Kinetics of cyclopropylcarbinyl radical ring openings measured directly by laser flash photolysis

Article abstract of DOI:10.1021/ja9819460

The kinetics of ring openings of cyclopropylcarbinyl radicals containing reporter groups were measured directly by laser flash photolysis (LFP) methods. The reporter groups are aryl-substituted cyclopropanes at the position of the radical center in the in

Full text of DOI:10.1021/ja9819460

J. Am. Chem. Soc. 1998, 120, 10379-10390
10379
Kinetics of Cyclopropylcarbinyl Radical Ring Openings Measured
Directly by Laser Flash Photolysis
John H. Horner,* Noriko Tanaka, and Martin Newcomb*
Contribution from the Department of Chemistry, Wayne State UniVersity, Detroit, Michigan 48202
ReceiVed June 3, 1998
Abstract: The kinetics of ring openings of cyclopropylcarbinyl radicals containing reporter groups were
measured directly by laser flash photolysis (LFP) methods. The reporter groups are aryl-substituted
cyclopropanes at the position of the radical center in the incipient product, and the initial ring-opening reaction
gives an aryl-substituted cyclopropylcarbinyl radical that opens “instantly” on the nanosecond time scale to
give benzylic and diphenylalkyl radical products that are detected by UV spectroscopy. Three reporter group
designs have been studied. The most useful design is that in substituted (trans-2-(2,2-diphenylcyclopropyl)-
cyclopropyl)methyl radicals (7). The important synthetic intermediate for production of this series is N-methoxy-
N-methyl-trans-2-(2,2-diphenyl-1R*-cyclopropyl)-1S*,2R*-cyclopropanecarboxamide (15a) which has been
prepared diastereomerically pure. The syntheses of 15a and a series of PTOC ester radical precursors derived
from 15a are described. Laser photolysis (355 nm) of PTOC esters gave acyloxyl radicals that decarboxylated
to give cyclopropylcarbinyl radicals that were studied. The substitutions at the cyclopropylcarbinyl position
of radicals 7 were H, H (7a); H, Me (7b); Me, Me (7c); H, CO2Et (7d); Me, CO2Et (7e); and H, Ph (7f). The
kinetics of ring openings of radicals 7 were measured in THF and in four cases in CH3CN in the temperature
range -41 to +50 °C. Alkyl radicals 7a and 7b displayed no kinetic solvent effect, whereas ester-substituted
radicals 7d and 7e did. The ester-substituted radicals react about as fast as the alkyl-substituted radicals due
to favorable polarization in the transition states for ring opening. The phenyl-substituted radical 7e ring-
opens about 3 orders of magnitude less rapidly than the parent radical 7a. The structures and energies of the
ground states, rotational transition states, and ring-opening transition states for a series of substituted
cyclopropylcarbinyl radicals corresponding to 7a-e were computed by the hybrid density functional theory
B3LYP/6-31G*, and the ring-opening kinetics were compared to those predicted from the computational barriers.
The precision in the Arrhenius functions for ring openings of radicals 7 permits meaningful comparisons of
the log A terms to those predicted from thermochemical considerations.
Knowledge of the rate constants of radical reactions is
necessary both for mechanistic work and for planning of radical-
based conversions in synthesis. For alkyl radicals, the linchpin
kinetic values are the rate constants for simple unimolecular
rearrangements, often referred to as “radical clocks”,1 such as
the cyclization of the 5-hexenyl radical and ring opening of the
cyclopropylcarbinyl radical. From numerous competition ki-
netic studies, the rate constants of these reactions have been
incorporated into rate constants of other radical reactions such
that an extensive, interrelated scale of alkyl radical kinetics
exists.2
The cyclopropylcarbinyl radicals, with rate constants for ring
opening on the order of 108 s-1 at ambient temperature, are
important for a number of reasons. Simple cyclopropylcarbinyl
radicals are the best calibrated of the “fast-reacting” radical
clocks, and their rate constants provide the foundation for the
kinetics of radicals that react faster. In addition, they provide
excellent platforms for the study of steric and electronic effects
of substituents due to the rigidity of the systems, and they are
among the more tractable from a computational perspective due
to the small number of atoms and the inflexible ring. It is
somewhat unusual, therefore, that virtually none of the rate
constants for cyclopropylcarbinyl ring-opening reactions have
been measured directly. ESR spectroscopic measurements of
the rates of ring opening of the cyclopropylcarbinyl radical were
conducted at low temperatures,3 and the muon-containing
analogues of 1-methyl- and 1,1-dimethylcyclopropylcarbinyl
radical were studied by muon spin-rotation spectroscopic
methods.4 However, the Arrhenius functions obtained in these
studies are unreasonable, and the results cannot be extrapolated
to ambient temperature with confidence. Laser flash photolysis
(LFP) kinetic units have adequate temporal resolution for direct
measurements of cyclopropylcarbinyl radical reactions at ambi-
ent temperature, but the lack of a prominent chromophore in
most of these radicals and their ring-opened products precludes
UV detection. Thus, the kinetics of ring openings of most
cyclopropylcarbinyl radicals are available indirectly from
competition trapping studies with calibrated trapping agents.2
We recently introduced the use of “reporter groups” for direct
LFP kinetic studies of radicals that do not otherwise contain
useful chromophores.5 The reaction of interest produces an aryl-
substituted cyclopropylcarbinyl radical that ring-opens “in-
stantly” to give a benzylic or diphenylalkyl radical that can be
observed in the UV. Examples of the application of the method
for measuring cyclopropylcarbinyl radical ring openings were
(3) Maillard, B.; Forrest, D.; Ingold, K. U. J. Am. Chem. Soc. 1976, 98,
7024-7026.
(4) Burkhard, P.; Roduner, E.; Hochmann, J.; Fischer, H. J. Phys. Chem.
1984, 88, 773-777.
(1) Griller, D.; Ingold, K. U. Acc. Chem. Res. 1980, 13, 317-323.
(2) Newcomb, M. Tetrahedron 1993, 49, 1151-1176.
(5) 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.
S0002-7863(98)01946-5 CCC: $15.00 © 1998 American Chemical Society
Published on Web 09/29/1998

10380 J. Am. Chem. Soc., Vol. 120, No. 40, 1998
Horner et al.
Scheme 1
Scheme 2a
reported in the original communication5 and more recently.6 In
this work we report the syntheses of a diastereomerically pure
intermediate and several precursors to substituted cyclopropyl-
carbinyl radicals, detailed LFP kinetic studies of cyclopropyl-
carbinyl radical ring openings, and analyses of the kinetics via
computational studies of the parent radicals.
a Key: (a) Na+(EtO)2P(o)C(-)HCO2Me; (b) (N,N-dimethylami-
no)(methyl)(phenyl)sulfoxonium tetrafluoroborate; (c) KOH, H2O; (d)
(i) (COCl)2, (ii) CH2N2, (iii) AgO; (e) LDA, CH3I.
Results
Design of Reporter Groups. The reporter group approach
as applied to cyclopropylcarbinyl radical ring openings is
exemplified in Scheme 1. The radical of interest (1) is produced
by laser irradiation. The ring opening of 1 will give both 2
and 3. Radical 3 is a 2-arylcyclopropylcarbinyl radical which
rapidly ring-opens to give a UV-detectable benzylic radical (4)
in this example. Because the rearrangements of aryl-substituted
cyclopropylcarbinyl radicals are extremely fast, k > 1 × 1011
s-1 at ambient temperature,7 the kinetics of the reporting reaction
are not convoluted with those of the reaction of interest. That
is, the observed kinetics are for the initial radical ring-opening
reactions. One should note that the sums of the rate constants
for reaction by both channels (i.e., 1 f 2 + 3) are measured
even though the observed products are from only one of the
reaction channels.
In principle, several designs for the reporting group moiety
are possible; the only requirement is that the final product is
detectable by UV spectroscopy. In practice, the molar absorp-
tivity of the reporter radical and the difficulty in synthesis of
diastereomerically pure compounds can place limits on the
practicality of a given design. The second point is especially
important for studies of cyclopropylcarbinyl radicals with
reporter groups because several asymmetric centers are present
in the initial radicals and it is likely that diastereomers will react
with different rate constants, thus precluding detailed analysis
of the kinetic effects of substituents.
reporting reaction are diphenylalkyl radicals which have larger
molar extinction coefficients than benzylic radicals,8 thus
permitting more precise kinetic measurements. An early
intermediate in the synthesis of the precursors to radicals 7 could
be crystallized to diastereomeric purity, and most of the studies
described here involve this series.
For studies of the relatively fast ring openings of cyclopro-
pylcarbinyl radicals, another limitation on the design of the
radical precursors exists. The target radicals must either be
produced directly from laser irradiation or result from very fast
unimolecular processes such as the decarboxylations of acyloxyl
radicals which occur with rate constants exceeding 1 × 109 s-1
at ambient temperature.9,10 The latter choice is desired for the
systems studied here because the immediate radical precursors
can be prepared from cyclopropylacetic acid derivatives that
are stable. Several peroxy acid and related derivatives afford
acyloxyl radicals upon irradiation. We employed Barton’s
PTOC ester derivatives,11,12 which are known to be excellent
sources of acyloxyl radicals when irradiated with 355 nm light
from a Nd:YAG laser.13-15 PTOC esters are prepared from the
We have studied three different reporter designs (shown in
radicals 5-7), each of which performed as expected. The
corresponding carboxylic acids which were our synthetic targets.
Syntheses of Precursors. The synthesis of the requisite
carboxylic acids for PTOC ester precursors to the series of
primary, secondary, and tertiary radicals 5 (Scheme 2) was
previously reported.5 Thus, Horner-Emmons olefination of
aldehyde 8 gave acrylate 9 which was cyclopropanated to give
10. Following saponification, acid 11 was homologated by a
(8) Chatgilialoglu, C. In Handbook of Organic Photochemistry; Scaiano,
J. C., Ed.; CRC Press: Boca Raton, FL, 1989; Vol. 2, pp 3-11.
(9) Falvey, D. E.; Schuster, G. B. J. Am. Chem. Soc. 1986, 108, 7419-
7420.
(10) Bockman, T. M.; Hubig, S. M.; Kochi, J. K. J. Org. Chem. 1997,
62, 2210-2221.
(11) The acronym PTOC derives from pyridinethioneoxycarbonyl. PTOC
esters are actually anhydrides of a carboxylic acid and the thiohydroxamic
acid N-hydroxypyridine-2-thione.
precursors to radicals 5 are prepared from commercially
available trans-2-phenylcyclopropanecarboxylic acid, but the
syntheses of the precursors for radicals 6 and 7 require additional
steps. An advantage of the precursors to radicals 6 is that the
symmetry of the reporting group reduces the number of
diastereomers produced in the syntheses. The reporter moiety
in radicals 7 offers the advantage that the products of the
(12) Barton, D. H. R.; Crich, D.; Motherwell, W. B. Tetrahedron 1985,
41, 3901-3924.
(13) Bohne, C.; Boch, R.; Scaiano, J. C. J. Org. Chem. 1990, 55, 5414-
5418.
(6) Newcomb, M.; Horner, J. H.; Emanuel, C. J. J. Am. Chem. Soc. 1997,
119, 7147-7148.
(7) Newcomb, M.; Johnson, C. C.; Manek, M. B.; Varick, T. R. J. Am.
Chem. Soc. 1992, 114, 10915-10921.
(14) Ha, C.; Horner, J. H.; Newcomb, M.; Varick, T. R.; Arnold, B. R.;
Lusztyk, J. J. Org. Chem. 1993, 58, 1194-1198.
(15) Aveline, B. M.; Kochevar, I. E.; Redmond, R. W. J. Am. Chem.
Soc. 1995, 117, 9699-9708.

