Correlation of gas-phase stability of bridgehead carbocations with rates of solvolysis and ab initio calculations

Article abstract of DOI:10.1021/ja962319i

The stability of bridgehead carbocations has been determined by Fourier transform ion cyclotron resonance spectroscopy (FT ICR) based on dissociative proton attachment (DPA) of bromides and alcohols. The stability of the ions correlates with the solvolytic reactivity of bridgehead derivatives over a rate range of 23 log units, and with theoretical calculations for hydride transfer of bridgehead hydrocarbons at the MP2/6-311G** level.

Full text of DOI:10.1021/ja962319i

2262
J. Am. Chem. Soc. 1997, 119, 2262-2266
Correlation of Gas-Phase Stability of Bridgehead Carbocations
with Rates of Solvolysis and ab Initio Calculations
Jose´-Luis M. Abboud,*,† Obis Castan˜o,‡ Ernest W. Della,*,§ Marta Herreros,†
Paul Mu1ller,*, Rafael Notario,† and Jean-Claude Rossier
Contribution from the Instituto de Quimica Fisica, “Rocasolano”, c/Serrano 119,
E-28006 Madrid, Spain, Departamento de Quimica Fisica, UniVersidad de Alcala´ de Henares,
Alcala´ de Henares (Madrid), Spain, Department of Chemistry, Flinders UniVersity,
Bedford Park, South Australia, 5042, Australia, and De´partement de Chimie Organique,
UniVersite´ de Gene`Ve, CH-1215 Gene`Ve, Switzerland
ReceiVed July 8, 1996X
Abstract: The stability of bridgehead carbocations has been determined by Fourier transform ion cyclotron resonance
spectroscopy (FT ICR) based on dissociative proton attachment (DPA) of bromides and alcohols. The stability of
the ions correlates with the solvolytic reactivity of bridgehead derivatives over a rate range of 23 log units, and with
theoretical calculations for hydride transfer of bridgehead hydrocarbons at the MP2/6-311G** level.
I. Introduction
but the experimentally accessible range of ion stabilities was
limited owing to apparent rearrangements of the highly strained
ions under the conditions of the experiments.7
Experimental insight into the structures of tertiary aliphatic
carbenium ions has become available through NMR studies1
and X-ray crystallography.2 Much less information exists,
however, with respect to their energies. Although some data
have been determined in the gas3 and in the condensed phase,4
much of our knowledge on carbenium ion stabilities is derived
from solvolytic studies.5 The early empirical force-field
calculations of Schleyer et al.6 correlating solvolytic reactivity
with strain changes between bridgehead derivatives and the
corresponding carbenium ions suggest that the transition state
for solvolysis should occur late on the reaction coordinate and
resemble the carbenium ion with respect to structure and energy.
However, lack of reliable experimental data on the stability
of carbenium ions in the bridgehead series made it impossible
to verify this hypothesis. Until very recently adamantane was
the only bridgehead derivative for which the stability of the
cation had been determined.3 An attempt was made to
determine the heterolytic bond dissociation energies D(R+-
X-) of bridgehead bromides in the gas phase by ICR methods,
The observation of rearrangements upon generation of
strained carbenium ions in the gas phase is, in part, due to the
methods of ionization. In the past, most bridgehead cations,
and also simple tertiary ions, were generated in the gas phase
by electron ionization of halogen derivatives with ionization
energies in the range of 9-12 eV (213-276 kcal/mol). Ions
thus obtained were then subject to halide exchange reactions,
and the equilibrium constants were determined by ICR and high
pressure mass spectrometry (HPMS).7 The energies used in
the ionization process are large enough to break not only the
carbon-halogen bond, but also other bonds, as shown by the
extensive fragmentation often observed, and the frequently low
yields of the ions of interest. Under these conditions, rear-
rangements of such ions are to be expected.
Recently, one of us8 used Fourier transform ion cyclotron
resonance spectroscopy (FT ICR) to develop a method for
determination of ion stabilities based on dissociative proton
attachment (DPA) of halides. Protonation of halides R-X
produces weakly associated complexes which decay almost
without activation to free ions and HX. The FT ICR experi-
ments allow one to determine the bases B such that their
conjugate acids BH+ are just able to transfer a proton to R-X,
according to reaction 1:
† “Rocasolano”, Madrid.
‡ Universidad de Henares.
§ Flinders University.
Universite´ de Gene`ve.
X Abstract published in AdVance ACS Abstracts, February 1, 1997.
(1) Wiberg, K. B.; Hadad, C. M.; Sieber, S.; Schleyer, P. v. R. J. Am.
Chem. Soc. 1992, 114, 5820-5828. Sieber, S.; Schleyer, P. v. R.; Gauss,
J. J. Am. Chem. Soc. 1993, 115, 6987-6988. Siehl, H.-U.; Mu¨ller, T.;
Gauss, J.; Buzek, P.; Schleyer, P. v. R. J. Am. Chem. Soc. 1994, 116, 6384-
6387.
