium tert-butyl
peroxide to a stirred solution of 1.07 g (3.95 mmol) of diphenylcyclo-
propylacetyl chloride in 75 mL of pentane at -10 °C. The reaction
mixture was maintained between -10 and 0 °C for 2 h. A sample
withdrawn after 1.5 h had an infrared absorption at 1765 cm-1 in place
of the carbonyl absorbance of the acid chloride at 1785 cm-1 indicating
that the reaction had gone to completion. The pentane solution was
filtered through a Celite bed and washed through with 50 mL of ice-
cold pentane. The solution was concentrated under reduced pressure
at 0 °C to about 3 mL and transferred to a small vessel with a nitrogen-
inlet arm. The distillation flask was washed with 5 mL of pentane, and
the resulting solution was added to that in the small vessel, upon which
some white crystals formed. The vessel was flushed with nitrogen and
cooled in several stages to -20 °C, whence crystallization appeared to
be complete. The pentane solution was withdrawn under positive
nitrogen pressure with a syringe. Fresh pentane was added, and the
crystals were dissolved by warming on a steam bath for a minimal
The other rate constants determined in this work were for
cyclization of radical 2 to radical 3 and for reactions of Et3SnH
with radicals 1 and 2 (Scheme 1). The values for tin hydride
trapping of the diphenylalkyl radical 1 (eq 6) should be useful
because we are not aware of any previous report of the kinetics
for reaction of a tin hydride with a diphenylalkyl radical. The
tin hydride trapping of radical 1 must be nearly isothermic; our
computed BDE for the hydrocarbon precursor to 1 is 79 kcal/
mol, and the calculated BDE for Bu3SnH based on corrections
of photoacoustic calorimetry data is 78.6 kcal/mol.33
(29) Newcomb, M.; Tanaka, N.; Bouvier, A.; Tronche, C.; Horner, J.
H.; Musa, O. M.; Martinez, F. N. J. Am. Chem. Soc. 1996, 118, 8505-
8506.
(30) Horner, J. H.; Tanaka, N.; Newcomb, M. J. Am. Chem. Soc. 1998,
120, 10379-10390.
(31) Furxhi, E.; Horner, J. H.; Newcomb, M. J. Org. Chem. 1999, 64,
4064-4068.
(32) Horner, J. H.; Lakshmipathy, G.; Newcomb, M. Unpublished results.
(33) Chatgilialoglu, C.; Newcomb, M. In AdVances in Organometallic
Chemistry; West, R., Hill, A. F., Eds.; Academic: San Diego, 1999; Vol.
44, pp 67-112.
(34) Esker, J. L.; Newcomb, M. J. Org. Chem. 1993, 58, 4933-4940.
(35) Graham, S. H.; Williams, J. S. J. Chem. Soc. 1959, 4066-4073.
(36) Tokuda, M.; Miyamoto, T.; Fujita, H.; Suginome, H. Tetrahedron
1991, 47, 747-756.

2994 J. Am. Chem. Soc., Vol. 122, No. 13, 2000
Halgren et al.
period; 15 mL of pentane were required to effect solution. On cooling
to -20 °C and scratching, the crystals reformed. After 0.5 h at -30
°C, the pentane solution was removed under positive nitrogen pressure.
The solvent that adhered to the crystals was largely removed by
maintaining the crystals in vacuo for 1 h at -10 to 0 °C. The yield
was 0.53 g (38%). Relative to 10 aromatic protons, integration of the
1H NMR spectrum at -10 °C in CCl4 showed 3.8 broad secondary
cyclopropyl protons much like those for the acid chloride, 9.2 tert-
butyl methyl protons, an 0.8 proton singlet at δ ∼2.1, possibly due to
water, and no olefinic proton resonances. A sample from another
preparation melted with effervescence at ca. 65 °C when heated rapidly.
Analysis of active oxygen by iodide oxidation as described by Silbert
and Swern37 gave an average active oxygen content from two
determinations of 94.5%.
LFP Kinetics. Kinetic measurements were carried out with an
Applied Photophysics LK-50 laser kinetic spectrometer using the third
harmonic (355 nm) of a Nd:YAG laser (7 ns pulse duration, 40 mJ/
pulse). The flow system consisted of a jacketed addition funnel
containing a fritted glass tube for helium sparging and attached by inert
tubing to a UV cuvette. A temperature-regulated circulating bath was
used to circulate fluid through the jacket of the funnel. Sample
temperatures were measured by means of a copper-constantan
thermocouple wire inserted into the interior of the cuvette through the
sample outflow opening. Each kinetic trace contained 512 data points.
For studies of 5, 14 kinetic traces were summed to improve the signal/
noise ratio. The impulse response of the system was measured to be
2.5 × 108 s-1
.
Indirect Kinetics. The experimental procedures have been reported.3
In brief, a small quantity (15-30 mg) of peroxyester 11 or 12, an
appropriate amount of Et3SnH (prepared39 by LAH reduction of the
bromide), and cosolvent were sealed in tubes after freeze-thaw
degassing. Following thermolysis in a controlled temperature bath, the
tubes were opened, and the contents were analyzed by GC. Products
13-15 were identified by comparison of the GC retention times to
those of authentic samples.
tert-Butyl 5,5-diphenylperoxy-4-pentenoate (12) was prepared by
a modification of the method reported by Howden,38 typically in 70%
yield when prepared from 5 g of 5,5-diphenyl-4-pentenoic acid.35
Samples of 12 had mp 40.5-42 °C (lit.38 mp 42-42.5 °C).
