13C and 15N Kinetic Isotope Effects on the Decarboxylation of 3-Carboxybenzisoxazole. Theory vs Experiment

Article abstract of DOI:10.1021/jo970852q

Nitrogen and carbon kinetic isotope effects were measured on the decarboxylation of 3-carboxybenzisoxazole at room temperature. The nitrogen isotope effect in acetone is 1.0312 ± 0.0006. The carbon isotope effect shows no dependence on the solvent polarit

Full text of DOI:10.1021/jo970852q

J . Org. Chem. 1997, 62, 7305 7309
7305
13C a n d 15N Kin etic Isotop e Effects on th e Deca r boxyla tion of
3-Ca r boxyben zisoxa zole. Th eor y vs Exp er im en t
P. Czyryca and P. Paneth*
Institute of Applied Radiation Chemistry, Department of Chemistry, Technical University of Ło´dz´,
Zeromskiego 116, 90-924 Ło´dz´, (Lodz), Poland
Received May 13, 1997X
Nitrogen and carbon kinetic isotope effects were measured on the decarboxylation of 3-carboxy-
benzisoxazole at room temperature. The nitrogen isotope effect in acetone is 1.0312
0.0006.
The carbon isotope effect shows no dependence on the solvent polarity: 1.0448 0.0007 in 1,4-
dioxane, 1.0445 0.0001 in acetonitrile, 1.0472 0.0013 in DMF, and 1.0418 0.0027 in water.
These isotope effects were modeled theoretically at the semiempirical (AM1, PM3, SAM1) and ab
initio (up to B3LYP/6-31
G**) levels. The comparison of the theoretical and experimental results
leads to the conclusion that none of the theory levels employed is capable of quantitatively predicting
these isotope effects.
Theoretical calculations of isotope effects are frequently
used as a research tool to obtain a detailed picture of
transition states. At the same time, experimental values
of isotope effects are used to test theoretical protocols on
which these calculations are based. Among recently
published studies on theoretical predictions of isotope
the dependence of calculated kinetic isotope effects on
the basis set. We have also indicated that, in the case of
the Menshutkin reaction,1b,6 neither of the semiempirical
NDDO methods was able to reproduce correctly all of the
experimental isotope effects. To use information from
isotope effects to analyze reaction mechanisms, these
disturbing findings require more attention.
Simple chemical reactions, with well-established mech-
anisms, are attractive models for the evaluation of the
newest methods of quantum chemistry. The so-called
Kemp’s reaction7,8 is one of them:
5
effects,1 however, some recent reports question their
predictive capabilities. J ensen et al.4a,c has shown theo-
retically the lack of the usually accepted correlation
between the kinetic isotope effect and the geometry of
the transition state in the case of E2 reactions as well as
X Abstract published in Advance ACS Abstracts, September 15, 1997.
(1) (a) Paneth, P. Comput. Chem. 1995, 19, 11 20 and references
therein. (b) Gawlita, E.; Szylhabel-Godala, A.; Paneth, P. J . Phys. Org.
Chem. 1996, 9, 41 49. (c) Czyryca, P.; Paneth, P. Proceedings of 1st
Electronic Computational Chemistry Conference; Carbondale, 1994,
ARI CD 101, ARInternet Corporation: Landover, MD, 1996. (d)
Czyryca, P.; Paneth, P. J . Mol. Struct. (Theochem) 1996, 370, 237
243. (e) Rakowski, K.; Paneth, P. J . Mol. Struct. 1996, 378, 35 43. (f)
Gawlita, E.; Anderson, V. E.; Paneth, P. Eur. Biophys. J . 1994, 23,
353 360. (g) Paneth, P. J . Mol. Struct. 1994, 321, 35 40.
(2) (a) Olson, L. P.; Niwayama, S.; Yoo, H.-Y.; Houk, K. N.; Harris,
N. J .; Gajewski, J . J . J . Am. Chem. Soc. 1996, 118, 886 892. (b) Wiest,
O.; Houk, K. N. J . Am. Chem. Soc. 1995, 117, 11628 11639. (c) Wiest,
O.; Black, K. A.; Houk, K. N.; J . Am. Chem. Soc. 1994, 116, 10336
10337. (d) Storer, J . W.; Raimondi, L.; Houk, K. N.; J . Am. Chem. Soc.
