Decomposition of malonic anhydrides

Article abstract of DOI:10.1021/ja301867s

Malonic anhydrides decompose at or below room temperature, to form a ketene and carbon dioxide. Rate constants for the thermal decomposition of malonic, methylmalonic, and dimethylmalonic anhydrides were measured by NMR spectroscopy at various temperatures, and activation parameters were evaluated from the temperature dependence of the rate constants. Methylmalonic anhydride is the fastest, with the lowest δH^?, and dimethylmalonic anhydride is the slowest. The nonlinear dependence on the number of methyl groups is discussed in terms of a concerted [2_s + (2_s + 2_s)] or [2_s + 2_a] cycloreversion that proceeds via a twisted transition-state structure, supported by computations.

Full text of DOI:10.1021/ja301867s

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Article
Decomposition of Malonic Anhydrides
Charles L Perrin, Agnes Flach, and Marlon N. Manalo
J. Am. Chem. Soc., Just Accepted Manuscript • DOI: 10.1021/ja301867s • Publication Date (Web): 24 May 2012
Downloaded from http://pubs.acs.org on May 30, 2012
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Decomposition of Malonic Anhydrides
Charles L. Perrin,* Agnes Flach, and Marlon N. Manalo†
Department of Chemistry, University of California—San Diego
La Jolla, CA 92093-0358 USA
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cperrin@ucsd.edu
Abstract. Malonic anhydrides decompose at or below room temperature, to form a ketene
and carbon dioxide. Rate constants for the thermal decomposition of malonic, methylmalonic and
dimethylmalonic anhydrides were measured by NMR spectroscopy at various temperatures, and
activation parameters were evaluated from the temperature dependence of the rate constants.
‡
Methylmalonic anhydride is the fastest, with the lowest ꢀH , and dimethylmalonic anhydride is the
slowest. The nonlinear dependence on the number of methyl groups is discussed in terms of a
concerted [2 +(2 +2 )] or [2 +2 ] cycloreversion that proceeds via a twisted transition-state
s
s
s
s
a
structure, supported by computations.
Introduction
Until 1978 malonic anhydrides ("2,4-oxetanediones", according to Chemical Abstracts) were
classic unknown substances, the goals of 70 years of synthetic attempts. Although heating a
succinic or glutaric acid with a dehydrating agent converts either of these to its anhydride,1 this
simple synthetic route fails to give malonic anhydride. Instead, carbon suboxide, O=C=C=C=O, is
produced.2 Furthermore, dehydration (or other transformation)3 of a substituted malonic acid
derivative leads to oligomeric or polymeric anhydrides.4 Clearly, the challenge to the formation of
the monomeric form is the strained four-membered ring. Indeed, the (calculated) enthalpy of
-1
hydrolysis of malonic anhydride is -134 kJ mol , considerably more exothermic than the -53 kJ
5
-1
mol of succinic anhydride. In contrast, a malonoyl peroxide, with a five-membered ring, is readily
accessible and is effective as a reagent for dihydroxylation of alkenes.6
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Malonic anhydrides were at last synthesized by Perrin and Arrhenius.7. The key to success
was to start with an already formed four-membered ring, as shown in Scheme 1. Ozonolysis of the
enol-lactone dimer (1) of a ketene at -78 ºC produces the malonic anhydride (2). According to
model studies on isopropenyl acetate and 6-phenyl-5-hydroxy-5-hexenoic acid ꢁ-lactone, cleavage
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of the molozonide (3) occurs so that the extra oxygen of ozone is acquired by the aldehyde, not by
the anhydride. The resulting carbonyl oxide (4) can be trapped with N-methylmorpholine N-oxide,8
or with benzaldehyde to form an ozonide (Caution!),9 or it can be allowed to dimerize, trimerize, or
oligomerize, to form peroxides (Caution!). Nevertheless, regardless of the fate of the carbonyl
oxide byproduct, the malonic anhydride itself is produced by this simple procedure. Its structure
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was characterized by derivatization and spectroscopically, especially by an IR band at 1820 cm
-1
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-1
and a Raman band at 1947 cm , which is a champion among organic C=O frequencies!
O
O
CRR'
R'
R
O
O
R'
R
R'
R
CRR'
O
O
3
+
-
+ RR'C=O -O
O
O
-78 C
O
O
O
1
a: R = H = R'
3
2
a: R = H = R'
4
b: R=H, R' = CH
c: R = CH = R'
b: R=H, R' = CH
c: R = CH = R'
3
3
3
3
Scheme 1. Synthesis of malonic anhydrides 2.
Malonic anhydrides are useful materials that can be easily derivatized to a variety of
monoesters and monoamides12 that are commonly used in the synthesis of pharmaceuticals, natural
products, and other biologically active compounds.13 Another proposed application is the
production of Meldrum's acid,14 which is useful in organic synthesis.15
The aspect of malonic anhydrides that is addressed here is their decomposition. The products
are carbon dioxide and a ketene (5 in Scheme 2), as has also been observed for a methylenemalonic
anhydride.16 Decomposition occurs near or below room temperature, which explains why they
eluded synthesis for so long and which demonstrates the advantage of an ozonolytic synthesis,
which can be performed at -78 ºC. But why is decomposition so fast? Also, why does the parent
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malonic anhydride (2a, R = H = R') decompose at a lower temperature than does dimethylmalonic
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anhydride (2c, R = CH = R'), even though a faster reaction might have been expected for the latter
3
(by weak analogy to the Saytzeff Rule for ꢂ-eliminations,17 due to stabilization of the more highly
7
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9
alkylated alkene)?
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R'
O
R
RR'C=C=O + O=C=O
ꢃ 20 C
O
5
O
2
a: R = H = R'
b: R=H, R' = CH
c: R = CH = R'
3
3
Scheme 2. Decomposition of malonic anhydrides
This decomposition is unquestionably a [2+2] cycloreversion. Because a [2 +2 ]
s
s
cycloreversion is forbidden, this reaction has been considered to be a [2 +2 ] process, via a twisted
s
a
transition-state structure, as illustrated in Fig. 1a. Notice that bonding to the C-C double bond of the
ketene is to the + lobe of one atomic orbital and to the – lobe of the other, so this serves as the
antarafacial component,18 while the O=C of the CO is the suprafacial component, with bonding to
2
the atomic orbitals projecting forward toward the ketene. This corresponds to a Möbius topology
for the cycle of atomic orbitals.19 An alternative is a [2 +(2 +2 )] process,20 with a cycle of six
s
s
s
atomic orbitals that avoids an antarafacial component by using two p orbitals on the central carbon
of the ketene. This is illustrated in Fig. 1b, with the vertical p orbitals forming the C-C ꢄ bond and
with the front lobe of the horizontal carbon p orbital in the ketene plane overlapping with the vertical
orbital on a CO oxygen. To achieve this overlap, this transition-state structure too must be twisted
2
around the vertical C-C bond that is breaking simultaneously with the breaking of the vertical C-O
bond.
