Uncatalyzed and amine catalyzed decarboxylation of acetoacetic acid: An examination in terms of No Barrier Theory

Article abstract of DOI:10.1006/bioo.2001.1231

Rate constants for decarboxylation of acetoacetic acid, its anion, and its imine with aminoacetonitrile have been calculated from equilibrium constants and distortion energies using No Barrier Theory. The mechanisms of decarboxylation of both acetoacetic acid and its imine involve preequilibrium formation of the zwitterion.

Full text of DOI:10.1006/bioo.2001.1231

Bioorganic Chemistry 30, 32–52 (2002)
doi:10.1006/bioo.2001.1231, available online at http://www.idealibrary.com on
Uncatalyzed and Amine Catalyzed Decarboxylation
of Acetoacetic Acid: An Examination in Terms
of No Barrier Theory1
J. Peter Guthrie
Department of Chemistry, University of Western Ontario, London, Ontario, Canada N6A 5B7
Received July 9, 2001
Rate constants for decarboxylation of acetoacetic acid, its anion, and its imine with aminoace-
tonitrile have been calculated from equilibrium constants and distortion energies using No
Barrier Theory. The mechanisms of decarboxylation of both acetoacetic acid and its imine
involve preequilibrium formation of the zwitterion.
᭧ 2002 Elsevier Science (USA)
Key Words: decarboxylation; amine catalysis; imine; No Barrier Theory; calculation of
rate constants.
INTRODUCTION
Decarboxylation of carboxylic acids is generally thermodynamically favorable but
kinetically unfavorable. For example, the decarboxylation of acetic acid in aqueous
solution is favored by a free energy change of Ϫ6 kcal/mol yet is a very slow reaction
under ordinary conditions; this value is calculated from values of the free energies
of formation in aqueous solution for acetic acid (1), methane (1), and carbon dioxide
(2). ␤-Ketoacids are famous exceptions to this generalization because they have a
low energy path for decarboxylation by way of the enol of the product ketone. This
decarboxylation can be made even easier by temporary conversion of the ketone to
an imine, which can give an iminium carboxylate zwitterion with a very good electron
sink to facilitate loss of CO2. Conversion of the keto acid to its anion makes decarboxyl-
ation more difficult because the immediate product must be the enolate and not the
enol. The difference is not large in absolute terms but noticeable on a human time
scale: the difference at 30ЊC is between a 7-h and a 430-h half-life.
1 This work is dedicated to F. H. Westheimer, on the occasion of his 90th birthday.
32
0045-2068/02 $35.00
᭧ 2002 Elsevier Science (USA)
All rights reserved.

DECARBOXYLATION OF ACETOACETIC ACID
33
Decarboxylation of ␤-ketoacids has been extensively studied (3–11). There remains
some uncertainty about details of the mechanism, and in particular about whether the
proton transfer is concerted with the C-C bond breaking (3,10,12,13). Amine catalysis
has been known for a long time (5,14,15,11,10,16), but is less understood in detail
because of the multistep nature of the catalysis. In the case of aminoacetonitrile,
which was an efficient catalyst for the decarboxylation of acetoacetic acid, a detailed
kinetic analysis was carried out, leading to a rate constant for the actual decarboxylation
of the imine (17). Amine catalysis is one of the mechanism used by enzymes which
catalyze decarboxylation (18,19,20,21,3) and has been incorporated into abzymes
(catalytic antibodies) (22).
This work will examine the decarboxylation of acetoacetic acid and its anion, and
the corresponding imine with aminoacetonitrile, which was found to be an efficient
catalyst for the decarboxylation. The catalysis will be shown to be explicable in terms
of No Barrier Theory, which offers a satisfactory explanation of the origins of the
intrinsic barrier for these reactions.
RESULTS
No Barrier Theory depends on the following postulates:
(1) Reactants are in equilibrium with starting material or product at each point
along each reaction coordinate.
(2) For any process where only one elementary reaction coordinate changes, the
energy will be a quadratic function of the corresponding reaction coordinate.
(3) Heterolytic bond cleavage constitutes an elementary reaction coordinate.
(4) Proton transfer between electronegative atoms can be treated as an elementary
reaction coordinate.
Reaction coordinates are defined to run from 0 to 1.
From these we can calculate the free energy hypersurface, and thus find the lowest
energy path over this surface from starting material to products. Transition state
energies so calculated are in good agreement with experiment for a variety of reactions:
proton transfer to form enolates (23), cyanohydrin formation (24), carbonyl hydration
(25), addition of amines to carbonyls (26), reaction of nucleophiles with carboca-
tions (27).
No Barrier Theory is in the spirit of Marcus Theory (28–31) and allows both an
explanation of, and a method for calculating the value of, the intrinsic barrier for a
reaction. The intrinsic barrier of Marcus Theory arises from the distortion energies
of No Barrier Theory. If the distortion energies for the simple processes are high then

34
J. PETER GUTHRIE
the intrinsic barrier will be high. The fact that different families of reactions can be
treated with no empirical intrinsic barriers speaks to the power of this new approach.
In order to apply No Barrier Theory we require equilibrium constants for the
decarboxylation reactions. These cannot be measured directly but must be calculated
using thermodynamic quantities. The relevant values are collected in Table 1. For
amine catalyzed decarboxylation, equilibrium constants for formation of imine from
starting material and of enamine from product are needed. The former is available
from kinetic analysis (17), but the latter has not been reported. The experimental rate
and equilibrium constants which are available are collected in Table 2. The calculations
involved in the application of No Barrier Theory require various pKa values not all
of which can be measured directly; various estimations were necessary. pKa values,
both measured and estimated are found in Table 3.
Thermodynamics of ethyl acetoacetate. The enthalpy of formation of ethyl acet-
oacetate in the gas phase has been determined by combustion calorimetry and is
Ϫ140.1 Ϯ 0.36 kcal/mol (32). In the gas phase ethyl acetoacetate is an equilibrium
mixture containing 47% keto and 53% enol at 298.15 K (33). The thermodynamic
quantities at 298.15K for
CH3COCH2COOC2H5 s CH3C(OH)ϭCHCOOC2H5
TABLE 1
Thermodynamic Quantities for Compound Discussed in This Papera
A. Compounds for which ⌬Gf (aq) has not previously been reported.
Compound
⌬Hf (g)
SЊ(g)
⌬Gf (g)
⌬Gtb
⌬Gf (aq)
CH3COCH2COOCH2CH3
CH3COCH2COOH
CH3C(ϭNCH2CN)CH3
CH3C(NHCH2CN)ϭCH2
Ϫ140.1 Ϯ 0.36c
106.21d
Ϫ100.89
Ϫ4.20d
Ϫ105.09
Ϫ120.04
33.08d
37.99d
91.95d
90.55d
62.81
68.13
B. Compounds for which ⌬Gf (aq) has been reported
Compound
⌬Gf (aq)
Compound
⌬Gf (aq)
Ϫ27.02 Ϯ 0.21f
CO2
CH3COCH3
Ϫ92.25 Ϯ 0.06e
Ϫ38.48 Ϯ 0.21f
CH3C(OH)ϭCH2
a All at 25ЊC; enthalpies and free energies are in kcal/mole, entropies are in cal/deg/mole, standard
states are ideal gas at 1 atm and 1M aqueous solution with an infinitely dilute reference state. Unless
otherwise noted, enthalpies of formation are from reference (92), entropies are from reference (93), free
energies of formation in the gas phase are calculated from the corresponding enthalpies of formation and
the standard entropies, and free energies of formation in aqueous solution are calculated from the
corresponding free energies of formation in the gas and free energies of transfer.
b Free energy of transfer from the gas at 1 atm to 1M aqueous solution.
c Reference (32).
d Calculated as described in the text.
e Reference (2).
f Reference (1).

