Search for high reactivity and low selectivity of radicals toward double bonds: The case of a tetrazole-derived thiyl radical

Article abstract of DOI:10.1021/jo061793w

The search for new radical structures having both low selectivity and high reactivity toward the addition reaction onto alkenes can be of interest in organic synthesis or polymer chemistry and has led us to propose a new tetrazole-derived thiyl radical. The reactivity of this sulfur-centered structure is compared to that of an aminoalkyl radical also efficient for alkene addition Worthwhile results are obtained; the new structure is more reactive on the complete range of alkenes with addition rate constants higher than 10 ⁷ M^-1 s^-1 for both electron-deficient (acrylonitrile, ...) or electron-rich (vinylether, ...) double bonds. Quantum mechanical calculations have allowed a better understanding of this unique feature.

Full text of DOI:10.1021/jo061793w

Search for High Reactivity and Low Selectivity of Radicals toward
Double Bonds: The Case of a Tetrazole-Derived Thiyl Radical
Jacques Laleve´e,* Xavier Allonas, and Jean Pierre Fouassier
Department of Photochemistry, Ecole Nationale Supe´rieure de Chimie de Mulhouse, 3 rue Alfred Werner,
68093 Mulhouse Cedex, France
j.laleVee@uha.fr
ReceiVed August 30, 2006
The search for new radical structures having both low selectivity and high reactivity toward the addition
reaction onto alkenes can be of interest in organic synthesis or polymer chemistry and has led us to
propose a new tetrazole-derived thiyl radical. The reactivity of this sulfur-centered structure is compared
to that of an aminoalkyl radical also efficient for alkene addition Worthwhile results are obtained; the
new structure is more reactive on the complete range of alkenes with addition rate constants higher than
107 M-1 s-1 for both electron-deficient (acrylonitrile, ...) or electron-rich (vinylether, ...) double bonds.
Quantum mechanical calculations have allowed a better understanding of this unique feature.
Introduction
(C•) (including aminoalkyl radicals)6-8 toward different alk-
enes: a clear separation and a quantification of both polar and
enthalpy factors were proposed. The reactivity of sulfur-centered
radicals (S•) has clearly deserved much less attention than the
reactivity of C•.1,9-12 The investigated C• are known to usually
exhibit a high selectivity toward double bonds;1 S• are usually
assumed to be less reactive toward double bonds than C• and
their selectivity remains unclear.10-11
The addition reaction of a radical to a double bond is usually
depicted by a state correlation diagram (SCD),1-5 which shows
the potential energy profiles of the four lowest doublet
configurations of the system consisting of the radical unpaired
electron and the attacked π-bond electron pair (the reactant
ground state, the reactant excited state, and two charge-transfer
configurations CTC R+/DB- and R-/DB+). The barrier obvi-
ously decreases upon increase of the exothermicity. The
involvement of the polar effects can also greatly influence the
reaction through a decrease of the barrier when decreasing the
CTC energies.1,4-8 This has been recently exemplified in the
study of the reactivity of a large class of carbon-centered radicals
The search for new radical structures having both low
(7) Laleve´e, J.; Allonas, X.; Fouassier, J. P. J. Am. Chem. Soc. 2003,
125, 9377-9380.
(8) Laleve´e, J.; Allonas, X.; Fouassier, J. P. J. Org. Chem. 2005, 70,
814-819. Laleve´e, J.; Allonas, X.; Fouassier, J. P. Macromolecules 2005,
38, 4521-4524.
(9) Tedder, J. M. Angew. Chem., Int. Ed. Engl. 1982, 21, 401-432.
(10) Ito, O.; Nogami, K.; Matsuda, M. J. Phys. Chem. 1981, 85, 1365-
1368.
(1) Fischer, H.; Radom, L. Angew. Chem., Int. Ed. 2001, 40, 1340-
1371.
(2) Heberger, K.; Lopata, A. J. Org. Chem. 1998, 63, 8646-8653.
(3) Shaik, S. S.; Shurki, A. Angew. Chem., Int. Ed. 1999, 38, 586-625.
(4) Shaik, S. S.; Canadell, E. J. Am. Chem. Soc. 1990, 112, 1446-1452.
(5) Wong, M. W.; Pross, A.; Radom, L. J. Am. Chem. Soc. 1994, 116,
6284-6292.
