Kinetics and thermodynamics of H? transfer from (η 5-C5R5)Cr(CO)3H (R = Ph, Me, H) to methyl methacrylate and styrene

Article abstract of DOI:10.1021/ja034927l

The rates of H/D exchange have been measured between (a) the activated olefins methyl methacrylate-d₅ and styrene-d₈, and (b) the Cr hydrides (η⁵-C₅Ph₅)Cr(CO) ₃H (2a), (η⁵-C₅Me₅)Cr(CO) ₃H (2b), and (θ⁵-C₅H ₅)Cr(CO)₃H (2c). With a large excess of the deuterated olefin the first exchange goes to completion before subsequent exchanges begin, at a rate first order in olefin and in hydride. (Hydrogenation is insignificant except with styrene and CpCr(CO)₃H; in most cases, the radicals arising from the first H? transfer are too hindered to abstract another HH?.) Statistical corrections give the rate constants k_reint for H? transfer to the olefin from the hydride. With MMA, k_reint decreases substantially as the steric bulk of the hydride increases; with styrene, the steric bulk of the hydride has little effect. At longer times, the reaction of MMA or styrene with 2a gives the corresponding metalloradical 1a as termination depletes the concentration of the methyl isobutyryl radical 3 or the α-methylbenzyl radical 4; computer simulation of [1a] as f(t) gives an estimate of k_tr, the rate constant for H? transfer from 3 or 4 back to Cr. These rate constants imply a ΔG (50 °C) of +11 kcal/mol for H? transfer from 2a to MMA, and a ΔG (50 °C) of +10 kcal/mol for H? transfer from 2a to styrene. The CH₃CN pK_a of 2a, 11.7, implies a BDE for its Cr-H bond of 59.6 kcal/mol, and DFT calculations give 58.2 kcal/mol for the Cr-H bond in 2c. In combination the kinetic ΔG values, the experimental BDE for 2a, and the calculated ΔS values for H? transfer imply a C-H BDE of 45.6 kcal/mol for the methyl isobutyryl radical 3 (close to the DFT-calculated 49.5 kcal/mol), and a C-H BDE of 47.9 kcal/mol for the α-methylbenzyl radical 4 (close to the DFT-calculated 49.9 kcal/mol). A solvent cage model suggests 46.1 kcal/mol as the C-H BDE for the chain-carrying radical in MMA polymerization.

Full text of DOI:10.1021/ja034927l

Published on Web 07/25/2003
Kinetics and Thermodynamics of H• Transfer from
(η5-C5R5)Cr(CO)3H (R ) Ph, Me, H) to Methyl Methacrylate and
Styrene
Lihao Tang,† Elizabeth T. Papish,† Graham P. Abramo,† Jack R. Norton,*,†
Mu-Hyun Baik,† Richard A. Friesner,† and Anthony Rappe´‡
Contribution from the Departments of Chemistry, Columbia UniVersity, 3000 Broadway,
New York, New York 10027, and Colorado State UniVersity, Fort Collins, Colorado 80523
Received February 28, 2003; E-mail: jnorton@chem.columbia.edu
Abstract: The rates of H/D exchange have been measured between (a) the activated olefins methyl
methacrylate-d5 and styrene-d8, and (b) the Cr hydrides (η5-C5Ph5)Cr(CO)3H (2a), (η5-C5Me5)Cr(CO)3H
(2b), and (η5-C5H5)Cr(CO)3H (2c). With a large excess of the deuterated olefin the first exchange goes to
completion before subsequent exchanges begin, at a rate first order in olefin and in hydride. (Hydrogenation
is insignificant except with styrene and CpCr(CO)3H; in most cases, the radicals arising from the first H•
transfer are too hindered to abstract another H•.) Statistical corrections give the rate constants kreinit for H•
transfer to the olefin from the hydride. With MMA, kreinit decreases substantially as the steric bulk of the
hydride increases; with styrene, the steric bulk of the hydride has little effect. At longer times, the reaction
of MMA or styrene with 2a gives the corresponding metalloradical 1a as termination depletes the
concentration of the methyl isobutyryl radical 3 or the R-methylbenzyl radical 4; computer simulation of
[1a] as f(t) gives an estimate of ktr, the rate constant for H• transfer from 3 or 4 back to Cr. These rate
constants imply a ∆G (50 °C) of +11 kcal/mol for H• transfer from 2a to MMA, and a ∆G (50 °C) of +10
kcal/mol for H• transfer from 2a to styrene. The CH3CN pKa of 2a, 11.7, implies a BDE for its Cr-H bond
of 59.6 kcal/mol, and DFT calculations give 58.2 kcal/mol for the Cr-H bond in 2c. In combination the
kinetic ∆G values, the experimental BDE for 2a, and the calculated ∆S values for H• transfer imply a C-H
BDE of 45.6 kcal/mol for the methyl isobutyryl radical 3 (close to the DFT-calculated 49.5 kcal/mol), and
a C-H BDE of 47.9 kcal/mol for the R-methylbenzyl radical 4 (close to the DFT-calculated 49.9 kcal/mol).
A solvent cage model suggests 46.1 kcal/mol as the C-H BDE for the chain-carrying radical in MMA
polymerization.
Introduction
Chain-transfer catalysis is thought to involve removal of H•
from the propagating radical chain, giving a vinyl-terminated
Metalloradicals have proven to be effective catalysts for chain
transfer during free radical polymerizations.1 Although the
original (and most effective) chain transfer catalysts have been
cobalt(II) complexes,2 we have found that the hindered chro-
mium metalloradical (η5-C5Ph5)Cr(CO)3•3 (1a) is also an
effective catalyst for chain transfer during the AIBN-initiated
polymerization of methyl methacrylate.4 Recently Poli and co-
workers have reported two Mo(III) complexes that are active
chain-transfer catalysts during the polymerization of styrene.5
polymer and a metal hydride (eq 1), followed by transfer of
that H• to monomer to start a new chain (eq 2). Such catalysis
reduces the molecular weight of the polymer.1 In effect, the
catalyst moves H• from the end of a growing chain to the
beginning of a new one.
† Columbia University.
‡ Colorado State University.
(1) (a) Gridnev, A. A.; Ittel, S. D. Chem. ReV. 2001, 101, 3611-3659. (b)
Gridnev, A. J. Polymer Sci: Part A: Polym. Chem. 2000, 38, 1753-1766.
(2) (a) Enikolopyan, N. S.; Smirnov, B. R.; Ponomarev, G. V.; Bel’govskii, I.
M. J. Polym. Sci., Polym. Chem. Ed. 1981, 19, 291. (b) Burczyk, A. F.;
O’Driscoll, K. F.; Rempel, G. L. J. Polym. Sci., Chem. Ed. 1984, 22, 3255.
(c) Gridnev, A. A. Polym. Sci. U. S. S. R. (Engl. Transl.) 1989, 31, 2369.
For reviews see: (d) Karmilova, L. V.; Ponomarev, G. V.; Smirnov, B.
R.; Belgovskii, I. M. Russ. Chem. ReV. (Engl. Transl.) 1984, 53, 132. (e)
Moad, G.; Solomon, D. H. The Chemistry of Free Radical Polymerization;
Pergamon: New York, 1995; Section 5.3.2.7
The instability of Co and Mo hydrides has made it difficult
to observe eq 2 directly. We have, however, prepared (η5-C5-
Ph5)Cr(CO)3H (2a) and observed eq 2 directly by treating 2a
with methyl methacrylate (MMA) monomer.4 Heating a solution
of (η5-C5Ph5)Cr(CO)3H in MMA causes polymerization to
(3) Hoobler, R. J.; Hutton, M. A.; Dillard, M. M.; Castellani, M. P.; Rheingold,
A. L.; Rieger, A. L.; Rieger, P. H.; Richards, T. C.; Geiger, W. E.
Organometallics 1993, 12, 116-123.
(5) Grognec, E. L.; Claverie, J.; Poli, R. J. Am. Chem. Soc. 2001, 123, 9513,
(4) Abramo, G. P.; Norton, J. R. Macromolecules 2000, 33, 2790-2792.
and references therein.