DECARBOXYLATION OF ACETOACETIC ACID
35
TABLE 2
Rate and Equilibrium Constants Used in This Worka
Reaction
log K
log k
CH3C(OH)ϭCH2 s CH3COCH3
ϩ8.33b
ϩ4.02
ϩ7.82
Ϫ0.50
Ϫ7.86
ϩ2.86
CH3C(NHCH2CN)ϭCH2 s CH3C(ϭNCH2CN)CH3
CH3COCH2COOH s CH3C(OH)ϭCH2 ϩ CO2
CH3COCH2COOH → CH3COCH3 ϩ CO2
Ϫ4.54c
Ϫ6.35c
1.0c
CH3COCH2COOϪ → CH3COCH2Ϫ ϩ CO2
CH3C(ϭNCH2CN)CH2COOH → CH3C(ϭNCH2CN)CH3 ϩ CO2
a In aqueous solution; calculated as described in the text unless otherwise noted.
b Reference (59).
c Reference (17).
are: ⌬H ϭ Ϫ3.17 kcal/mol, ⌬S ϭ Ϫ10.38 cal/K/mol, ⌬G ϭ Ϫ0.08 kcal/mol
(33,34). From this we may deduce that the heat of formation of the keto tautomer is
Ϫ138.42 kcal/mol, and that the heat of formation of the enol tautomer is Ϫ141.59
kcal/mol.
The entropy of both tautomers of gaseous ethyl acetoacetate was calculated using
DFT (35) and corrected for the number of low energy conformations. Exploration of
conformations for the keto tautomer by PCModel (36) showed that there are three
low energy conformations corresponding to rotation about the C-O bond of the ester,
three corresponding to rotation about the CH2-COO bond, and two corresponding to
TABLE 3
pKa Values for Compounds Discussed in This Worka
Compound
pKa
3.58b
1.19
Ϫ7.65
1.95
CH3COCH2COOH anti OH
CH3COCH2COOH syn OH
CH3C(OH+)CH2COOH
CH3C(OH+)CH2COOH
CH3C(ϭN(H+)CH2CN)CH2COOH
CH3C(ϭN(H+)CH2CN)CH2COOH
CH3C(ϭN(H+)CH2CN)CH2COOϪ
CH3C(ϭNCH2CN)CH2COOH
CH3C(OH)ϭCH2
0.53
2.62
2.17
4.26
10.94c
31
CH3C(ϪNHCH2CN)ϭCH2
CO2H+ linear
Ϫ39
Ϫ31
Ϫ21.34
1.95
CO2H+ bent
CH3C(OH+)CH2COOH (O+H perpendicular)
CH3C(OH+)CH2COOH (O+H perpendicular)
CH3C(OH)ϭCH2 (OH perpendicular)
7.41
a In aqueous solution; estimated as described in the text unless otherwise noted.
b Reference (44).
c Reference (59).

36
J. PETER GUTHRIE
rotation about the CH3CO-CH2 bond, for a total of 18 conformations. For the enol
tautomer there are three low energy conformations corresponding to rotation about
the C-O bond of the ester. The entropy values so calculated are: 110.15 cal/K/mol
for the keto tautomer, and 100.13 cal/K/mol for the enol tautomer. Combining these
values and the entropy of mixing, we obtain the free energy of formation of the
equilibrium mixture in the gas phase as Ϫ100.89 kcal/mol.
The solubility of ethyl acetoacetate in water is 14.3 g/100 ml at 16.5ЊC (37); this
corresponds to 1.1 M. In water ethyl acetoacetate is 0.5% enol (34,38). The vapor
pressure at 16.5ЊC can be calculated from the Antoine parameters (39), as 0.39 Torr.
The total free energy of transfer is thus Ϫ4.55 kcal/mol at 16.5ЊC. To correct this to
25ЊC one must estimate the enthalpy of transfer. This may be done using experimental
values for related compounds reported by Cabani et al. (40), starting with the value
for methyl butyrate (Ϫ11.50 kcal/mol). This is corrected using the difference between
methyl acetate (Ϫ10.16 kcal/mol) and ethyl acetate (Ϫ10.90 kcal/mol) to give the
heat of solvation of ethyl butyrate as Ϫ12.24 kcal/mol. This is corrected for the
introduction of a keto group using the difference between acetone (Ϫ9.77 kcal/mol)
and propane (Ϫ4.38 kcal/mol) to give the heat of solvation of ethyl acetoacetate as
Ϫ16.63. From this value and the free energy of transfer calculated above we obtain
the entropy of transfer as 41.65 cal/K/mol. The desired free energy of transfer at
25ЊC can now be calculated as Ϫ4.21 kcal/mol. The estimation of the heat of transfer
for ethyl acetoacetate is necessarily approximate, but even if the error were 5 kcal/
mol (larger than the effect of introducing a keto group in place of a methylene) the
resulting change in ⌬Gt at 25ЊC would be only 0.14 kcal/mol, because the temperature
change is small. The free energy of formation of the equilibrium mixture in aqueous
solution can now be calculated as Ϫ105.09 kcal/mol.
The free energy of hydrolysis of the ester may be estimated as Ϫ1.7 (the value
for methyl acetate (41) or methyl trifluoroacetate (42); the value is very insensitive
to the acyl substituent, and is the same, within the uncertainty of the data, as the free
energy of hydrolysis of ethyl acetate, calculated using tabulated free energy of forma-
tion data (1); equilibrium constants for methyl and ethyl acetate formation in 50%
acetic acid 50% water were within a factor of 1.6 (43)), and thus the free energy of
formation for the acid in aqueous solution may be calculated as Ϫ120.04 kcal/mol.
The pKa is 3.58 (44) and thus the free energy of formation of acetoacetate ion is
Ϫ115.15. The values in the literature are Ϫ118 kcal/mol (45) and Ϫ114 kcal/mol (46).
Thermodynamics of imine formation. The equilibrium constant for formation of
the imine from acetoacetate and aminoacetonitrile has been evaluated (17). The value
for the reaction of neutral acetoacetic acid and neutral aminoacetonitrile to give the
total (neutral plus zwitterionic) imine is K ϭ 0.25 (17). No value for the equilibrium
constant for formation of the imine from acetone and aminoacetonitrile has been
reported so it is necessary to estimate it. The equilibrium constants for imine formation
used in this estimation are: acetone plus methylamine (at 25ЊC) 0.23 MϪ1 (47);
isobutyraldehyde plus methylamine (at 35ЊC) 118 MϪ1 (48); and isobutyraldehyde
plus aminoacetonitrile (at 35ЊC) 11.28 MϪ1 (calculated from a value for KЈim
ϭ
([CA] ϩ [Im])[H2O]/(([Hy] ϩ [Al])[Am]) (49) by dividing by the concentration of
water, multiplying by 1 ϩ Kh (Kh ϭ 0.429 (48)) and dividing by 1 ϩ Kca (using the
value, 0.24 (48) for CF3CH2NH2, which has a similar pKa, since Kca is relatively