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R
C
a
R'
C
b
R'
R
C C O
O
O
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C
O C O
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O
Figure 1. Transition-state structures for (a) [2 +2 ] cycloreversion of malonic anhydrides. (b)
s
a
[2 +(2 +2 )] cycloreversion of malonic anhydrides, with atomic-orbital overlaps indicated by wavy
s
s
s
lines.
We now report the first measurements of rate constants and activation parameters for
decomposition of malonic anhydrides 2, including those of the monomethyl derivative (2b, R = H,
R' = CH ). The experimental data are reinforced by computations. The results provide definitive
3
answers to the questions above regarding the rapidity of decomposition and the substituent effects
on reactivities.
Experimental Section
Materials. Diketene (1a, Aldrich) was redistilled. The other two ketene dimers, 4-ethylidene-
3-methyl-2-oxetanone (1b,) and 3-hydroxy-2,2,4-trimethyl-3-pentenoic acid ꢂ-lactone (1c,), were
synthesized by established procedures.21 Other reagents were obtained from commercial suppliers
and used as received. Malonic (2a), methylmalonic (2b), and dimethylmalonic (2c) anhydrides were
22
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then produced by ozonolysis of the three ketene dimers. Details are available.
Sample Preparation. Solutions for ozonolysis were prepared in 200 µL CDCl in an NMR
3
tube, to contain approximately 0.2 M diketene 1a, 0.02 M methylketene dimer 1b, or 0.1 M
dimethylketene dimer 1c, along with 0.02 M cyclopentane (ꢁ 1.51), 0.02 M acetonitrile (ꢁ 2.10), or
0.2 M acetonitrile, respectively, as internal standard. To scavenge peroxides, 1 M or 0.1 M
propionaldehyde (6) was included in the solution of 1a or 1b, respectively. Addition of 6 to
scavenge dissolved peroxide dimers and trimers in the samples of 1b or 1c did not affect the
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kinetics. A combination sample of 0.1 M 1b, 0.05 M 1c, 0.2 M 6, and 0.1 M acetonitrile was also
prepared using a different distillation fraction of 1b that contained more propionic anhydride
byproduct, in order to test whether this anhydride interferes with the kinetic experiments. It does
not.
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Ozonolysis. The sample was placed in a dry ice/acetone cooling bath, and ozonolysis using
an Ozone Research and Equipment Corp. Model 03V5-O ozone generator was performed at -65
ºC. Ozone gas was bubbled through the sample until the solution turned light blue, at which point
O was bubbled through to remove excess ozone. After ozonolysis, additional chilled CDCl was
2
3
added into the NMR tube so that the total sample volume was 600-700 µL.
Peroxide solids in the sample of 2a were found to affect the rate of decomposition.
Reproducible rates were obtained only after the peroxides were filtered off by quickly pouring the
sample through a precooled 2-mL pipette tip equipped with a plug of cotton and pushing the liquid
through the filter with N pressure. Filtration had been also found applicable to the purification of
2
acetic formic anhydride, formed by ozonolysis of vinyl acetate.23 Peroxide solids in the samples of
2b and 2c were found not to interfere with the kinetics, because the results were the same regardless
of filtering. Therefore those peroxides were not removed. Finally, the NMR tube was capped and
the sample was frozen to permit transfer into the probe of the magnet. Caution: Peroxides are
potentially explosive, especially as solids and in larger quantities than here! It might be mentioned
that this study awaited instrumentation sensitive enough to measure kinetics safely at low
concentrations.
1
NMR Measurements. All H NMR spectra were acquired on a JEOL 500-MHz ECA
spectrometer. For 2a and 2b a tip angle of 68º and four acquisitions were used, with a repetition
time of 6-8 sec, sufficient for T relaxation, which was measured independently for anhydrides and
1
internal standards. For 2c a tip angle of 90º was used, with a single acquisition. The free-induction
decays were zero-filled (4X) to increase digital resolution, and line broadening of 0.2 Hz was
applied. The spectra were processed using JEOL Delta and iNMR software. For each run the
integration region was chosen by overlaying the spectra so that all the peaks would be integrated
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over the same region.
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Temperature adjustment. Prior to the experiment, the temperature of the probe was set in
the Delta software. The probe was first set to -50 ºC and 15-20 min was allowed for cooling. Once
the sample was inserted into the magnet, one spectrum was taken at -50 ºC and then the temperature
was set to the desired value. The sample was allowed to remain in the probe for 5 minutes to allow
for temperature equilibration, and then the kinetic experiment began. The temperature inside the
NMR probe was measured both before and after the run from the separation between the OH and
CH chemical shifts of an external 4% methanol in methanol-d standard.24 The change in
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temperature from before the run to after was considered to be the maximum variation in temperature
during the run. That variation was found to be less than 1 ºC for all of the runs.
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Characterization of Products. Malonic anhydride (2a): H NMR 4.1 ppm (s) (lit. 4.1)
7
and peroxides 5.0-6.0 ppm (lit. 5.0-6.0). Decomposition product ketene monomer (5a) was
1
observed at 2.3 ppm (s, 2H). Methylmalonic anhydride (2b): H NMR 4.30 ppm (q, 1H, J = 8.0
Hz), 1.65 ppm (d, 3H, J = 8.0 Hz) and peroxides 1.0-2.0 and 5.0-6.0 ppm. Decomposition product
methylketene (5b) was observed at 2.72 ppm (q, 1H, J = 7.3 Hz) and 1.69 ppm (d, 3H, J = 7.3 Hz).
1
Dimethylmalonic anhydride (2c): H NMR 1.63 ppm (s) (lit. 1.55) and acetone peroxides 1.0-2.0
7
ppm. Decomposition product dimethylketene (5c) was observed at 1.69 ppm (s).
Ketene formation was never quantitative. All three ketenes (5abc) undergo hydrolysis or
possibly polymerization during the course of the kinetic experiment. NMR signals that can be
assigned to hydrolysis products of 5a were at 2.1 and 2.2 ppm, corresponding to acetic acid and
anhydride. Signals at 2.7 ppm and 1.02 ppm, corresponding to isobutyric acid or anhydride (lit.25
2.66, 1.24), were observed from 5c. Signals attributable to propionic acid or anhydride from
hydrolysis of 5b were not observed, presumably because they were obscured by the added
propionaldehyde (6).
Kinetic Measurements. The time-dependence of integrated signal intensities was measured
at 5 ºC intervals between 0 ºC and 25 ºC for 2a, between -10 ºC and 15 ºC for 2b, and between 5 ºC
and 30 ºC for 2c. Time intervals between acquisitions were adjusted so that a minimum of 15
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spectra were acquired per run, and so that the reaction was monitored for more than one half-life.
Also, one decomposition reaction for each anhydride was monitored for > 10 half-lives to determine
whether any residual peaks were obscured by the anhydride signal.