9
10.1021/ja034927l CCC: $25.00 © 2003 American Chemical Society
J. AM. CHEM. SOC. 2003, 125, 10093-10102
10093

A R T I C L E S
Tang et al.
Scheme 1
k1 ) Skreinit
(5)
If we define kH in Scheme 2 as the second-order rate constant
for H• transfer to the metalloradical 1 from the deuterated methyl
isobutyryl radical 3-d5, and kD as the second-order rate constant
for D• transfer to 1 from 3-d5, then the selectivity factor S can
be written as in eq 6. (We neglect any secondary isotope effects,
and we defer consideration of cage effects.) By simplifying and
dividing by kD, S can be expressed in terms of kH/kD
begin, along with the slow conversion of the hydride 2a to the
metalloradical 1a.
5
6
There have been many previous reports of H• transfer from
transition-metal hydrides to carbon-carbon double bonds,
although the result has usually been hydrogenation. In 1975,
Feder and Halpern proposed that the HCo(CO)4-catalyzed
hydrogenation of anthracene to 9,10-dihydroanthracene involved
H• transfer.6 In 1977, Sweany and Halpern reported convincing
evidence (CIDNP and an inverse isotope effect for HMn(CO)5/
DMn(CO)5) for such a mechanism in the hydrogenation of
R-methylstyrene by HMn(CO)5 (Scheme 1).7 Other cases have
been summarized in a review.8
To assess the ability of different metalloradicals to catalyze
chain transfer, and to understand why (η5-C5Ph5)Cr(CO)3H does
not hydrogenate MMA when HMn(CO)5 is known to hydro-
genate R-methylstyrene, we have examined the kinetics and
thermodynamics of the reactions of (η5-C5R5)Cr(CO)3H (R )
Ph, 2a; R ) Me, 2b; R ) H, 2c) with MMA and styrene. This
variation in the cyclopentadienyl substituent provides a large
range of steric bulk in the hydride complexes.
kD[Cr•]
5
5
8
S )
)
≈
(6)
5
6
1
6
kH
kD
kD[Cr•] + kH[Cr•]
5 +
Of course, kH and kD are related by a normal primary kinetic
isotope effect. One estimate of its size can be obtained from
the observed isotope effect (2.93) on the disproportionation rate
constant for free radical polymerization of MMA at 60 °C.9
Another estimate (average value 3.5 between 40 and 80 °C)
can be obtained by comparing the efficiency of a cobalt chain
transfer catalyst for the polymerization of MMA with that for
the polymerization of MMA-d8.10 We have used the value of 3
shown in eq 6 to obtain the values of kreinit in Table 1.
Similar results, also without hydrogenation, were observed
when MMA-d5 was treated with the hydride 2b or 2c. The re-
sulting values of kreinit are also in Table 1. Comparison of kreinit
for 2a, 2b, and 2c at 323 K shows a substantial increase in the
rate of H• transfer as we decrease the steric bulk of the hydride
complex. (As will be seen, there is little variation in the Cr-H
bond strengths.) The temperature dependence of the observed
rate constants gives the activation parameters in Table 2.
Reaction of (η5-C5R5)Cr(CO)3H (R ) Ph, Me, H) (2a,b,c)
with Styrene-d8. In the case of styrene competition between
hydrogenation and H/D exchange was observed. The bright blue
color of (η5-C5Ph5)Cr(CO)3• (1a) appeared within a few minutes
of sealing an NMR tube with the C5Ph5 hydride 2a and styrene-
Results and Discussion
H/D Exchange Between (η5-C5R5)Cr(CO)3H (R ) Ph, Me,
H) (2a,b,c) and MMA-d5. When a solution of the hydride 2a
in C6D6 was treated with a large excess (g20 equiv) of MMA-
1
d5, H NMR showed smooth decay of the hydride resonance
and growth of the resonances of three isotopomers of MMA-d4
(eq 3); the cis and trans isotopomers were formed in equal
amounts. No methyl isobutyrate (which would be the product
of hydrogenation) was observed
1
d8, and traces of ethylbenzene could be seen in the H NMR
spectrum. With the C5Me5 hydride 2b and styrene-d8 more
ethylbenzene was formed. Depending on the initial concentration
we observed between 2 and 8% ethylbenzene in addition to the
main product styrene-d7.
When the C5H5 hydride 2c was treated with styrene-d8, the
Cp peak broadened and gradually shifted downfield to δ7.5
1
before disappearing completely from the H NMR spectrum
The first exchange proved cleanly separable from subsequent
exchanges, i.e., an exponential fitted to the hydride resonance
decayed to zero. The resulting rate constants (Table S1) and
plot (Figure S1) confirm that exchange is first-order in MMA-
d5 (eq 4)
(These results presumably arise from fast H• exchange between
CpCr(CO)3H and the product metalloradical CpCrCr(CO)3• (1c),
present in equilibrium with its dimer [CpCr(CO)3]2.). Mean-
while, the hydride peak disappeared and ethylbenzene appeared
(eq 7). A 2:1 ratio of 2c:styrene resulted in complete hydrogena-
tion to give the metalloradical 1c, which is in equilibrium with
its dimer (eq 7). ∆G for dissociation of the weak metal-metal
bond in [CpCr(CO)3]2 is only 4.6 kcal/mol at 300 K, so there
is only 10% monomer when [Cr] is 0.01 M11
d[CrH]
-
) k1[CrH][MMA-d5]
(4)
dt
Extracting the rate constant kreinit from an observed value of
k1 requires that we consider the fractional probability S that D•
will return to the chromium metalloradical 1 after the initial
transfer. S then relates k1 to kreinit as in eq 5
(6) Feder, H. M.; Halpern, J. J. Am. Chem. Soc. 1975, 97, 7186.
(7) Sweany, R. L.; Halpern, J. J. Am. Chem. Soc. 1977, 99, 8335.
(8) Eisenberg, D. C.; Norton, J. R. Israel J. Chem. 1991, 31, 55-66.
9
10094 J. AM. CHEM. SOC. VOL. 125, NO. 33, 2003

H•Transfer from (η5-C R )Cr(CO)3H (R ) Ph, Me, H)
A R T I C L E S
5
5
Scheme 2
a
Table 1. Values of kreinit from Isotopic Exchange between
(η5-C5R5)Cr(CO)3H and Excess MMA-d5
Table 2. Activation Parameters and kreinit at 323 K for Isotopic
Exchange between (η5-C5R5)Cr(CO)3H and Excess MMA-d5
k
reinit (10-3 M-1s-1
)
kreinit(323K),
‡
‡
R
10-3 M-1s-1
∆H , kcal/mol
∆S , eu
c
T(K)
R ) Phb
R ) Meb
R ) H
Ph
Me
H
1.74 (8) a
2.61 (5) a
14 (3) b
14.1 (8)
19.0 (6)
16 (1)
-28 (3)
-12 (2)
-17 (5)
333
323
318
313
308
303
298
293
288
3.00 (5)
1.74 (8)d
1.19 (2)
0.73 (1)
0.51 (1)
2.61 (5)
1.73 (1)
0.94 (2)
0.62 (1)
0.350 (6)
a Uncertainties from 323 K points in Table 1. b Extrapolated from
activation parameters. Uncertainties take into account covariance between
∆H‡ and ∆S‡.
4.0 (2)
2.5 (1)
1.23 (4)
0.97 (3)
0.59 (3)
With the C5Ph5 hydride 2a it is clearly appropriate to calculate
k
reinit from eq 10. With the C5Me5 hydride 2b we have still used
a Obtained using eqs 4, 5, and 6. Figures in parentheses are standard
eq 10; the error introduced thereby should be e5%. The results
are collected in Table 3.
deviation in least significant digit. b In C6D6. c In toluene-d8. d From Figure
S1.