1994, 116, 9675 9683. (e) Houk, K. N.; Li, Y.; Storer, J .; Raimondi,
L.; Beno, B. J . Chem. Soc. Faraday Trans. 1994, 90, 1599 1604. (f)
Wiest, O.; Houk, K. N.; Black, K. A.; Thomas, B. J . Am. Chem. Soc.
1995, 117, 8594 8599. (g) Olson, L. P.; Li, Y.; Houk, K. N.; Kresge, A.
J .; Schaad, L. J . J . Am. Chem. Soc. 1995, 117, 2992 2997. (h) Yoo, H.
Y.; Houk, K. N. J . Am. Chem. Soc. 1994, 116, 12047 12048. (i) Houk,
K. N.; Li, Y.; Mcallister, M. A.; Odoherty, G.; Paquette, L. A. J . Am.
Chem. Soc. 1994, 116, 10895 10913. (j) Bero, B. R.; Houk, K. N.;
Singleton, D. A. J . Am. Chem. Soc. 1996, 118, 9984 9985. (k) Zipse,
H.; Apaydin, G.; Houk, K. N. J . Am. Chem. Soc. 1995, 117, 8608
8617. l/ Goldstein, E.; Beno, B.; Houk, K. N.; J . Am. Chem. Soc. 1996,
118, 6036 6043.
(1)
Its advantages are high sensitivity to the polarity and
prototropicity of the solvent and simple, well-studied
kinetics. Furthermore, Hilvert et al.9 recently engineered
catalytic antibodies which catalyzed the above reaction,
and carbon kinetic isotope effects were measured.10 Since
then a number of contributions was published on model-
ing the reaction pathway,11 isotope effects,1c,d,2k and
14
solvent effects.12
In our approach to the problem of the reliability of the
calculations of isotope effects, we are using comparison
of experimental data with theoretical calculations to find
a dependable and cost-effective method that correctly
predicts the values of isotope effects. Differences in the
interpretation of the carbon isotope effects on the above
(3) (a) Lynch, G. C.; Truhlar, D. G.; Brown, F. B.; Zhao, J . G.
Hyperfine Interactions 1994, 87, 885 898. (b) Hu, W. P.; Truhlar, D.
G. J . Am. Chem. Soc. 1995, 117, 10726 10734. (c) Lynch, G. C.;
Truhlar, D. G.; Brown, F. B.; Zhao, J . G. J . Phys. Chem. 1995, 99,
207 225. (d) Allison, T. C.; Lynch, G. C.; Truhlar, D. G.; Gordon, M.
S. J . Phys. Chem. 1996, 100, 13588 13593. (e) Melissas, V. S.; Truhlar,
D. G. J . Chem. Phys. 1993, 99, 3542.
(6) Szylhabel-Godala, A.; Madhavan, S.; Rudzin˜ski, J .; O’Leary, M.
H.; Paneth, P. J . Phys. Org. Chem. 1996, 9, 35 40.
(7) Kemp, D. S.; Paul, K. G. J . Am. Chem. Soc. 1975, 97, 7305
7312.
(4) (a) Glad, S. S.; J ensen, F. J . Phys. Chem. 1996, 100, 16892
16898. (b) Nielsen, P. A.; Glad, S. S.; J ensen, F. J . Am. Chem. Soc.
1996, 118, 10577 10583. (c) Glad, S. S.; J ensen, F. J . Am. Chem. Soc.
1997, 119, 227 232. (d) Glad, S. S.; J ensen, F. J . Chem. Soc., Perkin
Trans 2 1994, 4, 871 876. (e) Glad, S. S.; J ensen, F. J . Am. Chem.
Soc. 1994, 116, 9302 9310.
(8) Kemp, D. S.; Cox, D. D.; Paul, K. G. J . Am. Chem. Soc. 1975,
97, 7312 7318.
(9) Lewis, C.; Kramer, T.; Robinson, S.; Hilvert, D. Science 1991,
253, 1019 1022.
(10) Lewis, C.; Paneth, P.; O’Leary, M. H.; Hilvert, D. J . Am. Chem.
Soc. 1993, 115, 1410 1412.
(5) (a) Rising, K. A.; Schramm, V. L. J . Am. Chem. Soc. 1997, 119,
27 37. (b) Huskey, W. P. J . Am. Chem. Soc. 1996, 118, 1663 1668.
(c) Yamataka, H.; Mishima, M.; Kuwatani, Y.; Tsuno, Y. J . Am. Chem.