(6) Laleve´e, J.; Allonas, X.; Fouassier, J. P. J. Phys. Chem. A 2004, 108,
4326-4334.
(11) (a) Alam, M. M.; Konami, H.; Watanabe, A.; Ito, O. J. Chem. Soc.,
Perkin Trans. 1995, 2, 263-268. (b) Ito, O.; Tamura, S.; Matsuda, M.;
Kenkichi, M. J. Polym. Sci,: Part A: Polym. Chem. 1987, 26, 1429-1438.
(12) Laleve´e, J.; Allonas, X.; Morlet-Savary, F.; Fouassier, J. P. J. Phys.
Chem. A 2006, 110, 11605-11612.
(13) Laleve´e, J.; Allonas, X.; Fouassier, J. P. J. Am. Chem. Soc. 2002,
124, 9613-9621.
10.1021/jo061793w CCC: $33.50 © 2006 American Chemical Society
Published on Web 11/23/2006
J. Org. Chem. 2006, 71, 9723-9727
9723

Laleve´e et al.
TABLE 1. Rate Constants ka of the Addition Reactions of I and II
to Different Alkenes and Equilibrium Constant K of the Addition/
Fragmentation Reactions of I
SCHEME 1
Ia
IIa
b
alkene
ka (M-1 s-1
)
K (M-1
)
ka (M-1 s-1
)
AN
MA
VA
2.5 × 107
1.0 × 108
2.0 × 108
4.4 × 108
2.4 × 108
8 × 108
1.9 × 109
4.5 × 105
8 × 104
33.3
16.7
4.17
16.7
2.56
16.7
25.6
37
6.0 × 107
3.0 × 107
<5 × 104
<5 × 104
<5 × 104
6.0 × 106
<5 × 104
<5 × 104
4.1 × 108
8.1 × 107
VE
ABE
AAM
NVP
VC
FU
MAL
selectivity and high reactivity relevant to organic synthesis or
polymer chemistry has led us to propose the tetrazole-derived
thiyl radical I (Scheme 1).
1 × 109
In this paper, the reactivity of I toward ten alkenes, chosen
among monomers (vinyl ethyl ether, VE; vinyl acetate, VA;
methyl acrylate, MA; acrylonitrile, AN; allyl butyl ether, ABE;
acrylamide, AAM; N-vinylpyrolidone, NVP; dimethyl fumarate,
FU; dimethyl maleate, MAL; vinylcarbazole, VC) will be
studied using laser flash photolysis and quantum mechanical
calculations. Double bonds having very different electron
acceptor/donor properties, strong enthalpy/polar effects on the
addition reactions are thus expected. We will outline the low
selectivity and the high reactivity of I toward both electrophilic
and nucleophilic alkenes. This study will offer a good op-
portunity to separate the relative contributions of the polar and
enthalpy effects in I and II and explain this unique feature of
I.
a The errors for the addition rate constants can be estimated to 5-10%.
b Using a k02 value of 3 × 109 M-1 s-1 (ref 28).
the reaction is found to be irreversible. The addition rate
constants of I and II as well as the equilibrium constants for
the addition/fragmentation reactions of I are presented in Table
1.
Quantum Mechanical Calculations. For a better character-
ization of I and II reactivity, quantum mechanical calculations
were carried out. The computational procedure has been already
discussed in detail.6-8 All of the calculations were performed
using the hybrid functional B3LYP from the G98 or G03
program suites.17,18 Reactants, products, and transition states
(TS) were fully optimized, allowing the determination of the
reaction enthalpy (∆HR), the amount of charge δTS transferred
from the radical to the alkene in the transition state structure,
and the barrier. The barrier corresponds to the energetic
difference between the TS and the reactants with the addition
Experimental Section
The chemical compounds used were selected with the best purity
available (5,5′-dithiobis(1-phenyl-1H-tetrazole, tert-butylperoxide).