For styrene kreinit from the hydride 2a is about an order of
magnitude faster than for MMA. However, in contrast to our
observations with MMA, there is little variation in kreinit with
the steric bulk of the hydride complexspresumably because
the double bond in styrene has fewer substituents. Completion
of hydrogenation by transfer of a second H•sto the methyl
isobutyryl radical 3 in Scheme 2 or the R-methylbenzyl radical
4 in Scheme 3sis not appreciable except in the least crowded
case, the C5H5 hydride 2c and styrene. A considerable difference
between 3 and 4 is apparent
Values of kreinit for H• transfer to styrene can be extracted
from the observed rate constants with styrene-d8 by procedures
similar to those in eqs 4-6. If we neglect hydrogenation and
consider the overall reaction to be that in eq 8, then we need
only consider the top part of Scheme 3; S for transfer to styrene
will be given by eq 9 and the rate law for disappearance of the
hydride resonance by eq 10. (Of course kH and kD now refer to
the H• and D• transfer from the R-methylbenzyl radical 4-d8.
2
3
kD[Cr•]
2
2
5
Formation of (η5-C5Ph5)Cr(CO)3• (1a) from (η5-C5Ph5)-
Cr(CO)3H (2a) and MMA. Kinetic Modeling. As we previ-
ously reported,4 the hydride 2a can initiate polymerization in
neat MMA. When heated to 100 °C under an inert atmosphere,
a 1.15 × 10-4 M solution of 2a in MMA turned from light
green to blue, the color characteristic of the metalloradical 1a;
IR confirmed that 1a had been formed. Use of the extinction
coefficient of 1a at 611 nm, determined in toluene as 720(80)
M-1 cm-1, suggested that the conversion of 2a to 1a was over
90%. Removal of excess monomer after 1 h afforded PMMA
with a number average molecular weight of approximately 6500,
close to the number average molecular weight from an AIBN-
initiated polymerization in the presence of a similar concentra-
tion of the metalloradical 1a.4
Similar conversions were obtained in a series of experiments
at lower temperatures, from 50 to 75 °C. Over a reaction time
of 8-12 h, 10-25% of the monomer was typically converted
to polymer.
At 65 °C with the hydride 2a in neat MMA the appearance
of the metalloradical 1a was monitored by UV-vis spectroscopy
S )
)
≈
(9)
1
3
2
3
k
H + 2
kH[Cr•] + kD[Cr•]
kD
kobs ) kreinit[styrene-d8]S
d[2c]
(10)
(11)
-
) 2kreinit[2c][styrene-d8]
dt
When, as with the C5H5 hydride 2c, hydrogenation is
complete we need only consider the bottom part of Scheme 3,
and can write the rate law in eq 11 and thereby calculate the
values of kreinit in Table 3 below.
(9) Ayrey, G.; Wong, D. J. D. Polymer 1975, 16, 623.
(10) Gridnev, A. A.; Ittel, S. D.; Wayland, B. B.; Fryd, M. Organometallics
1996, 15, 5116.
(11) (a) Adams, R. D.; Collins, D. E.; Cotton, F. A. J. Am. Chem. Soc. 1974,
96, 749. (b) Landrum, J. T.; Hoff, C. D. J. Organomet. Chem. 1985, 282,
215. (c) Madach, T.; Vahrenkamp, H. Z. Naturforsch. B.: Anorg. Chem.,
Org. Chem. 1978, 33B, 1301. (d) McLain, S. J. J. Am. Chem. Soc. 1988,
110, 643. (e) Woska, D. C.; Ni, Y.; Wayland, B. B. Inorg. Chem. 1999,
38, 4135.
9
J. AM. CHEM. SOC. VOL. 125, NO. 33, 2003 10095

A R T I C L E S
Tang et al.
Scheme 3
Figure 2. UV kinetic trace for the reaction of 2a (0.0121 M) with MMA
(0.268 M) in toluene at 50 °C. (Concentration of 1a from visible absorbance
at 611 nm [).
Figure 1. Absorbance of 1a at 611 nm (9) as a function of time when a
solution of 2a ([2a]0 ) 3.6 × 10-3 M) in neat MMA is heated at 65 °C.
(The solid line is the exponential curve fit.) The initial 1000 s are shown
in the inset.
kinetics of H• transfer in both directions. A typical plot of [1a]
as a function of time is shown in Figure 2.
Table 3. Values of kreinit for (η5-C5R5)Cr(CO)3H (R ) H, Me, Ph)
and Excess Styrene-d8 in C6D6
The H• transfer is thermodynamically uphill (see below), and
the hydride 2a converts to the metalloradical 1a only because
the methyl isobutyryl radicals 3 are consumed by dimerization
and disproportionation reactions (eq 12). The rate constant at
50 °C for both processes combined is 3.3 × 107 M-1 s-1 for
polymers with Pn (number average degree of polymerization)
) 104,13 but it increases as the chain length decreasessby about
a factor of 5 for chain lengths as short as the ones in this
experiment,14 making kterm equal to 1.65 × 108 M-1s-1. The
concentration of MMA is sufficiently high, and the conversion
so low, that to a first approximation we can neglect the
k
reinit (10-3 M-1s-1
)
c
T (K)
R ) Phb
R ) Meb
R ) H
323
318
313
308
303
18.4 (9)a
5.4 (3)
15.8 (6)
10.5 (3)
6.3 (5)
5.6 (3)
3.7 (3)
11.8 (7)a
7.2 (2)
4.6 (2)
3.6 (2)
a Average of two measurements. b Obtained using eq 9, 10. c Obtained
using eq 11.
reformation of MMA by eq 12. If we use kreinit as 0.0017 M-1 -1
s
(Figure 1). There was a significant deviation from exponential
behavior (see inset) at short reaction times.12
from Table 1, and simulate15 the growth of the metalloradical
1a as illustrated in Scheme 4, we can determine ktr by iteration
Using a solution of MMA in toluene instead of neat MMA
decreased the extent to which chain growth (rate constant
kp[MMA]) competed with H• return (rate constant ktr[Cr•]) for
the methyl isobutyryl radical 3. We were thus able to watch
the growth of the metalloradical 1a (20% to 30% conversion)
without significant changes in [MMA], and to determine the
(12) Kinetic modelling with [MMA] ) 9.3 M and the rate constants given in
this section produces (Figure S3) an initial sharp rise in [1a] like that
observed in Figure 1, although the agreement is not perfect (in neat MMA
polymerization changes the viscosity and significantly decreases [MMA],
making modelling difficult). High [MMA] pushes the equilibrium far
enough to the right that the rapid operation of kreinit and ktr generates
significant 1a before kterm begins to consume 3; as we would expect, no
such initial rise in [1a] is seen in the subsequent experiments at lower
[MMA] in toluene.
The resulting values of ktr, from experiments over a wide
range of initial MMA concentrations, are shown in Table 4. (A
(13) Extrapolated to 50 °C from equation given by Mahabadi, H. K.; O’Driscoll,
K. F. J. Macromol. Sci. A: Chem. 1977, 11, 967-976.
9
10096 J. AM. CHEM. SOC. VOL. 125, NO. 33, 2003

H•Transfer from (η5-C R )Cr(CO)3H (R ) Ph, Me, H)
A R T I C L E S
5
5
Scheme 4
a
Table 4. Values of ktr from MacKinetics15 Iteration of the
metal complexes18 and have provided access to absolute energy
values without having to neglect the entropy changes as above.
Because absolute energies obtained in quantum chemical
calculations are quite sensitive to the level of theory employed,
comparisons of reported BDEs from different studies are
problematic. Thus, we have computed both the Cr-H and C-H
bond strengths with the goal of obtaining values for the bond
strengths at the same level of theory to compare with those
derived from experimental methods. Because of computational
demands, however, the Cr-H bond strength has been computed
only for (η5-C5H5)Cr(CO)3H. Bond dissociation processes
require corrections for vibrational zero point energy (ZPE)
changes to the enthalpy, which are accessible by computing the
vibrational frequencies of all species involved. These computed
frequencies also provide reasonable estimates for vibrational
entropies and, thus, allow the explicit evaluation of free energies
of bond dissociation within the usual framework of the standard
approximations of statistical thermodynamics.