Kinetics of Ring Openings
J. Am. Chem. Soc., Vol. 120, No. 40, 1998 10381
Figure 2. ORTEP drawing of diastereomer 1 of acid 19b.
Figure 1. ORTEP drawing of 15a. The unit cell contains two
molecules.
Wolff rearrangement to give acid 12a that was sequentially
methylated to 12b and 12c. The reactions in Scheme 2
proceeded in good-to-excellent yield, but ester 10 was formed
as a 1:1 mixture of diastereomers that was not separated.
Therefore, acids 12 were diastereomeric mixtures, and acid 12b
was a mixture of up to four diastereomers. Each of the
diastereomeric mixtures of acids 12 was converted to the
corresponding mixture of PTOC esters for LFP studies.5
A
mixture of diastereomers of 2-(trans,trans-2,3-diphenylcyclo-
propyl)cyclopropylacetic acid was prepared from trans,trans-
2,3-diphenylcyclopropanecarboxaldehyde by a similar sequence
of reactions.16
In initial syntheses of the precursors for radicals 7, a
diastereomer problem similar to that arising in the preparation
of acids 12 was apparent. 2,2-Diphenylcyclopropancarbox-
aldehyde (13) was converted to the corresponding R,â-unsatur-
ated methyl ester, but a sluggish cyclopropanation reaction led
to an approximately 1:1 mixture of diastereomers.5 Therefore,
Figure 3. (A) Observed spectrum 34 ns after laser irradiation of the
PTOC precursor to radical 5a at ambient temperature. The benzylic
radical product (22a) has λmax at ca. 320 nm, and the pyridine-2-thiyl
radical has λmax at 490 nm. The strong bleaching is due to destruction
of the PTOC precursor which has λmax at ca. 360 nm. (B) Time-resolved
spectra from laser irradiation of precursor 21e at 20 °C. The spectra
are for 52, 72, and 160 (») ns after irradiation; the data at 32 ns have
been subtracted to give a baseline. Product radical 23e with λmax at
335 nm is forming with time; decay of the pyridine-2-thiyl radical is
insignificant on the time scale of these measurements. The inset shows
a kinetic trace at 338 nm where the x axis is time in nanoseconds.
acids 19a, 19b, and 19f. Esterification of acid 19b to the ethyl
ester (20b) followed by methylation of the lithium enolate gave
ester 20c, which was hydrolyzed to give acid 19c. Acid 19a
was esterified to ethyl ester 20a, which was converted to the
diethyl malonate 20d by ethoxycarboxylation of the lithium
enolate, and methylation of the enolate of 20d gave diethyl
malonate 20e. Partial hydrolysis of malonates 20d and 20e gave
the monoesters 19d and 19e. The PTOC ester precursors 21
were prepared from the corresponding acids 19 by reaction of
the corresponding acyl chlorides with N-hydroxypyridine-2-
thione sodium salt.
we examined the use of Weinreb amides for the syntheses of
the series of acids necessary for precursors to radicals 7.
Aldehyde 13 was converted to a 5:1 mixture of diastereomers
of the corresponding Weinreb amides from which amide (E-
14), the major diastereomer, was obtained by chromatography.
Cyclopropanation of (E-14) gave amide 15a and its diastereomer
15b as a 5.5:1 mixture. Diastereomerically pure 15a, obtained
by crystallization, was characterized by an X-ray crystal
structure determination (Figure 1).
Compound 15a was the starting point for the syntheses of
all of the precursors for radicals 7 (Scheme 3). The reduction
of 15a and reactions with methyl and phenyl Grignard reagents
gave aldehyde 16a and ketones 16b and 16f, respectively. The
carbonyl compounds were converted to enol ethers 17 by Wittig
reactions, and the enol ethers were hydrolyzed to give the
homologated aldehydes 18. The hydrolysis reaction of enol
ether 17f proceeded in poor yield, and several variations of the
reaction sequence were attempted with even poorer results.
Oxidation of aldehydes 18 gave the corresponding carboxylic
In the synthetic sequence for PTOC esters 21, only acids 19a
and 19c were produced as single diastereomers; each of the other
acids was obtained as a mixture of diastereomers. However,
the center of asymmetry that results in diastereomeric mixtures
for acids 19b and 19d-f is at the incipient radical position in
radicals 7, and the mixtures of diastereomers of PTOC esters
21 will give a single radical in each case and result in no
complications in the kinetic studies. This was explicitly
demonstrated in the case of PTOC ester 21b. The two
diastereomers of acid 19b were separated by column chroma-
tography, and one of these diastereomers was characterized by
X-ray crystallography (Figure 2). When the two diastereomeri-
cally pure PTOC esters 21b were prepared from the diastere-
(16) Tanaka, N.; Newcomb, M. Unpublished results.

