Hyperaromatic stabilization of arenium ions: Cyclohexa- and cycloheptadienyl cations-experimental and calculated stabilities and ring currents

Article abstract of DOI:10.1021/ja2071626

Measurements of pK_R show that the cycloheptadienyl cation is less stable than the cyclohexadienyl (benzenium) cation by 18 kcal mol ^-1. This difference is ascribed here to "hyperaromaticity" of the latter. For the cycloheptadienyl cation a value of K_R = [ROH][H⁺]/[R⁺] is assigned by combining a rate constant for reaction of the cation with water based on the azide clock with a rate constant for the acid-catalyzed formation of the cation accompanying equilibration of cycloheptadienol with its trifluoroethyl ether in TFE-water mixtures. Comparison of pK_R = -16.1 with pK_R = -2.6 for the cyclohexadienyl cation yields the difference in stabilities of the two ions. Interpretation of this difference in terms of hyperconjugative aromaticity is supported by the effect of benzannelation in reducing pK_R for the benzenium ion: from -2.6 down to -3.5 for the 1H-naphthalenium and -6.0 for the 9H-anthracenium ions, respectively. MP2/6-311+G* and G3MP2 calculations of hydride ion affinities of benzenium ions show an order of stabilities for substituents at the methylene group consistent with their hyperconjugative abilities, i.e., (H₃Si)₂ > cyclopropyl > H ₂ > Me₂> (HO)₂ > F₂. Calculations of ring currents show a similar ordering. No conventional ring current is seen for the cycloheptadienyl cation, whereas currents in the F ₂-substituted benzenium ion are consistent with antiaromaticity. Arenium ions where the methylene group is substituted with a single OH group show characteristic energy differences between conformations, with C-H or C-OH bonds respectively occupying or constrained to axial positions favorable to hyperconjugation. The differences were found to be 8.8, 6.3, 2.4, and 0.4 kcal mol^-1 for benzenium, naphthalenium, phenanthrenium, and cyclohexenyl cations, respectively.

Full text of DOI:10.1021/ja2071626

ARTICLE
pubs.acs.org/JACS
Hyperaromatic Stabilization of Arenium Ions: Cyclohexa- and
Cycloheptadienyl Cations—Experimental and Calculated
Stabilities and Ring Currents
David A. Lawlor,† David E. Bean,‡ Patrick W. Fowler,‡ James R. Keeffe,§ Jaya Satyanarayana Kudavalli,†
Rory A. More O’Ferrall,*,† and S. Nagaraja Rao†
†School of Chemistry and Chemical Biology, University College Dublin, Belfield, Dublin 4, Ireland
‡Department of Chemistry, University of Sheffield, Sheffield S3 7HF, U.K.
§Department of Chemistry and Biochemistry, San Francisco State University, San Francisco, California 91432, United States
S Supporting Information
b
ABSTRACT: Measurements of pKR show that the cyclohepta-
dienyl cation is less stable than the cyclohexadienyl
(benzenium) cation by 18 kcal molꢀ1. This difference is
ascribed here to “hyperaromaticity” of the latter. For the
cycloheptadienyl cation a value of KR = [ROH][H+]/[R+] is
assigned by combining a rate constant for reaction of the cation
with water based on the azide clock with a rate constant for the
acid-catalyzed formation of the cation accompanying equilibra-
tion of cycloheptadienol with its trifluoroethyl ether in TFEꢀ
water mixtures. Comparison of pKR = ꢀ16.1 with pKR = ꢀ2.6 for the cyclohexadienyl cation yields the difference in stabilities of the
two ions. Interpretation of this difference in terms of hyperconjugative aromaticity is supported by the effect of benzannelation
in reducing pKR for the benzenium ion: from ꢀ2.6 down to ꢀ3.5 for the 1H-naphthalenium and ꢀ6.0 for the
9H-anthracenium ions, respectively. MP2/6-311+G** and G3MP2 calculations of hydride ion affinities of benzenium ions show
an order of stabilities for substituents at the methylene group consistent with their hyperconjugative abilities, i.e., (H3Si)2 > cyclopropyl >
H2 > Me2> (HO)2 > F2. Calculations of ring currents show a similar ordering. No conventional ring current is seen for the cycloheptadienyl
cation, whereas currents in the F2-substituted benzenium ion are consistent with antiaromaticity. Arenium ions where the methylene group
is substituted with a single OH group show characteristic energy differences between conformations, with CꢀH or CꢀOH bonds
respectively occupying or constrained to axial positions favorable to hyperconjugation. The differences were found to be 8.8, 6.3, 2.4, and 0.4
kcal molꢀ1 for benzenium, naphthalenium, phenanthrenium, and cyclohexenyl cations, respectively.