DECARBOXYLATION OF ACETOACETIC ACID
37
insensitive to amine pKa (48))). Assuming that the substituent effect of the nitrile
is the same for isobutyraldehyde and acetone, and is the same at 25 as at 35ЊC,
we estimate that the equilibrium constant for imine formation from acetone and
aminoacetonitrile is 0.23 * 11.28/118 ϭ 0.022 MϪ1.
Thermodynamics of imine-enamine tautomerization. By an indirect calculation
based on an extended kinetic analysis Hine determined that the equilibrium constant
relating the imine from acetone and trans-2-dimethylaminomethylcyclopentylamine
and its enamine tautomer was 10Ϫ5 (50). It was necessary to estimate the corresponding
equilibrium constant for N-isopropylidenecyanomethylamine. This was done by calcu-
lating the free energies of formation in the gas phase and estimating the free energies
of transfer. Enthalpies of formation were calculated from B3LYP/6-31G**//RHF/6-
31G** energies as described (51) and entropies were calculated using results from
frequencies calculated at the B3LYP/6-31G**//B3LYP/6-31G** level (35), with care
to see that the correct rotational symmetry numbers were used and correcting for the
entropy of mixing due to low energy conformations.
Free energies of transfer were estimated using group additivity (1,52). It was
necessary to estimate some of the contributions since there are no free energy of
transfer data for either imines or enamines. For imines it was assumed that the imine
nitrogen was equivalent to a pyridine nitrogen, and that
⌬Gt(pyridine) Ϫ ⌬Gt(benzene) ϭ ⌬Gt(imine) Ϫ ⌬Gt(alkene),
where alkene corresponds to imine with N replaced by CH. This allows estimation
when the free energy of transfer for the analogous alkene is available or can be
calculated from well established parameters. The models for E-N-isobutylidenemeth-
ylamine and N-isopropylidenemethylamine are E-3-methyl-2-pentene (⌬Gt estimated
by group additivity (1) as 3.52 kcal/mol) and 2-methyl-2-butene (⌬Gt ϭ 3.21 kcal/
mol (1)). ⌬Gt is available for pyridine (⌬Gt ϭ Ϫ2.80 kcal/mol (53)) and benzene
(⌬Gt ϭ 1.03 kcal/mol (53)). Thus we estimate ⌬Gt for N-isopropylidenemethylamine
to be Ϫ0.62 kcal/mol, and for E-N-isobutylidenemethylamine to be Ϫ0.31 kcal/mol.
As an alternative approach we can calculate a value for [NI(C)] (where NI is an imine
nitrogen understood to be bonded to a double bonded carbon). The assumed equality
above is equivalent to:
⌬Gt(pyridine) Ϫ ⌬Gt(benzene) ϭ [NI(C)] Ϫ [CdH(C)]
Using the known value of [CdH(C)] (1) one obtains
[NI(C)] ϭ ⌬Gt(pyridine) Ϫ ⌬Gt(benzene) ϩ [CdH(C)] ϭ Ϫ4.13 kcal/mol
For enamines it was assumed that
⌬Gt(CH2ϭC(CH3)-OR) Ϫ ⌬Gt(C6H5-OR) ϳ ⌬Gt(CH2ϭC(CH3)-NHR)
Ϫ ⌬Gt(C6H5-NHR)

38
J. PETER GUTHRIE
and that
⌬Gt(CH2ϭCH-OR) Ϫ ⌬Gt(C6H5-OR) ϳ ⌬Gt(CH2ϭCH-NHR) Ϫ ⌬Gt(C6H5-NHR),
i.e., that the effect of changing from a benzene ring to an alkene is the same for enol
ethers and enamines
These assumptions are equivalent to:
{[Cd(C)(O)] ϩ [O(C)(Cd)]} Ϫ {[CB(O)] ϩ [O(C)(CB)]} ϳ {[Cd(C)(N)]
ϩ [NH(C)(Cd)]} Ϫ {[CB(N)] ϩ [NH(C)(CB)]}
and
{[CdH(O)] ϩ [O(C)(Cd)]} Ϫ {[CB(O)] ϩ [O(C)(CB)]} ϳ {[CdH(N)]
ϩ [NH(C)(Cd)]} Ϫ {[CB(N)] ϩ [NH(C)(CB)]}
Although individual group contributions for enol ethers are not available, the sums
are ({[Cd(C)(O)] ϩ [O(C)(Cd)]} ϭ Ϫ3.03 kcal/mol and {[CdH(O)] ϩ [O(C)(Cd)]} ϭ
Ϫ2.28 kcal/mol (54)). The contributions for substituted benzenes are available (1) or
can be calculated from literature data.
Values for [NH2(X)] (needed to calculate [CB(N)] from ⌬Gt for aniline), [CB(N)],
and [NH(C)(CB)] were calculated from the free energies of transfer of methylamine
(Ϫ2.70 kcal/mol (53)) aniline (Ϫ4.30 kcal/mol (55)) and N-methylaniline (Ϫ2.61
kcal/mol (56)) respectively.
The values so obtained were: [NH2(X)] ϭ Ϫ5.45 kcal/mol; [CB(N)] ϭ 0.60 kcal/
mol; and [NH(C)(CB)] ϭ Ϫ5.21 kcal/mol:
How good are the above assumptions likely to be? We can examine the first
by comparing
{[Cd(C)(O)] ϩ [O(C)(Cd)]} Ϫ {[CB(O)] ϩ [O(C)(CB)]} ϭ Ϫ3.03 Ϫ (Ϫ2.54)
ϭ Ϫ0.49 kcal/mol
with {[Cd(C)2] ϩ [CH2(C)(Cd)]} Ϫ {[CB(C)] ϩ [CH2(C)(CB)]} ϭ Ϫ0.60 Ϫ (Ϫ0.70) ϭ
0.10 kcal/mol.
The differences are clearly small, even for a more drastic change that is being
assumed here.
Similarly for the second assumption, comparing
{[CdH(O)] ϩ [O(C)(Cd)]} Ϫ {[CB(O)] ϩ [O(C)(CB)]} ϭ Ϫ2.28 Ϫ (Ϫ2.54)
ϭ 0.26 kcal/mol