10382 J. Am. Chem. Soc., Vol. 120, No. 40, 1998
Horner et al.
Scheme 3a
a Key: (a) LiAlH4; (b) MeMgBr; (c) PhMgBr; (d) LiHMDS, Ph3P+CH2OCH3Cl-; (e) LiHMDS, Ph3P+CH2OCH2CH2Si(CH3)3Cl-; (f) HCl, H2O,
heat; (g) CF3CO2H; (h) CrO3, H2SO4, acetone; (i) EtOH, TsOH, benzene, heat; (j) LDA, CH3I; (k) KOH, H2O; (l) LDA, NCCO2Et; (m) NaH, CH3I;
(n) LiOH (1 equiv), EtOH; (o) (i) (COCl)2, benzene, DMF (catalyst), (ii) N-hydroxypyridine-2-thione sodium salt
omers of acid 19b and studied independently by LFP, the results
were indistinguishable (see below).
Spectroscopy. Members of the PTOC family of radical
precursors have a strong, long wavelength absorbance centered
at approximately 360 nm, and irradiation with the third harmonic
of a Nd:YAG laser (355 nm) cleaves these compounds with
high efficiency.15 These two features require that LFP studies
are conducted with dilute, flowing solutions. To measure
kinetics at variable temperatures, solutions of the precursor were
thermally equilibrated in a jacketed addition funnel. Temper-
atures were controlled with a MeOH/H2O solution from a
temperature-regulated bath that was circulated through the jacket
of the addition funnel. After thermal equilibration and sparging
with helium, the PTOC ester solutions were allowed to flow
through a quartz flow cell. Temperatures were measured with
ing production of radicals 5a and 7e from the corresponding
PTOC esters. The spectrum from 5a shows the absorbance of
the benzylic radical product 22a with λmax at about 320 nm, a
strong bleaching centered at 370 nm from destruction of the
a thermocouple placed in the flowing stream about 1 cm above
PTOC ester, and a long wavelength absorbance due to the
the irradiation zone.
byproduct radical, pyridine-2-thiyl, with λmax at 490 nm.14,17
The time-resolved spectrum of 23e was obtained by subtracting
the signals observed at short reaction time from those observed
later, with the result that growing signals evolve in a positive
Low-temperature LFP studies with flowing solutions present
an additional problem in that condensation on the cell faces
must be avoided. For studies conducted below 0 °C, a flow
cell in an argon gas-filled, fabricated housing that contained
direction from the baseline and decaying signals evolve
quartz windows was employed. The practical lower temperature
negatively; virtually no decay of the pyridine-2-thiyl radical
limit with our unit is -40 °C, at which temperature we observed
signal at 490 nm occurs in the short time frame of the
cyclopropylcarbinyl radical ring openings.
variations of about (0.25 °C during the course of a series of
runs.
The benzylic radical 7f is a special case. The first observable
The ultimate detectable products from radicals 5 are benzylic
transient, radical 7f, absorbs with λmax at about 315 nm, but the
radicals 22 which were expected to have long wavelength λmax
initial UV spectrum contained a maximum absorbance close to
at about 315-320 nm, and those from radicals 7 are diphenyl-
310 nm due to the combined effect of the superimposition of
alkyl radicals 23 which should have λmax at about 330-335 nm.8
the spectrum of 7f with the bleaching spectrum from destruction
The PTOC esters absorb modestly in the region 300-340 nm,
of the PTOC precursor 21f. With time, the spectrum of the
so the initial photochemical reaction results in a decrease in
benzylic radical 7f evolved smoothly into the spectrum of the
signal intensity, a bleaching, in the region where the products
diphenylalkyl radical 23f (Figure 4). Because the extinction
absorb except for the special case of radical 7f, which is
coefficient of the diphenylalkyl radical is larger than that of
discussed below. Following the initial bleaching, benzylic or
diphenylalkyl radical signals grew in at the expected wave-
lengths. Figure 3 shows some typical spectra observed follow-
(17) Alam, M. M.; Watanabe, A.; Ito, O. J. Org. Chem. 1995, 60, 3440-
3444.

Kinetics of Ring Openings
J. Am. Chem. Soc., Vol. 120, No. 40, 1998 10383
constants smaller than 4 × 107 s-1 is insignificant (<3%) in
comparison to observed temperature variations of (0.25 °C.
For reactions faster than 4 × 107 s-1, the instrumental
response rate was deconvoluted from the observed kinetic traces
by standard Fourier transform (FT) methods using eq 1 where
Kdeconvol ) FT-1[FT(Kexp)/FT(Kinst)]
(1)
Kdeconvol is the deconvoluted kinetic trace, Kexp is the experi-
mentally measured kinetic trace with rate constant kexp, and Kinst
is the impulse response function of the system. In this case,
Kinst was taken to be a “noiseless” exponential function decaying
with a rate of 2.5 × 108 s-1 in order to avoid the introduction
of additional random error. The actual errors in values for kexp
were small in all cases (about 1% for reactions of radicals 7),
but the magnitude of the error after deconvolution increases in
an exponential fashion as the rate constant approaches the
instrumental limit. Thus, for example, the error in kexp ) (8.93
( 0.08) × 107 s-1 increased upon deconvolution to give k )
(9.89 ( 0.35) × 107 s-1. The fastest reaction studied in this
work had kexp ) 1.3 × 108 s-1 which gave k ) 1.6 × 108 s-1
when deconvoluted.
Figure 4. Time-resolved spectra obtained upon irradiation of 21f. (A)
Data collected 0.20, 1.00, 1.80, and 5.80 µs after irradiation; the arrows
show the direction of signal evolution with time. (B) Data from 1.00,
1.80, and 5.80 µs; the data at 0.20 µs have been subtracted to give a
baseline.
Radicals 5a-c and 6a were investigated in preliminary
demonstrations of feasibility before the kinetic unit was equipped
for operation below 0 °C, and a mixture of diastereomers of
the precursors was used in each case. For the primary radicals
5a and 6a in THF, rapid signal growth was observed at 315
nm even at 0 °C; the rate constants for these reactions were
greater than 1 × 108 s-1. Radicals 5b and 5c in THF displayed
measurable rate constants of 5.6 × 107 s-1 at 11 °C for 5b and
3.0 × 107 s-1 at 10.5 °C for 5c. The observed reduction in
rate constants with increasing substitutions was consistent with
expectations suggesting that the method was useful, but the rate
constants were clearly greater than those for the analogous parent
radicals that lacked the reporter groups, indicating that the
reporter groups imparted a small kinetic acceleration. Because
of the relatively weak signal growth from the ultimate benzylic
radical products, which reduced precision in the kinetic mea-
surements, and the fact that diastereomeric radicals were present,
we did not attempt variable-temperature studies with these
systems.
The kinetics of ring openings of radicals 7a-f were measured
in THF and, with the exceptions of 7c and 7f, in acetonitrile.
Each measurement is a sum of ca. 15 experimental runs. A
total of between 10 and 33 independent determinations for each
radical was obtained within the temperature range -41 to +50
°C. Standard errors in kexp were about 1%, and in duplicate
determinations made at a given temperature, the differences in
k were typically 1-3% although differences as small as 0.1%
were obtained in some cases. Two pairs of duplicate measure-
ments made in the -35 to -40 °C range at nominally the same
temperatures differed by 10-12%, suggesting that temperature
control and measurement were becoming significant problems.
Complete listings of observed rate constants for radicals 7
are given in the Supporting Information. Table 1 lists the
Arrhenius functions for the ring-opening reactions and values
of the rate constant at 20 °C calculated from these Arrhenius
functions, and Figure 5 shows the kinetics for 7a-f in graphical
form. The notable features of the kinetics are the following.
High precision was obtained in the Arrhenius functions for most
of the radicals 7, but radicals 7a and 7d reacted so fast that
only a limited range of temperatures could be studied. No
solvent effect was observed for the “alkyl” series of radicals
7a-c, but the polar radicals containing the R-ethoxycarbonyl
group (7d and 7e) displayed obvious solvent effects on
Figure 5. Observed rate constants (s-1) for fragmentations of radicals
7a-f. The hollow symbols are measurements in THF, and the solid
symbols are measurements in acetonitrile. The lines are the Arrhenius
functions in Table 1.
the benzylic radical, the initially observed absorbance at λmax
for 7f never decreased, but an isosbestic point was observed at
304 nm. Figure 4A shows the observed time-resolved spectra
with no corrections, and Figure 4B shows the same spectra with
the data at 200 ns subtracted from data obtained later. The
subtraction procedure removes negative signals from the bleach-
ing of precursor 21f and positive signals from the spectrum of
the initially formed radical 7f. The spectrum in Figure 4B is
mainly that of the diphenylalkyl radical product 23f because
the extinction coefficients of benzylic radicals are only about
25% as great as those of diphenylalkyl radicals at the respective
λ
max values and benzylic radicals have no appreciable absorbance
above 330 nm.8
Kinetics. The ring-opening reactions of cyclopropylcarbinyl
radicals have rate constants in the range of 108 s-1 at ambient
temperature, and the reporter groups impart a small kinetic
acceleration to these reactions as discussed below. Thus, we
performed studies with several systems at temperatures within
the range of -40 to +50 °C. The minimum represents the lower
limit of our apparatus. An upper temperature limit exists due
to the thermal instability of the PTOC esters, but there is also
a maximum kinetic limit due to the response time of the
electronics of the system. The measured response of our
apparatus to an “instantaneous” signal was 2.5 × 108 s-1. This
instrumental response will be convoluted into all kinetic
measurements, but the error introduced in reactions with rate