Triethylamine was purified by distillation. In the case of liquid
monomers, the stabilizer (hydroquinone-methyl ether, HQME) was
removed by column purification (AL-154). Vinylcarbazole was
purified by recrystallization.
of the zero point energy correction. The activation energy (EaTS
)
for the addition was obtained from the calculated barrier with
the usual addition of the RT term.12,19,20 The addition rate
constants were also calculated; determination of the preexpo-
nential factor in the Arrhenius equation was made by the
activatedcomplextheory:19,20theharmonicoscillatorapproximation18-20
was adopted for the activation entropy calculations. This
approach was assumed accurate enough for our purposes.21
Results
Experimental Addition Rate Constants. The tetrazole-
derived thiyl radical I was generated from the photodissociation
of the corresponding disulfide (5,5′-dithiobis(1-phenyl-1H-
tetrazole) under laser irradiation at 355 nm. The corresponding
radical I spectrum is centered at about 430 nm in agreement
with previous studies.14 The S-S bond cleavage occurs within
the risetime of our experimental setup (<10 ns). The reaction
used here for the observation of the aminoalkyl radical II
consists of two consecutive steps as already proposed.15,16 The
first step is the generation of a tert-butoxyl radical through the
photochemical decomposition of tert-butylperoxide; the second
step corresponds to an R(C-H) hydrogen abstraction reaction
from triethylamine. Radical II is observed at 340 nm.
The addition rate constants to the different alkenes were
determined by nanosecond laser flash photolysis (using the
equipment described in ref 13; resolution time, 10 ns) from a
classical Stern-Volmer analysis. To determine the addition and
fragmentation rate constants (ka and k-a) and the equilibrium
constant (K ) ka/k-a) of I, we used the selective radical trapping
flash photolysis method proposed in the literature.10-12 For II,
Adiabatic ionization potentials (IP) and adiabatic electron
affinities (EA) characterizing the reactants were calculated by
the previously used procedure(Table 2).6-8 The electron-
deficient or electron-rich character of the different alkenes is
represented by their absolute electronegativity (ø) calculated
(17) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb,
M. A.; Cheeseman, J. R.; Zakrzewski, V. G.; Montgomery, J. A., Jr.;
Stratmann, R. E.; Burant, J. C.; Dapprich, S.; Millam, J. M.; Daniels, A.
D.; Kudin, K. N.; Strain, M. C.; Farkas, O.; Tomasi, J.; Barone, V.; Cossi,
M.; Cammi, R.; Mennucci, B.; Pomelli, C.; Adamo, C.; Clifford, S.;
Ochterski, J.; Petersson, G. A.; Ayala, P. Y.; Cui, Q.; Morokuma, K.;
Salvador, P.; Dannenberg, J. J.; Malick, D. K.; Rabuck, A. D.; Raghavachari,
K.; Foresman, J. B.; Cioslowski, J.; Ortiz, J. V.; Baboul, A. G.; Stefanov,
B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Gomperts, R.;
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.; Andres, J. L.; Gonzalez, C.; Head-Gordon, M.; Replogle,
E. S.; Pople, J. A. Gaussian 98, Revision A.11; Gaussian, Inc.: Pittsburgh
PA, 2001.
(18) Foresman, J. B.; Frisch, A. In Exploring Chemistry with Electronic
Structure Methods, 2nd ed.; Gaussian Inc.: Pittsburgh, PA, 1996.
(19) Arnaud, R.; Subra, R.; Barone, V.; Lelj, F.; Olivella, S.; Sole´,
A.;Russo, N. J. Chem. Soc., Perkin Trans. 2 1986, 1517-1524.
(20) Pacey, P. D. J. Chem. Educ. 1981, 58, 612-615.
(14) Alam, M. M.; Watanabe, A.; Ito, O. Int. J. Chem. Kinet. 1996, 28,
405-411.
(15) Scaiano, J. C. J. Phys. Chem. 1981, 85, 2851-2855.
(16) Laleve´e, J.; Allonas, X.; Fouassier, J. P. Chem. Phys. Lett. 2005,
415, 202-205.
(21) Coote, M. L.; Henry, D. J. Macromolecules 2005, 38, 5774-5779.
