1. business and industrial
2. chemicals industry
3. plastics and polymers

Revisiting the Structure of the 2-Norbornyl Carbocation
Vernon G. S. Box
Department of Chemistry
City College
City University of New York
New York, NY, USA
Abstract - Only a few molecules have stimulated the discussion and understanding of reaction
mechanisms in organic chemistry. as has the 2-norbornyl Carbocation. New structural evidence
has shed more light on this enigma.
Key Words - 2-norbornyl, carbocation, singlet diradical, x-ray crystallography, molecular
modeling, StruMM3D
Introduction - The achievement of the crystal structure of the 2-norbornyl carbocation, 1, below,
was a watershed moment in the history of organic chemistry.[1] This important carbocation has
had an unprecedented impact on the history of organic reaction mechanisms.
H
H
H
+
H
H
1
A casual examination of the x-ray crystallographic data for the norbornyl carbocation could lead
one to conclude that the non-classical carbocation theory has at last proven to be correct.
However, a closer examination of its bond order data, derived only from its x-ray coordinate data,
has revealed some further insight into its structure and stability.
Discussion Historically, the solvolytic chemistry of chiral norbornanes bearing good leaving groups at C-2
revealed the core details of the overall reaction pathway, as shown in Scheme 1. It became
obvious that not only were these reactions much faster than the solvolyses of their simple
monocyclic analogues, but also they were stereospecific (the incoming group replaced the leaving
group retaining the same relative stereochemistry as the starting material), and importantly,
yielded a racemic product.[2] Thus, it was concluded that these solvolyses must have proceeded
via some symmetrical intermediate, and these possible carbocations are shown in Scheme 2.
5
H
H
H
6
4
1
3
H
ROH
H
H
+
H
H
H
OR
2
X
OR
Scheme 1
For brevity, the positive charge implied by the vacant p-orbital has been omitted. The structure
3D is an attempt to depict the resonance hybrid 3. as it is now popularly accepted.
H
H
H
_
H
H
H
H
-
X
H
H
H
H
H
X
_
H
+
H
H
H
2A
-
H
H
3E
2B
X
H
H
H
H
H
H
H
H
3A
H
H
H
H
H
H
+
H
H
H
H
H
3C
3B
H
3D
Scheme 2
The feud between believers in the classical[3], carbocation structures 2, and their rivals that
believed in the non-classical[4], carbocation structures 3, then ensued.
Advances in NMR spectroscopic methods and techniques eventually provided evidence in
support of the carbocation structure 3D.[5] The basic assumption that underpinned these
experiments was that performing NMR spectra at very low temperatures should slow down the
intramolecular equilibrium process between the classical carbocation structures 2A and 2B,
enough to detect their separate existence. Those low temperature NMR spectroscopic
experiments were not to be able to detect these classical ions, and so were seen to be congruent
with the existence of only one structure, 3D. Thus, popular opinion swung away from the notion
of the existence of the classical pair of carbocation structures, 2A and 2B.
The recent publication[1] of the crystal structure of the 2-norbornyl carbocation, 1, has supported,
unequivocally, the conclusions drawn from the NMR experiments. However, the structure 1 is
quite different from the structures 3D or 3E.
It is very important to note that the structures 1 3D and 3E are not identical. In structure 1, the
positive charge resides almost exclusively on the C-1 - C2 π-bond, whereas in the structure 3D
that positive charge is distributed over C-1, C-2 and C-6. If, somehow, the equilibration of the
classical carbocation structures 2A and 2B was faster than the NMR time scale, the “merging” of
these two structures would have generated an ion like 3E, in which the positive charge would
reside on C-1 and C-2. However, notice that the structure 1 shows the C-1 - C-2 bond to be a πbond, which would not be required for structure 3E, and so the x-ray data eliminated the structure
3E from consideration. The notion of classical carbocation structures 2A and 2B is therefore truly
dead.
However, as will be seen in the discussion below, considerable doubt must be cast on the validity
of the formulation of the non-classical 2-norbornyl carbocation as structure 3D, a simple
resonance hybrid between the simple cations 3A, 3B and 3C. Further, as will also be shown
below, the x-ray crystal structure of the 2-norbornyl carbocation, 1, denies the possibility of it
being the structure 3E.