10384 J. Am. Chem. Soc., Vol. 120, No. 40, 1998
Horner et al.
Table 1. Arrhenius Parameters and Rate Constants for the Ring Openings of Radicals 7a
radical
solvent
temp range (°C)
pointsb
log A
Ea (kcal/mol)
k(20)c (s-1
)
7a
THF
CH3CN
THF
THF
THF
CH3CN
THF
THF
CH3CN
THF
CH3CN
THF
-39 to -15
-39 to -15
-31 to 20
-41 to 12
18
10
18
30
12.89 ( 0.38
12.94 ( 0.30
12.81 ( 0.15
12.66 ( 0.16
12.74 ( 0.11
12.72 ( 0.16
13.10 ( 0.16
13.18 ( 0.58
13.84 ( 0.70
12.88 ( 0.10
12.79 ( 0.17
13.39 ( 0.32
5.75 ( 0.34
5.81 ( 0.34
6.18 ( 0.18
6.03 ( 0.19
6.11 ( 0.13
6.12 ( 0.15
6.86 ( 0.19
6.22 ( 0.65
6.76 ( 0.79
7.46 ( 0.13
7.23 ( 0.21
10.32 ( 0.43
3.9 × 108
4.0 × 108
1.57 × 108
1.43 × 108
1.50 × 108
1.41 × 108
0.95 × 108
3.4 × 108
6.2 × 108
2.04 × 107
2.46 × 107
4.81 × 105
7bd
7be
7bf
7be
7c
-40 to -5
-31 to 21
-39 to -10
-40 to -15
-37 to 49
-38 to 49
-9 to 50
16
18
12
10
22
33
14
7d
7e
7f
a Errors are at 2σ. b Number of independent determinations. c Rate constant at 20 °C. d Diastereomer 1. e Diastereomer 2. Weighted average of
both diastereomers.
f
Table 2. Relative Energies (kcal/mol) for Radicals 24a
radical antib
synb
rot TSc anti-TSd syn-TSd PMP2e
24a
24b
24c
24d
24e
24v
0
0
0
0
0
0
3.0
2.5
8.4
8.6
9.0
10.2
11.6
8.31
7.47
0.7
(1.2)f
1.2
9.5
(1.5)g
5.4
11.6
13.0
0.8
4.1
12.81
a Results at the B3LYP/6-31G*//B3LYP/6-31G* level. See Figure
6 for structures. b Energies for the bisected minima. c Transition state
for rotation. d Transition states for ring opening. e PMP2/6-31G* barriers
f
for the anti-TS for ring opening from ref 19. Energy of the
Figure 6. Representative computed minima and transition structures
for radicals 24: (a) anti-bisected minimum for 24b, (b) syn-bisected
minimum for 24b, (c) TS for rotation of 24b, (d) anti-TS for the ring
opening of 24b, (e) syn-TS for the ring opening of 24b, (f) perpendicular
(local) minimum for 24c.
perpendicular minimum. g Barrier for rotation between the bisected and
perpendicular minima.
proceeding from THF to acetonitrile. Despite intuitive notions
regarding radical stabilities, the ester-substituted secondary
radical 7d opened more rapidly than the methyl-substituted
secondary radical 7b. The benzylic radical 7f reacted nearly 3
orders of magnitude less rapidly than the unsubstituted parent
radical 7a, as one would expect. The observed rate constants
for 7f are listed, but this special system requires analysis in
terms of a prior equilibration (see Discussion).
barrier for the ring opening of the cyclopropylcarbinyl radical
(24a) computed at the G2 level was 7.89 kcal/mol,18,19 and
PMP2/6-31G* calculations with thermal corrections for the
barriers for the ring opening of 24a and 24b were 8.31 and
7.47 kcal/mol, respectively.18
The minimum-energy conformations of radicals 24 are
“bisected” structures with the substituents on the radical center
perpendicular to the C2-C3 bond of the cyclopropyl ring. Two
minima exist for the unsymmetrically substituted radicals 24b,
24d, and 24e, anti and syn with respect to the ring (Figure 6).
Low barriers for rotation through “perpendicular” transition
states were found. The dimethyl-substituted radical 24c is a
special case where the bisected conformer is the global minimum
and the perpendicular structure is a local minimum (Figure 6);
this unusual situation has the unpleasant result that the computed
global minimum-energy structure of 24c changes depending on
the level of theory employed. The low-energy rotational barriers
for the cyclopropylcarbinyl radicals permit production of an
equilibrium population of conformers before ring opening. Thus,
any differences in populations arising from the initial photo-
chemical generation of radicals from different diastereomers of
a precursor will not be important, as was specifically demon-
strated for the ring opening of radical 7b.
All of the transition structures for the ring openings of radicals
24 were similar; Figure 6 shows examples. The breaking bond
of the cyclopropyl ring (C1-C2) is offset slightly from collinear
with the p orbital of the radical center. This results in an
eclipsing interaction between C3 of the cyclopropyl ring and
one of the groups at the nearly sp2-hybridized radical center.
For the radicals that are not symmetrically substituted at the
radical center (24b, 24d, and 24e), the eclipsing interaction
resulted in differences in energies for the two possible transition
states for ring opening that amounted to 1-1.5 kcal/mol. From
Computational Studies. The LFP kinetic results for radicals
7 were quite precise, and it was of interest to compare them
with computational results. Affordable computational results
closely track with the experimental rate constants for reactions
of simple cyclopropylcarbinyl radicals,18,19 and the B3LYP20
hybrid density functional theory (DFT) method is known to be
quite accurate for radicals.21 We studied the simple cyclopro-
pylcarbinyl radicals 24 with B3LYP at the 6-31G* level.
Table 2 lists relative energy values for radicals 24. Our
objective was to compare the results for different substitution
patterns, and the barriers are not corrected with zero point
energies. More powerful computers than the PC we employed
would permit more accurate calculations in terms of absolute
values, and the barriers for the ring-opening reactions would
be slightly reduced by incorporation of thermal corrections due
to bond relaxations in the transition states. For example, the
(18) Martinez, F. N.; Schlegel, H. B.; Newcomb, M. J. Org. Chem. 1996,
61, 8547-8550.
(19) Martinez, F. M.; Schlegel, H. B.; Newcomb, M. J. Org. Chem. 1998,
63, 3618-3623.
(20) Becke, A. D. J. Chem. Phys. 1993, 98, 5648-5652.
(21) Fox, T.; Kollman, P. A. J. Phys. Chem. 1996, 100, 2950-2956.

Kinetics of Ring Openings
J. Am. Chem. Soc., Vol. 120, No. 40, 1998 10385
constants for the ring openings of radicals 5, 7, 24. Relative
rate constants at 20 °C are given in eqs 2-5 where R is the
Figure 7. Rate constants for radical ring openings at 20 °C.
(24, experimental) R ) 1.00:0.47:0.22
(5) R ) 1.00:0.38:0.20
(2)
(3)
(4)
(5)
the energies of the transition states, one can calculate the
reactivity through each channel. For example, at ambient
temperature, the reaction through the high-energy channel in
the methyl-substituted radical 24b (the methyl-eclipsing C3 of
the ring) will be 0.2 times as fast as the reaction through the
low-energy channel. The result will be that the log A term in
the Arrhenius function for the ring opening of 24b should be
slightly smaller (by about 0.1) than those for symmetrically
substituted radicals that have degenerate pathways for ring
opening.
A phenyl-substituted cyclopropylcarbinyl radical was too
large to calculate with the resources available, but the vinyl-
substituted radical 24v is a reasonable model for the a phenyl-
substituted cyclopropylcarbinyl radical that has been addressed
computationally.19 The low-energy transition-state barrier for
the ring opening of 24v was 4.5 kcal/mol larger than the barrier
for the opening of 24a at the PMP2/6-31G* level, and the
increased barrier for 24v was due mainly to a loss of resonance
energy of the allylic radical in the transition state.19
(7) R ) 1.00:0.37:0.24
(24, computed) R ) 1.00:0.44:0.37
ratio of rate constants for the 1°, 2°, and 3° radicals in the
indicated series. One should note that the relative errors in the
indirectly measured rate constants for radicals 24 are likely to
be significantly greater than the errors in the directly measured
rate constants for the reporter group series because the methods
for measuring the kinetics of radicals 24 differed. Equation 5
gives the relative rate constants for radicals 24 that one calculates
from the computational barriers to ring opening listed in Table
2 with the assumption that the entropy terms for all fragmenta-
tion channels are the same; the relative rate constants calculated
from the inexpensive computations are clearly useful at the
predictive level.
The absence of a solvent effect on the kinetics of ring
openings of radicals 7a and 7b is noteworthy (see Table 1 and
Figure 5A). It is commonly assumed that simple radical
reactions will not have polarized transition states and, thus, will
not display solvent effects. This is a reasonable assumption
when the radical centers in reactants and products do not have
functional groups, and it was previously demonstrated to hold
by indirect kinetic studies of cyclopropylcarbinyl ring openings
in competition with nitroxyl radical trapping reactions.25 The
demonstration of the absence of a solvent effect for 7a and 7b
at the level of precision available from the direct studies clearly
supports the premise that gas-phase kinetic values or computed
activation energies can be used to predict the kinetics of simple
radical reactions in solution.18,19 However, obvious solvent
effects on the ring-opening reactions of the ester-substituted
radicals 7d and 7e show that functional-group substitution at a
radical center can result in polarized transition states for
seemingly simple reactions.
Ester-Substituted Cyclopropylcarbinyl Radicals. Rota-
tions about the C-C bond between the cyclopropylcarbinyl
carbon and the cyclopropane ring are faster than ring openings
for cyclopropylcarbinyl radicals, as shown by the barriers listed
in Table 2. For the ester-substituted radicals 7d and 7e,
however, two distinct conformers can exist on the time scale
of the ring-opening reactions. Rotation about the bond between
the radical center and the carbonyl carbon that interconverts
the E- and Z-conformers of the ester-substituted radicals is
definitely slower than that of the ring-opening reaction of 7d
and most likely also is slower than the ring opening of 7e.
Discussion
Alkyl-substituted Cyclopropylcarbinyl Radicals. One can
compare the rates of ring openings of radicals 7a-c with those
of other cyclopropylcarbinyl radical reactions in order to
evaluate the kinetic effects of the reporter groups. A brief
comment on the Arrhenius log A terms for cyclopropylcarbinyl
radical fragmentations is given below, but we note here that
the values of log A can be predicted for cyclopropylcarbinyl
radicals due to the rigidity of the systems. This expediency
was previously employed by Bowry, Lusztyk, and Ingold.22
The rate constants at 20 °C for ring-opening reactions of 1°,
2°, and 3° cyclopropylcarbinyl radicals are shown in Figure 7.
The results for the reporter group-containing radicals 5 and 7
were measured by LFP in this work. The rate constant for
radical 24a is from the known Arrhenius function.23 The rate
constants for radicals 24b,22 24c,24 and 2522 are obtained from
Arrhenius functions calculated with the appropriate log A values
using a rate constant measured near room temperature. The
Arrhenius functions for ring openings of the muon-containing
analogues of radicals 24b and 24c do not appear to be
reasonable,4 and the kinetics obtained by this method were not
used. There is a regular increase in rate constants for ring
openings due to the reporter groups with the phenylcyclopropyl
group in radicals 5 giving about a 2.5-fold increase in rate, about
the same amount of acceleration as imparted by the methyl
group in 25. The diphenylcyclopropyl group in radicals 7 results
in a 4-5-fold acceleration.
That the kinetic effects of the reporter groups are relatively
benign is indicated by the consistency of the relatiVe rate
(22) Bowry, V. W.; Lusztyk, J.; Ingold, K. U. J. Am. Chem. Soc. 1991,
113, 5687-5698.
(23) Newcomb, M.; Glenn, A. G. J. Am. Chem. Soc. 1989, 111, 275-
277.
(24) Engel, P. S.; He, S. L.; Banks, J. T.; Ingold, K. U.; Lusztyk, J. J.
Org. Chem. 1997, 62, 1210-1214.
Studies from Fischer’s laboratory gave rate constants of (1-2)