R-X(g) + BH+(g) f R+(g) + HX(g) + B(g) ∆G°(1)
(1)
(2) Laube, T. Angew. Chem., Int. Ed. Engl. 1987, 26, 560-562. Laube,
T. HelV. Chim. Acta 1994, 77, 943-956. Laube, T. Angew. Chem., Int.
Ed. Engl. 1986, 25, 349-350. Hollenstein, S.; Laube, T. J. Am. Chem.
Soc. 1993, 115, 7240-7245. Laube, T. Acc. Chem. Res. 1995, 28, 399-
405.
(3) Lias, S. G.; Bartmess, J. E.; Liebman, J. F.; Holmes, J. L.; Levin, R.
D.; Mallard, W. G. NIST Standard Reference Database 19A, Computerized
Version 1.1. Standard reference data, NIST, Gaithersburg, MD 20899, 1989.
(4) Arnett, E. M.; Pienta, N. J. J. Am. Chem. Soc. 1980, 102, 3329-
3334. Arnett, E. M.; Flowers, R. A., II; Meekhof, A. E.; Miller, L. J. Am.
Chem. Soc. 1993, 115, 12603-12604. Arnett, E. M.; Flowers, R. A., II
Chem. Soc. ReV. 1993, 22, 9. Kramer, G. M.; Vicker, G. B. Acc. Chem.
Res. 1986, 19, 78.
X ) OH, halogen
For such a base, ∆G°(1) ≈ 0 (see ref 8).
The gas-phase basicity of B is expressed with respect to NH3,
according to:
+
NH4 (g) + B(g) f BH+(g) + NH3(g) ∆G°H+(g)
(7) (a) Mu¨ller, P.; Milin, D.; Feng, W. Q.; Houriet, R.; Della, E. W. J.
Am. Chem. Soc. 1992, 114, 6169-6172. (b) Mu¨ller, P.; Mareda, J.; Milin,
D. J. Phys. Org. Chem. 1995, 8, 507-528.
(8) Abboud, J.-L. M.; Notario, R.; Ballestros, E.; Herreros, M.; Mo´, O.;
Ya´n˜ez, M.; Elguero, J.; Boyer, G.; Claramunt, R. J. Am. Chem. Soc. 1994,
116, 2486-2492.
(5) Fort, R. C. In Carbonium Ions, Olah, G. A., Schleyer, P. v. R., Eds.;
Wiley: New York, 1972; Vol. IV, Chapter 32.
(6) Bingham, R. C.; Schleyer, P. v. R. J. Am. Chem. Soc. 1971, 93, 3189-
3199. Schleyer, P. v. R. In Cage Hydrocarbons Olah, G. A., Ed.; Wiley:
New York, 1990; Chapter 1.
S0002-7863(96)02319-0 CCC: $14.00 © 1997 American Chemical Society

Stability of Bridgehead Carbocations
J. Am. Chem. Soc., Vol. 119, No. 9, 1997 2263
+
of its supraconducting magnet, 4.7 T, allows the monitoring of ion
molecule reactions for relatively long periods of time.
∆G°H (g) is the basicity of the base B, relative to ammonia,
which leads to the DPA embodied in eq 1.9 In the DPA method,
ionization is effected essentially under thermal conditions, so
that the ions have much less opportunity to rearrange than when
generated upon electron impact as in the standard ICR approach.
We have now applied the method to a series of highly strained
bridgehead bromides. In addition, the method was extended
to alcohols, and this allowed the determination of ion stabilities
for structures where the bromo derivatives were not isolable.
C. Bromide Exchange Experiments. The equilibrium constant
Kp for reaction 2a, the exchange of bromide between the carbenium
+
+
ions R1 and R2 in the gas phase, has been determined directly in
some instances, by means of the standard experimental technique
already used by a number of workers, including Beauchamp,19 Taft,20
Kebarle21 (the latter used high pressure mass spectrometry instead of
ICR) and ourselves.7a
R1-Br(g) + R2+(g) a R2-Br(g) + R1+(g) Kp
(2a)
II. Experimental Section
Kp values defined through eq 2b were obtained by combining the ratio
of the intensities of R1+ to R2+ (taken as a measure of the ratio of the
partial pressures of these ions) with the ratio of the partial pressures of
the neutral reagents.