Reaction of (η5-C5Ph5)Cr(CO)3H (2a) with MMA in Toluene at 50
°C
[2a]
[MMA]
(M)
k
tr
init
init
(10-3M)
(103 M-1s-1
114
88.7
38.2
128
)
11.4
9.30
9.00
6.52
8.35
9.15
8.56
0.268
0.318
0.0791
0.281
0.212
0.186
0.221
84.3
91.0
94.7
a kreinit ) 0.0017 M-1s-1, kterm ) 1.65 × 108 M-1s-1, ꢀ of 1a ) 720
M-1cm-1
.
sample MacKinetics fit plot (Fig S4) is available in the
Supporting Information.) They have an average of 91 000
M-1s-1. The major source of uncertainty is the kterm estimate;
however, changing kterm by a factor of 2 only changes ktr by
30%.
For our Cr-H and C-H bonds the computed values are
summarized in Table 5 and the individual energy corrections
are listed in the Supporting Information. Calculated contributions
of the entropy to the bond dissociation indicate that the ∆S
values for the H• transfer reactions depicted in Schemes 4 and
5 are +2.36 and +1.65 kcal/mol at 298 K, respectively. The
computed bond dissociation energy terms indicate that changes
of the intrinsic entropy components, that is the vibrational,
rotational, and translational entropies of the molecule, are of
the same order of magnitude as the solvation free energy
changes upon bond dissociation. As can be expected, the
entropies favor the dissociated (H•) side of the reaction, while
solvation favors the reactant (M-H or C-H) side. Note that
the solvation free energy of H• is positive (estimated to be +5.12
kcal/mol in water19).
Determination of Cr-H Bond Strength in (η5-C5Ph5)Cr-
(CO)3H (2a). Experimentally, it is straightforward to determine
the strength of the Cr-H bond in 2a from a thermodynamic
cycle involving the pKa of the hydride and the redox potential
of the anion (the conjugate base of 2a). Breslow and co-workers
initially used such cycles to estimate the pKa values of some
weak carbon acids,20 Bordwell and co-workers have used such
cycles to estimate many C-H bond strengths in DMSO,21 and
Tilset and Parker,22 as well as Protasiewicz and Theopold,23
have estimated many M-H solution bond dissociation energies
in this way.
Kinetic Modeling of the Formation (η5-C5Ph5)Cr(CO)3•
(1a) from (η5-C5Ph5)Cr(CO)3H (2a) and Styrene. The met-
alloradical 1a was also formed when a toluene solution of
styrene and the hydride 2a was heated at 50 °C. Monitoring
the reaction by UV-vis spectroscopy, and taking ꢀ(1a) at 611
nm in toluene as 720 M-1cm-1, kreinit as 0.018 M-1s-1 from
Table 3, and kterm (Scheme 5) as 3.2 × 107 M-1s-1 16
,
we can
simulate the growth of 1a as shown in Scheme 5. For the data
set presented a ktr of 84 000 M-1s-1 gives the best fit. As was
the case with MMA, changing kterm by a factor of 2 only changes
ktr by 30%.
Thermodynamics of the H• Transfer Equilibrium: Bond
Strengths. The position of a reversible H• transfer equilibrium
like Schemes 4 or 5 depends on the strength of the Cr-H and
C-H bonds that are broken and made. To a first approximation,
assuming ∆S ≈ 0, we can express ∆G for such an equilibrium
by eq 13, where BDE(C-H) is the bond dissociation energy of
the C-H bond in the methyl isobutyryl radical 3 or the
R-methylbenzyl radical 4. Our experiments thus offer a way of
obtaining the BDE(C-H) of unstable radicals 3 and 4
∆G ) ∆H ) BDE(Cr-H) - BDE(C-H)
(13)
Computation of Cr-H and C-H Bond Strengths. Com-
putational methods, in particular those using density functional
theory (DFT),17 have become popular in recent years for
computing BDEs of a variety of molecules including transition
(18) Ziegler, T. Chem. ReV. 1991, 91, 651-667.
(19) Brunner, E. J. Chem. Eng. Data 1985, 30, 269.
(14) By extrapolation from the MMA/toluene data in Figure 2 and Table 3 in
Suddaby, K. G.; Maloney, D. R.; Haddleton, D. M. Macromolecules 1997,
30, 702-713. From polymerizations with the same [Cr•] we calculate Pn
as 2 (at such high concentrations of chain transfer catalyst Pn is very small).
(15) MacKinetics, written by and obtained from Leipold, W. S., III.; Weiher, J.
F.; McKinney, R. J. E. I. du Pont de Nemours, Inc., 1992-1995.
(16) Matheson, M. S.; Auer, E. E.; Bevilacqua, E. B.; Hart, E. J. J. Am. Chem.
Soc. 1951, 73, 1700.
(20) (a) Breslow, R.; Balasubramanian, K. J. Am. Chem. Soc. 1969, 91, 5182.
(b) Breslow, R.; Chu, W. J. Am. Chem. Soc. 1973, 95, 411. (c) Jaun, B.;
Schwarz, J.; Breslow, R. J. Am. Chem. Soc. 1980, 102, 5741-5748.
(21) Bordwell, F. G.; Cheng, J. P.; Harrelson, J. A., Jr. J. Am. Chem. Soc. 1988,
110, 1229.
(22) (a) Tilset, M.; Parker, V. D. J. Am. Chem. Soc. 1989, 111, 6711, as modified
by (b) Tilset, M.; Parker, V. D. J. Am. Chem. Soc. 1990, 112, 2843. Potential
sources of error in the determination of M-H bond strengths by this method
have been reviewed in ref 8 above.
(17) Parr, R. G.; Yang, W. Density Functional Theory of Atoms and Molecules;
Oxford University Press: New York, 1989.
(23) Protasiewicz, J. D.; Theopold, K. H. J. Am. Chem. Soc. 1993, 115, 5559.
9
J. AM. CHEM. SOC. VOL. 125, NO. 33, 2003 10097

A R T I C L E S
Tang et al.
Table 5. DFT-calculated Gas Phase Bond Dissociation Enthalpy (∆H), Entropy (∆S), and Free Energy (∆G), Solution Phase Bond
Dissociation Enthalpy (∆H(sol)) and Solution Phase Bond Dissociation Free Energy (∆G(sol))
−(298.15K)
∆S(gas)
∆H(gas)
∆H(sol)a
∆G(gas)
∆G(sol)a
X•
(kcal/mol)
(kcal/mol)
(kcal/mol)
(kcal/mol)
(kcal/mol)
(η5-C5H5)Cr(CO)3
methylisobutyryl
R-methylbenzyl
54.42
45.83
46.77
57.55/58.18
49.48/49.79
49.91/49.67
-8.56
-6.20
-6.91
45.86
39.64
39.86
48.99/49.62
43.28/43.59
43.00/42.76
All calculations are done for the reaction XH f X• + H•, where X denotes different fragments. See Computational Details for definitions of the energy
terms. a The solution phase values are given both for toluene and acetonitrile; toluene values are listed first, followed by those for acetonitrile.
Scheme 5
Scheme 6
Determining the pKa of 2a proved unusually difficult because
2a is insoluble in CH3CN (the solvent we have preferred in our
previous measurements24 of the thermodynamic acidity of
transition-metal hydrides). We therefore monitored the equi-
librium Keq for deprotonation of 2a by [PPN][CpCr(CO)3] (the
conjugate base of 2c) (eq 14) over a range of temperatures by
1H NMR in CD2Cl2. (Measurement of Keq by IR in CH2Cl2
proved impractical because of overlap of the peaks of both
hydrides and their anions.) From -50 to 0 °C, the cyclopen-
tadienyl signals belonging to CpCr(CO)3H (2c) and [PPN]-
[CpCr(CO)3] could be integrated separately and Keq determined
from their ratio and the initial concentrations of 2a and [PPN]-
[CpCr(CO)3]
Table 6. BDE of Different Cr Hydrides
Cr hydride
BDE, kcal/mol
H-Cr(CO)3(C5Ph5)a
59.6 (3)
62.3
61.5
59.8
59.9
H-Cr(CO)3(C5Me5)28
H-Cr(CO)3(C5H5)b
H-Cr(CO)2(PPh3)(C5H5)b
H-Cr(CO)2(PEt3)(C5H5)b
H-Cr(CO)2(P(OMe)3)(C5H5)b
62.7
a This work, in CH3CN. b The rest of the BDE values are from ref 27
and are in toluene.
in CH3CN,3,26 and our pKa estimate in the same solvent yield a
Cr-H bond dissociation energy of 59.6(3) kcal/mol in
CH3CN. In good agreement with this value, our DFT calculation
predicts a BDE of 58.2 kcal/mol in CH3CN (Table 5).