Soc. 1995, 117, 5829 5831. (d) Kupczyk-Subotkowska, L.; Saunders,
W. H., J r.; Shine, H. J .; Subotkowski, W. J . Am. Chem. Soc. 1994, 116,
7088 7093. (e) Boyd, R. J .; Kim, C.-K.; Shi, Z.; Weinberg, N.; Wolfe,
S. J . Am. Chem. Soc. 1993, 115, 10147 10152.
(11) Gao, J . J . Am. Chem. Soc. 1995, 117, 8600 8607.
(12) Grate, J . W.; Mcgill, R. A.; Hilvert, D. J . Am. Chem. Soc. 1993,
115, 8577 8584.
(13) Famini, G. R.; Wilson, L. Y. J . Chem. Soc., Perkin Trans 2. 1994,
1641 1650.
(14) Tarasow, T. M.; Levis. C.; Hilvert, D. J . Am. Chem. Soc. 1994,
116, 7959 7964.
S0022-3263(97)00852-9 CCC: $14.00 © 1997 American Chemical Society

7306 J . Org. Chem., Vol. 62, No. 21, 1997
Czyryca and Paneth
mentally in the case of nitrogen samples. The ratio of the
isotope ratios can be obtained from “deltas”sresults of mass
spectroscopic measurementssfrom the following equation:
reaction and discrepancies between values predicted by
different theoretical models have prompted us to make
additional measurements which promised to resolve our
doubts. Herein, we present results of nitrogen and
carbon kinetic isotope effects measured for the unsub-
Rf/R0 (1000 δf)/(1000 δ0)
(3)
stituted benzisoxazole (R
theoretical evaluations.
H) together with their
where δ relates the isotopic ratio of a measured sample to the
same ratio of home standard, e.g.,
Exp er im en ta l Section
Rsample
[13C]/[12C]sample
δ13C
1 × 1000
1 ×
Rea gen ts. 3-Carboxybenzisoxazole was synthesized as
described by Kemp et al.7 using o-nitrophenylacetic acid
(Aldrich) as the starting material. Triethylamine (Aldrich)
was distilled and stored over KOH. All solvents (diethyl ether,
acetone, acetonitrile, 1,4-dioxane, and DMF) were analytical
grade and were stored over molecular sieves. Organic solvents
and deionized water for carbon isotope effect determinations
were freed of traces of CO2 by 2 h purging with N2 passed
through an Ascarite trap, as described earlier.10
13
12
(
)
(
)
Rstandard
[ C]/[ C]standard
1000 (4)
Ca lcu la tion s. MOPAC 93, Amsol 5.4, and Ampac 5.0
packages17 19 running on DEC alpha workstations under OSF/
1; Gaussian 9420 running on a Cray J 916 under UNICOS 8.0.4;
HyperChem 521 running on a dual processor Pentium Pro 200
MHz PC under Windows NT 4.0; and GAMESS22 running on
a SGI Power Challange L under Irix 6.1 were employed.
Transition states were obtained by a coordinate driving
method from optimized structures of substrates, followed by
final reoptimization of the structures of maximum potential
energy. Then force field analysis was performed for both
substrate and transition state structures, and finally, kinetic
isotope effects were calculated by means of ISOEFF version
623 according to the Bigeleisen equation.16 In the case of
semiempirical Hamiltonians, two continuum solvent models
were also employed: COSMO24 (with two values of environ-
ment dielectric constant, 2.0 and 80.0) and SM425 (with the
parametrization for water). All the ab initio calculations were
performed in vacuum.
Nitr ogen Isotop e Effect. Samples for 15N isotope effect
measurement were prepared in the following way: to a
vigorously stirred solution of 3.1 mmol of 3-carboxybenzisox-
azole in 50 mL of acetone maintained at 21 °C was added 28.7
mmol of triethylamine. The reaction was quenched by the
addition of 5 mL of 70% H2SO4. The reaction mixture was
then diluted with cold water and extracted with ether. The
extract was dried and evaporated, and a small sample was
used to determine the conversion ratio (by means of 1H NMR).
Salicylonitrile was then separated by means of preparative
thin-layer chromatography (Merck, Kieselgel 60, without
fluorescent indicator). Quenching after 60 and 80 s yielded
conversions of 15.9 and 19.7%, respectively.