A. Synthesis of Alcohols and Bromides. The compounds used
in this study were either purchased or synthesized according to
procedures reported in the literature. Thus 2-tert-butyladamantan-2-
ol (1a) and 9-tert-butylbicyclo[3.3.1]nonan-9-ol (2b) were obtained by
reaction of tert-butyllithium with 2-adamantanone and 9-bicyclo[3.3.1]-
nonan-2-one, respectively.10 1-Bromobicyclo[2.2.2]octane (4) was
synthesized according to the procedure of Morita et al.11 Bromocubane
(6), 6-bromotricyclo[3.2.1.03,6]octane (10), homocubane-4-carboxylic
acid, and 1-bromohomocubane (8) were prepared as described.12
3-Bromonoradamantane (7) was synthesized in 94% yield by oxidative
decarboxylation of 3-noradamantanecarboxylic acid.13 1-Bromonor-
bornane (9)14 was accessible from the chloride by halide exchange.15
4-Bromohomocubane (5). Homocubane-4-carboxylic acid (0.30 g,
1.85 mmol) and 1-hydroxypyridine-1(1H)-thione (0.24 g, 1.85 mmol)
were dissolved in dichloromethane (15 mL); the solution was cooled
to 0 °C under an atmosphere of nitrogen. Dicyclohexylcarbodiimide
(0.40 g) was added in one portion, and the mixture was stirred for 2 h.
Dicyclohexylurea was filtered off and washed with dichloromethane
(2 mL) and the washings combined with the filtrate and evaporated at
room temperature. The residue was dissolved in 1-chloro-2,2,2-
trifluoroethane (4 mL) and the solution irradiated with a tungsten lamp
(300 W) for 1 h). The solution was cooled, washed succeedingly with
cold concentrated HCl (3 mL) and saturated sodium bicarbonate solution
(3 mL), and then dried (MgSO4). Careful removal of the solvent and
distillation (Kugelrohr: 90 °C/0.1 mm) of the residue gave 4-bromo-
homocubane (0.26 g, 71%), which had identical properties with those
reported.16
Kp ) [P(R2Br)/P(R1Br)][P(R1+)/P(R2+)]
(2b)
The standard Gibbs energy change for reaction 2a, ∆G°(2a) is given by
the equation
∆G°(2a) ) -RT ln Kp
D. Dissociative Proton Attachment Method (DPA). The basic
concepts of the method and its thermodynamic implications have been
developed in ref 8 and are summarized in the Introduction. The general
procedure for the generation of a carbenium ion R+(g) starting from
R-X(g) (X ) Br, OH) is as follows. A mixture of known composition
of R-X(g) and a base (B(g) is prepared. The mixture is introduced
into the high-vacuum section of the instrument and subjected to electron
ionization (generally using nominal energies of 10-13 eV). Nominal
pressures of R-X(g) are in the range of 1-2 10-7 mbar. Pressures of
B are some 3 to 20 times larger, depending on the system. Charged
fragments (mostly from B) act as primary ion sources. In general, after
1-2 s, the main ions present are BH+(g) and R+(g). Then, depending
on the system, one of the following series of experiments was
performed.
1. Determination of DPA Thresholds. This is carried out
according to the procedure described in ref 8: First, the system is
allowed to evolve for at least 5 s, and all ions, with the exception of
BH+(g), are ejected off the ICR cell22 by means of radiofrequency
ejection “chirps” (broad band). Great care is taken in order to avoid
the excitation of this ion, and so use is made of an “ejection safety
belt” (a feature of the Bruker software that strictly prevents the
irradiation of a preselected frequency range around the resonance energy
of BH+ in order to avoid its accidental excitation). BH+(g) is then
allowed to react for times of up to 100 s. During this period of time,
the main reactions observed are, first the formation of R+(g), and later
on that of the hydrogen-bonded dimers of B, B2H+(g), and, eventually,
variable amounts of (B-R)+(g). The formation of B2H+(g) is frequently
met in proton-exchange studies. The formation of (B-R)+(g) is a
consequence of both the electrophilicity of R+(g) and the stability of
this ion with respect to proton donation to B(g).
Given the very low working pressures prevailing in the experiments,
reaction 1 is essentially irreversible (the partial pressure of XH is
extremely small), and so, while a true equilibrium is not reached, the
onset of this process can be clearly determined.
2. DPA-Bromide Exchange Experiments. Here, features of both
methods are combined. It is useful when one of the halides, say R2-
Br, is likely to lead to secondary reactions. This is the case of the
cubyl derivatives (particularly 6 and 8) (this may be related to the fact
B. The FT ICR Spectrometer. The study was carried out on a
modified Bruker CMS-47 FT ICR mass spectrometer17 used in previous
studies.8,18 A detailed description is given in refs 10 and 11. Some
modifications have been introduced with respect to the standard
instrument. They are described in ref 18. The substantial field strength
(9) The values of the gas-phase basicities of the reference compounds
were taken from ref 3. They originate mostly from determinations carried
out in Professor R. W. Taft’s laboratory.