Scheme 1
’ INTRODUCTION
Two previous papers1,2 have explored evidence for hypercon-
jugative aromaticity of arenium ions based on (a) measurements
of high cis/trans reactivity ratios for acid-catalyzed formation of
the hydroxy-substituted ions from arene dihydrodiols and (b) the
dependence of these values on the expected aromaticity of the
ions, i.e., benzenium >1,2-naphthalenium > 9,10-phenanthrenium.3
Reaction of benzene cis-1,2-dihydrodiol 1 to form a hypercon-
jugatively stabilized 2-hydroxybenzenium ion 2 as the first and
rate-determining step of its acid-catalyzed dehydration to phenol
is illustrated in Scheme 1. It was proposed that the favorable
effect of hyperconjugation is enhanced by the aromatic character
of the no-bond structure 2b, which contributes to resonance
stabilization of the ion.
The slower reactions of the trans compared with cis isomers
of the arenedihydrodiols was suggested to arise from forma-
tion of the arenium ion intermediate in an unfavorable con-
formation 3 in which OH rather than H occupies an axial
position that is optimal for hyperconjugation. The advantage
of an aromatic resonance structure is then offset by the siting
of a positive charge on an oxygen rather than a hydrogen
atom.
Received: July 30, 2011
Published: October 18, 2011
r
2011 American Chemical Society
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Scheme 2
Scheme 3
Scheme 4
In the second paper,2 cis/trans reactivity ratios for 2-HO
groups were compared with those of other 2-substituents in
the acid-catalyzed dehydration of 1,2-dihydro-1-naphthols. With
the exception of groups subject to neighboring group participa-
tion in their trans configuration, an order H < Me < But < Ph <
NH3+ < HO ∼ MeO was established, which is consistent with a
reasonable expectation of relative capacities for σ-interaction
with a positively charged center. It was also shown that while a cis-
β-hydroxyl group caused a nearly constant rate reduction of
∼103-fold for a carbocation-forming reaction, consistent with the
influence of an inductive effect, the effect of a trans-β-hydroxyl
substituent was highly sensitive to the “aromatic” stability of
the arenium ion intermediate, with a maximum rate reduction of
107-fold for formation of a β-hydroxybenzenium ion, consistent
with an additional contribution from loss of hyperconjugative
stabilization of the cation.
intermediate but deprotonation of the cation to form the
cycloheptatriene product.
Determination of a rate constant for carbocation formation is
nevertheless required to evaluate an equilibrium constant for
carbocation formation KR = [ROH][H+]/[R+], where R+ is the
2,4-cycloheptadienyl cation 5, ROH is the 2,4-cycloheptadienol
6, and a value for KR may be deduced from the ratio of rate
constants for formation and reaction of the carbocation with
water, i.e., KR = kH O/kH in Scheme 3.
2
In these circumstances, Richard and Jencks have shown that a
rate constant for carbocation formation may be deduced from
measurements of a rate constant for equilibration of the alcohol
and trifluoroethyl ether in solvent mixtures of water and trifluoro-
ethanol (TFE) (Scheme 4).4 As reaction of the carbocation
with water or TFE is much faster than loss of a proton to form
cycloheptatriene, the latter reaction can be neglected on the time
scale of the equilibration.
The approach to equilibrium may be monitored by HPLC.
Tables S2 and S3 list HPLC peak intensities for cycloheptadienol
and its trifluoroethyl ether as a function of time, for 0.1 and
1.0 M HClO4 in aqueous mixtures containing 30, 50, and 70%
TFE (plus 10% of acetonitrile). From these measurements rate
constants kobs and equilibrium constants Keq for equilibration of
the alcohol and ether may be determined. Expressions for kobs
and Keq in terms of the microscopic rate constants in Scheme 4
are shown in eqs 1 and 2. These equations contain three
unknowns, the rate constants kH and kꢀ2, which represent
acid-catalyzed conversion of cycloheptadienol and its trifluoro-
ethyl ether, respectively, to the carbocation intermediate, and the
ratio of rates for reaction of the carbocation with H2O and TFE,
In the present paper the stability of the benzenium ion
(cyclohexadienyl cation) 4 is compared with that of the cyclo-
heptadienyl cation 5, using equilibrium measurements of ease of
formation from the corresponding alcohol (KR). In the absence
of hyperconjugative aromatic stabilization, the difference in
stability should reflect uncanceled ring strain effects between
cycloheptadienol and the cation 5. Although it is difficult to
predict exact magnitudes for ring strain effects, a sufficiently
large difference may be taken as indicative of stabilization of the
cyclohexadienyl cation not available to its seven-membered
counterpart, for which a no-bond resonance structure contribut-
ing to hyperconjugation does not contain an aromatic ring.