Ca r bon Isotop e Effects Sa m p les. 13C isotope effects were
determined by means of a general procedure described by
O’Leary.15 All experiments were carried out at 21 °C. For
each sample, to a 4 mL solution (under nitrogen) containing
0.31 mmol of 3-carboxybenzisoxazole was added 1 mL (0.57
mmol) of a solution of triethylamine dissolved in the same
solvent through a stopper. The reaction was stopped by
anaerobic addition of 1.5 mL of 70% phosphoric acid. Then
the CO2 formed during the reaction was purified by cryodis-
tillation through two dry ice/2-propanol traps and a liquid
nitrogen-cooled trap. The amount of the carbon dioxide was
measured manometrically and then it was distilled into a
sample tube. Extents of the reaction were of about 5 20%
(lower in the case of reactions carried out in water). Samples
of CO2 for isotopic composition measurements after full
conversion were prepared in the similar manner. Desired full
conversion was achieved by leaving the reaction overnight (in
DMF) and confirmed manometrically.
Isotop e Effects Mea su r em en ts. The samples for nitrogen
isotope effects were combusted, then the products were passed
through a catalyzer system in order to convert the nitrogen
compounds to N2. The procedure was automatic in a Heareus
system coupled on-line with the mass spectrometer. Then the
nitrogen was introduced into a Finnigan Delta S isotope ratio
mass spectrometer. Carbon dioxide samples were introduced
directly through a direct inlet system. Isotope effects were
calculated according to the following formula:16
Resu lts
The results of experiments and calculations are shown
in the Tables 1 3. The 15N kinetic isotope effect (Table
1) is an average of nine individual values from two
independent series: five samples of the series of 16%
reaction completion and four samples of 20% conversion.
The 13C kinetic isotope effects are averages of five or six
independent samples for each solvent. The large stan-
dard deviation in the case of the reaction carried out in
water was caused by measurements of very small amounts
of CO2, due to the very slow decarboxylation rate in this
solvent. For a comparison, Table 1 contains also a set of
(17) Stewart, J . J . P., Fujitsu, MOPAC 93 rev. 2, 1993.
(18) Hawkins, G. D.; Lynch, G. C.; Giesen, D. J .; Rossi, I.; Storer, J .
W.; Liotard, D. A.; Cramer, C. J .; Truhlar, D. G. Amsol 5.4, QCPE
program 606.
(19) AMPAC 5.0, Semichem, 7128 Summit, Shawnee, KS 66216.
(20) Frisch, M. J .; Trucks, G. W.; Schlegel H. B.; Gill, P. M. W.;
J ohnson, B. G.; Robb, M. A.; Cheeseman, J . R.; Keith T.; Petersson, G.
A.; Montgomery, J . A.; Raghavachari, K.; Al-Laham, M. A.; Zakrzewski,
V. G.; Ortiz, J . V.; Foresman, J . B.; Cioslowski, J .; Stefanov, B. B.;
Nanayakkara, A.; Challacombe, M.; Peng, C. Y.; Ayala, Y.; Chen, W.;
Wong M. W.; Andres, J . L.; Replogle, E. S.; Gomperts, R.; Martin, R.
L.; Fox, D. J .; Binkley, J . S.; Defrees, D. J .; Baker, J .; Stewart, J . J .
P.; Head-Gordon, M.; Gonzalez, C.; Pople, J . A. Gaussian 94, Revision
C.3, 1995, Gaussian, Inc., Pittsburgh PA, 1995.
kL
kH
ln(1 f)
(2)
(21) HyperChem 5.01a, Hypercube, Inc., Waterloo, Ontario, Canada
N2L 3X2.
ln(1 fRf/R0)
(22) Schmidt, M. W.; Baldrige, K. K.; Boatz, J . A.; Elbert, S. T.;
Gordon, M. S.; J ensen, J . H.; Koseki, S.; Matsunaga, N.; Nguyen, K.
A.; Su, S. J .; Windus, T. L.; Dupuis, M.; Montgomery, J . A. J . Comput.
Chem. 1993, 14, 1347 1363.