10386 J. Am. Chem. Soc., Vol. 120, No. 40, 1998
Horner et al.
× 106 s-1 at 20 °C for this rotation in ester-substituted
radicals,26,27 and 5-exo cyclizations of ester-substituted radicals
with rate constants of (2-5) × 107 s-1 were shown to be faster
than conformational interconversion.28 Therefore, it is possible
that two reactive forms of 7d and 7e were present in the LFP
experiments. Nevertheless, the kinetic data was well-fit by
single-exponential solutions; that is, double-exponential solutions
of the data gave the same values for the one rate constant,
obtained in single-exponential solutions and small values for
the second rate constant. This requires either that 7d and 7e
were produced primarily in one conformation or that both
conformations reacted with the same rate constants.
An ethoxycarbonyl group is considered to be a radical
stabilizing group, although a consensus on the extent of
stabilization is not apparent. Bordwell’s estimate29 that the
C-H bond-dissociation energy (BDE) of ethyl acetate is about
7.5 kcal/mol less than that of methane appears to be reasonable
and can be compared to the 4.2 kcal/mol reduction in BDE for
ethane relative to methane.30 An intuitive conclusion from the
radical stabilizing effect of the ester group might be that the
ester-substituted radicals 7d and 7e should ring-open less rapidly
than their alkyl-substituted counterparts 7b and 7c. This
conclusion is supported by the computational results at the
B3LYP/6-31G* level which give estimated ring-opening rate
constants at 20 °C for the secondary and tertiary methoxycar-
bonyl-substituted radicals 24d and 24e that are only 0.03 and
0.003 times as fast, respectively, as that for the parent radical
24a.
Nevertheless, the secondary ester-substituted radical 7d reacts
faster than the secondary alkyl radical 7b, and in acetonitrile,
the activation free energy for the fragmentation of 7d is nearly
1 kcal/mol less than that for the ring opening of 7b. The
seemingly counterintuitive kinetic results for 7d must arise from
a polarized transition state for the reaction and are consistent
with previous results. Specifically, thermodynamic cycles for
the additions of an alkyl radical to an alkene and to an acrylate
(the reverse of the fragmentation reactions of 7d and 7e) indicate
that the additions to acrylates are more exothermic by about 2
kcal/mol.31 This value is smaller than the differences in BDE
between alkyl- and ester-substituted radicals because the ester
group also stabilizes the double bond in the acrylate. From
kinetic studies of the additions of alkyl radicals to alkenes and
acrylates, one finds that the ∆Gq for additions to acrylates is
about 4 kcal/mol smaller than that for additions to alkenes.32
The increased stabilization in the transition states for the
additions to acrylates is due to favorable polarization, and the
same polarization will be present in the reverse reaction, the
fragmentation of an ester-substituted radical.
solvent effects with accelerated rearrangements proceeding from
THF to the more polar solvent acetonitrile. Another obvious
effect is that the gas-phase calculated barriers for ring openings
of the ester-substituted radicals are clearly inconsistent with
those for the alkyl radicals.
The tertiary ester-substituted radical 7e fragments less rapidly
than the tertiary alkyl radical 7c by about a factor of 4 at 20
°C, but this appears to be the result of steric effects and not
electronic effects. In the computed transition structures for the
fragmentation reactions of radicals 24, an eclipsing interaction
is produced between one of the substituents at the radical center
and the C3 of the cyclopropyl ring (Figure 6). This eclipsing
interaction can be relieved by distorting the planar radical center
which will produce a minor energy penalty for an alkyl radical
but a more significant penalty for the conjugated ester-
substituted radical. The net result is that the computed energy
barrier for the tertiary alkyl radical 24c is only 0.4 kcal/mol
greater than the lower energy barrier for the ring opening of
the secondary radical 24b; whereas, both energy barriers for
the ring opening of the tertiary ester-substituted radical 24e are
1.4 kcal/mol greater than the corresponding barriers for the
secondary ester-substituted radical 24d.
Polarized transition states for R-ester radical fragmentations
were previously implicated. Metzger and co-workers studied
high-temperature fragmentation reactions of R-methoxycarbonyl
radicals in competition with hydrogen atom transfer trapping
reactions. They found that radical 26 eliminates an ethyl radical
more readily than it eliminates a methyl radical33 and that the
stabilized (methoxycarbonyl)methyl radical cleaves from radical
27 less rapidly than the 2-propyl radical cleaves from 28.34 In
both cases, the less thermodynamically favored fragmentation
is faster because loss of the more nucleophilic radical is favored
by transition-state polarization effects.
The kinetics of ring opening of another ester-substituted
cyclopropylcarbinyl radical, the tert-butoxycarbonyl-substituted
radical 29, was previously studied by Beckwith and Bowry.35
They reported rate constants for the the ring opening of 29 from
competition kinetic studies with nitroxyl radical trapping. Their
rate constants were about 2 orders of magnitude smaller than
those we find for 7d. For example, from the Arrhenius function
for ring opening of 7d in THF, one calculates a rate constant at
80 °C of 2 × 109 s-1, but the reported rate constant for the ring
One effect of polarized transition states is that, unlike the
case of the alkyl-substituted radicals, the rates of the ring
opening of the ester-substituted radicals 7d and 7e displayed
opening of 29 at this temperature is 1.4 × 107 s-1 35
.
Two factors
that should result in a larger rate constant for the ring opening
of 7d are (1) the reporter group in radicals 7a-c resulted in a
4-5-fold acceleration in the rate constants for ring opening in
comparison to those of radicals 24, and a similar acceleration
would be expected for 7d in comparison to 29, and (2) Beckwith
and Bowry’s kinetic studies with 29 were performed in
cyclohexane, a nonpolar solvent that would be expected to
reduce the rate constant for the fragmentation relative to that
observed in THF.
(25) Beckwith, A. L. J.; Bowry, V. W.; Ingold, K. U. J. Am. Chem. Soc.
1992, 114, 4983-4992.
(26) Lung-Min, W.; Fischer, H. HelV. Chim. Acta 1983, 66, 138-147.
(27) Strub, W.; Roduner, E.; Fischer, H. J. Phys. Chem. 1987, 91, 4379-
4383.
(28) Newcomb, M.; Horner, J. H.; Filipkowski, M. A.; Ha, C.; Park, S.
U. J. Am. Chem. Soc. 1995, 117, 3674-3684.
(29) Bordwell, F. G.; Satish, A. V. J. Am. Chem. Soc. 1994, 116, 8885-
8889.
(30) Griller, D.; Kanabus-Kaminska, J. M.; Maccoll, A. THEOCHEM
1988, 40, 125-131.
(31) Benson, S. W. Thermochemical Kinetics, 2nd ed.; Wiley: New York,
1976.
(32) Zytowski, T.; Fischer, H. J. Am. Chem. Soc. 1996, 118, 437-439.
Walbiner, M.; Wu, J. Q.; Fischer, H. HelV. Chim. Acta 1995, 78, 910-
924.
(33) Klenke, K.; Metzger, J. O.; Lu¨bben, S. Angew. Chem., Int. Ed. Engl.
1988, 27, 1168-1170.
(34) Metzger, J. O.; Klenke, K. Chem. Ber. 1990, 123, 875-879.
(35) Beckwith, A. L. J.; Bowry, V. W. J. Am. Chem. Soc. 1994, 116,
2710-2716.