In addition, high-level calculations of the stabilization have
been undertaken to ensure that arguments based on a simple
valence-bond representation of resonance and hyperconjugation
have a firm foundation. The computations assess both energies
and magnetic ring currents.
Finally, a review of the literature identifies other possible
examples of aromatic hyperconjugation. The evidence comes
from spectroscopic properties (IR and NMR) and effects of
benzannelation on the stabilities of arenium ions. It also comes
from reactivities of aromatic molecules toward electrophilic
aromatic substitution and from comparisons of acid-catalyzed
dehydration of arene hydrates (or cis-dihydrodiols) and ring-
opening of arene oxides. It is argued that the breadth and
importance of the influence of this type of aromaticity justifies
the designation “hyperaromatic” for the stabilization of arenium
ions.
k
ꢀ1[H2O]/k2[TFE], denoted x.
kH
xk
ꢀ2
ð1 þ xÞ
kobs
¼
þ
ð1Þ
ð1 þ xÞ
k
½H2Oꢂ
ꢀ1
where
x ¼
k2½TFEꢂ
’ RESULTS
kHk2½TFEꢂ
Keq
¼
k
ð2Þ
Experimental Results. A rate constant for acid-catalyzed
dehydration of 1-hydroxy-2,4-cycloheptadiene (2,4-cyclohepta-
dienol 6, Scheme 2) to form cycloheptatriene 7 in aqueous
solution was determined spectrophotometrically as 6.8 ꢁ
10ꢀ6 Mꢀ1 sꢀ1 (see Experimental Section, Table S1, and Figure S1).
For this reaction, unlike that of arene dihydrodiols,1ꢀ3 the
rate-determining step is not formation of a carbocation
ꢀ1k ½H2Oꢂ
ꢀ2
Experimentally, the value of Keq was taken as the ratio of
concentrations of alcohol 6 and ether when the equilibration
reaction was complete. For both kinetic and equilibrium mea-
surements it was supposed that the extinction coefficients of the
alcohol and trifluoroethyl ether were equal. A value of x was
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Scheme 5
Table 1. Rate and Equilibrium Constants from Kinetic and
Product Analyses of Equilibration of Cycloheptadienol and
Its Trifluoromethyl Ether in TFEꢀH2O Mixtures (v/v) and
0.1 M H+ at 25 °C
%
TFEa
104kobs
(sꢀ1
103kH
(Mꢀ1 sꢀ1
104k
(Mꢀ1 sꢀ1
)
ꢀ2
xb
)
Keq
)
log k/ko
c
30
50
70
27.6
12.6
7.2
6.0
0.195
0.56
1.31
3.3
2.9
8.9
6.1
4.2
ꢀ0.02
0.23
6.05
22.2
11.2
0.66
a Reaction solutions also contain 10% acetonitrile. b [ROH]/[ROTFE]
from ratio of products for solvolysis of dichloroacetoxycycloheptadienol 8.
c Log of ratio of rate constants for dehydration of benzothiophene
hydrate 9 in TFEꢀH2O (k) and water (ko).5
Scheme 6
Scheme 7
Figure 1. Plots of % cycloheptadienol (ROH, b) and its trifluorometh-
yl ether (ROCH2CF3, O) versus time for equilibration in 70% TFE:30%
H2O (v/v) with 0.1 M HClO4 at 25 °C.
determined by generating the carbocation in TFEꢀH2O mix-
tures of the same composition as used for the kinetic and
equilibrium measurements. Partitioning between the two solvent
components gave x as the ratio of alcohol and trifluoroethyl ether
products formed (eq 3). As shown in Scheme 5, the dichlor-
oacetate ester of the cycloheptadienol 8 was used as a precursor
to generate the carbocation. This substrate was chosen because it
of the derived values of kobs is probably not better
than 50%. As will be seen, this level of precision is nevertheless
satisfactory for the purpose of the analysis.