(23) Paneth, P. ISOEFF version 6ha, available upon request from
the author. This program extracts all data necessary for calculations
of isotope effects from outputs of quantum chemistry packages and
performs calculations of isotope effects; MOPAC/AMPAC, AMSOL,
SIBIQ, GAMESS, GAUSSIAN and HYPERCHEM formats are cur-
rently supported.
where f is fraction of reaction, R0 is the isotopic ratio (ratio of
heavy to light isotope concentration) of the reactant before the
reaction, and Rf is the isotopic ratio of the product after the
fraction of reaction f. From the mass balance, R0 equals R∞,
the isotopic ratio of the product after full conversion. We have
used this latter ratio in determinations of the carbon kinetic
isotope effects. The equality of R0 and R∞ was tested experi-
(24) Klamt, A.; Shu¨u¨rman, G. J . Chem. Soc., Perkin Trans. 2 1993,
799 805.
(25) Giesen, D. J .; Storer, J . W.; Cramer, C. J .; Truhlar, D. G. J .
Am. Chem. Soc. 1995, 117, 1057 1068.
(15) O’Leary, M. H. Methods Enzymol. 1980, 64, 83 104.
(16) Melander, L. Isotope Effects on Reaction Rates; Ronald Press
Co.: New York, 1960.

Decarboxylation of 3-Carboxybenzisoxazole
J . Org. Chem., Vol. 62, No. 21, 1997 7307
One could try to put some meaning to the difference
of averaged values of the carbon isotope effects in the
aqueous solution for unsubstituted and 5-nitro-substi-
tuted compounds (0.4%) disregarding the precision. How-
ever, if this difference was meaningful, the increase of
the isotope effect in aqueous solution compared to the
isotope effect on the reaction in dioxane, which is
observed for the 5-nitro derivative, should be paralleled
by a similar tendency for the unsubstituted compound,
which is not the case. Second, we have measured the
carbon kinetic isotope effect for the unsubstituted 3-car-
boxybenzisoxazole in a number of solvents of different
polarity and properties. Two solvents, dioxane and
water, were chosen in order to make the results compa-
rable to those previously obtained for the 5-nitro deriva-
tive and because of the large difference in their polarity.
Since the hydrogen-bonding network present in water
dramatically affects the rate constant of the reaction, we
have also used two other, considerably polar solvents:
acetonitrile and DMF. These two solvents constitute an
interesting pair since while their apparent polarity is
similar, the rate constants are different by an order of
magnitude. Comparison of the results obtained in diox-
ane, acetonitrile, and DMF indicates that a relative
increase of the rate constant of 2 3 orders of magnitude
does not change the carbon isotope effects. Thus, upon
inspection of all of the experimental values together with
their statistical precision, we conclude that the carbon
kinetic isotope effect is unperturbed by substituents or
solvents, supporting the original assumption of Kemp
that the transition state structure is very similar under
all conditions. Consequently, we assume that the carbon
kinetic isotope effect is about 1.045, regardless of the
environment.
F igu r e 1. Carbon kinetic isotope effects on decarboxylation
of 3-carboxybenzisoxazole and 3-carboxy-5-nitrobenzisoxazole.
Ta ble 1. Mea su r ed Nitr ogen a n d Ca r boxylic Ca r bon
Isotop e Effects on Deca r boxyla tion of
3-Ca r boxyben zisoxa zole a n d
3-Ca r boxy-5-n itr oben zisoxa zole a t 21 °C.
kinetic isotope effect
a
solvent
acetone
R
H
R
5-NO2
nitrogen
1.0312 0.0006
carbon
1,4-dioxane
acetonitrile
DMF
1.0448 0.0007
1.0445 0.0001
1.0472 0.0013
1.0418 0.0027
1.0434 0.0007
1.0458 0.0007
water
a
From ref 10.
carbon kinetic isotope effect values measured previously
for the decarboxylation of 5-nitrobenzisoxazole.10
We now turn our discussion to the results of theoretical
calculations. If what we have concluded thus far is
correct, then the criterion for the evaluation of a theoreti-
cal protocol can be formulated: “a theory level properly
modeling the carbon kinetic isotope effect should yield
the value of about 4.5%”. Following this line of argument
it seems that desolvation equilibrium isotope effects
deduced by Zipse et al. result from the erroneous value
of the carbon isotope effect obtained at the 6-31G* level
in the gas phase (1.0320).
Discu ssion
We start our discussion with the problem of transition
state location on the reaction pathway. Kemp postulated
that, despite the tremendous rate change with solvent
polarity, the transition state for reaction 1 remains
unchanged. This was recently questioned on the basis
of theoretical modeling of carbon kinetic isotope effects.2k
We have argued earlier10 that experimental results
obtained for 5-nitro-substituted substrate (see Figure 1)
support Kemp’s postulate. Also QM/MM calculations
performed at the AM1/TIP3P level led to similar conclu-
sions.11
It should be noticed that the experimental data was
obtained for the 5-nitro derivative while the calculations
were performed on the unsubstituted substrate (R H).