DECARBOXYLATION OF ACETOACETIC ACID
39
with
{[CdH(C)] ϩ [CH2(C)(Cd)]} Ϫ {[CB(C)] ϩ [CH2(C)(CB)]} ϭ 0.02 Ϫ (0.70)
ϭ 0.72 kcal/mol
Again the difference is small.
Thus we end with the following estimated values:
{[Cd(C)(N)] ϩ [NH(C)(Cd)]} ϭ Ϫ5.10
{[CdH(N)] ϩ [NH(C)(Cd)]} ϭ Ϫ4.35
Using these values we may now estimate free energies of transfer for the simple
enamines:
(CH3)2CϭCH-NHCH3 ⌬Gt ϭ Ϫ0.33 kcal/mol
CH3C(NHCH3)ϭCH3 ⌬Gt ϭ Ϫ0.45 kcal/mol
For the next step what we want is the difference, ⌬Gt (enamine) Ϫ ⌬Gt(imine), which
is Ϫ0.70 kcal/mol for E-N-isobutylidenemethylamine and Ϫ0.33 kcal/mol for
N-isopropylidenemethylamine.
Using the free energies of transfer estimated above and the free energies in the
gas phase calculated as described, the free energy change for conversion of
N-isopropylidenemethylamine to N-isopropenylmethylamine can be calculated as 6.1
kcal/mol, in satisfactory agreement with the value estimated by Hine from a kinetic
analysis for the imine of acetone and trans-2-dimethylaminomethylcyclopentylamine,
i.e., 6.8 kcal/mol (50).
For the case of interest in this paper, the imine and enamine derived from acetone
and aminoacetonitrile, there will be additional terms required for the nitrile group
and for the interaction between the nitrile and the amino or imino nitrogen. For
lack of information permitting a more detailed examination we must make the (not
unreasonable) assumption that the distant polar interactions between nitrile and ena-
mine nitrogen or imine nitrogen will be the same. This means that the difference
between the free energy of transfer of enamine and imine pairs will be the same for
all cases. This clearly is only an approximation, yet should be close because absent
steric bulk which causes shielding from solvent the only difference is in the distant
polar interactions which are not expected to be very different; the pKa value of the
two nitrogens should be similar since a simple imine has a pKa of about 7 (7.6 for
N-isopropylidenemethylamine (57), 6.88 for E-N-isobutylidenemethylamine (58)) and
an enamine is expected to have pKa similar to aniline, i.e., 4.58 (44) (just as an enol
(e.g., vinyl alcohol, pKa 10.50 (59)) has a pKa similar to a phenol (phenol itself, pKa
9.95 (44))). This means that the equilibrium constant for imine–enamine conversion
in solution can be calculated from the equilibrium constant in the gas using only this
roughly constant difference in free energies of transfer.

40
J. PETER GUTHRIE
We must, however, consider the uncertainties in the estimated values. Conversion
of DFT energies into heats of formation (51) requires an extrapolation because there
are very few calorimetric values (and none for simple imines (60)), which can be
used for calibration. For a set of five heats of formation for imines, three of which
were calculated at the G2 (62) level of theory (63,64), and two of which
(1-azacyclopentene (65) and N-methylbenzaldimine (66)) are experimental, the atomic
level parameter set (51) (supplemented by one new parameter for doubly bonded
nitrogen) gave an rms error of 3.67 kcal/mol; the modified atomic level parameter
set (51) (which needed no new parameters) gave an rms error of 1.81 kcal/mol. The
method for estimating entropies gives an rms error of 1.28 cal/K/mol for a set of 128
compounds (35). The calculation of free energies of transfer requires a number of
estimated contributions so we will take the uncertainty as 1.0 kcal/mol. These uncer-
tainties lead to an uncertainty in each free energy of formation of 2.10 kcal/mol, and
in the free energy for the imine–enamine equilibrium of 2.97 kcal/mol.
Alternatively the quality of the estimation process can be assessed by comparing
the estimated free energies of formation for N-isopropylidenemethylamine and E-N-
isobutylidenemethylamine with values calculated from free energies of formation of
methylamine (2), the carbonyl compounds (1), and water (2), and the equilibrium
constants. The values are: N-isopropylidenemethylamine, estimated 24.11 kcal/mol,
experimental 24.12 kcal/mol; and E-N-isobutylidenemethylamine, estimated 27.99
kcal/mol, experimental 28.82 kcal/mol. The estimated values are within 1 kcal/mol
of the experimental values, which is in excellent agreement considering the expected
uncertainties in the method.
pKa values. In the application of No Barrier Theory, the energies of various “corner
intermediates” must be calculated. These often involve proton transfer processes, and
thus various pKa values are required some of which had to be estimated.
The pKa of acetoacetic acid in water (where it is almost entirely the keto tautomer
(34)) is 3.58 (44). For carbonyl protonated acetoacetic acid, the pKa for dissociation
of the protonated carbonyl may be estimated starting with acetone, for which Yates
and Cox reported a value of Ϫ5.37 using an X-function to extrapolate from sulfuric
acid solutions (67). The effect of substituents will be assumed to be similar to that
in amidines R-C(NH2)ϭNHϩ2 , for which ␳ ϭ Ϫ11.98, with ␴
(68). From values
meta
for CH3 and CH2COOCH3 (assumed to be the same as for CH2COOH) taken from
Perrin et al. (68) we calculate the pKa difference as Ϫ2.28, leading to a pKa of
Ϫ7.65. The effect of carbonyl protonation on the pKa of the carboxylic acid is assumed
to be the same as the effect of N-protonation on 2-pyridylacetic acid, for which Button
and Taylor (69) report microscopic pKa values for the neutral and cationic species
of 4.26 and 2.63, respectively, for an effect of the plus charge equal to Ϫ1.63. This
leads to a pKa for the carboxylic acid in carbonyl protonated acetoacetic acid of 1.95.
If direct proton transfer is to be part of the concerted transition state, the initial
carboxylic acid must be in the less stable conformation with the OH syn to the
C-COOH bond. This conformation is less stable but more acidic. DFT calculations
(B3LYP/3-21ϩG*) lead to an energy difference of 3.26 kcal/mol. Thus the pKa of
the syn conformation of acetoacetic acid would be 1.19 if it were not hydrogen
bonded; an intramolecular hydrogen bond would lower the acidity by stabilizing the
acid form.