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Possible interferences. Small residual signals near the chemical shift of 2c were detected
after the signal of 2c had disappeared. These signals were assigned as peroxides, whose signals
were also found in that region. Although these signals could erroneously augment the anhydride
signal, the nonlinear analysis described below corrects for this, and the errors in the measured rate
constants for 2c are not larger than the errors for the other two samples, where no such interference
was seen.
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Even though water and chloroform are immiscible, trace water might hydrolyze an anhydride
and deceptively increase the rate of its disappearance. To test this, the reaction of water with malonic
anhydride (2a) was simulated by adding 2 equivalents of ethanol to a sample of 2a at -65 ºC,
immediately inserting it into the NMR probe cooled to -10 ºC, and monitoring the subsequent
1
reaction. As expected, the anhydride disappeared rapidly, with the immediate formation of H NMR
peaks at 1.31 ppm (t, 3H), 3.43 ppm (s, 2H), and 4.24 ppm (q, 2H), which are assigned to 3-ethoxy-
3-oxopropanoic acid (monoethyl malonate), along with other signals at 2.1 ppm (s) and 4.11 ppm
(q), which may be assigned to ethyl acetate from reaction of ketene 5a. Inasmuch as malonic acid
was not detected among any of our products, we conclude that residual water does not interfere with
our kinetic experiments.
Data Analysis. At each time point the concentration of anhydride, A, normalized to the
(constant) concentration of the standard, was obtained by dividing the integrated peak area of the
anhydride by the integrated peak area of the standard. The first-order rate constant k for
disappearance of the anhydride was then obtained by two methods. First, k was obtained from the
slope of the linear plot of ln A vs. time t (eq. 1), which also gives ꢅ, the standard error of that slope.
Second, k was obtained using non-linear regression analysis ("Solver" routine in an Excel
spreadsheet) to fit the data to eq. 2, where estimates for the initial concentration A and the rate
o
constant k were obtained from the fit to eq 1, and the residual intensity A was estimated as the
ꢆ
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intensity at the final time point. The term A accounts for any extraneous signals hidden under the
ꢆ
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anhydride peak, which might be seen at the end of the reaction. Non-linear regression analysis also
has the advantage of eliminating error caused by heteroskedasticity (time-dependent variance),
arising from the increased error of the logarithm of a diminishing concentration. To distinguish
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these two rate constants, they will be designated as k and k , respectively.
lin NL
ln A = ln A - kt
o
(1)
(2)
A = (A - A ) exp(-kt) + A
ꢆ
o
ꢆ
‡
For each anhydride, activation parameters ꢀH and ꢀS (enthalpy and entropy of activation)
‡
as well as the standard errors in these quantities, were then obtained from a plot of ln(k /T) or
lin
ln(k /T) versus 1/T (eq 3, where T = absolute temperature, k = Boltzmann's constant, h =
NL
B
‡
Planck's constant, and R = gas constant), which has a slope of -ꢀH /R and an intercept of ln(k /h) +
B
‡
ꢀS /R.
‡
ln(k/T) = ln(k /h) + ꢀS /R - ꢀH /RT
‡
(3)
B
Computational Methods. All calculations were carried out on a Dell Optiplex PC with Intel
Core 2 Duo processor. Structures of malonic anhydride (2a), ketene (5a), and CO were built using
2
GaussView 4.1.2 (Gaussian, Inc.) and optimized with the Gaussian03W program.26 An initial
transition-state structure was calculated at the HF/6-31G(d) level using the Synchronous Transit-
Guided Quasi-Newton (STQN) method and the QST2 option. The validity of the transition-state
structure was verified by calculating frequencies and reaction-path following along the intrinsic
reaction coordinate (IRC). Geometry optimizations of reactants and products were next performed
at the MP2/6-31G(d) level. The transition-state structure was found by the STQN method using the
QST3 option, with the transition-state structure obtained from the HF method as the initial guess.
IRC calculations were then performed using the MP2 transition-state structure. Vibrational
frequencies were calculated for each structure, and the zero-point energy (ZPE) was included in the
total energy. No correction was applied for scaling factors,27 because they affect total energies by <
1 kcal/mol and relative energies by < 0.1 kcal/mol. No correction was applied for basis-set
superposition error.
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To obtain more accurate energies, calculations at the MP2/cc-pVDZ, MP2/aug-cc-pVDZ
(which was found suitable for modeling [2+2] cycloadditions involving allene, ketene, and other
X=C=Y),28 B3LYP/6-31G(d), B3LYP/cc-pVTZ, BPW91/6-31G(d), BPW91/6-311+G(3df,2p),
B3LYP/6-311+G(3df,2p), and G3 levels were also done. Transition-state structures were calculated
using the QST3 option, except for G3. Some of these calculations were also performed for the
methyl and dimethyl analogs. Optimization of the transition structure using MP2/cc-pVTZ,
MP2/cc-pVQZ, or B3LYP/cc-pVQZ was unsuccessful.
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In addition to the above closed-shell calculations, unrestricted MP2, B3LYP, and BPW91
calculations using the 6-31G(d), cc-pVDZ, or 6-311G+(3df,2p) basis set and the QST3 option
were performed to search for other transition-state structures. The UBPW91 method seems to be
adequate for diradicals.29 Larger basis sets, 6-311++G(2d,2p) and cc-pVTZ, did not converge. The
possibility of a stepwise mechanism was tested further by breaking the C-O bond of the malonic
anhydride ring and optimizing the structure. A QST3 calculation using UB3LYP/6-31G(d),
BPW91/6-31G(d), or UBPW91/6-31G(d) gave a transition structure similar to that obtained by the
UMP2/6-31G(d) calculation. Unrestricted calculations (UB3LYP) using larger basis sets such as
cc-pVTZ and 6-311++G(2d,2p) failed to converge.
Finally, the effect of solvation was tested at the B3LYP/6-31G(d), UBPW916-31G(d), and
UBPW91/6-311+G(3df,2p) levels using the polarizable continuum model (PCM) with chloroform
(ꢇ = 4.90) as solvent, but only the first two converged.
Results
Rates of decomposition of malonic anhydrides. The first-order rate constants k ,
lin
determined from the logarithmic plots (eq 1), and k , from nonlinear regression analysis (eq 2),
NL
for the decomposition of all three anhydrides 2abc at each temperature can be found in Tables 1, 2,
and 3. The tabulated values show only significant figures, but insignificant figures were retained for
further calculations. Tables 1, 2, and 3 also list ꢅ (the standard error in k ), %ꢅ (the % relative
lin
lin
lin
error of k ), r (the correlation coefficient of the linear fit), and 100(A /A ) (the percent infinity
lin
ꢆ
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absorbance not due to anhydride, determined from the nonlinear fit).