Kinetics of Ring Openings
J. Am. Chem. Soc., Vol. 120, No. 40, 1998 10387
Nevertheless, it seems unlikely that the combination of the
solvent effect and the reporter group effect could amount to
more than an order of magnitude difference in the rate constants
for the ring openings of 7d and 29. Another factor that might
be involved in the large apparent difference in the two sets of
results is the fact that the rate constants for the nitroxyl radical
coupling reaction with the ester-substituted radical 29, the
competing reaction in the Beckwith and Bowry study, were not
available and were estimated to be about 0.25 times as large as
those for reaction of the nitroxyl radical with a secondary alkyl
radical. It is conceivable that the rate constants for nitroxyl
trapping of 29 are as great as those for reaction with an alkyl
radical given that the enthalpies of nitroxyl radical coupling
reactions do not appear to have a large effect on the kinetics.36
It is also possible that the products of nitroxyl radical trapping
were not stable and equilibrated partially by homolysis, radical
rearrangement, and coupling.
The ramifications of the kinetic results with the ester-
substituted radicals 7d and 7e should be emphasized. Cyclo-
propylcarbinyl radical ring openings have often been employed
as mechanistic probes for reactions in which putative radical
intermediates might exist, and He and Dowd have used an ester-
substituted cyclopropane probe (30) and an ester-substituted
2-phenylcyclopropane probe (31) in attempts to determine
whether radicals are involved in model studies of the vitamin
B12-catalyzed methylmalonyl-CoA to succinyl-CoA rearrange-
ment.37 They found that the rearrangements occurred with no
competition with Bu3SnH trapping.39 Beckwith and Bowry later
reported rate constants for cyclization of 33 to 32 determined
via nitroxyl radical trapping reactions;35 their values for the
cyclization (k ) 0.8 × 107 s-1 at 42 °C) are in reasonable
agreement with the rate constant determined by Ingold’s group.
In unpublished work, our group has studied rate constants for
cyclization of 33 by direct LFP methods; the rate constant at
42 °C from direct measurements is virtually identical to that
found by Ingold’s group (1.1 × 107 s-1).40
Because 32 is favored at equilibrium, one cannot directly
measure the rate constants for the ring opening of this radical
in a conventional LFP experiment. Indirect kinetic studies
involving competing trapping reactions are possible,2 and
Beckwith and Bowry35 reported rate constants for ring opening
of 32 determined via nitroxyl radical trapping. In addition, rate
constants for the ring opening of a bicyclic version of radical
32, determined by competitive trapping by t-BuSH, were
reported by Venkatesan and Greenberg.41 In these indirect
studies, however, the rate constants for the competition trapping
reactions were not known and had to be estimated.
The reporter group approach provides a way to circumvent
the equilibrium problem, thus permitting direct LFP kinetic
studies of the ring opening of a benzyl-substituted cyclopro-
pylcarbinyl radical. Product 34a from the ring opening of
radical 7f fragments to 23f with a rate constant in excess of 1
× 1011 s-1,7 several orders of magnitude larger than the rate
constant for the back reaction of 34a to 7f. Nevertheless, the
detectable amount of radical ring opening. Because the ester
substitution has a minimal effect on the kinetics of the ring
openings of cyclopropylcarbinyl radicals and given that the
(trans-2-phenylcyclopropyl)methyl radical is known to ring-open
with a rate constant of 3 × 1011 s-1, the absence of ring-opened
products in their studies with probe 31 requires that the
maximum lifetime of a radical intermediate in the rearrangement
was <5 ps even with conservative estimates of detection
limits,37,38 a value within an order of magnitude of the “lifetime”
of a transition state and much too short for any diffusively free
intermediate.
measured rate constants for formation of 23f are not equal to
those for fragmentation of radical 32 and, in fact, are not
necessarily equal to those for fragmentation of 7f. A small
accelerating effect of the reporter group is expected on the basis
of the results with the simple cyclopropylcarbinyl radicals 7a-
c, and 7f should react faster than 32. In addition, a small
decelerating effect will result from the production of radical
34b in the initial fragmentation of 7f. Because the cyclization
of radical 34b must be on the order of 5 × 106 s-1 at ambient
temperature, about an order of magnitude faster than fragmenta-
tion of 7f, an “equilibrium” between 7f and 34b will be
established, and any 34b present serves as an unreactive
reservoir of 7f with regard to the ultimate production of the
detectable radical 23f.
Phenyl-Substituted Cyclopropylcarbinyl Radicals. The
equilibrium between the phenyl-substituted cyclopropylcarbinyl
radical 32 and its ring-opened product 33 is known to lie on
the side of cyclic radical 32. This was demonstrated by Ingold’s
One can estimate the kinetic effect of production of 34b in
the following manner. The (trans-2-methylcyclopropyl)methyl
radical (25) is known to fragment about equally to the two
possible ring-opened products,22 a result mainly due to ap-
proximately equal amounts of relief of steric compression in
the two possible transition states.18 Therefore, one might assume
that the accelerating effect of the reporter group is also due
mainly to steric effects and that 7f partitions approximately
equally to 34a and 34b. Through the use of this assumption
and the use of the rate constants for cyclization of radical 33
discussed above and that measured for reactions of 7f, the
group in a 1990 paper that disproved claims to the contrary
and showed that the use of phenyl-substituted cyclopropanes
in mechanistic studies could be complicated.39 The Ingold group
established a rate constant of 1.2 × 107 s-1 at 42 °C for the
cyclization of 33 to 32 via isotopic scrambling in 33 in
(36) Bowry, V. W.; Ingold, K. U. J. Am. Chem. Soc. 1992, 114, 4992-
4996.
(37) (a) He, M.; Dowd, P. J. Am. Chem. Soc. 1996, 118, 711. (b) He,
M.; Dowd, P. J. Am. Chem. Soc. 1998, 120, 1133-1137.
(38) Reference 37b places the limit at 50 ps, but this appears to be a
typographical error.
(40) Horner, J. H.; Martinez, F. M.; Tronche, C.; Newcomb, M.; Halgren,
T. A.; Roberts, J. D. To be submitted for publication.
(41) Venkatesan, H.; Greenberg, M. M. J. Org. Chem. 1995, 60, 1053-
1059.
(39) Bowry, V. W.; Lusztyk, J.; Ingold, K. U. J. Chem. Soc., Chem.
Commun. 1990, 923-925.