DECARBOXYLATION OF ACETOACETIC ACID
41
The pKa for protonated carbon dioxide was estimated using the same procedure
as was used for protonated ketene (70). The proton affinity of carbon dioxide has
been measured (71). The free energy of transfer is known (2). Then from the equation
in Ref. (70) we obtain Ϫ39 as the pKBH+ for carbon dioxide. The pKa would shift if
the carbon dioxide were bent to the angle of a carboxylic acid; the extent of this shift
was estimated by calculating the energies of the four species by DFT/COSMO meth-
ods, assuming that the differences would be more meaningful than the absolute values.
CO2(linear) ϩ CO2Hϩ(bent) s CO2Hϩ(linear) ϩ CO2(bent).
The products of the equation as written are 11.10 kcal/mol less stable than the
starting materials meaning that protonated bent CO2 is 8.12 pKa units less acidic than
protonated linear CO2. The calculations were carried out with planar protonated bent
CO2, with the H anti to the remote oxygen; this corresponds to the product of
decarboxylation without proton transfer of the syn conformation of the carboxylic acid.
The acidity of the OH in acetoacetic acid protonated on the ketone oxygen using
the p-orbital rather than a lone pair orbital was estimated using the energy difference
between normally and orthogonally protonated acetone (72), i.e., 18.8 kcal/mol. The
pKa so estimated was Ϫ21.34. To a first approximation it was assumed that the pKa
of the carboxylic acid in ketone protonated acetoacetic acid was independent of the
mode of protonation.
The conformation of the enol of acetone with the OH in the plane orthogonal to
the plane of the double bond was calculated (B3LYP/3ϭ21ϩG*) to be 3.53 kcal/mol
higher energy than the planar form. The pKa was accordingly reduced to 7.41.
The pKa of the iminium ion in the N-protonated cyanomethylimine of acetoacetic
acid is estimated starting from the accepted value for the N-methyliminium ion of
acetone, 7.6 (57). The effect of the carboxylic acid is assumed to be the same as
for 2-carbomethoxymethylpyridinium (4.15) vs 2-methylpyridinium (5.94 (69), i.e.,
Ϫ1.79, and the effect of the cyanomethyl group is assumed to be the same as
the effect on an ammonium, i.e., Ϫ5.28 [5.34 (cyanomethylamine) (44) Ϫ 10.62
(methylamine) (44)ϭ Ϫ5.28]. The result is an estimated pKa of 0.53. The pKa of
the carboxylic acid in the N-protonated cyanomethylimine of acetoacetic acid is
estimated to be the same as for 2-carboxymethylpyridinium, i.e., 2.62 (69).
The pKa of the carboxylic acid in the neutral form of the cyanomethylimine of
acetoacetic acid was estimated to be 4.26, the value in neutral 2-pyridylacetic acid.
The pKa of the iminium ion in the zwitterion of this imine was calculated from the
other three pKa values as 2.17.
The pKa of the cyanomethylenamine of acetone was estimated starting from an
estimate of the pKa of the methylenamine of acetone, 35 (73). The effect of a
cyanomethyl group in RCH2NHRЈ acting as an acid should be similar to the effect
in RCH2OH as an acid. The latter is described by a ␳* of Ϫ1.32 (74), and CN
has ␴* ϭ 3.30 (68); thus the effect of CN is ⌬pKa ϭ 4.35, and the pKa of the
cyanomethylenamine of acetone is estimated to be 31.
Estimated pKa values should be reliable to within Ϯ1 or 1.5 pK unit except for
protonated carbon dioxide (probably no better than Ϯ5 pK), orthogonally protonated

42
J. PETER GUTHRIE
acetoacetic acid (probably no better than Ϯ3 pK), and the cyanomethylenamine of
acetone, (probably no better than Ϯ4 pK).
Mechanistic models for the decarboxylation processes. A detailed model for decar-
boxylation, needed for No Barrier Theory, potentially involves four or more reaction
dimensions if proton transfers are involved. Three dimensions are inevitably required
by No Barrier Theory for decarboxylation: geometrical distortion at the carboxylate;
geometrical distortion at the CH2; and breaking of the carbon–carbon bond. For the
decarboxylation of acetoacetate anion, the simplest case, the reaction cube is shown
in Fig. 1. For other mechanism analogous reaction cubes (or hypercubes) can be
drawn. If proton transfer are involved in the transition state for decarboxylation of
acetoacetic acid or its imine, then there must be additional dimensions, at least one
per proton transfer process. There are problems with such mechanisms because of
the conflicting stereoelectronic requirements for C–C cleavage (the breaking bond
must be orthogonal to the plane of the keto or imino function) and hydrogen bonding
(the hydrogen bond should be to a lone pair of the keto or imino function and the
hydrogen should be in the plane of the function and should also be in the plane of
the carboxylic acid group). These requirements are incompatible with a direct proton
transfer and such a transfer demands an energetically unfavorable distortion at both
oxygen atoms. In addition such direct proton transfer requires the syn conformation
of the carboxylic acid which is 3.26 kcal/mol less stable (by DFT calculation) imposing
an additional penalty on what is already a difficult reaction.
With two water molecules it was possible to build a structure with nearly linear
hydrogen bonds and nearly normal bond angles. However, such a mechanism would
require six reaction dimensions, three of which were proton transfer dimensions.
Calculations for such a model would be onerous, and seems needless since simpler
FIG. 1. Reaction cube for the decarboxylation of acetoacetate anion.