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-1
-1
Table 1. Rate constants k (s ), standard error (s ), % relative error, and correlation coefficient
lin
9
-1
from logarithmic plots, along with k (s ) and 100(A /A ) from nonlinear fits for decomposition
NL
ꢆ
o
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13
14
15
16
17
18
19
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21
22
23
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43
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47
48
49
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53
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of 2a at various temperatures (ºC).
4
4
10 ꢅ
4
10 k
%ꢅ
10 k
100(A /A )
ꢆ
T
r
lin
lin
lin
NL
o
25.9
20.7
20.5
15.7
10.7
5.8
18.1
10.1
9.3
0.2
0.1
1.1
1.4
2.0
1.1
1.2
1.9
0.8
1.1
0.9990
0.9976
0.9939
0.9979
0.9975
0.9960
0.9988
0.9978
18.0
0.007
0.017
0.022
0.001
-0.102
0.067
0.008
0.018
10.2
9.3
0.2
6.70
4.49
2.79
1.73
1.63
0.08
0.05
0.05
0.01
0.02
6.76
4.42
2.85
1.73
1.61
0.8
0.8
-1
-1
Table 2. Rate constants k (s ), standard error (s ), % relative error, and correlation coefficient
lin
-1
from logarithmic plots, along with k (s ) and 100(A /A ) from nonlinear fits for decomposition
NL
ꢆ
o
of 2b at various temperatures (ºC).
4
4
10 ꢅ
4
10 k
%ꢅ
10 k
100(A /A )
o
T
r
lin
lin
lin
NL
ꢆ
15.6
10.6
10.6
10.6
10.7
10.7
10.7
14.08
8.34
7.38
7.38
8.32
8.04
7.14
0.07
0.03
0.17
0.19
0.03
0.05
0.08
0.5
0.3
2.4
2.6
0.4
0.7
1.2
0.9997
0.9999
0.9958
0.9938
0.9998
0.9997
0.9985
14.15
8.21
7.42
7.63
8.37
7.73
7.21
0.005
0.003
0.009
0.009
0.003
0.003
0.007
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5.7
0.8
5.24
3.51
2.29
1.43
0.04
0.03
0.04
0.01
0.8
0.9
1.6
0.9
0.9993
0.9988
0.9960
0.9988
5.18
3.45
2.29
1.29
0.002
0.003
0.001
0.003
-3.8
-9.1
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-1
Table 3. Rate constants k (s ), standard error (s ), % relative error, and correlation coefficient
-1
lin
-1
from logarithmic plots, along with k (s ) and 100(A /A ) from nonlinear fits for decomposition
NL
ꢆ
o
of 2c at various temperatures (ºC).
4
4
10 ꢅ
4
10 k
%ꢅ
10 k
100(A /A )
ꢆ
T
r
lin
lin
lin
NL
o
31.4
26.0
20.9
15.6
15.6
15.6
10.6
5.6
11.15
7.11
0.04
0.04
0.4
0.5
0.3
0.3
0.3
0.5
0.9
0.6
0.9999
0.9998
0.9999
0.9999
0.9999
0.9998
0.9992
0.9994
12.33
7.86
5.7
3.8
2.9
3.2
2.7
7.0
6.8
6.5
4.54
0.01
4.89
2.614
2.671
2.621
1.476
0.891
0.008
0.009
0.014
0.014
0.006
2.78
2.797
2.981
1.697
1.036
The logarithmic fits all give correlation coefficients r > 0.99, reflecting good linearity in the fit
to eq 1. Therefore these reactions indeed follow first-order kinetics, with no indication of a second-
order component that could be ascribed to dimerization or to reaction with the peroxide byproduct.
The logarithmic fits give rate constants with an average relative error of 1%, which is excellent
precision. The nonlinear fits give values of 100(A /A ) for 2a and 2b very close to zero,
ꢆ
o
corresponding to "complete" disappearance of the signals of these two anhydrides. However, the
average value of 100(A /A ) for 2c corresponds to a residual signal intensity of 5% of the initial
ꢆ
o
anhydride intensity. These infinity values agree well with the spectra, where no residual signal was
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observed for 2a and 2b, but where small residual peaks were observed in the spectrum of 2c.
Nevertheless, those residual signals in the sample of 2c do not lead to an increase in the relative
7
8
error %ꢅ , which is no worse than the error for 2a and 2b. Moreover, the nonlinear fit
lin
9
compensates for this residual intensity.
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For all three anhydrides the values of k are more reliable because they account for both
NL
residual absorbance and heteroskedasticity. Errors in k and k are compared below.
lin NL
The rate constants in Tables 1, 2, and 3 confirm the previous qualitative observations that
malonic anhydrides 2a and 2c decompose near or below room temperature, as does 2b.
Decomposition is fastest for methylmalonic anhydride (2b) and slowest for dimethylmalonic
anhydride (2c). This nonlinear dependence on the number of methyl groups is a puzzle parallel to
the lower reactivity of 2c that was noted originally.
Activation Parameters. Figures 2 and 3 show plots of ln(k/T) vs. 1/T for rate constants k
lin
from the logarithmic fits and for rate constants k from the nonlinear fits, respectively, for all three
NL
anhydrides 2abc. The two plots appear very similar. The slopes, standard errors of the slope,
intercepts, standard errors of the intercepts, correlation coefficients, and standard error of the y
estimate (ꢅ ) found from these plots are listed in Table 4. The values hardly differ between linear
lnk
and nonlinear fits. The correlation coefficients found from these plots are all > 0.99. The activation
‡
parameters ꢀH and ꢀS for each anhydride were determined from the slopes and intercepts of
‡
‡
those plots. Insofar as the plots are adequately linear, there is no evidence that ꢀH is temperature-
‡
dependent or that there is any detectable ꢀC . The values, along with their errors, are listed in
p
Table 5.
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-12
-12.5
-13
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-13.5
-14
-14.5
-15
3.3
3.4
3.5
3.6
3.7
3.8
1000/T
Figure 2. Eyring plot for anhydrides 2abc using the rate constants from linear fits: parent (o),
methyl ([]), dimethyl (ꢀ).
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-12.5
-13
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-13.5
-14
-14.5
-15
3.3
3.4
3.5
3.6
3.7
3.8
1000/T
Figure 3. Eyring plot for anhydrides 2abc using the rate constants from nonlinear fits: parent (o),
methyl ([]), dimethyl (ꢀ).
Table 4. Slope, standard error of the slope, intercept, standard error of the intercept, correlation
coefficient, and standard error of y for the plots in Figures 2 and 3.
ꢅ
Anhydride slope
±
intercept
11.7
11.7
9.7
±
r
lnk
2a (Lin)
2a (NL)
2b (Lin)
2b (NL)
2c (Lin)
2c (NL)
-7.1
-7.1
-6.4
-6.6
-8.1
-8.0
0.2
0.2
0.3
0.2
0.1
0.1
0.8
0.8
0.9
0.9
0.5
0.4
0.9972 0.068
0.9972 0.068
0.9928 0.080
0.9941 0.075
0.9991 0.037
0.9994 0.028
10.6
14.2
13.8
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Table 5. Enthalpy (kcal/mol,) and entropy of activation (cal/mol-K), along with their errors, for
anhydrides 2abc from linear and nonlinear fits.