Furthermore, our experimental value for 2a fits well with
calorimetric determinations on related chromium hydrides (Table
6).27 In the Hoff study, the monomer-dimer equilibrium of [(η5-
C5Me5)Cr(CO)3]2 was used to measure the Cr-Cr bond en-
thalpy,28 and the enthalpy of reaction of the (η5-C5Me5)Cr(CO)3•
radical with H2 was measured calorimetrically, so the value of
62.3 for the Cr-H BDE of C5Me5Cr(CO)3H in toluene should
be quite accurate. In the same study, the Cr-H BDE of CpCr-
(CO)3H was also determined to be 61.5 kcal/mol in toluene,
which compares reasonably well to our DFT value of 57.6 kcal/
mol for toluene (Table 5). The agreement between the calori-
metric numbers, our BDE value derived from the Keq measure-
ment and DFT-computed numbers gives reassurance that the
assumptions used in the proton-transfer treatment are reasonable.
[PPN][CpCr(CO)3] +
Keq
C Ph Cr(CO) H
y
z [PPN][C5Ph5Cr(CO)3] +
5
5
3
CD2Cl2
2a
CpCr(CO)3H
(14)
2c
+
PPN ) Ph3P)N)PPh3
The value of Keq (80) measured at 250 K was corrected to
298 K by assuming ∆G to be approximately constant and using
∆G ) -RTlnKeq. If we assume that for such large bases Keq
will be similar in CH2Cl2 and CH3CN,23,25 and take the pKa of
2c in CH3CN as 13.3,24 then we can estimate the pKa of 2a in
CH3CN as 11.7(3).
The thermodynamic cycle in Scheme 6 yields eq 15 if we
add the reactions and substitution the appropriate physical
constants22
Strength of the C-H Bond in the Methyl Isobutyryl
Radical 3. The literature yields conflicting evidence about the
strength of the C-H bond in 3. Of course we can obtain that
bond strength if we know the heats of formation of both sides
of eq 16. The gas-phase enthalpy of formation of methyl
BDE(M-H) ) 1.37 pKa(M-H) + 23.06 E°(M•/M-) +
58.4 kcal/mol (15)
-
The known redox potential of C5Ph5Cr(CO)3•/C5Ph5Cr(CO)3
(24) The work has been summarized in a review: Kristja´nsdo´ttir, S. S.; Norton,
J. R. “Acidity of Hydrido Transition Metal Complexes in Solution”. In
Transition Metal Hydrides; Dedieu, A., Ed.; VCH: New York, 1991,
Chapter 9.
(26) To convert the redox potential of 1 vs (Fc/Fc+) in CH3CN to a redox
potential vs (H+/H2) in CH3CN a value of 0.049 V is added. Kiolthoff, I.
M.; Chantooni, M. K., Jr. J. Phys. Chem. 1972, 76, 2024-2034.
(27) Kiss, G.; Zhang, K.; Mukerjee, S. L.; Hoff, C. D. J. Am. Chem. Soc. 1990,
112, 5657-5658.
(28) Watkins, W. C.; Jaeger, T.; Kidd, C. E.; Fortier, S.; Baird, M. C.; Kiss,
G.; Roper, G. C.; Hoff, C. D. J. Am. Chem. Soc. 1992, 114, 907-914.
(25) Proton-transfer equilibria of η2-dihydrogen complexes measured in CD2-
Cl2 have been used to estimate aqueous pKa values in the same fashion:
Jia, G.; Morris, R. H. Inorg. Chem. 1990, 29, 582-584.
9
10098 J. AM. CHEM. SOC. VOL. 125, NO. 33, 2003

H•Transfer from (η5-C R )Cr(CO)3H (R ) Ph, Me, H)
A R T I C L E S
5
5
methacrylate is -82.4 kcal/mol,29 but the gas-phase enthalpy
of formation of a methyl isobutyryl radical 3 is less accurately
known. Engel and co-workers have calculated -78(2) kcal/mol30
by using -111 kcal/mol31 as the enthalpy of formation of methyl
isobutyrate and estimating32 the C-H BDE for the tertiary
carbon of methyl isobutyrate as 85 kcal/mol. By using the same
C-H BDE of 85 kcal/mol, but using the enthalpy of formation
of methyl isobutyrate (-117.3 kcal/mol) measured calori-
metrically by Kharasch,33 one can calculate a value of -84(2)
kcal/mol for the enthalpy of formation of the methyl isobutyryl
radical. Combining either of these two values for 3 with 52.1
kcal/mol for H• implies that the gas-phase C-H BDE in the
methyl isobutyryl radical 3 is 48 or 54 kcal/mol. Our DFT
calculations give a gas-phase BDE of 45.8 kcal/mol (Table 5),
which is in better agreement with the former estimate
Strength of the C-H Bond in the r-Methylbenzyl Radical
4. We can similarly infer the strength of the C-H bond in the
R-methylbenzyl radical 4. Reported C-H BDE’s are as high
as 54.3 kcal/mol and as low as 46.9 kcal/mol. The former
number comes from the gas phase heats of formation (kcal/
mol) of styrene (35.2),34 H• (52.1), and the R-methylbenzyl
radical (33).35 This value (54 kcal/mol) is also supported by
the equilibrium constant for the reversible decomposition of a
Co(III)(R-phenethyl) complex to liberate styrene and half an
equivalent of H2.36 The lower experimental estimate for the
C-H BDE of R-methylbenzyl radical 4, 46.9 kcal/mol, comes
from a ∆Hf for this radical derived from very-low-pressure
pyrolysis, 39.6 kcal/mol.37 A similar value (41.3 kcal/mol)
comes from proton affinity experiments by a thermodynamic
cycle.38 In good agreement with previous quantum chemical
studies on MP4/CBS-4 level of theory39 that reported a bond
dissociation energy of 45.5 kcal/mol for R-methylbenzyl radical
4, our DFT calculations suggest a gas-phase BDE of 46.8 kcal/
mol, and lend support to the lower values in the set of estimates.
Comparing our Cr-H BDE (59.6 kcal/mol in CH3CN) with
the C-H BDE values from our DFT calculations and with
literature bond strength estimates suggests that H• transfer from
(η5-C5Ph5)Cr(CO)3H to styrene (eq 18) is between 5 and 14
kcal/mol uphill. This range is slightly lower than an estimate,
16.1(4) kcal/mole, that has been published40 for a similar H•
transfer, between 2c and R-cyclopropyl styrene
Comparing our Cr-H BDE (59.6 kcal/mol in CH3CN) with
any of these C-H results for methyl isobutyryl radical 3 makes
it clear that the equilibrium in eq 17 is uphill, and that treatment
of the hydride 2a with MMA converts it to the metalloradical
1a only because of the operation of kterm (Scheme 4). Com-
parison of the Cr-H and C-H DFT calculations in Table 5
suggests a gas phase ∆H for reaction 17 of 8.6 kcal/mol.
Addition of ∆S and solvation energies from the continuum
solvation model gives an overall theoretical ∆G of 6.3 kcal/
mol for the equilibrium in eq 17 in toluene (Table S10)
If we again assume that Keq ) kreinit/ktr, our rate constants at
50 °C in toluene imply a value of 9.87 kcal/mol for ∆G (eq
18) at that temperature. Now our “experiment/theory hybrid”,
using ∆S from our gas-phase DFT computations (5.54 eu) and
our Cr-H BDE from CH3CN (59.6 kcal/mol), gives a C-H
bond strength for 4 of 47.9 kcal/mol in toluene, which is in
good agreement with our 49.9 kcal/mol in that solvent from
DFT calculations.