10388 J. Am. Chem. Soc., Vol. 120, No. 40, 1998
Horner et al.
equilibrium constant for 34b and 7f is found to be about 10
(favoring 7f). Because of the (assumed) equal partitioning of
7f to 34a and 34b, the measured rate constants for production
of 23f would be about 5% smaller than the rate constants for
fragmentation of 7f, about 4.6 × 105 s-1 at 20 °C.42
The symmetry-breaking features of radicals 7 will have only
minor effects on the entropy terms.43 Increasing moments of
inertia for radicals 7 containing substituents at the radical center
will reduce log A slightly, but increasing barriers to rotation
will mitigate that effect somewhat.31 The net result is that log
A should be in the range of about 12.6-13.0 for 7b-f. This
was generally found for the cases in Table 1 where the precision
in log A was good. It is apparent that one can accurately
estimate an Arrhenius function for a cyclopropylcarbinyl radical
ring opening from one precisely measured kinetic value and an
estimated log A term, but estimating log A will require some
computational or experimental results. In the absence of those
results, log A ) 12.8 ( 0.2 is a good approximation for any
substituted cyclopropylcarbinyl radical.
In regard to the specific case of radicals 32 and 33, one might
estimate that the reporter group effect in all radicals 7 is due to
sterics. In this case, the same 4-5-fold acceleration in ring-
opening kinetics at 20 °C would be present in 7f in comparison
with 32. Therefore, the estimated rate constant for the ring
opening of 32 at 20 °C is 1 × 105 s-1. This value can be
compared with a rate constant for the opening of 32 of 4 × 104
s-1 at 20 °C extrapolated from the nitroxyl radical trapping
studies35 and to a total rate constant for two (nondegenerate)
ring openings of a bicyclic version of 32 of 5 × 106 s-1 at 25
°C from t-BuSH trapping studies.41 It is likely that the estimates
for the trapping rate constants in both of the indirect studies
introduced errors, and it would appear that the error in the
estimate of the t-BuSH trapping rate constant is considerable,
although the rigid bicyclic structure of the radical studied might
have had a kinetic effect. Combination of the rate constant for
the ring opening of 32 estimated from our results with the
directly measured rate constant for cyclization of 33 at 20 °C
Conclusion
The reporter group approach permits highly precise direct
measurements of the kinetics of cyclopropylcarbinyl radical ring
openings, a group of reactions for which most of the previously
available kinetic data were obtained by indirect kinetic methods.
The precision in both the kinetic measurements and the derived
Arrhenius functions for the radicals studied here provides highly
reliable radical clocks that might be employed in competition
kinetic and mechanistic studies of radicals or putative radical
intermediates. The power of the approach was shown in the
measurement of the rate constants for the ring openings of ester-
and phenyl-substituted radicals which were studied previously
by competition methods for which the rate constants of the
competing basis reactions were not available. The ester-
substituted radical 7d reacted at least an order of magnitude
faster than one would have predicted on the basis of an earlier
report, and solvent effects on the ring openings of ester-
substituted radicals 7d and 7e were readily demonstrated. The
synthetic route presented gives a diastereomerically pure
intermediate (15a) that can be converted to a wide range of
radical precursors.
(k ) 5.6 × 106 s-1 40
gives an equilibrium constant of K ≈ 60
)
favoring 32; the benzyl-substituted cyclopropylcarbinyl radical
32 is clearly favored, as demonstrated by Ingold’s group.39
Entropic Terms. One of the attractions of studying cyclo-
propyl systems is that the rigidity of the compounds precludes
much of the conformational freedom one would have in an
acyclic compound and the transition states for its reactions. In
the case of the ring opening of the cyclopropylcarbinyl radical
(24a), Ingold has previously noted that the entropy of activation
(∆Sq) could be predicted with confidence.3 To obtain the
transition state, the rotation of the methylene group must be
“frozen”, which results in an entropic penalty. However, the
cyclopropylcarbinyl radical has four equivalent reaction channels
available for ring opening (two by virtue of the symmetrical
substitution at the radical center and two from the different
bonds in the cyclopropyl ring that can break), and this increases
log A. At ambient temperature, these two effects cancel such
that ∆Sq ) 0 and log A ) 13.15 at ambient temperature.3
The calibration of the cyclopropylcarbinyl radical ring
opening using rate data obtained from kinetic ESR, nitroxyl
trapping, and PhSH trapping results that span a total of about
250 °C gives exactly the above value, log A ) 13.15.23 The
agreement of the experimental result with the result predicted
thermochemically leads to the reasonable expectation that one
can compute an accurate Arrhenius function for a cyclopropyl-
carbinyl radical ring opening from one precisely determined rate
constant and the assumption that log A must be 12.85 for each
bond that can break; this expedient has been employed previ-
ously.22
Experimental Section
General Methods. Commercially available reagents were purchased
from either the Sigma or the Aldrich chemical companies and were
used as received. Tetrahydrofuran (THF) and diethyl ether were
distilled under a nitrogen atmosphere from sodium benzophenone ketyl.
Methylene chloride was distilled under nitrogen from phosphorus
pentoxide. Dimethyl sulfoxide (DMSO) and dimethylformamide
(DMF) were distilled under reduced pressure from calcium hydride.
The sodium salt of N-hydroxypyridine-2-thione was purified as
described previously.44 2,2-Diphenylcyclopropanecarboxaldehyde was
prepared by PCC oxidation of (2,2-diphenylcyclopropyl)methanol.45 1
H
NMR spectra (300 or 500 MHz) and 13C NMR spectra (75 or 125 MHz)
were obtained on Varian Gemini 300 and Unity 500 spectrometers.
Melting points were obtained on a Thomas-Hoover capillary melting
(43) Two symmetry-breaking features are possible for radicals 7, the
reporter group and the substituents at the radical center. On the basis of (1)
the observation that the C1-C2 and C1-C3 bond breaking in trans-2-
methylcyclopropylcarbinyl radical (25) are nearly equal,22 (2) the compu-
tational results that suggest that the effect of the methyl group in 25 is
almost entirely due to sterics,18 and (3) the observation by NMR
spectroscopy that reactions of 5a, 6a, and 7a in the presence of PhSH gave
products containing some intact cyclopropyl groups, we assume that the
C1-C2 and C1-C3 bond breakings in radicals 7 occur with equal rates.
The maximum possible effect of the substituent at the radical center in
radicals 7b and 7d-f would be to preclude one reaction channel which
would reduce log A by 0.3. From the computational results in Table 2, the
minimum effect of the substituent would be for radical 24b where log A
would be reduced by 0.1.
(42) We note in passing that the kinetic effect due to the initial
partitioning of 7f is a result of the fact that the back cyclization of 37b to
7f is faster than fragmentation of 7f. Similar effects are not possible for the
other reporter group radicals studied in this work because the back reactions
are slower than the initial fragmentations. The 3-butenyl radical has a rate
constant for cyclization on the order of 104 s-1 at ambient temperature,2
and that for the 4-(tert-butoxycarbonyl)-3-butenyl radical is about 1 × 107
s-1 35
The effects of back reactions for these cases would be the
.
superimposition of a slow reaction (the back cyclization reaction) with the
fast reaction fragmentation with a net effect of double-exponential kinetic
behavior if the transients 23 were persistent and data were acquired for an
extended period. For all cases except 7f, the measured kinetics are the sum
of the rate constants for fragmentation to both possible products.
(44) Esker, J. L.; Newcomb, M. J. Org. Chem. 1993, 58, 4933-4940.
(45) Walborsky, H. M.; Barash, L.; Young, A. E.; Impasato, F. J. J.
Am. Chem. Soc. 1961, 83, 2517-2525.