7
8
9
‡
‡
ꢀH
ꢀS
Anhydride
2a (Lin)
2a (NL)
2b (Lin)
2b (NL)
2c (Lin)
2c (NL)
±
±
14.2
14.2
12.7
12.6
16.2
15.9
0.4 -24.0 1.5
0.4 -23.9 1.5
0.5 -27.9 1.8
0.5 -28.1 1.7
0.3 -18.9 1.0
0.2 -19.8 0.8
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Error Analysis. Errors in the rate constants were determined by three different methods. The
first was ꢅ , from the error in the slope of the logarithmic plots, as listed in Tables 1-3. The
lin
second method was from ꢅ , the standard deviation of the y estimate in Table 4. Because this
lnk
could be converted to ꢅ as in eq 4, it represents the relative error in the rate constant. Multiplying
k
this by 100 gives the % error in k, designated as %ꢅ . Thus the values of %ꢅ for the linear fits are
k
k
6.8, 8.0, and 3.7 % for 2a, 2b, and 2c, respectively, and 6.8, 7.5, and 2.8 % for the nonlinear fits.
Because the relative errors from the nonlinear fits are slightly smaller, they are confirmed to be
more reliable.
ꢅ
lnk
= (ꢈlnk/ꢈk)ꢅ = (1/k)ꢅ
k
(4)
k
The third measure of the error in the rate constants is the variation between experiments
repeated at the same temperature. These repetitions are included in Tables 1-3 and in Figures 2-3.
T
They are summarized in Table S1, expressed as %ꢅ , the % deviation of rate constant at that
k
T
temperature, from linear and nonlinear fitting. The values of %ꢅ are comparable to the % errors
k
in k or to ꢅ in Table 4. However, the latter errors are more reliable because they are determined
lnk
from more data points.
It should be noted that the error %ꢅ in Tables 1-3 is the smallest of all error estimates,
lin
because it is a within-run error, rather than a run-to-run error. The error %ꢅ includes error due to
lin
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the variation in temperature during a single experiment, whereas the error %ꢅ from Table 4
k
5
6
7
8
includes error due to the variation in temperature from run to run. The contribution due to this
variation is given in eq 5, where the first term is negligible compared to the second. The uncertainty,
ꢅ , previously reported as ±0.8 K,30 is entirely consistent with the observed %ꢅ . Therefore we
9
T
k
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conclude that the major source of errors in the rate constants is due to imperfect control of
‡
temperature, but those errors are small. Moreover, the errors in ꢀH and ꢀS in Table 5 are realistic
‡
estimates.
‡
2
ꢅ
lnk
= (ꢈlnk/ꢈT)ꢅ = (1/T + ꢀH /RT )ꢅ
T
(5)
T
Summary of Kinetics Experiments. These experimental results confirm and quantify the
7
previous observation that 2a decomposes faster than 2c. Moreover, we find that 2b decomposes
even faster than either 2a or 2c. This can be seen by comparing data in Tables 1-3 at similar
-4 -1 -4 -1
temperatures or more explicitly from rate constants (6.4±0.4)x10 s , (11.3±0.9)x10 s , and
-4 -1
(2.7±0.1)x10 s for 2a, 2b, and 2c, respectively, interpolated at 15.0 ºC from Fig. 3. Alternatively,
‡
these rate constants correspond to values of ꢀG of 21.06±0.04 kcal/mol, 20.73±0.05 kcal/mol,
‡
and 21.55±0.02 kcal/mol for 2a, 2b, and 2c. Parallel to the rate constants, 2b shows a ꢀG
significantly lower than that of the other two anhydrides.
‡
According to the data in Table 5, ꢀH is highest for 2c and lowest for 2b. This result
reinforces the nonlinear dependence of the rate constants on the number of methyl groups. The
entropy of activation is least negative for 2c and is most negative for 2b, although the difference
between 2b and 2a is barely significant at a 95% confidence level. Indeed, an apparent
compensation between enthalpy and entropy is often an artifact of experimental error.31
Computational Results. Calculated energies for each of the species, by the various
computational methods, are listed in Table S2. All reactants and products are minima, with no
imaginary frequencies, whereas the transition states have one imaginary frequency. It may be noted
that the four atoms of the malonic anhydride ring are not coplanar, although the barrier to ring
inversion is too small to calculate. Energies of the transition state and of the products, ketene (5a) +
CO , relative to the reactant malonic anhydride (2a), are summarized in Table 6. Table 7 presents
2
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these values for methyl (2b) and dimethyl (2c) malonic anhydrides.
5
6
7
8
Table 6. Calculated energies (kcal/mol) of transition state and product, relative to malonic
9
anhydride (2a).
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‡
E
E
rel,pdt
Method
rel
a
HF/6-31G(d)
39.16
33.45
31.06
28.84
26.55
-4.32
-1.07
-5.13
-9.60
-5.96
-3.89
---
a
MP2/6-31G(d)
MP2/6-31G(d)
MP2/cc-pVDZ
MP2/aug-cc-pVDZ
UB3LYP/6-31G(d)
b
29.71
c
B3LYP/6-31G(d)
25.88
B3LYP/cc-pVTZ
26.28 -11.86
B3LYP/6-311+G(3df,2p)
UBPW91/6-31G(d)
25.75 -11.85
b
26.05
-2.95
---
c
UBPW91/6-31G(d)
23.88
b
UBPW91/6-311+G(3df,2p) 22.98
G3 ---
-9.46
-4.61
a
b
Uncorrected for zero-point energies. Same with restricted. PCM(solvent=chloroform).
c
Table 7. Calculated energies (kcal/mol) of transition state and product, relative to methyl (2b) or
dimethylmalonic (2c) anhydride .
‡
E
E
rel,pdt
Method
rel
a
B3LYP/6-31G(d)
28.30
25.19
24.80
---
-1.43
-8.80
-8.64
-0.40
a
B3LYP/cc-pVTZ
a
B3LYP/6-311+G(3df,2p)
a
G3
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b
B3LYP/6-31G(d)
29.86
27.19
26.79
---
-0.29
-7.18
-6.86
3.08
b
B3LYP/cc-pVTZ
b
B3LYP/6-311+G(3df,2p)
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b
G3
a
b
Methylmalonic (2b). Dimethylmalonic (2c).
Discussion
Computed Exothermicity. As starting points, the decomposition of malonic anhydride (2a)
was calculated at the HF/6-31G(d) level without ZPE-correction and at MP2/6-31G(d) including
ZPE. According to the results in Table 6, an exothermicity of 4.3 or 5 kcal/mol is obtained.