9724 J. Org. Chem., Vol. 71, No. 26, 2006

New Tetrazole-DeriVed Thiyl Radical
TABLE 2. Electronic Properties for the Ten Alkenes and Two
Radicals Used
TABLE 3. Thermodynamical Data and Transition State Properties
for the Different Radical/Alkene Systems (see text)
a
IP (eV)a
EA (eV)a
ø (eV)a
∆HR
d(X-C)
barriera
(kJ/mol)
system
(kJ/mol)
δTS,b
(Å)
log(ka,calc)
AN
MA
VA
VE
ABE
AAM
NVP
VC
FU
10.5 (10.9)
9.64 (9.9)
8.91 (9.2)
8.31 (8.8)
8.77
9.3
8.06
7.18
9.56
0.12 (-0.2)
0.09 (-0.5)
-0.48 (-1.2)
-1.5 (-2.2)
-1.01
5.3 (5.4)
4.9 (4.7)
4.2 (4.0)
3.4 (3.3)
3.88
4.59
3.68
3.6
5.38
I/AN
I/MA
I/VA
-30.4
-25.1
-12.1
-23.3
-7.3
-26.5
-20.02
-21.03
16.42
-0.135
-0.124
-0.25
-0.304c
-0.223
-0.15
-0.276c
-0.312c
-0.06
-0.12
0.195
0.189
0.124
0.06
0.109
0.177
0.08
2.647
2.498
2.401
11.5
8.72
0.2
0
2.2
4.5
0
5.4
5.8
7.3
7.4
6.4
6.6
7.4
7.4
2.7
3.0
6.7
6.4
0.6
-1.3
-0.3
5.0
0.3
1.3
6.8
6.8
I/VE
-0.11
I/ABE
I/AAM
I/NVP
I/VC
2.574
2.563
-0.7
0.00
1.21
1.00
3.33
-0.35
0
MAL
I
II
9.3
8.93
4.96
5.15
6.13
2.31
I/FU
2.317
2.37
25.05
23.7
1.9
2.0
36.3
49.3
40.2
7.6
40.3
37.1
0
I/MAL
II/AN
II/MA
II/VA
II/VE
II/ABE
II/AA
II/NVP
II/VC
II/FU
II/MA
9.40
-53.1
-41.1
-29.1
-22.4
-24.1
-48.5
-29.5
-22.6
-31.2
-43.0
2.553
2.448
2.251
2.297
2.27
2.439
2.306
2.323
a At UB3LYP/6-31+G* and ZPE corrected. In parentheses are the
experimental data from ref 1.
from eq 1.22-23 The same procedure was used to obtain the
absolute electronegativity (øR)) of the radicals.
0.131
0.36c
0.32c
0
ø ) (IP + EA)/2
(1)
a Single points at UB3LYP/6-311++G** level on the geometry deter-
mined at 6-31G* level; ZPE corrected at 6-31G* level. b UB3LYP/6-31G*
and ZPE corrected at 6-31G* level. c Charge transfer for d(X-C) con-
strained to 2.4 Å for I and 2.5 Å for II.
Discussion
The High Reactivity and Low Selectivity of I. For the
monosubstituted alkene monomers, a striking feature is that the
ka valuesswhich span at least 4 orders of magnitude for IIs
change by less than 1 order for I and always remain very high
(ka > 107 M-1 s-1). I appears highly reactive and exhibits a
low selectivity. To the best of our knowledge, there has neVer
been a report of such an enhanced property. For example, for
the phenylthiyl radical and the corresponding derivatives, the
reactivity is strongly decreased (the rate constants of addition
are found lower by a factor of about 1 000! for the alkenes
investigated) and the selectivity is rather high (this structure
being mainly reactive with alkenes bearing withdrawing sub-
stituents).11
For a better understanding of this unusual behavior, quantum
mechanical calculations were carried out. The different param-
eters characterizing the addition process of I and II to the
different alkenes (∆HR, δTS, and Ea) and the calculated addition
rate constants (ka) are presented in Table 3. For the I/VE, I/NVP,
I/VC, II/FU, and II/MAL systems, barrierless reactions were
found and the TS structure cannot be determined. For these
systems, the ka values were calculated using the activation
entropy determined for I/VA and II/AN (these two reactions
also being almost barrierless).
The calculated and experimental ka values are compared for
I and II in Figure 1. An excellent general agreement is observed.