has a convenient half-life (∼100 s, k = (7.4 ( 0.55) ꢁ 10ꢀ3 sꢀ1
)
for solvolysis in water. The solvolysis was monitored by HPLC
Combination of x with kobs and Keq gave the values of kH and
(Table S4).
k
shown in Table 1. However, it should be noted that these
ꢀ2
measurements refer to TFEꢀH2O mixtures. To extrapolate a
value for water, log kH was plotted against values of log k/ko for
the dehydration of benzothiophene hydrate 9, where k and ko are
rate constants for its reaction in a TFEꢀH2O mixture and H2O,
respectively.5 As shown in Scheme 6, formation of the carboca-
tion 10 is rate-determining for this dehydration reaction, which is
judged to be a suitable model for representing solvent effects on
the analogous carbocation formation from cycloheptadienol.
The three-point plot of log kH for cycloheptadienol 6 against
log k/ko for benzothiophene hydrate is shown in Figure S2. The
straight line through the points is drawn with slope 1.0 as
observed for a number of comparable reactions.5 The extra-
polated value of kH in water is (2.6 ( 1.0) ꢁ 10ꢀ3 Mꢀ1 sꢀ1. The
scatter evident in this plot is tolerable because an error as large as
2-fold in kH affects a derived value of pKR for the cyclohepta-
dienyl cation by only 0.3 log unit. As indicated below, the
measurement for water is corroborated by a value for 50%
aqueous TFEꢀH2O mixture requiring no extrapolation.
k
½H2Oꢂ
½ROHꢂ
ꢀ1
x ¼
¼
ð3Þ
k2½TFEꢂ
½ROCH2CF3ꢂ
Plots of percentages of cycloheptadienol and its trifluoro-
ethyl ether as a function of time during their equilibration in 70%
TFE and 30% water in the presence of 0.1 M HClO4 are shown in
Figure 1. As can be seen, instead of reaching constant fractions of
dienol and ether as the reaction approaches equilibrium, at longer
times the mixture contains decreasing percentages of ether. This
is attributed to evaporation and was corrected for as described in
the Experimental Section to give the satisfactory fit of calculated
to experimental measurements shown in the figure. Values of Keq
were based not on measurements of dienol and ether at 0.1 M
HClO4 but on a ratio of concentrations at 1 M acid, at which
(acid) concentration the reaction was much faster than at 0.1 M
and the limiting ratio of dienol to ether remained constant on the
time scale of the experiment (Table S3). For the kinetic
measurements in 50% and 30% TFE, greater scatter of the HPLC
measurements than in Figure 1 was observed, and the precision
To obtain KR for the cycloheptadienyl cation, kH must be
combined with a rate constant kH O for reaction of the ion with
2
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Table 2. Products from Solvolysis of 2,4-Cycloheptadienyl
Dichoroacetate 8 in Aqueous Solution at 25 °C in the
Presence of Sodium Azide
Scheme 8
Scheme 9
[NaN3] (M)
% dienol
% azide
[azide]/[dienol]
0.00
0.10
0.20
0.40
0.60
0.80
100
0.00
11.9
22.3
39.1
44.1
58.2
0.0
88.1
77.7
60.9
55.9
41.9
0.14
0.29
0.64
0.79
1.39
water (Scheme 3). A value of kH O can be obtained from the azide
clock4,6 by trapping the carbocat2ion formed from solvolysis of the
cycloheptadienyl dichloroacetate 8 by reaction with azide ion in
competition with water as shown in Scheme 7. Product proportions
were determined by HPLC. The cycloheptadienyl azide 11 was not
isolated, but the HPLC peak was identified from its retention time
relative to the alcohol, based on the fact that its rate of formation was
the same as that of other products, and by the dependence of the
final peak intensity on the concentration of azide ions.