DECARBOXYLATION OF ACETOACETIC ACID
43
models worked well. A two reaction dimension model requires the energies of 4
corner species and can be explored by calculating a 10 ϫ 10 grid of 100 points
(including the 4 known to start with) in a short time. A six reaction dimension model
requires the energies of 64 corner species and a similar exploration involves 106
points and thus 10,000 times as much computer time. It is commonly found that
high dimensional transition states are rare, and only to be expected when all corner
intermediates are high energy. In the present case the zwitterion corresponding to
complete transfer of the proton from COOH to ketone oxygen was only 13 kcal/mol
higher in energy than the neutral starting material, while the transition state was 24
kcal/mol higher. Thus there is no need to avoid the zwitterion by being fully concerted:
it is far too low in energy for there to be a need for it to be avoided. As a further
test of the cyclic concerted mechanism, we used Multidimensional Marcus Theory
(MMT), since this can treat the mechanism with only four dimensions, by using an
intrinsic barrier for the zwitterion decarboxylation. MMT necessarily assumes the
same intrinsic barrier for the decarboxylation whatever the degree of proton transfer;
as will be seen below this is probably a poorer approximation for this reaction than
for other reactions where MMT has been used, but any error is in the sense of biasing
the results toward concerted processes, by not disfavoring decarboxylations which
do not have an anionic carboxylate. In the event the reaction is predicted to occur
with complete proton transfer, and the same free energy of activation as for the
stepwise process by way of the zwitterion.
In all cases, the initial conformation was assumed to be one with the bond to the
carboxylate perpendicular to the plane of the ketone or imine, as shown in Newman
projection (a), and with the O–C–O plane orthogonal to the bond, which will become
a double bond, as in Newman projection (b). This conformation minimizes the cost
of distorting the carboxylate to linearity, i.e., to the conformation of the product CO2.
The cost of attaining this conformation relative to the preferred conformation is small.
Models for acetoacetic acid decarboxylation. The direct transfer mechanism was
modeled by assuming that the OH of the protonated ketone would be orthogonal to
the plane of the ketone (since this would be the stereoelectronic result of protonation
on the ␲-bond). In this case the starting point was the neutral acid with the C–C,
which is to break, in the plane orthogonal to that of the ketone, and the OH syn to
the C–C bond. The syn OH is 3.26 kcal/mol higher in energy than the anti conforma-
tion. The product is an encounter complex of the enol and carbon dioxide with the
enol OH in the plane orthogonal to the plane of the double bond. Distortions used
were for the neutral keto acid with the OH syn to the C–C bond. The starting material,
with both carboxylate and CH2 distorted, showed a strong tendency for the OH to

44
J. PETER GUTHRIE
flip to the anti conformation, and only remained syn if the OH were initially set to
point at the ketone oxygen. Distortion energies for the syn isomer were considerably
higher than for the anti isomer. This model led to a much slower reaction (⌬GÞ was
40.4 kcal/mol, see Table 5, while the experimental value was 24 kcal/mol) than the
preferred zwitterionic model, so no attempts were made to refine it.
For the concerted mechanism with two water molecules (treated by MMT) the
various corner intermediates involved varying numbers of proton transfers and thus
commonly involved ionic aggregates with hydrogen bonds linking members of the
chain. Models were constructed based on optimized structures of starting material
and products with a hydrogen bonded chain of water molecules joining the ketone
(enol) oxygen with one oxygen of the carboxylic acid (carbon dioxide) with standard
distances and angles as close to normal as possible. For the purpose of calculating
the electrostatic energies, proton transfers were assumed to occur without motion of
the oxygens. This is a crude approximation, but the electrostatic energies in water
are small, amounting to a few kcal/mol at most, and thus there is no need for an
elaborate refinement. The electrostatic energy was calculated from the distances
between charged atoms, and scaled to the ion pairing energy for spherical ions in
contact, taken as Ϫ1.19 kcal/mol, derived from the free energy of 1:1 ion pair
formation in water (75). Hydrogen bond energies were calculated using the Stahl-
Jencks equation (76) as before (72). This model leads to a prediction of fast pre-
equilibrium formation of the zwitterion, which then decarboxylates in the rate lim-
iting step.
For the zwitterion model, the reaction cube begins with the zwitterion, which is
estimated to be 13.02 kcal/mol higher in energy than the neutral acid. Since proton
transfers between oxygens are fast, and the overall transition state is 23.65 kcal/mol
higher in energy than the starting materials, this equilibrium is established in a rapid
preequilibration. The four corners with the C–C bond broken all represent encounter
complexes of the two products, and there is an entropic cost associated with forming
such complexes from the products free in solution, which is calculated following Hine
(77). Together with the distortion energies already described this permits calculation of
the free energy of each corner. This model, with only three reaction dimensions, led
to a satisfactory calculated free energy of activation: see Table 5.
Models for acetoacetate anion. In the case of the decarboxylation of acetoacetate
anion, only three dimensions are relevant. The distortion energies and entropic costs
of complex formation suffice to calculate the energies of the corners.
Models for imine decarboxylation. In the case of amine catalyzed decarboxylation
it seemed probable a priori that proton transfer dimensions would not be relevant
because proton transfer was relatively favorable. The initial state for the reactions is
the conformation where the C–COO bond is orthogonal to the plane of the ketone
or iminium.
For decarboxylation of the imine, only two models were examined. One was the
cyclic concerted mechanism, with a chain of two water molecules conducting a proton
from the carboxylic acid to the imine nitrogen. This was treated by MMT as in the
decarboxylation of the acid. Here also the proton transfers were found to be complete
before the transition state, so that the reaction was in effect that of the zwitterion.
The second was decarboxylation of the zwitterion itself, treated by No Barrier

DECARBOXYLATION OF ACETOACETIC ACID
45
Theory with three reaction dimensions. The reaction cube begins with the zwitterion,
which is estimated to be 2.85 kcal/mol higher in energy than the neutral acid. This
energy for the corners with the C–C intact, the entropic costs of complex formation
for corners with C–C broken, and the distortion energies permit calculation of the
free energy of each corner.
Distortion energies. Although gas phase distortions can be calculated for the anion
(the keto carboxylate does not fall apart, although the C–C bond does lengthen) this
cannot be done for the zwitterions of the keto acid or imino acid. In the gas phase
these simply fall apart to give the neutral products. However, it was possible to
calculate distortions based on the zwitterions using the COSMO procedure (78,79)
to estimate solvation effects (COSMO has been used for zwitterions in water (80)):
in these calculations geometry optimization was carried out with solvation included
at all times. It seems unlikely that the absolute solvation energies will be correct but
it seems reasonable to assume that differences between the total energies (including
solvation) of two conformers of the same compound will be useful. In solution, as
approximated by the COSMO procedure, the zwitterions did not spontaneously fall
apart although the bond joining the carboxylate to the rest of the molecule did lengthen,
and the O–C–O angle did open, though less than for the anion in the gas phase.
Strictly, the distortions should be based on the initial and final states of the mechanis-
tic model being considered for a particular reaction. However, it is tempting to see
if distortions based on one system can be used for related reactions, in a process
analogous to the use of a transferable intrinsic barrier in Marcus Theory. Thus one
could us the distortions for acetoacetate anion for all three mechanisms, assuming
that acetoacetate anion was a model for the zwitterion of acetoacetic acid or its imine.
This has the advantage that calculations on the anion can be done in the gas phase
whereas calculations on the zwitterions can not. Less plausibly one could try distortions
for acetoacetic acid for all three. Similarly the anion of the imine of acetoacetate
could be used as a proxy for the zwitterion. The only cases where these short cuts
TABLE 4
Distortion Energies Relative to the Equilibrium Conformation in the Medium Indicateda
Starting acid
CH2
Products
CH2 Both
Reactive
conformer
CO2
Both
CO2
Acetoacetic acid anti (gas phase)
Acetoacetic acid syn (gas phase)
Acetoacetate anion (gas phase)
Acetoacetate anion (solution)
Acetoacetate zwitterion (solution)
Acetoacetic acid imine (gas phase)
Acetoacetate anion imine (gas phase)
Imine zwitterion (solution)
0.69
4.89
2.17
0.84
0.25
1.40
3.61
0.46
112.72 38.42 164.62 60.70 15.49 76.19
124.47 42.48 188.95 65.22 15.45 80.67
91.70 30.88 129.63 42.22 12.97 55.19
108.86 34.35 154.40 51.97
8.33 60.30
83.48 21.35 113.85 43.48 11.35 55.83
115.27 39.55 169.56 61.20 17.67 78.87
95.89 24.72 135.78 46.02 24.72 70.71
98.57 28.44 135.10 47.08 12.82 59.90
a All at 25ЊC; energies in kcal/mol. Products are carbon dioxide and the enol of acetone or the
cyanomethylenamine of acetone.