According to the MP2/cc-pVDZ and MP2/aug-cc-pVDZ calculations, the exothermicity is 10
and 6 kcal/mol, respectively. The exothermicity obtained at the B3LYP/6-31G(d) level is 4 kcal/mol,
comparable to that at MP2/6-31G(d). According to the B3LYP/cc-pVTZ, B3LYP/6-311+G(3df,2p),
and BPW91/6-311+G(3df,2p) calculations, the exothermicity is increased, approaching 12
kcal/mol. According to the G3 method, which generally gives enthalpies of formation accurate to ±1
kcal/mol,32 the exothermicity is only 4.6 kcal/mol. However, Table S2 shows that the B3LYP/6-
31G(d), B3LYP/cc-pVTZ, B3LYP/6-311+G(3df,2p), and BPW91/6-311+G(3df,2p) absolute
energies for 2a, ketene, and CO are all more negative than the G3 energies. Therefore, by the
2
Variation Principle of quantum mechanics,33 the G3 energies are not sufficiently reliable for this
study. We therefore accept a calculated value of 10-12 kcal/mol for the exothermicity of conversion
of 2a to 5a + CO .
2
Computed Activation Energy. According to the result in Table 6, an activation energy of
39 kcal/mol is obtained at the HF/6-31G(d) level without ZPE-correction. The resulting transition-
state structure has all the heavy atoms lying in essentially the same plane, but with an increased
separation between the atoms involved in bond breaking. Electron correlation is known to be
especially significant in transition states,34 as confirmed by the MP2/6-31G(d) calculations, which
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predict an activation energy ~6 kcal/mol lower than that of the HF method. Inclusion of ZPE
corrections leads to a slight further lowering of the activation energy.
7
8
9
The importance of electron correlation becomes more apparent when the calculated transition-
state structures are compared. Whereas a planar structure was calculated by the HF method, a
twisted transition-state structure (Fig. 4) was found by the MP2 calculation. The OCCC dihedral
angle is 32º. This twisting is much less than in Fig. 1a, where the twisting is exaggerated in order to
depict the atomic-orbital overlaps. Figure 5 shows the framework and two contours of the highest
occupied molecular orbital of the B3LYP6-31G(d) transition state. Atomic orbitals on all six atoms
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are involved, including both oxygens of CO and also including two p orbitals on the central carbon
2
of the ketene. This is consistent with a [2 +(2 +2 )] process, but the interaction of one C=O of
s
s
s
CO with the C=C of ketene is antarafacial, which is consistent with a [2 +2 ] process. Although
2
s
a
this process was rejected for the dimerization of ketene,35 we choose not to distinguish between
them.
Figure 4. Transition-state structure for thermal decomposition of malonic anhydride, as calculated
at the MP2/6-31G(d) level.
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Figure 5. Atomic framework and two contours of the highest occupied molecular orbital of the
5
6
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8
transition-state structure for decomposition of malonic anhydride, as calculated at the B3LYP/6-
31G(d) level.
9
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According to the MP2/cc-pVDZ and B3LYP/6-31G(d) calculations, the activation energy is
29 and 30 kcal/mol, respectively, or slightly lower, ~26 kcal/mol, by MP2/aug-cc-pVDZ, B3LYP/cc-
pVTZ, and B3LYP/6-311+G(3df,2p) methods, and 23 kcal/mol by BPW91/6-311+G(3df,2p). The
transition-state structures look similar in all cases and also similar to that in Fig. 4 or 5, but with an
OCCC dihedral angle of 27º.
The possibility of a stepwise mechanism was also explored by using the unrestricted
UMP2/6-31G(d), UB3LYP/6-31G(d), UBPW91/6-31G(d), and UBPW91/6-311+G(3df,2p)
methods, which allow for a stepwise mechanism, but the calculated activation energies are
unchanged. Moreover, the transition-state structures are virtually identical to those obtained using
the corresponding restricted methods.
The possibility of a stepwise mechanism was further explored by searching for reaction
intermediates, but this calculation converged only to the optimized malonic anhydride structure. In
another calculation, the CO moiety was twisted by 90º after breaking the C-O bond of the ring.
2
Geometry optimization of this structure did not reach a minimum. For another attempt at geometry
optimization to a stable intermediate, the C-C bond parallel to the C-O bond of the ring was broken
instead, but this calculation led to the optimized malonic anhydride structure. Similar results were
obtained for the calculations in the presence of a solvent continuum. Thus, no reaction intermediates
were found. We therefore conclude that the reaction is concerted, not stepwise.
According to the BPW91/6-311+G(3df,2p) calculations, the C-C bond that is being broken
has elongated from 1.524 Å in 2a to 1.780 Å in the transition-state structure, while the C-O bond
that is being broken has elongated from 1.426 Å to 2.130 Å, in part because of the twisting of the
OCCC dihedral angle by 30º. Therefore, although this is a concerted process, it is quite
asynchronous, with C-O cleavage occurring in advance of C-C cleavage. However, in contrast to the
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cycloaddition of alkenes with isocyanates, for which the transition-state structure is zwitterionic,36
5
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ꢁ+ ꢁ-
the B3LYP/6-311+g(3df,2p) Mulliken charges show a C –O character smaller than in the
7
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ꢁ-
anhydride, whereas the UBPW91/6-311+G(3df,2p) charges show a greater O character in the
9
ꢁ+
transition-state structure than in the anhydride but a smaller C character.
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The above calculations ignore solvation. The importance of solvation is demonstrated by the
B3LYP/6-311+G(3df,2p) calculation that shows that the dipole moment of the transition-state
structure is 5.26 D, appreciably larger than the 2.91 D of the reactant 2a. Therefore a polar solvent
is likely to accelerate the reaction. Such solvation can be taken into consideration by PCM
simulation, with chloroform as solvent. Then the activation energy calculated by the B3LYP/6-
31G(d) method drops from 29.7 kcal/mol to 25.9 kcal/mol, or from 26.05 kcal/mol to 23.9 kcal/mol
with UBPW91/6-31G(d), a decrease of 2-4 kcal/mol.
Experimental Enthalpy of Activation. As can be seen from Table 5, the experimentally
‡
measured ꢀH is quite low, 14.2±0.4, 12.6±0.5, or 15.9±0.2 kcal/mol for the thermal
decomposition of 2a, 2b, or 2c, respectively. Low values are consistent with a concerted
cycloreversion, where a stabilization due to bond formation compensates for the energy rise due to
bond breaking. In contrast, for a representative stepwise process, the decomposition of cyclobutane,
the activation enthalpy is much higher, 61 kcal/mol experimentally or 63 kcal/mol
computationally.37 Lower activation enthalpies, 27.5 and 48 kcal/mol, are found for two concerted
cycloreversions, of dicyclopentadiene and diketene, respectively.38 Yet our observed values are
considerably lower even than these. Indeed, the unusually low activation energy, or the
correspondingly rapid decomposition, is the reason why malonic anhydrides eluded synthesis for
so long.