As depicted in Scheme 2, it is widely suggested that the ion 3 is a resonance hybrid of the
possible canonical forms 3A, 3B and 3C. The NMR spectroscopic evidence suggests that C-6
does not ever bear a significant positive charge,[6] as in resonance form 3C, and since 3C would
also be a highly unstable primary carbocation, then it would not be expected to be a significant
contributor to any resonance hybrid. Thus if there is any double bond character in the C-1 - C-2
bond, as depicted in 3D, then the order of this bond must be closer to 1, rather than to 2. That
would make the resonance hybrid more akin to the structure 3E than to 3D, an unhappy
conclusion.
Since the C-6 - C-1 bond of resonance structure 3A, and the C-6 - C-2 bond of resonance
structure 3B, would be two electron bonds flanking a carbocation center, then their bond orders
would be expected to be quite close to, if not greater than 1, due to the massive inductive effect of
the carbocation center.[7] So these bonds should be expected to be of near normal strengths and
lengths. However, the x-ray structure of the carbocation 1 shows that these two C-C bonds have
bond orders of about 0.17, showing that these bonds are extremely weak and extremely long.
Further, the fundamental "Rules for Resonance" states that one cannot imply the movement of
atoms in going from one resonance structure to another, and only electrons may be redistributed.
Thus, if 3A, 3B and 3C are "normal", planar carbocations, then all the resonance structures 3A,
3B and 3C violate this rule. Indeed, the hydrogens shown would be fluttering from one
orientation to another as the tetrahedral sites become trigonal and vice versa. If the resonance
hybrid is definitely to be depicted as 3D, then we must invoke the participation of non-planar
carbocations, and a non-planar π-bond, in the structure 3D. These features are known to be
highly unstable.[8]
The experimentally determined crystal structure of the 2-norbornyl carbocation, 1, has shown that
C-7, C-1, C-2, H-2 dihedral angle is about 153 degrees (as too is the C-3, C-2, C-1, H-1 dihedral
angle). So while the H-1, C-1, C-2 and H-2 are coplanar, the data clearly showed that the C-1 and
C-2 atoms were not planar. This fact, highlighted another issue with the involvement of the
possible resonance structures 3C in the resonance hybrid 3D.
Thus, the ion 3 cannot be a resonance hybrid of the simple carbocation structures 3A, 3B and 3C,
and since the 2-norbornyl cation cannot be depicted as 3E, there is a problem with the
formulation of the 2-norbornyl carbocation as a simple non-classical carbocation.
The crystal structure of the 2-norbornyl carbocation, 1, has therefore not only cast doubts on the
validity of previous thoughts on its structure, but also has revealed a third possible structure for
the norbornyl carbocation, which is significantly more congruent with the experimentally
determined structure, both energetically and in the structural details.
In order for us to better understand the bond length features that the C-1 - C-2 bond of the 2norbornyl carbocation would show, if it was indeed representable by structure 3E, it is useful for
us to consider the crystal structures of four derivatives of adamantylideneadamantane,4.
X
4
5
6
7
8
X=O
X = Cl+
X = Br+
X = I+
These heterocyclic derivatives of adamantylideneadamantane, 4, are stable, in large part, because
of the inability of nucleophiles to approach the backsides of the C-X bonds in attempted Sn2
reactions.
Table 1 - Bond lengths (pm) and Bond Orders†
Compound
C-X
C-X
C-C
CCDC Code
Epoxide, 5
145.2, 0.81
145.9, 0.78
148.4, 1.12
GICJUX
Chloronium ion, 6 192.4, 0.59
192.4, 0.59
148.6, 1.21
NOCHUI
Bromonium ion, 7 211.9, 0.54
208.8, 0.62
214.0, 0.49
211.7, 0.54
149.0, 1.19
149.0, 1.19
WEVPIW
Iodonium ion, 8
233.8, 0.51
236.2, 0.46
145.3, 1.36
WEVPOC
Norbornyl cation,
181.5, 0.10
181.2, 0.10
181.2, 0.10
180.3, 0.13
138.5, 1.71
138.8, 1.69
HIGNAO02
Benzene
†
139, 1.667
StruMM3D (www.exorga.com) was used as the molecular modeler
The experimentally determined crystal structures of all of the molecules, 5 to 8, are available, and
will be the sole sources of the data used here. While bond length data, derived from the
experimentally determined atomic coordinates of these molecules will be discussed, the bond
orders (B.O.) of the relevant bonds will be more useful. No theoretical derived data for these
molecules will be used in this discussion in an effort to avoid pointless political controversies.