46
J. PETER GUTHRIE
led to useful results was the use of acetoacetate anion (in gas phase or solution) as a
proxy for the two zwitterions, or the acid zwitterion as a proxy for the imine zwitterion.
The distortion energies are distinctly smaller for the anion than for the free acid.
This is a consequence of a slight lengthening of the C–C bond linking the carboxylate
anion to the rest of the molecule and a consequent opening of the OCO angle, which
means the cost of opening the angle to 180Њ becomes smaller. There is also a flattening
of the CH2, which lowers the distortion energy at this center.
The distortion energies calculated for various models are summarized in Table 4.
Free energies of activation calculated by the various models are summarized in
Table 5. The values based on distortion appropriate to the mechanistic model, shown
in bold in Table 5, are in excellent agreement with experiment: the rms error is 2.38
kcal/mol. The use of anion distortions for all mechanisms is also successful, although
this leads to underestimating the distortions needed for the zwitterion mechanism if
the gas phase anion distortions are used, and to overestimating the cost of these
distortions if the solution phase anion distortions are used. The errors turn out to be
small enough that the anion can be used as a model. If the gas phase anion distortions
are used the rms error in calculated free energies of activation is 1.99 kcal/mol; if
TABLE 5
Observed and Calculated Free Energies of Activationa
Reaction path ⌬GÞ
Acid
Anion
Imine
decarboxylation decarboxylation decarboxylation
Experimentalb
24.08
32.03
26.60
(32.02)
27.64
16.39
3-D mechanismsc
Neutral distortions of the acid (gas)
Neutral distortions of the imine (gas)
Acetoacetate anion distortions (gas)
Acetoacetate imine anion distortion (gas)
Acetoacetate anion distortions (aqueous)
Acid zwitterion distortions (aqueous)
Imine zwitterion distortions (aqueous)
4-D mechanisms
(21.85)
25.79
(26.20)
(19.31)
(23.20)
(20.61)
(17.52)
19.93
(27.86)
25.05
28.48
Fully concerted, neutral distortions of the acid
(syn, gas)
Acetoacetic acid cyclic concerted path
involving two water moleculesd
Acetoacetic acid imine, cyclic concerted path
involving two water moleculesd
40.40
25.10
19.94
Note. Calculated values were obtained using various sets of distortion energies as identified in column
1. Free energies of activation in bold type are based on correct distortion energies; those in ordinary type
are based on distortions of an incorrect species/medium combination: values in parentheses are based on
distortions of the wrong overall protonation state and/or the ketone rather than the imine.
a All in aqueous solution at 30ЊC.
b Calculated from rate constants in Table 2.
c 3-D mechanisms involve zwitterions for acetoacetic acid and its imine.
d Calculated using Multidimensional Marcus Theory, as described in the text.

DECARBOXYLATION OF ACETOACETIC ACID
47
the solution distortions are used the rms error is 2.53. The trends in distortion energies
can readily be rationalized in terms of the nature of the electron sinks available for
hyperconjugative stabilization of the carboxylates.
What uncertainties are to be expected in the calculated free energies of activation?
Experience with a number of reaction families treated by No Barrier Theory suggests
an average error for a group of reactions will be between 1 and 2 kcal/mol. Such
errors are not surprising in view of the numerous approximations in the theory. An
alternative approach is to examine the sensitivity of the result to the various numerical
values used to calculate it. This calculation was carried out for the acetoacetic acid
zwitterion; the effect of uncertainties in: the zwitterion equilibrium, the overall free
energy of reaction, and each of the distortion energies were determined by carrying
out the calculation with each value in turn perturbed by 2 kcal/mol, chosen to be
large enough to make a significant difference for each value. This led to a set of
partial derivatives of ⌬GÞ with respect to each of the input quantities. With these
and estimates of the uncertainty in each of these quantities, the overall uncertainty
in ⌬GÞ could be calculated. The uncertainties in input quantities used were: 2 kcal/
mol in zwitterion content, 1 kcal/mol in overall free energy of reaction, 0.1 kcal/mol
in conformational cost of going to the reactive conformation of starting material (a
cost of only 0.25 kcal/mol) and 5 kcal/mol in each of the corner distortion energies.
The result was an uncertainty of 1.8 kcal/mol in ⌬GÞ, about the value expected
empirically. If each individual uncertainty were taken as 2 kcal/mol, then the overall
uncertainty in ⌬GÞ was 1.9 kcal/mol. A similar analysis for the decarboxylation of
the imine was carried out. The uncertainties in input quantities used were: 2 kcal/
mol in zwitterion content, 3.2 in overall free energy of reaction (calculated from 1
kcal/mol for decarboxylation of acetoacetic acid, 0.5 kcal/mol in each imine formation
equilibrium free energy change, 2.97 kcal/mol in imine:enamine tautomerization free
energy), 0.1 kcal/mol in conformational cost of going to the reactive conformation
of starting material (a cost of only 0.46 kcal/mol), and 5 kcal/mol in each of the
corner distortion energies. The result was an uncertainty of 2.6 kcal/mol in ⌬GÞ,
somewhat larger than for reaction of the acid alone because of the greater uncertainty
in the thermodynamics.
DISCUSSION
Intrinsic barrier for decarboxylation. Decarboxylation, despite its familiarity (ev-
ery chemist has seen carbonic acid decarboxylation) is an inherently difficult reaction
because of the large distortion energy if only the geometry of the carboxylate were
to change from initial to final value. This inherent difficulty is responsible for the
observation that carbonic acid itself is surprisingly unreactive to decarboxylation (81).
Thus it is very advantageous if the driving force for the actual decarboxylation reaction
is as large and favorable as possible. If this is achieved by providing a better electron
sink by internal proton transfer, then it will have a double effect, increasing the driving
force and causing an initial state geometry change in the direction of reaction, just
as having a better leaving group on an sp3 center will cause the bond to the leaving
group to lengthen and the geometry at that center to shift towards the planar geometry
of the cation, which had lost the leaving group (82).
In terms of Marcus Theory, decarboxylation has a high intrinsic barrier, consistent