(10) (a) Bartlett, P. D.; Lefferts, E. B. J. Am. Chem. Soc. 1955, 77, 2804,
2805. (b) Peters, E. N.; Brown, H. C. J. Am. Chem. Soc. 1975, 97, 2892-
2895.
(11) Suzuki, Z.; Morita, K. J. J. Org. Chem. 1967, 32, 31-34. Morita,
K.; Kobayashi, T. J. Org. Chem. 1966, 31, 229-232.
(12) (a) Compound 6: Della, E. W.; Tsanaktidis, J. Aust. J. Chem. 1989,
42, 61-69. Della, E. W.; Head, N. J.; Mallon, P.; Walton, J. J. Am. Chem.
Soc. 1992, 114, 10730-10738. (b) Compound 10: Della, E. W.; Janowski,
W. K.; Pigou, P. E. Aust. J. Chem. 1992, 45, 1205-1211. (c) Compound
8: Eaton, P. E.; Yip, Y. C. J. Am. Chem. Soc. 1991, 113, 7692-7697. (d)
Homocubane-4-carboxylic acid: Della, E. W.; Head, N. J.; Janowski, W.
K.; Schiesser, C. H. J. Org. Chem. 1993, 58, 7876-7882.
(13) (a) Della, E. W.; Patney, H. K. Synthesis 1976, 251-252. (b) Olah,
G. A.; Lee, C. S.; Prakash, G. K. S.; Moriarty, R. M.; Rao, R. M. S. J. Am.
Chem. Soc. 1993, 115, 10278-10732.
(14) Rieke, R. W.; Bates, S. E.; Hudnell, P. M.; Pointdexter, G. S. Org.
Synth. 1980, 59, 85-94.
(15) MacKinley, J. W.; Pincock, R. E.; Scott, W. B. J. Am. Chem. Soc.
1973, 95, 2030-2032.
(19) Staley, R. H.; Wieting, R. D.; Beauchamp, J. L. Am. Chem. Soc.
1977, 99, 5964-5972 and references therein.
(16) Paquette, L. A.; Ward, J. S.; Boggs, R. A.; Farnham, W. B. J. Am.
Chem. Soc. 1975, 97, 1108-1112.
(20) Abboud, J.-L. M.; Hehre, W. J.; Taft, R. W.; J. Am. Chem. Soc.
1976, 98, 6072-6073.
(17) Laukien, F. H.; Allemann, M.; Bischofberger, P.; Grossmann, P.;
Kellerhals, Hp.; Kofel, P. In Fourier Transform Mass Spectrometry,
EVolution, InnoVation and Applications; Buchanan, M. V., Ed.; ACS
Symposium Series 359; American Chemical Society: Washington, DC,
1987; Chapter 5, p 81.
(21) Sharma, R. D.; Ben Charma, D. K.; Hiraoka, K.; Kebarle, P. J.
Am. Chem. Soc. 1985, 107, 3747-3573.
(22) Soo, O. G.; Buchanan, M. V.; Comisarow, M. R. In Fourier
Transform Mass Spectrometry, EVolution, InnoVation and Applications;
Buchanan, M. V., Ed.; ACS Symposium Series 359; American Chemical
Society: Washington, DC, 1987; Chapter 1.
(18) Abboud, J.-L. M.; Herreros, M.; Notario, R.; Esseffar, M.; Mo´, O.;
Ya´n˜ez, M. J. J. Am. Chem. Soc. 1996, 118, 1126-1130.

2264 J. Am. Chem. Soc., Vol. 119, No. 9, 1997
Abboud et al.
a
Table 1. Experimentally Determined Gibbs Energy Changes for Reaction 2a, ∆G°(2a)
+
+
R1Br
R2
∆G°(2a)
R1Br
R2
∆G°(2a)
1-bromoadamantane
2-bromo-2-methylpropane
bromocubane
2-norbornyl
-2.3 (0.3)b
3.0 (0.3)b
0.5 (0.3)d
4-bromohomocubane
1-bromohomocubane
bicyclo[2.2.2]octylc
1-norbornylc
2.5 (0.3)d
2-norbornyl
-0.6 (0.3)d
3-noradamantylc
a All values in kcal mol-1. Estimated uncertainties are given in parentheses. b Values obtained by the standard bromide exchange method. c Ions
generated by the DPA technique. d Values obtained by combining DPA and bromide exchange. See text.