One might expect that the transition states for these two
reactions (R H and R NO2) may differ since the nitro
group in the para position to the phenolate oxygen of the
product should strongly stabilize the transition state, the
phenomenon which manifests itself experimentally by the
activation barrier being over 5 kcal/mol lower in the case
of the nitro derivative. We have addressed this question
experimentally by measuring carbon kinetic isotope
effects for the unsubstituted substrate in a variety of
solvents, as reported in the Results.
Furthermore, the calculated values of the oxygen
isotope effect seem to be erroneous, too. Intuitively one
would expect that this isotope effect should be very small
or even inverse (less than unity) since bonding to car-
boxylic oxygens increases along the reaction coordinate.
Apart from one semiempirical result (AM1 Hamiltonian),
all our calculations yielded inverse values, as listed in
Tables 2 and 3. And even in this exception the value of
the oxygen isotope effect is only 1.0007. We have also
an experimental indication that this isotope effect is in
18O values
fact inverse. It can be deduced from the δ
obtained during isotopic ratio measurements (peaks 46/
44 in the CO2 isotopic analysis). The experimental
procedure, however, may be the source of systematic
error since the reaction is quenched by acidification with
phosphoric acid. This promotes 18O exchange between
carbon dioxide and water and causes a wash-out of the
isotope label. We have demonstrated earlier that under
experimental conditions only a few percent of oxygen is
being exchanged,28 but since no tests were carried out
A few observations are worth noting. First, isotope
effects in the presence and absence of the 5-nitro sub-
stituent are the same within the experimental error (note
that standard deviations and not statistical errors are
reported), as illustrated in Figure 1.
(26) Dewar, M. J .S.; Zoebisch, E. G.; Healy, E. F.; Stewart, J . J . P.
J . Am. Chem. Soc. 1985, 107, 3902.

7308 J . Org. Chem., Vol. 62, No. 21, 1997
Czyryca and Paneth
Ta ble 2. Ca lcu la ted Nitr ogen , Ca r boxylic Ca r bon , a n d Oxygen Kin etic Isotop e Effects on Deca r boxyla tion of
3-Ca r boxyben zisoxa zolesResu lts of Sem iem p ir ica l Ca lcu la tion s
AM1
COSMO
2.0
PM3
COSMO
2.0
method
solvent model
SM4
H2OSRP
SM4
H2OSRP
ꢀ
ꢀ
80.0
ꢀ
ꢀ
80.0
SAM1
k14/k15
1.0540
1.0300
1.0007
1.0560
1.0332
0.9995
1.0604
1.0380
1.0617 (1.0558)a
1.0391 (1.0368)
1.0146
1.0369
0.9898
1.0148
1.0458
0.9866
1.0200
1.0619
0.9881
1.0114 (1.0110)
1.0503 (1.0490)
1.0754
1.0199
k
k
12/k13
16,16/k18,18
a
Values given in parentheses were obtained from scaled frequencies.
solvent effect by Hilvert et al.12 It should be noted here
that perturbations of the reacting system upon changing
solvents may be different from those caused by going from
gas phase to a solvent. Our previous calculations of
isotope effects using the COSMO model indicate that the
value obtained for the gas-phase coincides with the one
extrapolated from the dependence of the isotope effect
on the solvent polarity.1d This supports the assumption
that the gas-phase results can be used in the present
case. However, caution is necessary since COSMO was
developed for polar systems. Furthermore, contributions
to isotope effects from specific interactions, e.g. hydrogen
bonding, are lost by using continuum solvent models
(COSMO and SM4 in our case).