The decomposition of malonic anhydrides must be concerted, without any intermediate
diradical or zwitterion, because neither the C-O bond nor the C-C bond is so weak that the
activation energy for its cleavage would be < 16 kcal/mol. A concerted process is supported by the
calculations that fail to find an intermediate. Thus we avoid the mechanistic uncertainty that has long
plagued the study of cycloaddition and cycloreversion reactions.
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One reason for the low activation energy is the exothermicity of the reaction, due to the
stability of CO . According to the experimental ꢀ Hº of CO and of ketene (-393.5 and -47.5 kJ
2
f
2
-1 39a
-1 5
mol ) and the estimated ꢀ Hº of malonic anhydride (-407 kJ mol ), the decomposition of
f
9
malonic anhydride is exothermic by 8 kcal/mol (although this is an underestimate owing to
comparison of malonic anhydride with reference four-membered-ring compounds that lack the
carboxyls in the destabilizing anti conformation). This agrees quite well with our computational
results of 10-12 kcal/mol at the B3LYP/cc-pVTZ, B3LYP/6-311+G(3df,2p), and BPW91/6-
311+G(3df,2p) levels.
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Our computational results lead to an activation energy of 23-26 kcal/mol. This is a substantial
overestimate relative to the experimental 13-16 kcal/mol. The discrepancy between these calculated
activation energies and the experimental ones can be attributed largely to the neglect of solvation.
When solvation by chloroform is taken into consideration with PCM, the activation energy
calculated by the B3LYP/6-31G(d) or UBPW91/6-31G(d) method drops by 2-4 kcal/mol. If this
decrease is applied to the activation energy calculated at the UBPW91/6-311+G(3df,2p) level
(which did not converge with PCM), the activation energy is estimated to drop to 19-21 kcal/mol,
which is still higher than the experimental value, but not so much as to invalidate the calculations or
the experiments. Because the activation energy has not reached a limiting value even with cc-pVTZ
or 6-311+G(3df,2p), it is possible that a larger basis set or an alternative methodology might give a
lower value, as might a more accurate treatment of solvation, but such computations are unlikely to
justify the effort when their chief purpose is to complement the experimental results.
Despite the discrepancy, both the calculated activation energy and the experimental values are
much lower than for other cycloreversions. Indeed, most cycloreversions have quite high activation
energies, because those reactions are so endothermic that they are usually studied in the direction of
the cycloaddition. The activation energy for the cycloreversion is then the sum of the activation
energy of the cycloaddition and the reaction enthalpy. The closest analog to a malonic anhydride is
a malonimide (2,4-azetidinedione), which is prepared from a ketene and an isocyanate,40 a reaction
that is slightly exothermic,41 or by cyclization of a malonic acid derivative,42 and which does not
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decompose. One of the most studied classes of cycloadditions is of ketenes with imines, which
proceeds stepwise but is not fully understood.43 Similar is the cycloaddition of ketenes (or
isocyanates) with aldehydes, but this is concerted.44
9
Yet exothermicity cannot be the only reason. For example, the decomposition of oxetanone
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(ꢂ-propiolactone) to ethylene + CO is slightly more exothermic (12 kcal/mol).45 Nevertheless, the
2
activation energy for this decomposition is much higher, 45.8 kcal/mol.46
We suggest that the other reason for the low activation energy is the [2 +(2 +2 )] or [2 +2 ]
s
s
s
s
a
nature of the reaction pathway. An sp-hybridized central C, as in the ketene product, is needed to
provide two p orbitals for the cycle of six atomic orbitals or for the antarafacial component. In the
(also exothermic) decomposition of oxetanone only the carbon atom of CO can provide two p
2
orbitals for the cycle,47 but the required twisting decreases the stabilization of the CO below what
2
will be realized in the products.
‡
Effects of Methyl Substitution. The remaining puzzle regarding ꢀH for decomposition of
‡
malonic anhydrides is the nonlinear dependence on the number of methyl groups, with ꢀH lowest
‡
for the monomethyl (2b) and highest for the dimethyl (2c). The lowest ꢀH might have been
expected for the latter, whose methyl groups could stabilize the C-C double bond forming in the
transition-state structure.
However, the stabilization of ketenes by methyl substitution is much less than the stabilization
48
2
of alkenes. It is even doubtful whether there is any net stabilization by methyl of an sp carbon in
-
ketene. The calculated effect of one or two added methyls on ꢀH º of ketene is -16 or -40 kJ mol
f
l 49
-1 39b
, whereas the effect of one or two added methyls on ꢀH º of ethane is -19.8 or -50.2 kJ mol .
f
2
Therefore a methyl group appears to destabilize the sp carbon of ketene by ~4 kJ mol more than
-1
3
it does an sp carbon.
The data in Tables 6 and 7 support this conclusion. According to the B3LYP/6-31G(d)
calculations, the exothermicity decreases from 3.89 kcal/mol for 2a to 1.43 and 0.29 kcal/mol for
2b and 2c. For the G3 calculations, which we consider less reliable, these values are 4.61, 0.40, and
-3.08 (endothermic), respectively. For the more reliable B3LYP/cc-pVTZ calculations, the
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exothermicities are 11.86, 8.80, and 7.18 kcal/mol, respectively, and 11.85, 8.64, and 6.86 for
B3LYP/6-311+G(3df,2p). In short, methylation destabilizes the product ketene, relative to the
reactant anhydride.
9
Therefore the methyls should not have been expected to accelerate the decomposition. Instead
the methyls retard decomposition through steric destabilization of the twisted transition-state
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structure (Fig. 1b), which brings one of them closer to one of the oxygens of the CO . According
2
to the B3LYP/cc-pVTZ calculation on the parent 2a, the distances between an H and the oxygens of
the CO have shortened from 2.889 and 3.043 Å in the anhydride to 2.647 and 2.925 Å in the
2
transition-state structure. For the dimethyl (2c) the distances between an H on each methyl and one
or the other oxygen of CO have shortened from > 3.214 Å to 2.664 and 2.783 Å. For comparison,
2
50
the sum of the van der Waals radii for hydrogen and oxygen is 2.72 Å. A similar increase in ꢀH
‡
due to steric repulsion was seen for [2+2] cycloaddition of ethoxyketene to cis- vs. trans-2-
butene.51
‡
The higher ꢀH for 2c is reproduced by the results in Tables 6 and 7. According to the more
reliable B3LYP/cc-pVTZ calculations, the activation energies for 2a and 2c are 26.28 and 27.19
kcal/mol, respectively, or 25.75 and 26.79 according to B3LYP/6-311+G(3df,2p). The difference of
1 kcal/mol is small but consistent with the experimental difference of 1.7±0.45 kcal/mol from Table
5.