For II, only the limiting values are reported for the addition to
VA, VE, ABE, NVP, and VC. The calculated values are found
systematically lower than the experimental ones by about 1 order
of magnitude. This kind of behavior has been recently observed
for other sulfur-centered radicals,12 and such a difference is
known for other systems in the literature.1,24,25 Keeping in mind
the difficulty18 in acquiring an accurate determination of the
transition state structure and knowing than ka values spanmore
than 4 order of magnitude, the observed agreement can be
(22) Parr, R. G.; Pearson, R. G. J. Am. Chem. Soc. 1983, 105, 7512-
7516.
FIGURE 1. Plot of log(ka,exp) vs log(ka,calc) for I (A) and II (B).
(23) Pearson, R. G. J. Am. Chem. Soc. 1985, 107, 6801-6806.
(24) Coote, M. L. Macromolecules 2004, 37, 5023-5031.
(25) Henry, D. J.; Coote, M. L.; Gomez-Balderas, R.; Radom, L. J. Am.
Chem. Soc. 2004, 126, 1732-1740.
considered an excellent (Figure 1) reproduction of the evolution
trend. Determination of accurate calculated values obviously
requires the use of more sophisticated quantum calculations.
J. Org. Chem, Vol. 71, No. 26, 2006 9725

Laleve´e et al.
formation. Through such an analysis of I reactivity, the
proposition of new efficient sulfur-centered structures will be
possible in forthcoming studies.
The charge transfers observed for the different radical/alkene
systems are presented in Table 3. For I, δTS is always found to
be negative, indicating its electrophilic character. II appears to
be nucleophilic with a net charge transfer from the radical to
the alkene for all of the monomers studied. These behaviors
are also reflected, as expected, by the radical electronegativity
(øR) as the absolute electronegativity difference (radical/alkene)
and the driving factor for the charge transfer.6,22,23 For øR
>
øM, charge transfer is observed from the alkene to the radical
and for øR < øM, from the radical to the alkene. Interestingly,
clear relationships are found between δTS and ø. For I, this
transfer (in absolute value) increases from AN to VE (δTS
)
-0.692 + 0.112øM (r ) 0.96)). For II, an opposite trend is
observed: δTS increases from VE to AN (δTS ) -0.296 +
0.107øM (r ) 0.86)).
TS Structures. The distances determined by quantum me-
chanical calculations in the TS between the radical center
(carbon or sulfur atom) and the attacked carbon of the double
bond d(X-C) are presented in Table 3. For I and II, the bond
formation in the TS structure correlates with ∆HR (for I, d(X-
C) ) 2.421 - 0.0056∆HR; for II, d(X-C) ) 2.093 -
0.0080∆HR), in agreement with Hammond’s postulate, which
states that the placement of a transition structure is directly
related to reaction exothermicity. Interestingly, the points
concerning II are still clearly beyond the correlation obtained
for I; i.e., the structures of the corresponding TS’s are earlier
for I than for II. The d(X-C) shift between these compounds
is about 0.25 Å: for an exothermicity of 25 kJ/mol, d(C-C) is
about 2.25 Å for II and about 2.50 Å for I.
Polar and Enthalpy Contributions for C• and S•. From
the SCD approach, the barrier is affected by the reaction
exothermicity and the participation of a charge transfer in the
TS. The polar effect (∆Epol) is proportional to (δTS).22,23
Therefore, a multiple regression analysis of the dependence of
EaTS vs ∆HR and (δTS)2 can be obtained for I (eq 2) and II (eq
3) using the Origin 7.5 software26 (obviously, the barrierless
reactions were not included in the analysis).
FIGURE 2. Plot of log(ka,exp) vs ø for I (A) (the experimental data
for bisubstituted monomers MAL and FU are given in brackets) and
II (B).
For I, the experimental equilibrium constants of K for the
addition/fragmentation process correlate with the addition
reaction exothermicity (ln(K) ) 0.424 - 0.107 ∆HR (r ) 0.86)).
The same effect observed in mercaptobenzoxazoles12 was
ascribed to the large influence of ∆HR on k-a. A more detailed
analysis of the factor governing k-a is beyond the scope of this
paper.
The electron acceptor properties of the different alkenes
decrease with the absolute electronegativity in the series FU >
AN > MAL > MA > AAM > VA > ABE > NVP > VC >
VE (Table 2). The ka change with the monomer electronegativity
is depicted in Figure 2.