Ta ble 3. Ca lcu la ted Nitr ogen , Ca r boxylic Ca r bon , a n d
Oxygen Kin etic Isotop e Effects on Deca r boxyla tion of
3-Ca r boxyben zisoxa zolesResu lts of a b In itio
Ca lcu la tion sa
theory level
STO-3G
k14/k15
k12/k13
k16,16/k18,18
1.0667
1.0370
1.0153
1.0322
1.0307b
1.0322
(1.0367)
1.0292
1.0320b
1.0421
1.0238
1.0276
1.0276
0.9808
0.9850
3-21G*
UHF/3-21G*
1.0370
(1.0416)c
1.0184
0.9850
B3LYP/3-21 G*
6-31G*
UHF/6-31G*
B3LYP/UHF/6-31G*
B3LYP/UHF/6-31 G*
B3LYP/6-31
0.9808
1.0115b
0.9850
0.9915
0.9893
0.9894
1.0448
1.0259
1.0275
1.0275
G**
The goal was to find methods which properly model
all three isotope effects and, if more then one can be
identified, to pinpoint the most cost-effective one. We
have started with the cheapest semiempirical methods
and moved through ab initio to DFT methods. Unfortu-
nately, as can be seen from results collected in Tables 2
and 3, there is no level among those studied that correctly
reproduces the isotope effects of carbon and nitrogen
simultaneously. Thus it is not possible to argue the
details of the transition state structure, such as bond
lengths and timing of bond breaking, and extent of bond
breakage, based on our calculations. Nevertheless, a few
general observations are worth mentioning. The transi-
tion state structures obtained using the 3-21G basis sets
are planar, while those obtained in other calculations
have the carboxyl rotated about 90°. Occasionally we
were able to identify a transition state for this rotation
for which the imaginary frequency was at the level of
50/i cm 1, the same value as reported by Houk’s group.2k
a
Scaling factors appropriate for each basis set were taken from
ref 32. From ref 2k. c Values given in parentheses were obtained
using unscaled frequencies.
b
for the oxygen exchange in the present studies, we are
reluctant to report quantitative values of the carboxylic
oxygens isotope effect. Nevertheless, we can safely say
qualitatively that this isotope effect is inverse. This
conclusion agrees with the experimental data of Headley
and O’Leary, who have found an inverse oxygen isotope
effect of 0.5% per oxygen atom for the decarboxylation
of 4-pyridylacetic acid in aqueous solution.29 Thus we
formulate the second criterion of the correctness of
theoretical calculations: the predicted oxygen isotope
effect should be inverse.
Initially we restricted our theoretical modeling to the
semiempirical level, which is most cost-effective among
quantum chemical theory levels. We have found a huge
difference between the nitrogen kinetic isotope effect
obtained by the AM1 and PM330 methods (see Table 2).
Thus, we thought measuring this value experimentally
was “the unequivocal experiment”. As can be seen from
Tables 1 and 2, measuring this value raised more
questions than it answered (a typical outcome of un-
equivocal experiments). On the basis of this experiment
we have formulated the third condition a good theoretical
method should fulfill: the modeled nitrogen kinetic
isotope effect should be around 3.1%.
A large k14/k15 isotope effect of over 3% suggests that
the N O bond is significantly cleaved in the transition
state and that its structure is probably closer to the
salicylonitrile anion than to the substrate. This leads
to the conclusion that the “transition state with delocal-
ized charge” is in the present case misleading: the net
negative charge in the transition state is probably mostly
localized on the oxygen atom of the former isoxazole ring
and similarly delocalized as in the substrate anion. This
supports, on the molecular level, the explanation of the
influence of the solvent properties on the reaction rate
given by Hilvert,12 who suggested that the reaction is
running slower in dipolar, nonprototropic solvents, in
agreement with the Ingold rule, and the net acceleration
observed is due to the ion pairing effect.
Armed with criteria derived from the analysis of
carbon, oxygen, and nitrogen isotope effects, we started
on our quest for the “best theoretical approach” to
modeling of isotope effects on the Kemp’s reaction. Since
we have argued that the environment has little to no
effect on isotope effects, the logical choice was to study
the gas-phase reaction. This choice was also supported
by the results of simulations using combined QM/MM
calculations carried out by Gao11 and studies of the
While the calculated values of the nitrogen isotope
effect tend to approach the experimental one with the
increase of the basis set, the same is not true in the case
of the carbon isotope effect. Most of the calculations
yielded this kinetic isotope effect at the level of 3%. We
(27) J orgensen, W. L.; Chandrasekhas, J .; Madura, J . D.; Impley,
R. W.; Klein, M. L. J . Chem. Phys. 1983, 79, 926.
(28) Paneth, P.; O’Leary, M. H. Biochemistry 1985, 24, 5143 5147.