Kinetics of Ring Openings
J. Am. Chem. Soc., Vol. 120, No. 40, 1998 10389
point apparatus and are uncorrected. High-resolution mass spectral
analyses and X-ray structural determinations were performed by the
Central Instrumentation Facility at Wayne State University.
(37), 205 (17), 193 (16), 192 (11), 191 (32), 178 (19), 167 (56), 165
(31), 155 (16), 154 (29), 141 (12), 129 (16), 115 (26), 105 (13), 91
(100), 77 (12), 55 (34). HRMS of 15b, C21H23NO2: calcd, 321.1729;
found, 321.1723.
X-ray Crystallography. Crystallographic data were collected at
room temperature on a S/N/S automated R3 diffractometer with
monochromated Cu radiation. The structures were solved using the
programs in SHELXL-93.46
The syntheses of amides 14 and 2-(2,2-diphenylcyclopropyl)-
cyclopropanes 15, the starting point for all precursors to radicals 7,
are given here. Synthetic details for preparation of PTOC esters 21
are in Supporting Information.
(E)-N-Methoxy-N-methyl-3-(2,2-diphenylcyclopropyl)propen-
amide ((E)-14) and (Z)-N-Methoxy-N-methyl-3-(2,2-diphenylcyclo-
propyl)propenamide ((Z)-14). 2,2-Diphenylcyclopropanecarboxal-
dehyde (13.75 g, 0.061 mol) and N-methoxy-N-methyl-2-(triphenyl-
phosphoranylidene)acetamide (24.5 g, 0.067 mol) were dissolved in
methylene chloride and stirred at room temperature overnight. The
solvent was removed under reduced pressure to give a brown semisolid
mass. Addition of hexanes/EtOAc (3/1, 1 L) caused a tan precipitate
to form. After filtration through a bed of silica to remove the
precipitate, the filtrate was concentrated under reduced pressure to give
a yellow oil. The crude product was chromatographed on silica (3/1
hexanes/EtOAc) to give, in order of elution, (Z)-14 (2.62 g, 14%) as
an oil and (E)-14 (14.35 g, 76%) as a white solid. Mp: 78-81 °C. 1H
NMR of (E)-14 (300 MHz): δ 1.73 (t, J ) 5.3 Hz, 1 H), 1.80 (dd, J
) 8.5, 4.9 Hz, 1 H), 2.45 (ddd, J ) 10.1, 8.5, 5.8 Hz, 1 H), 3.19 (s, 3
H), 3.67 (s, 3 H), 6.33 (dd, J ) 15.5, 10.1 Hz, 1 H), 6.53 (d, J ) 15.5
Hz, 1 H), 7.1-7.3 (m, 10 H). 13C NMR of (E)-14 (75 MHz): δ 23.4,
30.7, 32.3, 39.6, 61.6, 117.6, 126.2, 127.0, 127.2, 128.4, 128.6, 130.7,
140.5, 145.8, 148.3, 166.5. MS of (E)-14 m/z (rel int): 307 (4), 277
(10), 276 (35), 219 (55), 217 (21), 204 (18), 203 (15), 202 (16), 191
(14), 178 (16), 165 (30), 141 (33), 127 (100), 115 (33), 97 (17), 95
(35), 91 (97). HRMS of (E)-14, C20H21NO2: calcd, 307.1572; found,
307.1568. 1H NMR of (Z)-14 (300 MHz): δ 1.65 (t, J ) 5.2 Hz, 1 H),
1.72 (dd, J ) 8.5, 4.9 Hz, 1 H), 3.27 (s, 3 H), 3.67 (s, 3 H), 3.92 (ddd,
J ) 10.6, 8.5, 5.8 Hz, 1 H), 5.30 (t, J ) 11.1 Hz, 1 H), 6.22 (d, J )
11.6 Hz, 1 H), 7.1-7.3 (m, 10 H). 13C NMR of (Z)-14 (75 MHz): δ
23.9, 26.1, 32.3 (br), 39.8, 61.5, 126.1, 126.6, 127.9, 128.3, 128.4, 130.5,
141.5, 145.9, 148.9, 167.9. MS of (Z)-14 m/z (rel int): 276 (6), 219
(13), 178 (11), 141 (12), 127 (100), 115 (14), 105 (16), 96 (35), 91
(34), 77 (11). HRMS of (Z)-14, C19H18NO (M+ - OCH3): calcd,
276.1388; found, 276.1383.
Structure of Compound 15a. Crystals of 15a suitable for X-ray
crystallography were grown by slow (1 week) crystallization from
diethyl ether/hexanes. Compound 15a consisted of colorless, striated,
flat rods. Compound 15a belongs to the triclinic space group P(-1)
with a ) 11.1311(12) Å, b ) 12.983(2) Å, c ) 14.162(2) Å, R )
67.597(12)0, â ) 88.428(11)0, γ ) 70.483(10)°, Z ) 4, and D ) 1.205
g/cm3. Absorption corrections were applied on the basis of ψ scans.
The asymmetric unit contains two crystallographically independent
molecules. R ) 0.0470, and Rw2 ) 0.1328 for 3348 reflections with I
> 2σ(I). [R ) 0.0615 for all data.] GOF ) 1.074. Other experimental
parameters along with positional and anisotropic thermal parameters
are given in Supporting Information.
Structure of Compound 19b (Diastereomer 1). Crystals of 19b
(diastereomer 1) suitable for X-ray crystallography were grown by slow
(1 week) crystallization from hexanes/EtOAc. Diastereomer 1 of 19b
belongs to the monoclinic space group P21/c with a ) 10.2756(14) Å,
b ) 23.384(4) Å, c ) 7.6671(8) Å, â ) 111.831(9)°, Z ) 4, and D )
1.190 g/cm3. R ) 0.0372, and Rw2 ) 0.0957 for 2113 reflections with
I > 2σ((I). [R ) 0.0442 for all data.] GOF ) 1.029. Other
experimental parameters along with positional and anisotropic thermal
parameters are given in Supporting Information.
Kinetic Measurements and Data Analysis. All kinetic measure-
ments 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 for low-
temperature measurements consisted of a jacketed funnel attached
directly to a UV cuvette. A Neslab ULT-80 circulating bath was used
to circulate chilled fluid through the jacket of the funnel. For
measurements below 0 °C, the entire funnel and cuvette assembly was
enclosed in a box made of black Delrin. The box was equipped with
four optical windows which allowed the laser and analyzing beams to
pass through the sample cuvette. The interior of the box was flushed
with argon to prevent water condensation. Sample temperatures were
measured by means of a copper-constantan thermocouple wire inserted
into the interior of the cuvette through the sample outflow opening.
Data were digitized using a Hewlett-Packard 54522 oscilloscope with
a maximum time resolution of 0.5 ns. Each kinetic trace contained
512 data points. Typically, two sets of data, each containing 14 kinetic
traces, were collected at one temperature. Each set was summed to
improve the signal/noise ratio. For kinetic traces with rates greater
than 4 × 107 s-1, the observed kinetic trace is the convolution of the
impulse response of the instrument with the real kinetic trace. To carry
out deconvolution, the traces were zero-filled to 512 points and Fourier
transformed. This Fourier transformed trace was then divided by the
“noiseless” Fourier transform calculated to match the instrument impulse
response function. The resulting function was inverse Fourier trans-
formed to generate the deconvoluted kinetic trace.
N-Methoxy-N-methyl-trans-2-(2,2-diphenyl-1R*-cyclopropyl)-
1S*,2R*-cyclopropanecarboxamide (15a) and N-Methyl-N-methoxy-
trans-2-(2,2-diphenyl-1R*-cyclopropyl)-1R*,2R*-cyclopropanecar-
boxamide (15b). Trimethylsulfoxonium iodide (26.5 g, 0.12 mol) was
added slowly over 2 h via a solids addition funnel to a stirred suspension
of NaH (2.90 g, 0.12 mol) in DMSO (70 mL). After this mixture was
stirred for an additional 0.5 h, a solution of (E)-14 (11.5 g, 0.037 mol)
in DMSO (70 mL) was added, and the reaction mixture was stirred for
30 h at room temperature. The reaction mixture was poured into brine
(300 mL) and extracted with ether/methylene chloride (1/1). The
organic layer was washed with brine and dried over MgSO4. The
solvent was removed under reduced pressure, and the resulting crude
product was chromatographed on silica gel (3/1 hexanes/EtOAc) to
give a white solid (7.1 g) as a 5.5/1 mixture of diastereomers (15a and
15b). The major isomer (15a) was obtained by recrystallization from
hexanes/EtOAc (5.8 g, 60%). Mp: 83-84 °C. Slow concentration of
the mother liquors gave 15b (0.21 g, 2%). Mp: 91-92 °C. 1H NMR
of 15a: δ 0.65 (ddd, J ) 8.0, 6.0, 3.9 Hz, 1 H), 0.90-1.2 (m, 2 H),
1.22-1.38 (m, 2 H), 1.58 (dt, J ) 8.5, 6.1 Hz, 1 H), 2.10 (br m, 1 H),
3.19 (s, 3 H), 3.78 (s, 3 H), 7.1-7.5 (m, 10 H). 13C NMR of 15a: δ
14.4, 17.6, 19.3, 23.2, 28.8, 32.7, 35.4, 61.6, 125.6, 126.5, 127.2, 128.2,
130.7, 141.3, 146.9, 174.0. MS of 15a m/z (rel int); 321 (7.6), 290
(15), 261 (6), 233 (14), 217 (26), 206 (40), 205 (17), 193 (16), 192
(11), 191 (33), 178 (16), 167 (62), 165 (30), 155 (16), 154 (31), 141
(11), 129 (16), 115 (27), 105 (14), 91 (100), 77 (11), 55 (29). HRMS
Instrument Response Time. When the (2,2-diphenylcyclopropyl)-
carbinyl radical was generated by flash photolysis from the corre-
sponding PTOC ester, a kinetic trace corresponding to a growth of 2.5
× 108 s-1 was observed. Because this radical was previously found
by indirect methods to open with a rate constant of 6 × 1011 s-1 at 20
(46) Sheldrick, G. M. SHELXL-93: Program for Crystal Structure
Refinement; University of Go¨ttingen, Germany, 1993.
(47) 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.; and Pople, J. A. Gaussian-94; Gaussian, Inc.:
Pittsburgh, PA, 1995.
1
of 15a, C21H23NO2: calcd, 321.1729; found, 321.1725. H NMR of
15b (500 MHz): δ 0.95 (m, 2 H), 1.22 (m, 1 H), 1.34 (m, 3 H), 2.06
(br m, 1 H), 3.11 (s, 3 H), 3.66 (s, 3 H), 7.13 (m, 3 H), 7.21 (m, 3 H),
7.30 (t, J ) 7.4 Hz, 2 H), 7.42 (d, J ) 7.3 Hz, 2 H). 13C NMR of 15b
(125 MHz): δ 15.1, 17.4, 20.2, 23.2, 29.8, 32.5 (br), 35.5, 61.4, 125.6,
126.5, 127.2, 128.2, 128.4, 130.8, 141.4, 146.9, 173.6 (br). MS of
15b m/z (rel int): 321 (11), 290 (15), 261 (5), 233 (15), 217 (27), 206
(48) Hariharan, P. C.; Pople, J. A. Theor. Chim. Acta 1973, 28, 213.

10390 J. Am. Chem. Soc., Vol. 120, No. 40, 1998
Horner et al.
°C,7 the rate observed in the kinetic traces must correspond to the
electronic response of the detection system. The impulse response of
the system for use in deconvolution was therefore taken as a decaying
Dr. M. J. Heeg for performing the X-ray structural determina-
tions.
Supporting Information Available: Tables of kinetic data
for radicals 7; tables of crystallographic data, atomic coordinates,
and anisotropic displacement parameters for 15a and 19b
(diastereomer 1); and synthetic procedures for preparation of
all compounds in Scheme 3 (34 pages, print/PDF). See any
current masthead page for ordering information and Web access
instructions.
exponential with a rate of 2.5 × 108 s-1
.
Computational Methods. Ab initio molecular orbital calculations
were performed using the Gaussian 94 series of programs47 on a PC.
Reactants and transition structures were optimized with the B3LYP20
hybrid density functional theory using the 6-31G*48 basis set.
Acknowledgment. We thank the National Science Founda-
tion for financial support via grant CHE-9614968. We thank
JA9819460