Table 2. Experimentally Determined DPA Thresholds for Reaction 1a
e
referenceb (∆GB)c
referenced (∆GB)a
∆G°H (g)
+
compound
1a 2-tert-butyl-2-adamantanol
2a 9-tert-butyl-9-bicyclo[3.3.1]nonanol
3a 1-adamantanol
n-BuNH2 (-15.6)
n-PrNH2 (-15.1)
n-Bu2S (-5.6)
EtC(O)NMe2 (-16.6)
n-BuNH2 (-15.6)
pyrazine (-6.1)
t-BuOMe (2.2)
-16.1
-15.4
-5.9
2.5
3b 1-bromoadamantane
Et2CO (2.8)
4 1-bromobicyclo[2.2.2]octane
7 3-bromonoradamantane
Me2CHCN (10.6)
MeCHO (18.0)
Cl3CCN (27.5)
(CF3CH2)2O (33.3)
HCO2n-Pr (10.5)
MeSH (16.9)
Cl3CCH2OH (26.0)
H2CO (30.8)
10.6
17.5
26.8
32.1
9 1-bromonorbornane
10 6-bromotricyclo[3.2.1.03,6]octane
a All values in kcal mol-1 b Strongest base able to lead to DPA. c Gas-phase basicities of the reference bases, relative to ammonia (see test).
.
d Weakest base not leading to DPA. e Average of two (∆GB) values.
that cubane has a high gas-phase basicity, well above the DPA
IV. Discussion
thresholds of all the bromides studied in this work23).
Consider two compounds, R1X and R2X. It can be easily
shown that the difference of their DPA thresholds equals the
standard Gibbs energy change for reaction 3:
The study is carried out with a mixture of known amounts of R1-
Br(g) and R2-Br(g) and B(g) under conditions similar to those given
above. The gas-phase basicity of B is close to, but lower than the
DPA threshold of R1-Br(g), the “well-behaved halide”. Some 5 s after
electron ionization of the mixture, BH+(G) is selcted and allowed to
react with R1-Br(g) and R2-Br(g). Of the various ions formed, R1+(g)
is selected and its reaction monitored. The relevant process taking place
under these conditions is reaction 2a. After reaction time of up to 20
s, Kp values are determined by means of eq 2b as in the standard halide
exchange method.
+
+
R1X(g) + R2 (g) a R2X(g) + R1 (g)
(3)
This important fact allows us to unify the results obtained by
halide exchange and DPA (see Experimental Section). The
+
results are summarized as ∆G°H (g) values in Table 4. Also
given are the ion stabilities expressed relative to the 1-adamantyl
cation (Ad+) by means of ∆G°(4), the standard Gibbs energy
change for reaction 4:
The experimental uncertainties on ∆G°(2a) are estimated to be at least
0.3 kcal mol-1. This is the usual size of uncertainties affecting relative
gas-phase basicities studied by means of proton-exchange reactions.
Here, the situation is less favorable because of (a) the absence of
appropriate references to carry out multiple overlap studies and (b) the
fact that some of the Kp values are large. As indicated above,
R+(g) + Ad-X(g) f R-X + Ad+(g) ∆G°(4)
(4)
+
uncertainties on ∆G°H (g), the DPA thresholds, are estimated to 2 kcal
The ∆G°(4) values for 2-bromo-2-tert-butyladamantane (1b)
and 9-bromo-9-tert-butylbicyclo[3.3.1]nonane (2b) were deter-
mined by combining the experimental ∆G°(4) values of the
corresponding alcohols 1a and 2a, respectively, relative to
1-adamantanol (Ad-OH, 3a) with the standard Gibbs energy
changes for the isodesmic reactions 4a:
mol-1
.
Tables 1 and 2 summarize the experimental results obtained in this
work.
III. Computational Details
All the structures studied in this work were fully optimized
at the HF/6-31G* level.24 The harmonic vibrational frequencies
were determined analytically and used to compute the corre-
sponding zero-point energies (scaled by a factor of 0.9135),25
thermal corrections, and entropies. The structures of the carben-
ium ions R+ having between 4 and 10 carbon atoms as well as
those of the corresponding hydrocarbons, R-H, were further
subject to a complete optimization at the MP2/6-311** level.
All calculations were performed on a Silicon Graphics “Chal-
lenge” Computer, using the Gaussian 94 (Revision B.3)26 pro-
gram. The results of these calculations are collected in Table
3.
Ad-Br(g) + R-OH(g) f Ad-OH(g) + R-Br(g) ∆G°(4a)
(4a)
The ∆G°(4a) values for 1b and 2b amount to 5.68 and 5.64
kcal/mol, respectively, at the 6-31G* level.24 It should be
emphasized that the ranking of stabilities of carbenium ions is
independent of the nature of X. Results to be published
elsewhere obtained with chlorides, bromides and alcohols are
in remarkably good agreement.
In Figure 1 ∆G°(4) values are plotted against the standardized
rates of solvolysis (log k for solvolysis with OTs leaving groups,
in 80% EtOH at 70°, relative to 1-adamantyl-p-toluene-
sulfonate).27,28 The correlation spans about 23 log units for k.