The bond length and bond order data are presented in Table 1.
The structure of the epoxide, 5,[9] shows normal lengths for the C-O bonds of 145 pm (B.O. 0.8) and the C-C bond of 1.48 pm (B.O. - 1.12). Oxygen is the second most electronegative
atom, and so the shortened C-C bond reflects the expected consequence of the oxygen's inductive
effect.[7]
As has been emphasized,[10] the single bonds of the stable, non-delocalized, tub conformation of
cyclooctatetraene are 146 pm long. Delocalization in this tetraene molecule cannot occur because
of the large dihedral angles between adjacent double bonds. The single bond lengths in
cyclooctatetraene are therefore due to the reduced covalent radii of the sp2 hybridized carbon piatoms. Thus, the bond lengths of 148 pm in the epoxide cannot be due to
resonance/delocalization effects.
For the halogenonium ions, 6 to 8,[11 to 13 respectively] the C-X bond orders are uniformly
greater than 0.5, showing that these are highly extend, though fully formed, bonds. The C-C
bonds are all between 148 to 149 pm, similar in length to the epoxide's C-C bond, with bond
orders of about 1.2. These shortened C-C bonds again reflect the enhanced inductive effects of
the positively charged atom X, but their lengths all fall very comfortably within the normally
observed range (B.O < 1.5) of lengths for C-C single bonds. This data re-enforces the notion that
structures such as 9 cannot be possible for these molecules.
X+
π complex
X+
9
σ complex
The 2-norbornyl carbocation, 1, shows quite different features than these adamantane derivatives.
The carbocation 1 shows a much shorter C-1 - C-2 bond, 138 pm, with the same length and
similar bond order (B.O. > 1.5) as that of the benzene C=C bond. Thus the C-1 - C-2 bond of
carbocation 1 has the features of a delocalized C=C double bond.
The crystallographic data show that C-1 - C-2 bond of carbocation 1 is a pyramidalized π-bond,
and that the degree of the deformation from planarity is well within the range experimentally
observed for pyramidalized alkene and benzenes.[14] Pyramidalized alkenes are known to be
neutral (no charge separation) and highly reactive,[14] undoubtedly because of their significant
singlet diradicaloid properties.
The only logical structural explanation for these observations on carbocation 1 is shown in
Scheme 3. The structures 1A and 1B are meant to indicate that the CH2 radical center is weakly
bonded to the C-1 - C-2 radical cation π-bond, a sigma complex. The structures 1A, 1B and 1C
are intended to be slightly different representation of one structure and not a resonance hybrid.
Notice that the positive charge is explicitly shared by only C-1 and C-2, in contrast to structure
3D or 3E.
H
.
+
H
H
H
.
H
.
H
H
H
+.
H
H
1A
H
H
1B
H
+
H
H
1C
Scheme 3
The length of the C-1 - C-2 bond, 138 pm, clearly suggests that unlike the halogenonium ions 6 to
8, the center of positive charge is borne by the radical-cation C-1 - C-2 π-bond, and so very little
if any positive charge can reside on C-6. This is consistent with previous NMR studies.[6]
Thus, the carbocation 1 must be a singlet diradicaloid entity, with the tetrahedral C-6 bearing a
radical orbital, as in structures 1A and 1B, and the pyramidalized C-1 - C-2 double bond being a
delocalized radical carbocationic π-bond entity.
The halogenonium ions, 6 to 8, all show bond orders greater 0.5 for the bonds joining the halogen
atoms to the central carbons. The epoxide 5, which is uncharged, shows bond orders of about 0.8
for the C-O bonds. On the other had, the carbocation 1 shows bond orders of about 0.17 for the
bonds between C-6 and C1 and C2. These bonds are clearly almost broken, and so must be quite
weak, while for the halogenonium ions the corresponding bonds are almost fully formed, and so
must be much stronger.