The behavior of I is particularly worthwhile. The remarkable
low selectivity toward the addition process is still outlined for
the complete range of monomer electronegativity going from
the electron-rich π-system (VE, NVP, VC, ...) to the electron-
deficient alkenes (AN, MA, AAM, ...), except for the two
bisubstituted alkene monomers FU and MAL. In the latter case,
the steric hindrance destabilizes the adduct radical: the reaction
is less exothermic than expected from the electronegativity
values. Comparatively, the carbon-centered structure II is found
to be rather selective with an enhanced reactivity toward
electron-deficient alkenes (particularly for monomer exhibiting
ø > 4.5 eV) and a very low reactivity toward electron-rich
structures (ka , 5 × 104 M-1 s-1). The behavior of I probably
corresponds to a unique feature. This behavior can be worth-
while for synthesis applications including C-S single bond
Ea ) 22.8 + 0.30∆HR - 326.5(δTS)2
Ea ) 63.9 + 0.45∆HR - 1 010(δTS)2
r2 ) 0.90
r2 ) 0.98
(2)
(3)
Equation 3 is close to the expression derived for many C•/
alkene couples:6 Ea ) 64.9 + 0.41∆HR - 775(δTS)2. These two
equations underline this important difference between carbon-
and sulfur-centered radicals.
From eqs 2 and 3 (Ea ) E0 + R∆HR + â(δTS)2), we have an
access to E0 (called hereafter the intrinsic barrier) which
represents the barrier for ∆HR ) 0 without any polar effects.
This term is about 3 times lower for I than for II. This is clearly
a new point.
The second term in these equations (R) describes the enthalpy
and basically represents the Evans-Polanyi relationship which
(26) Origin 7.5; OriginLab Corporation: Northampton, MA, 2003.
(27) Semenov, N. N. Some Problems in Chemical Kinetics and ReactiVity;
Princeton Press: Princeton, NJ, 1958.
(28) Laleve´e, J.; Allonas, X.; Fouassier, J. P. Chem. Phys. Lett. 2005,
415, 287-290.
9726 J. Org. Chem., Vol. 71, No. 26, 2006

New Tetrazole-DeriVed Thiyl Radical
states that the barrier decreases when there is an increase in
exothermicity.27 About one-third and one-half of the ∆HR
change are transferred to the TS structures for I and II,
respectively. Interestingly, the transfer coefficient (R) is lower
for I. For II, the transfer coefficient is in excellent agreement
with the value previously found for a large variety of carbon-
centered radicals.6
For I, the polar and enthalpy factors exhibit antagonist effects
from VE to AN. This is not the case for II; i.e., both factors
increase in this series. Therefore, the barrier change in the VE-
AN series is lower for I, explaining its lower selectivity.
Concomitantly, the associated lower E0 of I will also lead to a
higher reactivity (lower EaTS).
All of these behaviors can probably be ascribed to the
symmetry and the overlap of the molecular orbitals involved in
the TS’s, which are different for I and II. Indeed, in the SCD
approach the reaction surface is strongly related to the mixing
of the potential energy profiles of the lowest doublet configura-
tions of the R/alkene system. This mixing strongly depends on
the orbitals involved.3,4 Nowadays, a quantification of this factor
remains an outstanding problem in quantum chemistry.3 How-
ever, from the different frontier orbitals involved in I and II, it
can be reasonably assumed that this factor influences both E0
and R.
The third part (â) of these equations differs with the Evans-
Polanyi approach and takes into account the polar term. For II,
the coefficient for the polar factor (1 010) is close to that recently
found for carbon-centered radicals (775).6 For I, a lower value
is noted (326). This is in agreement with the different elec-
tronegativity of the sulfur- and carbon-centered structures.
Conclusion
One fascinating aspect of radical I should be its ability to
initiate the polymerization processes of a large variety of
monomers; this cannot be done with any known initiating
radicals. From the chemical reactivity point of view, a large
panel of radical/double bond situations could be expected
through a careful selection of sulfur-centered radicals thereby
allowing a further general discussion of the observed properties.
The addition of S• onto double bonds can also give access to a
large variety of C-S single bond formations.
Acknowledgment. The authors thank the CINES (Centre
Informatique National de l’Enseignement Supe´rieur) for the
generous allocation of time on the IBM SPsupercomputer.
JO061793W
J. Org. Chem, Vol. 71, No. 26, 2006 9727