If we assume that Keq ) kreinit/ktr, our rate constants at 50 °C
in toluene imply a value of 11.4 kcal/mol for ∆G (eq 17) at
that temperature. Converting this number to a BDE requires
that we separate the enthalpic and entropic contributions. In eq
13 we assumed ∆S ≈ 0, making ∆G and ∆H the same. A second
possibility is to define an “experiment/theory hybrid” by using
the DFT-computed gas phase ∆S of 7.93 eu (from Table S10)
for the reaction shown in eq 17. If we begin with our
experimental ∆G in toluene, estimate ∆S in that solvent from
the gas-phase value, and assume that our Cr-H BDE in CH3-
CN (59.6 kcal/mol) is approximately correct in toluene, then
we obtain a C-H bond strength for methyl isobutyryl radical 3
of 45.6 kcal/mol in toluene, which is in reasonable agreement
with our 49.5 kcal/mol in that solvent from DFT computations
(Table 5).
The â C-H bonds in the methyl isobutyryl radical 3 and the
R-methylbenzyl radical 4 are both much weaker than ordinary
C-H bonds. They are, however, stronger than the â C-H bond
in the ethyl radical (35.7 kcal/mol).41
Cage Effects and their Influence on the Kinetic Determi-
nation of Bond Strengths. In Schemes 4 and 5 and eqs 17 and
18 we have assumed that the rate constant kreinit corresponds to
a single step. There are, however, many reasons to assume that
such H• transfers occur within a solvent cage. The observation
of CIDNP in Scheme 1 and related reactions7,8 implies competi-
tion between H• return and cage escape after H• transfer.
Exchange between the hydride ligand and the substrate (ac-
(29) Viclu, R.; Perisanu, S. ReV. Roumaine Chemie 1980, 25, 619-624.
(30) Engel, P. S.; Chen, Y. Wang, C. J. Org. Chem. 1991, 56, 3073-3079.
(31) Group addition thermochemical calculation using data from and methods
of Pedley, J. B.; Naylor, R. D.; Kirby, S. P. Thermochemical Data of
Organic Compounds; Chapman and Hall: London, 1986. This type of
estimate should approximate the gas-phase enthalpy of formation.
(32) The C-H BDEs were estimated using three different approaches: ther-
molysis of azoalkanes, thermolysis of dimethyl tetramethylsuccinate, and
ESR determination of carboalkoxyalkyl radical rotational barriers.
(33) Kharasch, M. S. J. Res. Natl. Bur. Stand. 1929, 2, 359-430. It is unclear
from the tables of thermodynamic data if the Kharasch measurement is a
gas-phase enthalpy. If it is a condensed-phase measurement, then the heat
of vaporization of methyl isobutyrate must be added to the measured value
of -117.3 kcal/mol, which would essentially make the Engel and Kharasch
numbers equal.
(34) Prosen, E. J.; Rossini, F. P. J. Res. Natl. Bur. Stand. 1945, 34, 59.
(35) Kerr, J. A. Chem. ReV. 1966, 66, 465.
(36) Ng, F. T. T.; Rempel, G. L.; Mancuso, C.; Halpern, J. Organometallics
1990, 9, 2762.
(37) Robaugh, D. A.; Stein, S. E. Int. J. Chem. Kinetics 1981, 13, 445-462.
(38) Meot-Ner, M. J. Am. Chem. Soc. 1982, 104, 5-10.
(39) Zhang, X. M. J. Org. Chem. 1998, 63, 1872-1877.
(40) Bullock, R. M.; Samsel, E. G. J. Am. Chem. Soc. 1990, 112, 6886-6898.
(41) Blanksby, S. J.; Ellison, G. B. Acc. Chem. Res. 2003, 36, 255-263.
9
J. AM. CHEM. SOC. VOL. 125, NO. 33, 2003 10099

A R T I C L E S
Tang et al.
Scheme 7
Scheme 8
complished by the k2 and k-2 steps) is considerably faster than
the overall reaction in the system in Scheme 7.42
terminated polymer 6, eq 19 means that we can determine a
true ∆G for Scheme 8 from ktr(polymer)/kreinit. Our values of
these rate constants at 50 °C give a ∆G of -13.5 kcal/mol in
toluene. Neglecting ∆S and using our Cr-H BDE give 46.1
kcal/mol as the BDE at 50 °C for the C-H bond in 3-Psto
our knowledge the first determination of the strength of a C-H
bond in the chain-carrying radical of a polymerization reaction.
Unfortunately, the BDE(C-H) that we have just calculated
for 3-P (46.1 kcal/mol) cannot be compared with the BDE(C-
H) that we calculated earlier from our “experiment/theory
hybrid” for 3 (45.6 kcal/mol), since the BDE for 3-P neglected
∆S. It is better to compare ∆G for H• transfer to the polymer-
substituted double bond in the vinyl-terminated polymer 6
(+13.5 kcal/mol), with the ∆G we obtained (from kreinit and ktr
without allowing for cage effects) for H• transfer to MMA (eq
17) (+11.4 kcal/mol). The fact that ∆G is larger for H• transfer
to the polymer-substituted double bond suggests that the C-H
BDE in 3-P is lower than that in 3 itself, which is not
unreasonable: 3 and 3-P differ in the number of equivalent C-H
bonds by a factor of 2, and the C-H bond strength may be
influenced by the substituent effect of the polymer chain. We
have explored the latter possibility by calculating (at the
suggestion of a reviewer) the gas-phase BDE for the “mono-
substituted” radical 7 (3 + MMA); the results (Table S10)
indicate that the C-H bond in 7 is indeed 0.8 kcal/mol weaker.
(Although we have calculated entropy corrections for 7, they
are unlikely to be good approximations for the polymer-
substituted radical 3-P.)
Such cage effects may explain the difference between the ktr
value we obtained above (9.1 × 104 M-1s-1 by kinetic
modeling) for methyl isobutyryl radical 3 and the one we have
obtained (1.6 × 106 M-1s-1 from molecular weight measure-
ments as a function of [1]) for the polymer-containing radical
3-P.43 Cage effects may also explain why our ktr(polymer) Value
decreases with temperature. The forward step (and by micro-
scopic reversibility the reverse step) in reactions 17 and 18 may
occur in more than one step, and may involve an associative
pre-equilibrium;44 if H• transfer occurs only after the formation
of a solvent cage, then we have the sequence of events in
Scheme 8. The first step kcapture is merely the microscopic reverse
of cage escape, driven by the interaction between the metal-
loradical Cr• and the chain-carrying radical 3-P.45-47
The observed rate constant ktr will then be given by eq 19.
The cage-forming equilibrium kcapture/kescape will lie further to
the left with increasing temperature, making ktr(polymer)
decrease with increasing temperature as observed
k
capturekCfCr
kcapturekCfCr
ktr )
≈
(19)
kescape + kCfCr
kescape
If we assume kreinit for H• transfer from Cr hydride to MMA
is equal to kCrfC for H• transfer from Cr hydride to the vinyl-
(42) Jacobsen, E. N.; Bergman, R. G. J. Am. Chem. Soc. 1985, 107, 2023-
2032.
(43) Tang, L.; Norton, J. R. in preparation, to be submitted to Macromolecules.
(44) A similar “negative activation energy” has been seen, and a similar
explanation (reversible formation of a dissociable intermediate) offered,
for a carbene/alkene cycloaddition in Turro, N. J.; Lehr, G. F.; Butcher, J.
A., Jr.; Moss, R. A.; Guo, W. J. Am. Chem. Soc. 1982, 104, 1754-1756.
(45) The bond between the sterically encumbered (η5-C5Ph5)Cr(CO)3• (1a) and
the tertiary radical 3-P will be weak. Formation of such a bond would
reduce the efficiency of 1a as a chain transfer catalyst,46 as the resulting
alkyl complex 5 cannot be an intermediate in formation of the hydride 2a
(5 would have no vacant coordination site and thus be unable to undergo
â-hydrogen elimination).47 Weak interaction between the metalloradical
1a and the carbon-centered radical 3-P can, however, contribute to the
formation of the cage in Scheme 6.