48
J. PETER GUTHRIE
with its being an inherently difficult reaction. The intrinsic barriers, based on the
observed rate constants, are: for the decarboxylation of acetoacetic acid, via the
zwitterion, 15.42 kcal/mol; for acetoacetate anion, 19.10 kcal/mol; and for the cyano-
methylimine of acetoacetic acid, via the zwitterion, 15.54 kcal/mol. The average is
16.69 Ϯ 2.09 kcal/mol, but the variation is considerable, and there is a trend for the
intrinsic barrier to become smaller as the reaction becomes more thermodynamically
favorable. By comparison for a set of aldol additions, the intrinsic barrier for the
C–C bond forming step, the analogous process to the once considered here, was
13.89 Ϯ 0.80 kcal/mol (83).
No Barrier Theory uses three distortion energies to calculate the rate constant for
decarboxylation from the corresponding equilibrium constant, in effect calculating
the intrinsic barrier. These distortion energies, and particularly the distortions involving
the carboxylate/carbon dioxide distortion to or from the linear sp geometry are very
high. Thus the intrinsic barriers are expected, and found, to be high.
Concerted vs stepwise decarboxylation mechanisms. A concerted mechanism is
commonly written (84) for the decarboxylation of ␤-ketoacids despite concerns that
it is inconsistent with the stereoelectronic requirements (3). A theoretical study of
the decarboxylation of formylacetic acid (85) found that the transition state was very
zwitterion-like even in the gas phase, but had an intramolecular hydrogen bond. This
was severely non-linear (O–H–O angle of 151.0Њ) and out of both O–C–C planes.
In the gas phase zwitterions are high energy species and the need for stabilization
by hydrogen bonding would drive formation of even a strongly distorted hydrogen
bond. In solution, where abundant solvent molecules are available, such distorted
hydrogen bonds need not form. Thus the zwitterionic nature of the transition state,
despite the large energetic barrier to charge separation in the gas phase, seems a
compelling argument that the decarboxylation must proceed by way of the zwitterion.
On the other hand, the hydrogen bond seen in the calculated transition state seems
likely to be an inherently undesirable feature enforced by the absence of solvation.
An argument in favor of a concerted mechanism rather than the zwitterion mecha-
nism, was that the rate of decarboxylation of dimethylacetoacetic acid was essentially
unchanged as the solvent changed from water to 75% methanol or 50% acetone. Hine
argued that as the zwitterion became less stable in a lower dielectric constant medium
it also became more reactive, and the two effects might cancel (86). As an attempt
to shed light on the phenomenon, the dipole moments calculated by molecular orbital
theory for various structures were compared. For acetoacetic acid, the dipole moment
of the zwitterion, 13.00 D, is much larger than that of the equilibrium conformation
of the neutral acid, 4.42 D. However, the distorted forms, and in particular the form
with both carboxylate and CH2 of the zwitterion distorted actually has a smaller dipole
moment than the neutral molecule, at 4.19 D. Although the cleaving C–C bond will
be longer and the angular distortions less at the transition state than in the “corner
intermediate,” the charges will also be less. Similarly the imine zwitterion has a much
larger calculated dipole moment, 13.20 D in its equilibrium conformation than the
neutral imine, 7.10 D, but the “corner intermediate” with both carboxylate and CH2
of the zwitterion distorted has a dipole moment of only 6.12 D. Thus these calculations,
though too crude to be compelling, permit the suggestion that the transition state for
reaction may be of very similar polarity to the neutral starting material, even though the

DECARBOXYLATION OF ACETOACETIC ACID
49
reaction proceeds by way of the very polar zwitterion. Two very different calculational
approaches, that of Bach (85) and the present work, have found strong arguments in
favor of the zwitterion mechanism.
Nonobservation of acid catalysis. The model here proposed, that angle changes in
the carboxylate ion have an important role in lowering the activation barrier for
decarboxylation, also offers a satisfying explanation for the absence of acid catalysis
of decarboxylation of keto acids. Protonation of the ketone would give a good electron
sink, and loss of CO2 with accompanying loss of a proton would be thermodynamically
favorable, but aside from the rate retarding effect of having an additional reaction
dimension (87) the kinetic barrier would be higher because the O–C–O angle would
not be expanded before embarking on the reaction coordinate. In fact no sign of acid
catalysis was seen in moderately concentrated sulfuric, perchloric, or hydrochloric
acids (88).
Prospects for No Barrier Theory. In applying No Barrier Theory various models
must be tested. It is common to find several models which lead to excessively high
free energies of activation; these correspond to incorrect detailed mechanisms. Model
leading to excessively low free energies of activation are not found, barring errors in
the application of the theory. That is to say that the theory provides an approach to test
mechanistic models, and reject those which do not lead to agreement with experiment.
It is my hope that No Barrier Theory will develop into a general and reliable
procedure for testing mechanistic proposals and rejecting those which do not match
reality. It principle it should be possible to extend this approach to enzyme cata-
lyzed reactions.
CALCULATIONS
Methods
Molecular orbital calculations were carried out with Gaussian 98 (89). Data files
were created and given preliminary optimization using PCModel (36), which was
also used to examine the structures after DFT optimization. DFT calculations used
the B3LYP (90,91) method from Gaussian 98.
Transition states were located using the procedure previously described to search
an energy surface for the saddle point (87). The algorithm for calculating the energy
at any point on the hypersurface has been revised to a simpler implementation of the
assumptions of No Barrier Theory. With one reaction dimension the energy at any
point along the dimension can be calculated from the appropriate equation based on
the energies of the initial and final points. With two dimensions, the energy at any
point can be calculated using the one-dimensional formula and the energies at the
correct positions along a pair of opposite edges of the square reaction diagram. There
are two ways in which this can be done, and the lower of the two energies is taken.
With three dimensions, the energy at any point can be calculated using the one-
dimensional formulas and the energies at the appropriate positions on a pair of opposite
faces of the cubic reaction diagram. There are three ways in which this can be done,
and the lowest of the three energies is taken. This can be extended to more dimensions
as needed.

50
J. PETER GUTHRIE
ACKNOWLEDGMENTS
I thank the Natural Sciences and Engineering Research Council of Canada for financial support of this
work and the Killam Trust for a Killam Research Fellowship.
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