(29) (29) Headley, G. W.; O’Leary, M. H. J . Am. Chem. Soc. 1990,
112, 1894.
have argued earlier that the rotation around the C
C
bond has a surprisingly large influence on the isotope
(30) Stewart, J . J . P. J . Comput. Chem. 1989, 10, 209, 221.
effect.1d This may also be the reason the calculated value

Decarboxylation of 3-Carboxybenzisoxazole
J . Org. Chem., Vol. 62, No. 21, 1997 7309
is different from the observed isotope effect. For example,
for the reaction going from the flat substrate, the carbon
isotope effect changes from 1.0286 for the rotated transi-
tion state to 1.0414 for the flat transition state.
severe with most of the post-Hartree Fock methods,
where the scaling factor for low-frequencies is larger than
unity while the standard scaling factor is fractional.
Because of the problems with scaling frequencies, one
should expect about 0.5% uncertainty in the accuracy of
the calculated isotope effects. The problem of scaling is
even more serious with semiempirical methods. Tradi-
tionally frequencies obtained with these methods were
used directly without scaling. We have shown a small
scaling effect previously.1a Radom et al., suggest scaling
factors of 0.9532 and 0.9761 for frequencies obtained by
means of AM1 and PM3, respectively. This can lead to
changes in isotope effects of about 0.5%, as illustrated
by the results given in Table 2.
Another possible explanation of this situation could be
that the calculated isotope effect for the reaction in
question is correct and it is the experimental value that
is more complex and represents an apparent isotope
effect. Hilvert argued that the reaction is actually
stepwise with preequilibrium tight ion pair separation
and subsequent decarboxylation. In such a case, the
observed isotope effect would be a product of the equi-
librium isotope effect on ion pair separation and the
kinetic isotope effect on decarboxylation. However, the
equilibrium carboxylic carbon isotope effect on the tight
ion pair separation has to be very small. By far the upper
limit of its value is the equilibrium isotope effect on the
deprotonation of an carboxylic acid. Bron31 reported the
secondary carbon equilibrium isotope effect on deproto-
nation of benzoic acid to be 1.001 at 30 °C. The preequi-
librium mechanism is an extreme case. Other stepwise
mechanisms would introduce isotopically insensitive
steps to the apparent rate, causing the observed carbon
isotope effect to be even smaller. Thus we can discard
this explanation.
The highest theory level used here is B3LYP/6-
31
G*. This level may still not be sufficient for the
qualitative calculations of isotope effects. Glad and
J ensen have shown4a considerable variation of isotope
effects, calculated by means of DFT method, upon the
change of basis set. Results of Melissas and Truhlar
indicate3e that higher correlation corrections and bigger
basis sets are necessary to quantitatively model isotope
effects.
Con clu sion s
The carbon isotope effect on the Kemp’s reaction shows
no dependence on the solvent polarity despite tremendous
dependence of the rate constant. The comparison of the
theoretical and experimental results of kinetic isotope
effects leads to the conclusion that none of the theory
levels employed, neither semiempirical nor ab initio, are
capable of predicting isotope effects. While it is possible
that by using higher theory levels one can correctly model
these isotope effects, our results warn against drawing
mechanistic conclusions from the low-to-medium calcula-
tion levels. Clearly more research is needed to establish
acceptable computational framework.
A dogma in isotope effect calculations states that the
absolute values of normal modes are not important since
the true source of isotope effects lies in isotopic differ-
ences. While this is basically true, it is not always
appreciated how large these “not important” effects could
be. We have used our results to shed some light on this
problem. We illustrate this issue with the 3-21G* results.
In their excellent study of over a thousand frequencies
Scott and Radom32 evaluated optimal scaling factors
relating theoretical harmonic frequencies calculated at
different levels of theory to the observed fundamentals.
The values given in Table 3 in parentheses show the
dependence of the calculated kinetic isotope effects on
the scaling factor. It is apparent that an incorrectly
chosen scaling factor can considerably change the value
of the calculated isotope effect. The problem is even more
Ack n ow led gm en t. We thank Dr. S. Madhavan for
the help with measurements of isotope effects. Financial
support from the State Committee for Scientific Re-
search (KBN, Poland) and the computational grant from
the Poznan Supercomputer & Networking Center are
gratefully acknowledged.
(31) Bayles, J . W.; Bron, J .; Paul, S. O. J . Chem. Soc., Faraday
Trans. 1976, 72, 1546 1552.
(32) Scott, A. F.; Radom, L. J . Phys. Chem. 1996, 100, 16502 16513.
J O970852Q