(46) Reversible formation of a Co-C bond has been observed with Co(II) chain
transfer catalysts and the R-methylbenzyl radical 4 in styrene polymeri-
zation, but it is insignificant with the isobutyryl radical 3 in MMA
polymerization. Heuts, J. P. A.; Forster, D. J.; Davis, T. P. Macromolecules
1999, 32, 2511-2519.
(47) Similarly, the release of alkenes from alkyl cobalamins occurs not by
â-hydrogen elimination but by C f Co H• transfer after homolysis of the
Co-C bond. See Halpern, J. Pure Appl. Chem. 1979, 51, 2171, and
Bonhoˆte, P.; Scheffold, R. HelV. Chim. Acta 1991, 74, 1425-1444.
It is also possible that our ∆G for H• transfer to the vinyl-
terminated polymer 6 (+13.5 kcal/mol) differs from our ∆G
for H• transfer to MMA (+11.4 kcal/mol) because our kinetic
analysis of the latter situation (eq 17) did not include cage
effects.
Experimental Section
General. All manipulations were carried out using Schlenk,
high-vacuum, or inert-atmosphere-box techniques, unless oth-
erwise indicated. THF, C6D6, and toluene-d8 were distilled under
9
10100 J. AM. CHEM. SOC. VOL. 125, NO. 33, 2003

H•Transfer from (η5-C R )Cr(CO)3H (R ) Ph, Me, H)
A R T I C L E S
5
5
N2 from Na/benzophenone. Et2O, hexanes, CH2Cl2, benzene,
and toluene were degassed and passed through columns of
activated alumina and supported copper catalyst.48
data for H/D exchange between 2c53 and MMA-d5, so toluene-
d8 was used as a solvent instead of benzene; the rate constants
obtained from 308 K to 288 K are given in Table S4.
Materials. Styrene was washed 3 times with 5% NaOH and
NaCl solutions to remove inhibitors. It was dried over CaH2,
distilled under reduced pressure, and stored in the freezer at
-30 °C. It was then distilled immediately prior to use.
Methyl methacrylate was predried over MgSO4, and then ran
down an Aldrich Inhibitor Removal Column to remove inhibitor.
It was vacuum-transferred over CaH2, stored at -30 °C, and
vacuum-transferred immediately prior to use.
With styrene-d8 modification was required because the
reaction was considerably faster. The solution of 2 with the
internal standard was placed in an NMR tube and frozen inside
an inert atmosphere box, the styrene-d8 solution was added by
syringe, and the tube was immediately put back in the freezer
of the inert atmosphere box. The tube was flame-sealed while
frozen. The solution was thawed and mixed just before it was
placed in the NMR probe.
MMA-d5 and styrene-d8 were purchased from Aldrich in
sealed ampules. The inhibitor was removed from the MMA-d5
by vacuum-transfer from CaH2, and from the styrene-d8 by
vacuum-transfer alone.
(η5-C5Ph5)Cr(CO)3• (1a),3 (η5-C5Ph5)Cr(CO)3H4 (2a), (η5-
C5Me5)Cr(CO)3H (2b),49 and (η5-C5H5)Cr(CO)3H (2c)50 were
prepared by literature procedures. AIBN was recrystallized by
methanol twice and stored at -35 °C. Hexamethylcyclotrisi-
loxane was purified by vacuum-transfer. Bis(triphenylphosphi-
ne)iminium cyclopentadienyl chromium tricarbonyl ([PPN]-
[CpCr(CO)3]) was synthesized according to a published procedure
for the molybdenum species.51
The rate constants for styrene-d8 and (η5-C5Ph5)Cr(CO)3H
(2a), (η5-C5Me5)Cr(CO)3H (2b), are shown in Table S5, S6;
the rate constants for styrene hydrogenation with (η5-C5H5)Cr-
(CO)3H (2c) are shown in Table S7.
Determination of the Rate Constants ktr for H• Transfer
to (η5-C5Ph5)Cr(CO)3• (1a) from the methyl isobutyryl
radical 3 and r-methyl benzyl radical 4. Solutions of (η5-
C5Ph5)Cr(CO)3H (2a) and MMA or styrene in toluene (see Table
4) were made in an inert atmosphere box and placed in a UV
cell (quartz, 1 cm path length) that could be attached to a
Schlenk line with a Teflon stopcock. The cell, filled with an
inert atmosphere, was detached from the Schlenk line and placed
in the Peltier temperature controller (previously equilibrated to
the desired temperature) inside the UV spectrometer. Absor-
bance data at 611 nm were collected every 30s for the first h;
thereafter, the time between spectra was incremented by 10%
on each scan. The reaction was complete after 20 h.
The value of ktr was obtained using MacKinetics15 simulation
software, with initial concentrations for all species and the time
dependence of the chromium radical 1a (calculated from the
absorbance data with ꢀ ) 720 M-1cm-1) as input. The rate
constants kreinit ) 0.0017 M-1s-1 (for methyl isobutyryl radical
3, from Table 1) and 0.018 (for R-methyl benzyl radical 4, from
Table 3) and kterm ) 1.65 × 108 M-1s-1 (for 3)13,14 and 3.2 ×
107 M-1s-1 (for 4)16 were fixed and ktr determined by iteration.
The results for MMA are in Table 4.
Measurement of the Extinction Coefficient of (η5-C5Ph5)-
Cr(CO)3• (1a) in Toluene is described in the Supporting
Information.
NMR Kinetic Measurements. Rate Law for H• Transfer
from (η5-C5Ph5)Cr(CO)3H (2a) to MMA. All NMR kinetic
measurements were recorded on a 300 MHz instrument. In a
typical experiment, a C6D6 solution (300 µL) of 2a (0.030 M)
and hexamethylcyclotrisiloxane (as an internal standard) (0.002
M) was placed in a J. Young NMR tube. A C6D6 solution (300
µL) of 2.00 M MMA-d5 was added to the same tube and frozen
in liquid N2. The tube was placed in the NMR probe (equili-
brated to a temperature calibrated by ethylene glycol52 as 323.0
( 0.5 K, and already tuned with a similar tube) and allowed to
thaw. The extent of reaction was determined by monitoring the
decrease in the peak height (related to the internal standard) of
the hydride resonance (δ -3.98). The time-dependent hydride
concentrations were fitted to eq 4, 5, 6 with KaleidaGraph; both
[CrH]∞ and kobs were refined. A plot of kobs vs [MMA-d5] is
shown as Figure S2
Determination of the pKa of (η5-C5Ph5)Cr(CO)3H (2a) A
typical experiment is described. Two 1 mL solutions of [PPN]-
[CpCr(CO)3] (23.5 mg) and 2a (15.2 mg) in CD2Cl2 were
prepared. A weighed aliquot from each solution was measured
into an NMR tube with a resealable Teflon stopcock to give a
final volume of approximately 1 mL. Spectra were taken
between 230 and 270 K, and the Cp resonances of CpCr(CO)3H
obst
[CrH]t ) [CrH]∞ + ([CrH]0 - [CrH]∞)e-k
(20)
-
Rate Constants kreinit for H• Transfer from (η5-C5R5)Cr-
(CO)3H (R ) Ph, Me, H) (2a,b,c) to MMA-d5 and Styrene-
d8. The same general procedure as in the previous paragraph
was followed with MMA-d5. To obtain activation parameters,
and CpCr(CO)3 were integrated. From the known initial
amounts of 2a and [PPN][CpCr(CO)3] and the ratios of the Cp
resonances the equilibrium constant for proton exchange was
calculated. Four NMR equilibrium measurements yielded a pKa
of 11.7(3).
k
reinit from 2a to MMA-d5 was measured from 333 K to 308 K
(Table S2). Similarly, the kinetics of H• transfer from 2b to
MMA-d5 were observed from 323 K to 303 K in C6D6 (Table
S3). Lower temperatures were needed to obtain accurate kinetic
Computational Details. All calculations were carried out
using the Jaguar 4.1 suite54 of ab initio programs. The geometries
(53) During the 1H/2D exchange experiments between excess MMA-d5 and the
hydride complex 2c (η5-C5H5)Cr(CO)3H, the 1H NMR resonance of the
Cp of 2c broadened and shifted downfield (to δ 5.2 at the end of the
experiment), although that of the hydride remained sharp. The extent of
the broadening varies from experiment to experiment. It appears to arise
from fast H• exchange between CpCr(CO)3H and traces of the metalloradi-
cal 1c (CpCrCr(CO)3•), present in equilibrium with its dimer [CpCr(CO)3]2.