Taking into account that at 70° one order of magnitude in rate
constants corresponds to 1.57 kcal mol-1 in Gibbs energy of
activation, this amounts to 36.1 kcal mol-1 and almost 50 kcal/
mol in Gibbs energies for bromide exchange. It covers
practically the full experimental rate range for solvolytic
bridgehead reactivities, including the previously not accessible
1-homocubyl (8+), 1-norbornyl (9+), and 6-tricyclo[3.2.1.03,6]-
(23) Santos, I.; Balogh, D. W.; Doecke, C. W.; Marshall, A. G.; Paquette,
L. J. Am. Chem. Soc. 1986, 108, 8184-8189.
(24) Hehre, W. J.; Radom, L.; Schleyer, P. v. R.; Pople, J. A. Ab Initio
Molecular Orbital Theory; Wiley-Interscience: New York, 1986; Chapter
4.
(25) Pople, J. A.; Scott, A. P.; Wong, M.; Radom, L. Isr. J. Chem. 1993,
33, 345-350.
(26) Frisch, M. J.; Trucks, C. W.; Schlegel, H. B.; Cill, D. M. C.; Johnson,
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.; Peng, C. Y.; Ayala, P. Y.; Chen, W.;
Wong, M. W.; Andre´s, J. L.; Replogle, E. S.; Gomperts, R.; Martin, R. L.;
Fox, D. J.; Binley, J. S.; Defrees, D. J.; Baker, J.; Stewart, J. P.; Head-
Gordon, M.; Gonza´lez, C.; Pople, J. A. Gaussian, Inc.: Pittsburgh, PA,
1995.
(27) Mu¨ller, P.; Milin, D. HelV. Chim. Acta 1991, 74, 1808-1816.
(28) Della, E. W.; Janowski, W. K. J. Org. Chem. 1995, 60, 7756-
7759.

Stability of Bridgehead Carbocations
J. Am. Chem. Soc., Vol. 119, No. 9, 1997 2265
Table 3. Total Energiesa at HF/6-31G* and MP2/6-311G** Levels, Zero-Point Vibrational Energies (ZPE)a Thermal Correction to Enthalpies
(TCE)a and Total Entropy Values (S)b for the Species Studied in this Work
compound
HF/6-31G*
MP2/6-311G**
ZPEa,d
TCEa
Sd
2-tert-butyladamantane
2-tert-butyl-2-adamantanol
9-tert-butylbicyclo[3.3.1]nonane
9-tert-butylbicyclo[3.3.1]nonanol
adamantane
1-adamantyl
adamantanol
1-bromoadamantane
bicyclo[2.2.2]octane
bicyclo[2.2.2]oct-1-yl
1-bromobicyclo[2.2.2]octane
homocubane
1-homocubyl
1-bromohomocubane
4-homocubyl
4-bromohomocubane
cubane
cubyl
bromocubane
noradamantane
3-noradamantyl
3-bromonoradamantane
norbornane
1-norbornyl
1-bromonorbornane
2-norbornyl
-544.143 796
-618.988 536
-506.257 855
-581.102 266
-388.026 478
-387.180 304
-462.882 909
-295.345 085
-311.103 599
-310.246 490
-2880.421 136
-346.504 487
-345.615 165
-2915.819 435
-345.623 485
-2915.821 215
-307.393 906
-306.507 589
-2876.710 581
-348.970 068
-348.101 166
-2918.285 595
-272.061 201
-271.181 170
-2841.376 669
-271.200 613
-2841.375 277
-309.903 129
-309.011 188
-2879.217 708
-157.298 978
-156.442 549
-2726.614 852
0.349 717
0.354 724
0.342 348
0.347 479
0.238 762
0.226 767
0.242 844
0.229 210
0.202 363
0.190 446
0.192 931
0.162 206
0.149 358
0.152 663
0.148 791
0.152 729
0.132 288
0.118 599
0.122 858
0.209 766
0.197 097
0.200 176
0.173 604
0.161 343
0.164 133
0.160 967
0.164 463
0.179 783
0.167 197
0.170 292
0.128 600
0.107 725
0.119 514
0.354 133
0.359 711
0.347 478
0.353 159
0.239 823
0.228 254
0.245 876
0.232 853
0.204 244
0.192 716
0.197 301
0.163 174
0.150 943
0.156 227
0.150 585
0.156 351
0.133 396
0.120 335
0.126 558
0.215 414
0.198 642
0.203 675
0.174 930
0.163 263
0.167 951
0.163 067
0.168 159
0.180 847
0.168 928
0.173 921
0.131 140
0.111 480
0.124 134
102.08
103.48
104.25
106.15
79.86
80.27
84.58
88.80
81.85
80.73
90.07
72.43
73.41
81.89
74.28
82.37
69.62
70.45
79.55
76.38
77.62
85.55
73.79
74.92
82.99
76.84
83.14
73.68
74.88
83.05
71.18
75.65
77.15
-389.592 731
-388.705 010
-312.388 487
-311.464 498
-347.859 363
-346.924 581
-346.947 954
-308.580 611
-307.665 563
-350.376 567
-349.461 809
-273.164 341
-272.235 168
-272.269 098
2-bromonorbornane
tricyclo[3.2.1.03,6]octane
6-tricyclo[3.3.1.03,6]octyl
6-bromotricyclo[3.2.1.03,6]octane
2-methylpropane
tert-butyl
2-bromo-2-methylpropane
-311.146 170
-310.205 790
-157.964 175
-157.056 582
a In hartree. b In kcal mol-1 K-1 c Evaluated at HF/6-31G* level. d ZPE values corrected by the factor 0.9135.25
.