(37) Silbert, L. S.; Swern, D. Anal. Chem. 1958, 30, 385-387.
(38) Howden, M. E. H. Ph.D. Thesis, California Institute of Technology,
1962.
(39) Kriegsmann, H.; Ulbricht, K. Z. Anorg. Chem. 1964, 328, 90-104.
(40) Jaguar, version 3.5; Schro¨dringer Inc.: Portland, OR 97204.
(41) Gaussian 94 (Revision E.2); Frisch, M. J.; Trucks, G. W.; Schlegel,
H. B.; Gill, P. M. W.; Johnson, B. G.; Robb, M. A.; Cheeseman, J. R.;
Keith, T.; Petersson, G. A.; Montgomery, J. A.; Raghavachari, K.;
Al-Laham, M. A.; Zakrzewski, V. G.; Ortiz, J. V.; Foresman, J. B.;
Cioslowski, J.; Stefanov, B. B.; Nanayakkara, A.; Challacombe, M.; Peng,
C. Y.; Ayala, P. Y.; Chen, W.; Wong, M. W.; Andres, J. L.; Replogle, E.
S.; Gomperts, R.; Martin, R. L.; Fox, D. J.; Binkley, J. S.; Defrees, D. J.;
Baker, J.; Stewart, J. P.; Head-Gordon, M.; Gonzalez, C.; Pople, J. A.;
Gaussian, Inc.: Pittsburgh PA, 1995.
(42) Gaussian 98 (Revision A.6); Frisch, M. J.; Trucks, G. W.; Schlegel,
H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Zakrzewski, V. G.;
Montgomery, J. A.; Stratmann, R. E.; Burant, J. C.; Dapprich, S.; Millam,
J. M.; Daniels, A. D.; Kundin, K. N.; Strain, M. C.; Farkas, O.; Tomasi, J.;
Barone, V.; Cossi, M.; Cammi, R.; Mennucci, B.; Pomelli, C.; Adamo, C.;
Clifford, S.; Ochterski, J.; Petersson, G. A.; Ayala, P. Y.; Cui, Q.;
Morokuma, K.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman,
J. B.; Cioslowski, J.; Ortiz, J. V.; Stefanov, B. B.; Liu, G.; Liashenko, A.;
Piskorz, P.; Komaromi, I.; Gomperts, R.; Martin, R. L.; Fox, D. J.; Keith,
T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Gonzalez, C.;
Challacombe, M.; Gill, P. M. W.; Johnson, B. G.; Chen, W.; Wong, M.
W.; Andres, J. L.; Head-Gordon, M.; Replogle, E. S.; Pople, J. A.; Gaussian,
Inc.: Pittsburgh, PA, 1998.
Computations. Quantum calculations for radicals 1, 2, 4, 5, 9, and
10 were performed using Jaguar v3.540 or the Gaussian 9441 or 9842
series of programs. Calculations also were performed on unsubstituted,
monophenyl-substituted, and 1,1-diphenyl-substituted ethanes and
ethenes as model systems. Geometries were optimized using Jaguar at
the restricted-open-shell B3LYP level of theory43 using the 6-31G*
basis set.44 This level of theory is especially appropriate for determining
the geometries of open-shell species because density functional
calculations are less susceptible to geometry distortions resulting from
spin contamination than are unrestricted Hartree-Fock (UHF)45
calculations.27 For the radical species, vibrational frequencies were also
calculated at this level of theory to compute zero-point energies, thermal
vibrational contributions to the enthalpy, and entropies. Better quality
single-point energies were obtained using the larger and more flexible
cc-pVTZ(-f) basis set.46 Where feasible, Mo¨ller-Plesset correlation
corrections to the UHF wave function were computed through fourth
order47 (singles, doubles, and quadruples), with spin projection48
computed through third order.
Acknowledgment. We are grateful to the National Science
Foundation for financial support (CHE-9614968 to M.N. and
GP-8540 to J.D.R.).
(43) (a) Becke, A. D. J. Chem. Phys. 1993, 98, 5648-5652. (b) Lee,
C.; Yang, W.; Parr, R. G. Phys. ReV. B 1988, 37, 785-789.
(44) Hehre, W. J.; Radom, L.; Schleyer, P. v. R.; Pople, J. A. Ab Initio
Molecular Orbital Theory; Wiley: New York, 1986, Chapter 4.
(45) Pople, J. A.; Nesbet, R. K. J. Chem. Phys. 1954, 22, 571-572.
(46) Here, cc-pVTZ(-f) refers to the triple-ú correlation-consistent basis
set of Dunning, excluding f functions on second-row elements and d
functions on hydrogen; see: Dunning, T. H. J. Chem. Phys. 1989, 90, 1007-
1023.
Supporting Information Available: Tables of product
yields from thermal decompositions of peroxyesters, additional
experimental details, and additional references (PDF). This
material is available free of charge via the Internet at
http://pubs.acs.org.
(47) Krishnan, R.; Frisch, M. J.; Pople J. A. J. Chem. Phys. 1980, 72,
4244-4245. Krishnan, R.; Pople, J. A. Int. J. Quantum Chem. 1978, 14,
91-100.
(48) Schlegel, H. B. J. Chem. Phys. 1986, 84, 4530.
JA991114H