(It is difficult to avoid introducing traces of 1c during the synthesis of 2c,
and some 1c is formed in the course of the 1H/2D exchange.)
(48) Pangborn, A. B.; Giardello, M. A.; Grubbs, R. H.; Rosen, R. K.; Timmers,
F. J. Organometallics 1996, 15, 1518.
(49) Leoni, P.; Landi, A.; Pasquali, M. J. Organomet. Chem. 1987, 321, 365.
(50) Keppie, S. A.; Lappert, M. F. J. Organomet. Chem. 1969, 19, P5.
(51) Darensbourg, M.Y.; Jimenez, P.; Sackett, J. R.; Kanckel, J. M.; Kump, R.
L. J. Am. Chem. Soc. 1982, 104, 1521-1530.
(52) Cavanagh, J.; Fairbrother, W. J.; Palmer, A. G., III; Skelton, N. J. Protein
NMR Spectroscopy Principles and Practice; Academic Press New York,
1996.
(54) Jaguar 4.1, Schro¨dinger Inc, Portland, OR, 2000.
9
J. AM. CHEM. SOC. VOL. 125, NO. 33, 2003 10101

A R T I C L E S
Tang et al.
of all species were fully optimized using the B3LYP functional55
and the 6-31G** basis set. Although this basis set is known to
give reliable geometries, the energies are expected not to be
sufficiently accurate, in particular for the radical species that
require a high-quality basis. Therefore, we re-evaluated the
energies using the correlation consistent triple-ú basis56 cc-
pVTZ(-f)++ including two sets of diffuse functions in addition
to the standard set of two polarization functions. The chromium
atom was represented using the Los Alamos LACVP** basis,57
which contains effective core potentials and corresponds to the
6-31G** basis used for all main-group elements, in geometry
optimizations. For single point calculations, we used a modified
version of LACVP**, denoted LACV3P**++, where the
exponents were decontracted and diffuse functions were added
to match the cc-pVTZ(-f)++ basis of the main group elements.
All calculations made use of the unrestricted spin formalism.
Cartesian coordinates of all optimized structures are given in
Supporting Information.
Vibrational frequencies based on analytical second derivatives
were computed at the B3LYP/6-31G** level of theory and
unscaled frequencies were used to deduce vibrational zero-point
energy (ZPE) corrections. For both chromium complexes this
level of theory gave rise to a physically meaningless imaginary
frequency at ∼40 cm-1 that was assigned to a rotation of the
Cp-ring around an axis connecting the Cr center with the center
of mass of the Cp-ring. Re-evaluation of the vibrational
frequencies for both Cr-complexes at the B3LYP/cc-pVTZ(-f)/
LACV3P** level of theory gave no imaginary frequency
confirming the widely accepted practice of ignoring all imagi-
nary frequencies below 100 cm-1. The thermodynamic proper-
ties derived from these two levels of theory are practically
identical for both cases and are given in the Supporting
Information.
the solvation energy in single point calculations at the B3LYP/
6-31G**/LACVP** level of theory with the dielectric constant
set to 2.379 and 37.5 to emulate toluene and acetonitrile,
respectively. Basis set effects on solvation energy and the
general performance of this protocol have been investigated
explicitly elsewhere,60 and found to be sufficiently small that a
re-evaluation of the solvation energy at the cc-pVTZ(-f)++ level
of theory is not necessary.
Bond Dissociation Energies. To compute the gas-phase bond
dissociation enthalpy, ∆H(gas), the vibrational zero-point energy
difference (∆ZPE) and thermal corrections ∆HT (HT ) ∫CpdT;
Cp ) heat capacity; T ) temperature) have been added to the
electronic bond dissociation energy ∆HSCF: ∆H ) ∆HSCF
+
∆ZPE + ∆HT + 5/2RT. The electronic energy HSCF is the single
point energy computed at the B3LYP/cc-pVTZ(-f)++ level of
theory. The electronic energy of H• at the B3LYP/cc-pVTZ(-
f)++ level of theory is 13.667 eV. The last term (5/2RT) is the
thermal correction for free H• and amounts to 1.48 kcal/mol at
room temperature. ∆S, the entropy corrections in gas phase are
derived using standard approximations of statistical mechanics.
The translational entropy of free hydrogen is computed using
the Sackur-Tetrode equation (26.04 eu). In evaluating the
solution phase energies, it is desirable to obtain the enthalpy
and entropy of solvation separately, which would allow for
computing bond dissociation enthalpy and the free energy of
bond dissociation in solution. However, continuum solvation
models are by default unable to separate these terms and simply
give the overall free energy of solvation. Thus ∆H(sol) we list
in Table 5 is ∆H(sol) ) ∆H(gas) + ∆G(solvation). Although
the hybrid energy ∆H(sol) is therefore rigorously not meaning-
ful, it is a helpful one because it gives an estimate for the
solvation corrected bond dissociation enthalpy. The solvation
energy of H• is assumed to be the same as that of the H2
molecule and set to +3.40 kcal/mol. We use the experimental
solvation enthalpy (∆HSolv ) 5.773 kJ/mol) and entropy (∆SSolv
) -47.68 J/(mol K)) determined by Brunner19 for toluene (ꢀ
) 2.379). Appropriate values for acetonitrile have been used
accordingly (see the Supporting Information).
Solvation effects were taken into account using a continuum
solvation model58 by numerically solving the Poisson-Boltz-
mann equation.59 Rather than reoptimizing the geometry with
the self-consistent-reaction-field potential added to the Hamil-
tonian, we simply used the gas phase geometry and computed
Acknowledgment. This work was supported by grants from
the DOE to J.R.N. (DE-FG02-97ER14807) and from the NIH
to R.A.F. (GM40526). The authors are grateful to Prof. N. Turro
and A. Maliakal for helpful discussions.
(55) (a) Becke, A. D. J. Chem. Phys. 1993, 98, 5648. (b) Lee, C. T.; Yang, W.
T.; Parr, R. G. Phys. ReV. B 1988, 37, 785.
(56) Dunning, T. H. J. Chem. Phys. 1985, 89, 4207.
(57) Hay, P. J.; Wadt, W. R. J. Chem. Phys. 1985, 82, 270.
(58) (a) Cramer, C. J.; Truhlar, D. G. Structure and ReactiVity in Aqueous
Solution, ACS Symposium Series 568; American Chemical Society:
Washington, D. C., 1994. (b) Tomasi, J.; Persico, M. Chem. ReV. 1994,
94, 2027. (c) Patterson, E. V.; Cramer, C. J.; Truhlar, D. G. J. Am. Chem.
Soc. 2001, 123, 2025.
(59) (a) Friedrichs, M.; Zhou, R. H.; Edinger, S. R.; Friesner, R. A. J. Phys.
Chem. B 1999, 103, 3057-3061. (b) Edinger, S. R.; Cortis, C.; Shenkin,
P. S.; Friesner, R. A. J. Phys. Chem. B 1997, 101, 1190-1197. (c) Marten,
B.; Kim, K.; Cortis, C.; Friesner, R. A.; Murphy, R. B.; Ringnalda, M. N.;
Sitkoff, D.; Honig, B. J. Phys. Chem. 1996, 100, 11 775-11 788.
(60) Baik, M.-H.; Friesner, R. A. J. Phys. Chem. A 2002, 106, 7407.
Supporting Information Available: Measurement of extinc-
tion coefficient of (η5-C5Ph5Cr(CO)3•, details of (η5-C5R5Cr-
(CO)3H/MMA-d5 and (η5-C5R5Cr(CO)3H/styrene-d8 isotope
exchange, and details of DFT computation (PDF). This material
is available free of charge via the Internet at http://pubs.acs.org.
JA034927L
9
10102 J. AM. CHEM. SOC. VOL. 125, NO. 33, 2003