A R T I C L E S
Tripp et al.
While these experiments add a few more pieces, the puzzle
here is not quite complete. We could reliably observe the
absence of presence of the small extra methyl ester resonances
and GC peaks on the basis of whether the crude product was
treated with mCPBA, and these effects did not exhibit a
significant temperature dependence. In contrast, Ihara did not
treat any crude reactions products with mCPBA and reports that
the peaks appear or not as a function of temperature. Thus, we
cannot explain this experimental discrepancy between our work
and Ihara’s.
Nonetheless, the correlation of the minor NMR peaks with
the minor GC peaks and the disappearance of all these peaks
on mCPBA treatment support our conclusion that these arise
from constitutional isomers and not other diastereomers. Further,
we have identified and tentatively assigned other diastereomers
29a and 30a by GC, and NMR experiments show that they do
not have any methyl ester resonances in the region integrated
by Ihara. We conclude that NMR integration is simply not up
to the task of determining product ratios because there are two
major products and at least five minor products, each of which
has three nonequivalent methyl esters. Even though the GC
analysis is incomplete because we cannot rigorously assign
structures to all the minor peaks, it is still much more
informative than NMR integration because the GC peaks can
be individually classified as tricyclic or not and can be
individually integrated.
Figure 8. BHLYP/6-311G** optimized transition structures 41-44 for
cyclization of radical 14. MP2/6-311G** data are in parentheses, and
BHLYP/cc-pVDZ data are in brackets.
Table 4. Calculated Differences in Activation Energy (kJ mol-1
for the Different Modes of Ring-Closure of Radical 14
)
entry
method
cis-chair 41 trans-chair 42 cis-boat 43 trans-boat 44
Calculations. Clearly then, the computational methods
employed in the earlier study of Beckwith and Schiesser predict
the incorrect stereochemical outcome for the cyclization of 14
and would presumably also fail for other hexenyl radicals
bearing bulky substituents at position 1. What is special about
these 1-substituted systems such that simple steric arguments
fail to compute the correct reaction outcome? To explore this
question further, it is necessary to employ computational
methods that are designed to provide a more holistic approach
to this chemistry. Accordingly, we sought recourse to ab initio
and density functional quantum techniques.
1
2
3
4
5
6
MP2/6-311G**
BHLYP/6-311G**
BHLYP/6-311G**+ZPE
BHLYP/cc-pVDZ
BHLYP/cc-pVDZ+ZPE
BHLYP/aug-cc-pVDZ
0
0
0
0
0
0
1.1
2.2
2.5
2.7
3.0
1.5
9.0
12.5
12.8
13.4
13.5
12.6
4.6
4.5
3.8
5.0
4.3
4.2
Inspection of Figure 8 reveals the length of the forming C-C
bond in each transition state to lie in a narrow range around
2.2 Å, with BHLYP calculations predicting a slightly later
transition state in each case, as has been observed previously
for other systems. Inspection of Table 4 clearly indicates that
higher level quantum calculations do indeed predict the correct
stereochemical outcome for the ring-closure of 14; the cis-chair
structure 41 is calculated to be the lowest energy transition state
at all levels of theory. The magnitude of the preference for the
cis mode of cyclization is somewhat underestimated, the largest
energy difference of 3.0 kJ mol-1 calculated at the BHLYP/
cc-pVDZ + ZPE level of theory being some 10 kJ mol-1 less
than that determined for the ring-closure of 14 in hexane. The
cyclization of 14 displays a pronounced solvent dependence,
while the calculated data reflect gas-phase chemistry more
closely. Alternatively, very accurate data may only be achievable
Previous work has shown that, without going to very high
levels of theory (e.g. G3-RAD),26 the BH and HLYP (BHLYP,
density functional) method provides a very cost-effective
computational technique for studying free-radical reactions,27
while B3LYP often provides poor data for radicals and MP2
calculations are often highly spin contaminated;25,28 indeed, the
MP2/6-311G** calculated transition states for 14 provided s
values approaching unity, while the analogous BHLYP data
were typically below 0.82.
Searching for the C10H19 potential energy surface at all levels
of theory29 employed in this study, we located four transition
states for the cyclization of 14: cis-chair (41), trans-chair (42),
cis-boat (43), and trans-boat (44), in keeping with the earlier
publication by Beckwith and Schiesser.13 The BHLYP/
6-311G** optimized structures (41-44) are displayed in Figure
8, while the calculated differences in activation energy are listed
in Table 4. Full details (Gaussian Archive Entries) are available
as Supporting Information.
(29) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M.
A.; Cheeseman, J. R.; Montgomery, J. A., Jr.; Vreven, T.; Kudin, K. N.;
Burant, J. C.; Millam, J. M.; Iyengar, S. S.; Tomasi, J.; Barone, V.;
Mennucci, B.; Cossi, M.; Scalmani, G.; Rega, N.; Petersson, G. A.;
Nakatsuji, H.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa,
J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Klene, M.;
Li, X.; Knox, J. E.; Hratchian, H. P.; Cross, J. B.; Adamo, C.; Jaramillo,
J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.;
Pomelli, C.; Ochterski, J. W.; Ayala, P. Y.; Morokuma, K.; Voth, G. A.;
Salvador, P.; Dannenberg, J. J.; Zakrzewski, V. G.; Dapprich, S.; Daniels,
A. D.; Strain, M. C.; Farkas, O.; Malick, D. K.; Rabuck, A. D.;
Raghavachari, K.; Foresman, J. B.; Ortiz, J. V.; Cui, Q.; Baboul, A. G.;
Clifford, S.; Cioslowski, J.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz,
P.; Komaromi, I.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.;
Peng, C. Y.; Nanayakkara, A.; Challacombe, M.; Gill, P. M. W.; Johnson,
B.; Chen, W.; Wong, M. W.; Gonzalez, C.; Pople, J. A. Gaussian 03,
revision B.05; Gaussian, Inc.: Pittsburgh, PA, 2003.
(26) Go´mez-Balderas, R.; Coote, M. L.; Henry, D. J.; Radom, L. J. Phys. Chem.
A 2004, 108, 2874-2883.
(27) Mohr, M.; Zipse, H.; Marx, D.; Parrinello, M. Phys. Chem. A 1997, 101,
8942-8948.
(28) For examples, see: Morihovitis, T.; Schiesser, C. H.; Skidmore, M. A. J.
Chem. Soc., Perkin Trans. 2 1999, 2041-2047.
9
5526 J. AM. CHEM. SOC. VOL. 127, NO. 15, 2005