‡
Because 2c has the highest ꢀH , steric effects are a dominant influence on the rates of
decomposition of methyl-substituted malonic anhydrides. Yet if steric effects were the only
influence, then the order of reactivity would be 2a > 2b > 2c. Instead there is a nonlinear
‡
dependence of rate on the number of methyl groups, with 2b faster than 2a, and with a ꢀH lower
by 1.6±0.6 kcal/mol, according to the data in Table 5. This is opposite to any steric effect. Of
course, steric repulsion can be avoided, because the single methyl group of 2b can project away
from the CO , as does the R' in the rear of Fig. 1b.
2
‡
The lower ꢀH for 2b represents a stabilization of its transition state. According to the
calculated exothermicities, this is a stabilization that does not appear in the product. Yet this lower
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ꢀH is reproduced by the results in Tables 6 and 7. According to the more reliable B3LYP/cc-
pVTZ calculations, the activation energies for 2a and 2b are 26.28 and 25.19 kcal/mol, respectively,
or 25.75 and 24.80 according to B3LYP/6-311+G(3df,2p). This difference of 1 kcal/mol is also
small but consistent with the experimental difference of 1.6±0.6 kcal/mol from Table 5.
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What is the origin of this stabilization, which appears only in the transition state and not in the
product? One possibility is hyperconjugation, whereby an electron-donating methyl stabilizes the
delocalized electronic structure of the transition state. In support, the B3LYP/6-311+G(3df,2p) total
‡
charge on the methyl group in the transition-state structure 2b is +0.166, greater than the total
charge either of +0102 in reactant 2b or of +0.049 in product methylketene (5b). Thus electron
donation by the methyl is strongest in the transition state (although the effect is less marked with
B3LYP/cc-pVTZ charges).
‡
The increase in ꢀH due to the steric destabilization of the transition-state structure by one
‡
‡
methyl can be estimated. This is the difference between the experimental ꢀH for 2c and ꢀH for
2b, which lacks steric destabilization, but this difference must be corrected for the 1.6±0.6 kcal/mol
of stabilization in 2c due to one extra methyl group. Thus the steric destabilization of the transition-
state structure by one methyl group is 15.9 - 12.6 + (14.2 - 12.6) kcal/mol, or 4.9 ± 1.1 kcal/mol.
These estimates are plotted on an energy diagram in Fig. 6, which shows the relative activation
enthalpies of the transition-state structures for decomposition of 2a, 2b, and 2c. The dashed line for
2c represents the enthalpy of the hypothetical transition-state structure without the electronic
‡
stabilization by the two methyl groups. The figure also reproduces the observation that ꢀH is not
‡
linear in the number of methyl groups. In summary, the reason why 2c has the highest ꢀH is that
the steric retardation by the second methyl is greater than the stabilization of the delocalized
electronic structure of the transition state by two methyls.
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H(2c‡)
H
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H(2a‡)
H
stab'n = 1.6
H(2b‡)
Figure 6. Relative transition-state enthalpies for decomposition of malonic anhydrides.
‡
Entropy of Activation. As can be seen from Table 5, ꢀS is substantially negative for
decomposition of all three malonic anhydrides (2abc). This might be thought unusual for a
decomposition that converts one molecule to two and where the overall ꢀSº is > 0. However, a
52
‡
negative ꢀS is also seen in the classic example of the decomposition of dicyclopentadiene.
‡
The negative ꢀS is due to the necessity of organizing the structure to permit the orbital
overlaps in the transition-state structure (Fig. 1b, 4,5). The least negative is for 2c. This may be a
consequence of the steric repulsion, whereby the transition-state structure has a more pronounced
character of a fragmentation. The more interesting result is the 4.2±2.3 cal/mol-deg more negative
‡
ꢀS for 2b than for 2a. This is consistent with a contribution of Rln2, arising from the ability of 2a
to twist in two directions to reach the transition-state structure of Fig. 1b or 4, whereas 2b can twist
in only one way to avoid methyl repulsion.
Conclusions
The rate constants and activation parameters for the thermal decomposition of malonic
anhydrides 2a, 2b, or 2c were reliably obtained. The parent malonic anhydride 2a was found to
decompose at a higher rate than that of 2c, and methylmalonic anhydride 2b decomposes at an even
higher rate than either 2a or 2c.
Computations support a twisted transition-state structure as illustrated in Figure 4 or 5. The
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low ꢀH values provide additional evidence supporting a [2 +(2 +2 )] or [2 +2 ] cycloreversion
s
s
s
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a
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mechanism, but they are exceptionally low, owing to the formation of the stable CO product. The
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‡
ꢀH values increase in the order 2b < 2a < 2c, owing to opposition between steric hindrance by a
9
methyl group and its hyperconjugative ability to stabilize the delocalized transition-state structure,
which is less effective.
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‡
The ꢀS values for all three anhydrides are large and negative, consistent with a highly
ordered transition-state structure, as predicted for [2 +(2 +2 )] or [2 +2 ] cycloreversions and as
s
s
s
s
a
‡
supported by calculations. The ꢀS for 2a is less negative than that of 2b because 2a can twist in
two different ways to reach the transition-state structure.
Despite the long-standing controversies and uncertainties regarding whether 2+2
cycloadditions and cycloreversions are concerted or stepwise, all these results are consistent with a
‡
concerted but asynchronous mechanism. The unusually low ꢀH decisively excludes a stepwise
process because there is no bond so weak that the activation energy for its cleavage would be < 16
kcal/mol.
Acknowledgments. This research was supported by NSF Grants CHE03-53091 and
CHE07-42801 and by Instrumentation Grant CHE97-09183. We are grateful to Prof. Tom Tidwell
for insightful comments.
Supporting Information Available: Complete Reference 26. Table S1 summarizing rate
constants for decomposition of malonic anhydrides (2abc) from repeated runs at the same
temperature. Table S2 of energies, as calculated by HF/6-31G, MP2/6-31G(d), MP2/cc-pVDZ,
MP2/aug-cc-pVDZ, B3LYP/6-31G(d), B3LYP/cc-pVTZ, G3, B3LYP/6-311+G(3df,2p), and
UBPW91/6-311+G(3df,2p). Tables S3-63 listing optimized geometries of malonic anhydride,
ketene, CO , the transition-state structure, and their methyl and dimethyl analogs, as calculated by
2
HF/6-31G, MP2/6-31G(d), MP2/cc-pVDZ, MP2/aug-cc-pVDZ, B3LYP/6-31G(d), B3LYP/cc-
pVTZ, G3, B3LYP/6-311+G(3df,2p), and UBPW91/6-311+G(3df,2p). This material is available
free of charge via the Internet at http://pubs.acs.org.
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† Current address: Institute of Chemistry, University of the Philippines Los Baños College, Laguna
4031, Philippines.
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References
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-1
and 1949 cm (Knunyants, I. L.; Cheburkov, Yu. A. Izv. Akad. Nauk SSSR, Ser. Khim. 1960,
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-1
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24 . Berger, S.; Braun, S. 200 and More NMR Experiments; Wiley-VCH: Weinheim 2004.
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