Fang et al.
a late transition state with a short NC-CR bond and significant
CR-Cl bond rupture. It is important to note, however, that
changing the solvent only causes a slight tightening of the SN2
transition state, but does not cause the large shift required to
change the transition state from product-like in DMSO to
reactant-like in THF even though THF bridges the gap between
the reaction in DMSO and the gas phase to as large an extent
as possible experimentally. Even though the solvation in THF
is far from that in the gas phase,5 the great difference in the
polarity of the two solvents should show a trend toward an early
transition state if it is mainly the absence of solvent in the gas
phase calculations that is responsible for the difference in the
transition states predicted by the two methods. Therefore, it is
highly unlikely that the absence of solvent in the gas-phase
calculations is responsible for the very different transition states
that were predicted by interpreting the experimental KIEs found
in DMSO and by the gas-phase calculations.
that the KIEs calculated by theory for several SN2 reactions
have been close to the KIEs found experimentally.25
A fourth reason for suggesting the transition state predicted
by theory is correct is that the difference between the best set
of KIEs calculated from the transition structures and the
experimental values, although outside experimental error, are
small,2 i.e., the ∆(KIEcalc - KIEexp) are 0.004 (R-D2), 0.009
(â-D3), 0.04 (R-C), 0.008 (nucleophile C), 0.0001 (nucleophile
N), and 0.0000 (leaving group Cl). This means theory, without
solvent modeling, reproduces the experimental KIEs quite well.
Also, finding that the transition state structure and the KIEs
calculated with the solvent continuum model were close to those
obtained in the gas-phase calculations2 suggests that solvent does
not affect transition state structure significantly. This is not
surprising since the results of this study suggest the transition
state is not affected significantly by solvent.
Finally, it is worth noting that this lack of change in transition
state structure with solvation found in this experimental study
is supported by theoretical calculations. For instance, Yamataka
and Aida26 showed that adding 10 more water molecules to the
SN2 reaction between water and methyl chloride, i.e., changing
the solvating water molecules from 3 to 13 and changing the
∆Gq by 13.5 kcal/mol, did not change the transition structure
significantly, i.e., the change in the CR-O transition state bond
was only 0.18 Å while that in the CR-Cl transition state bond
was only 0.074 Å. This very small change in transition state
structure with the change in solvation is surprising because this
is a Type II (the charges on the nucleophile and leaving group
are different) SN2 reaction where Saunders and co-workers27
and Westaway and Jiang28 found the transition state was altered
significantly by a change in solvent. In another study of the
SN2 reaction between chloride ion and methyl chloride, Mo-
hamed and Jensen29 found that microsolvation by four water
molecules did not affect the transition state structure significantly
although they changed the rate constant (the ∆Gq) for the
reaction by approximately 16 kcal/mol. The results from our
study show experimentally that a significant change in solvation
does, indeed, not alter transition state structure significantly and
gives some assurance that transition state predicted by theory
is also correct. It is worth noting that both the above theoretical
results and our experimental results suggest that the lack of
solvent modeling is not the reason the transition state structure
predicted by theory and by interpreting the experimental KIEs
using the traditional method differ.
Apart from the minor variations in transition structures, every
level of theory that was investigated predicted the transition
state was reactant-like. In fact, it now appears likely that the
theoretical calculations, even in the absence of solvent modeling,
give the most accurate transition state structure. The following
arguments appear to support this view: First, a recent theoretical
investigation has demonstrated that the observed chlorine leaving
group KIE for a particular SN2 reaction cannot be simply related
to the amount of CR-Cl bond rupture in the transition state17
as had been previously believed. In fact, the product-like
transition state for the reaction between cyanide ion and ethyl
chloride was suggested originally because the chlorine KIE was
large suggesting there was significant CR-Cl bond rupture in
the transition state. It is worth noting that the experimental
R-deuterium, the â-deuterium, the R-carbon, the nucleophile
carbon, and the nucleophile nitrogen KIEs are all consistent with
a reactant-like transition state and since the chlorine KIE of
1.0070 could be found for a reactant-like transition state, there
is no good reason to conclude that the transition state is product-
like.
Second, another finding which suggests that the theory gives
a good model for the transition state is that the experimental
∆Hq (18.7 kcal mol-1) for the reaction in DMSO was very well
reproduced with use of several continuum solvent models.2 For
example, SM5.42/HF/6-31G(d) calculated the ∆Hq exactly,
while COSMO/PM3 calculated it within 0.4 kcal/mol, and
several others gave values that were within 4 kcal/mol of the
experimental value. It is worth noting that Almerindo and
Pliego24 calculated a ∆Gq in DMSO with the geometry
optimized at the B3LYP/6-31G(d) level and the activation
energy calculated at the MP2/6-311+G(2df,2p) level with the
PCM continuum solvent model, that is within 1.5 kcal/mol of
the experimental ∆Gq if one uses the experimental ∆Sq.2 Also
the transition state found by Almerindo and Pliego and that in
our 2003 paper using different levels of theory were similar,
i.e., the NC-CR transition state bonds were 2.156 and 2.392 Å
and the CR-Cl transition state bonds were 2.332 and 2.134 Å,
respectively.
Finally, it is interesting that the rate constant for the reaction
is not very sensitive (it only changes from 4.2 × 10-4 to 6.58
× 10-4 M-1 s-1, see Table 7) to the significant change in solvent
from DMSO to THF. The larger rate constant in THF indicates
the change in solvation is greater at the cyanide ion than at the
SN2 transition state. This is what one would expect because the
cyanide ion has a greater negative charge density than the charge
dispersed transition state.
A discussion of the lack of change in transition state structure
with a significant change in solvent is warranted. Several
investigations of the effect of changing the solvent on transition
(25) Davico, G. E.; Bierbaum, V. M. J. Am. Chem. Soc. 2000, 122,
1740-1748 and references therein.
Another reason for favoring the transition state found by
theoretical calculations rather than the one suggested by
interpreting the experimental KIEs in the traditional manner is
(26) Yamataka, H.; Aida, M. Chem. Phys. Lett. 1998, 289, 105-109.
(27) Hargreaves, R. T.; Katz, A. M.; Saunders, W. H., Jr. J. Am. Chem.
Soc. 1976, 98, 2614-2617.
(28) Westaway, K. C.; Jiang, W. Can. J. Chem. 1999, 77, 879-889.
(29) Mohamed, A. A.; Jensen, F. J. Phys. Chem. A 2001, 105, 3259-
3268.
(23) Jobe, D. J.; Westaway, K. C. Can. J. Chem. 1993, 71, 1353-1361
(24) Almerindo, G. I.; Pliego, J. R., Jr. Org. Lett. 2005, 7, 1821-1823.
4746 J. Org. Chem., Vol. 71, No. 13, 2006