Table 4. Experimental and Theoretical Data for Gas-Phase and Solution Reactionsa
+
compound
∆G°H (g)
∆G°(4)
∆G°(5)
-8.0
∆G°(6)
2.2
2.2
1.4
1.4
0.0
∆G°(6)(th)
∆log ksolv
1a 2-tert-butyl-2-adamantanol
1b 2-tert-butyl-2-bromoadamantane
2a 9-tert-butyl-9-bicyclo[3.3.1]nonanol
2b 9-tert-butyl-9-bromobicyclo[3.3.1]nonane
3a 1-adamantanol
3b 1-bromoadamantane
4 1-bromobicyclo[2.2.2]octane
5 4-bromohomocubane
-16.1
10.2b
15.9c,d
9.5b
8.8
8.6
-15.4
-8.1
15.1c,d
0.0b
-5.9
2.5
10.6
0.0d
0.0d
-0.9
-1.0
-0.6
-1.8
-2.1
-2.0
-2.5
-2.9
-2.6
0.0
-9.0
0.0
8.5
0.0
-3.6
-8.1d
-10.6d,e
14.5d,e
-15.0d
-23.7d,e
-24.3d
-29.6d
-2.3d,f
-5.9d,f
-11.6
-15.1
-16.8
-25.8
-26.3
-32.1
-5.2 (-5.9)g
-8.5 (-8.2)g
-14.7
-16.3
-16.9
-29.3
-26.2
-33.1
-5.3
-5.9h
-7.3
6 bromocubane
7 3-bromonoradamantane
8 1-bromohomocubane
17.5
-6.9
-11.0h
-10.1
-13.9h
9 1-bromonorbornane
26.8
32.1
10 6-bromotricyclo[3.2.1.03,6]octane
11 2-bromonorbornane
12 2-bromo-2-methylpropane
-8.6
a All Gibbs energies in kcal mol-1 b Relative to 3a. c Calculated as indicated in the text. d Relative to 3b. e Determined as indicated in the text.
.
f Determined by the standard bromide method. See text and Table 1. g Experimental value from Kebarle and co-workers.21 h Extrapolated from
triflate solvolysis.28
octyl (10+) cations. To our knowledge, this is the widest range
ever reported for correlation of gas-phase data and solution
kinetics. Correlation coefficient (r ) 0.9957) and standard
deviation (σ ) 0.77 on log k) are very satisfactory. The slope
of the correlation between log k and the ion stabilities (-0.49)
implies that 77% of the energy difference between the bromides
and the respective cations are expressed in the rates of solvoly-
sis. This slope compares favorably with that of -0.39 relating
log k with strain changes between R+ and R-Br.5-7 The
consistency between the two sets of experimental data supports
fully the basic mechanistic concepts on bridgehead solvoly-
sis.
ions more strained than bicyclo[2.2.2]octyl (4+). The rear-
rangement of the norbornyl cation (9+) under ICR conditions
has been noted previously.7a It now appears, that, in addition,
the cubyl (6+) and 3-noradamantyl (7+) cations might also have
undergone rearrangement in the ICR spectrometer and are
slightly less stable than previously suggested.
Since the ion stabilities in the gas phase are free of solvation
effects, they represent intrinsic properties and are, therefore,
amenable to rigorous quantum chemical calculations. Since no
experimental data are available for the energy of the majority
of the neutral species, a leaving group correction (∆G°(5)) was
applied to the ∆G°(4) values as defined by eq 5:
Comparison of the present set of cation stabilities with the
previous one, determined by ICR,7a reveals discrepancies for
R-X(g) + Ad-H(g) f R-H(g) + Ad-X(g) ∆G°(5) (5)

2266 J. Am. Chem. Soc., Vol. 119, No. 9, 1997
Abboud et al.
Figure 2. Calculated (MP2/6-311G**) Vs experimental standard Gibbs
energy changes for reaction 6. Values in parentheses are standard
deviations.
Figure 1. Log ksolv values relative to 1-adamantyl Vs experimental
standard Gibbs energy changes (∆G°(4) for bromide exchange in the
gas phase (reaction 4). Values in parentheses are standard deviations.