Essentially, while the halogenonium ions are fully, and discretely, bonded entities, the carbocation
1 shows us a much more weakly coherent structure with C-6 flirting with C-1 and C-2, via their
π-bond, and being bonded strongly to neither. In effect, the activation energy to transition
between two structures 2A and 2B should be almost zero, as is normally accepted for incipient
bonding between radicals.
If this is true, then since the two entities 2A and 2B could interchange freely, without energetic
restriction, then any NMR study performed at low temperature would give inconclusive results,
since on the NMR time scale, only one molecule would be observed. So, the classical
carbocation formulation for this entity, requiring a rapid equilibrium between the two molecules
1A has not been disproved.
This singlet diradical carbocation rationalization completely avoids the pitfalls inherent in the
simple resonance stabilized carbocation structural rationalization shown in Scheme 2. all of
whose structures violate the rules for resonance in one way or another.
Another look at the possible processes leading to the formation of the carbocation 1 is shown in
Scheme 4. Thus, as the C-2 carbocation forms, an electron transfer from the C-6 - C-1 bond to
the cation center then creates the singlet radical cations 1Z, and thence to 1A. Indeed, this
mechanism might also be applied to all thermally induced suprafacial-suprafacial cation-induced
[1,n] sigmatropic rearrangements.[15]
5
H
4
H
6
7
H
1
H
_
H
+
H
X
H
H
1
H
H
H
.
H
1Z
H
H
+
H
H
+.
-
X
2
3
H
H
H
H
.
.
H
H
H
+.
1B
H
H
H
H
H
+.
1A
Scheme 4
Acknowledgements - The molecular modeler used in this study was StruMM3D,[16] which drew
attention to the presence of the delocalized C-1 - C-2 double bond. While any other molecular
modeler could have been used, no other molecular modeler tried called attention to this unusual
bond. Any molecular modeler can be used to corroborate the data discussed above.
References
1. Scholz, F.; Himmel, D.; Heinemann, F. W.; Schleyer, P. V. R.; Meyer, K.; Krossing, I., Science
2013, 341(6141), 62-64.
2. Winstein, S.; Trifan, D. S., J. Am. Chem. Soc., 1949, 71(8), 2953
3. Brown, H. C., "The nonclassical ion problem", Plenum Press, New York, 1977, and references
cited therein
4. Winstein, S. in "Carbonium Ions", Vol. III, Olah, G. A. and Schleyer, P. v. R., Eds., WileyInterscience, New York, 1972, Chapter 22, and references cited therein
5. Yannoni, C. S.; Macho, V.; Myhre, P. C., J. Am. Chem. Soc., 1982, 104(25), 7380-7381.
6. Olah, G. A.; Liang, G.; Matescu, G. D.; Riemenschneider, J. L., J. Am. Chem. Soc., 1973,
95(26), 8698-8702.
7. Fodi, B.; McKean, D. C.; Palmer, M. H. J. Mol. Struct.: THEOCHEM., 2000, 500, 195–223.
8. 14. Della, E. W.; Abboud, J. L. M.; Castano, O.; Herreros, M.; Muller, P.; Notario,R.; Rossier,
J.-C., J. Am. Chem. Soc., 1997, 119(9), 2262-2266.
9. Watson, W. H.; Nagl, A., Acta Cryst. 1988, C44, 1627-1629. (GICJUX)
10. Box, V. G. S., J. Chem. Educ., 2011, 88(7), 898-906
11. Mori,T.; Rathore, R.; Lindeman, S.V.; Kochi, J.K., Chem.Commun. 1998, 927-928.
(NOCHUI)
12. Rathore, R.; Lindeman,S.V.; Zhu, C.-J.; Mori, T.; Schleyer, P.v.R.; Kochi, J.K., J. Org. Chem.
2002, 67, 5106-5116. (UGIDAP)
13. Brown, R. S.; Nagorski, R. W.; Bennet, A. J.; McClung, R. E. D.; Aarts, G. H. M.;
Klobukowski, M.; McDonald, R.; Santarsiero, B. D., J. Am. Chem. Soc. 1994, 116, 2448.
(WEVPIW and WEVPOC)
14. Borden, W. T., Chem. Rev., 1989, 89(5), 1095–1109
15. Woodward, R.B.; Hoffmann, R., "The Conservation of Orbital Symmetry" Verlag Chemie
Academic Press. 2004.
16. StruMM3D can be obtained from Exorga, Inc at www.exorga.com