Data from Table 4.
confirms that no rearrangements took place in the DPA
experiments. It also lends credibility to the empirical force-
field calculations which predicted the same trends with much
simpler means.7
Owing to the large number of atoms in these molecules, and
since only neutral species are involved, this corrective term
(∆G°(5)) was computed only at the HF 6-31G*//6-31G* level,
but, nevertheless, with full energy optimization (see Experi-
mental Details). In the bridgehead series, ∆G°(5) varies in a
rather narrow range from -0.9 to -2.6 kcal/mol; however, in
the case of 1a and 2a the values are -8.0 and -8.1, respectively.
This suggests that the high solvolytic reactivity of 1a and 2a,
as well as that of the corresponding bromides, is due to a front-
strain effect,29 and not to some particular stabilization of the
carbenium ions. Although this F-strain effect is treated
adequately by force-field calculations of 1a,b and 2a,b,
respectively, it was not recognized as such in the past.27
Combination of eqs 4 and 5 leads to eq 6 for hydride exchange
between R+ and adamantane (Ad-H):
The unusually high stability of the 2-norbornyl cation (11+)
has been the subject of much controversy in the past.30 It is of
interest to note that the secondary 11+ lies nicely on the
correlation line in Figure 2, although the latter is defined by
tertiary ions. The stability of the 2-norbornyl cation (11+) is
close to that of the 1-adamantyl cation (3+). It is much more
stable than simple “classical” secondary or strained tertiary
carbenium ions (see below). Our MP2/6-311G** calculations
lead to a structure of 11+ in which the carbon-carbon bond
lengths agree within 0.04 Å or better with that reported by
Jorgensen, Schleyer, Schaefer, and co-workers31 in a recent high-
level theoretical study on the stability of this ion in the gas phase
and in solution. All these results are obviously in agreement
with the nonclassical structure of 11+.
R+(g) + Ad-H(g) f R-H(g) + Ad+(g) ∆G°(6) (6)
Our results demonstrate the overwhelming significance of
strain on the stability of tertiary carbenium ions, which may be
destabilized to such a degree that they lie in the range of
secondary ions. Chloride exchange reactions in the gas phase
reveal an enthalpy difference of 14.6 kcal/mol between the tert-
butyl and the 2-propyl cation.21 With the same difference we
assign a ∆G°(6) value of about -20.6 kcal/mol to the 2-propyl
cation, which would place it between the 3-noradamantyl (7+)
and 1-homocubyl (8+) cations, but almost 10 kcal/mol above
10+ (6-tricyclo[3.2.1.03,6]octyl cation), the least stable of the
tertiary cations of this series.
Kebarle et al. have used high-pressure mass spectrometry to
directly determine ∆G°(4) for the 2-norbornyl (11+) and tert-
butyl (12+) cations.21 Their experimental values, which are also
included in Table 4, are in excellent agreement with the values
reported here.
In order to secure completely independent evidence for the
absence of rearrangements for the systems studied in this work,
thermodynamic Gibbs energy changes for the relevant reactions,
∆G°(6)(th), were determined by means of high-level ab initio
calculations (see Experimental Details) for compounds having
up to 10 carbon atoms. The calculated values for ∆G°(6)(th)
are given in Table 4. Figure 2 shows a plot of ∆G°(6)(th) in
function of the experimental values for hydride transfer ∆G°(6)-
(exp), after leaving group correction according to eq 4a and eq
5.
Acknowledgment. This work was supported by the Spanish
D.G.I.C.Y. T. (Grant PB93-0142-C03-01 to J.-L.A., and Grant
PB93-0289-C-02-02 to R.N.), the Swiss National Science
Foundation (Grant No. 20-32′117.91 to P.M.) and the Australian
Research Council (Grant No. A 29232151 to E.W.D.).
As Figure 2 shows, the two sets of data correspond almost
perfectly. The agreement between theoretical and experimental
values provides strong support for the experimental method and
JA962319I
(30) (a) Grob, C. A. Acc. Chem. Res. 1983, 16, 426-431. (b) Brown,
H. C. Acc. Chem. Res. 1983, 16, 432-440. (c) Olah, G. A.; Prakash, G.
K. S.; Saunders, M. Acc. Chem. Res. 1983, 16, 440-448.
(31) Schreiner, P. R.; Severance, D. L.; Jorgensen, W. L.; Schleyer, P.
v. R.; Schaefer, H. F., III J. Am. Chem. Soc. 1995, 117, 2663-2664.
(29) (a) Slutsky, J.; Bingham, R. C.; Schleyer, P. v. R.; Dickason, W.
C.; Brown, H. C. J. Am. Chem. Soc. 1974, 96, 1969, 1970. (b) Tidwell, T.
T. J. Org. Chem. 1974, 39, 3533-3537.