Scheme 10
Product ratios of cycloheptadienyl azide (RN3) to cyclo-
heptadienol (ROH) for different concentrations of azide ion
are shown in Table 2 and plotted against [N3ꢀ] in Figure S3, to
give a straight line with slope 1.58. The relationship between
product ratio and [N3ꢀ] based on Scheme 7 is given by eq 4, so
that the slope of the plot corresponds to the ratio of rate
constants for reaction of the cycloheptadienyl cation with azide
1,4-cyclohexadiene9 leads to a difference in values of pKR at 25 °C
of 5.5/1.36 = 4.0 and pKR = ꢀ16.1 for 2,6-cycloheptadienol.10
We also wished to estimate the equilibrium constant for
dehydration of the cycloheptadienols to form cycloheptatriene
(eq 5). Guthrie has reported a free energy of formation ΔG°f(aq)
for cycloheptatriene,11 and ΔG° for the equilibria can be found if
ΔG°f(aq) for the cycloheptadienols is known. A value of ΔG°f(g)
for 1,3-cycloheptadiene has been reported,12 and the required
ΔG°f(aq) can be derived if ΔGt, the free energy of transfer to
aqueous solution, and the increment in free energy for re-
placement of H by OH can be estimated. The derivation of
corresponding values for 1,3- and 1,4-cyclohexadienes has been
described,9 and Table S6 summarizes data for saturated and
unsaturated seven-membered rings. Assuming that the effect of
OH substitution in the 1,3-cycloheptadiene is the same as for
1,3-cyclohexadiene (ꢀ39.7 kcal molꢀ1),9 one obtains a value of
ΔG°f(aq) which may be combined with values for cyclohepta-
triene and water in eq 6 to give ΔG° = ꢀ4.9 kcal molꢀ1 and
ions and water, kAz/kH O. With the usual assumption for a
2
carbocation of this stability,6 that the reaction with azide ions is
diffusion controlled with rate constant kAz = 5.0 ꢁ 109 Mꢀ1 sꢀ1, we
obtain from the slope of the plot kH O = (3.2 ( 0.3) ꢁ 109 sꢀ1
.
2
Combining kH O with kH = 2.6 ꢁ 10ꢀ3 Mꢀ1 sꢀ1 gives KR =
1.23 ꢁ 1012 an2d pKR = ꢀ12.1.
½RN3ꢂ=½ROHꢂ ¼ kAz½N3ꢀꢂ=kH O
ð4Þ
2
A value of kH O was also determined for a 1:1 TFEꢀH2O
2
mixture (v/v). Product percentages of azide (RN3), alcohol
(ROH), and trifluoroethyl ether (ROCH2CF3) are listed in
Table S5, and [RN3]/[ROH] is plotted against concentration
of azide ions in Figure S4 to give a straight line of slope kAz/kH O
=
2
3.7 ( 0.1, from which kH O = 1.5 ꢁ 109. Combination with kH =
2
2.9 ꢁ 10ꢀ3 Mꢀ1 sꢀ1 (from Table 1) gives pKR = ꢀ11.7. As found
previously for carbocation-forming reactions,5 values in water
and in the TFEꢀH2O mixture show rather small differences.
This directly determined value thus reinforces the value extra-
polated (with greater uncertainty) for water. The rate constant
for formation of the trifluoroethyl ether from the cycloheptadie-
nyl cation is 1.2 ꢁ 108, which on combination with kꢀ2 = 4.2 ꢁ
10ꢀ4 from Scheme 4 gives pK = ꢀ11.5 in 1:1 TFEꢀH2O, where
K = [ROCH2CF3][H+]/[R+].
pKH O = ꢀ4.9/1.36 = ꢀ3.6 at 25 °C, where KH O = 2.5 ꢁ 10ꢀ4
2
refer2s to the reverse hydration reaction. The dehydration is cor-
respondingly favorable, with equilibrium constant 1/KH O = 4000.
2
A value of pKR was also required for the isomeric 2,6-
cycloheptadienol 12 (Scheme 8). This was estimated by suppos-
ing that the difference in free energy of formation of the parent
hydrocarbons, 1,3- and 1,4-cycloheptadiene, corresponds to the
difference in their heats of hydrogenation7,8 to form cyclo-
heptane, ΔΔH = 6.0 kcal molꢀ1. Assuming that the free energies
of transfer of the two hydrocarbons to aqueous solution are the
same, a correction of 0.5 kcal molꢀ1 from the estimated
difference between substitution of an OH group in 1,3- and
This equilibrium constant may be combined with pKR
=
ꢀ12.1 to derive a pKa = ꢀ15.7 for deprotonation of 1,3-
cycloheptadienyl cation to cycloheptatriene based on the cycle
in Scheme 9. Arrows in the cycle indicate the directions of
reaction to which equilibrium constants refer.
The availability of a pKa for the 1,3-cycloheptadienyl cation
leads to a complete evaluation of rate constants for the dehydra-
tion reaction based on the relationships in Scheme 10, in which
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kA and kp are rate constants respectively for protonation of
cycloheptatriene by H3O+ and deprotonation of the 1,3-cyclo-
heptadienyl cation in water. The measured rate and equilibrium
constants for acid-catalyzed dehydration of the cycloheptadienol,
Chart 1
kde and 1/KH O, can be expressed in terms of the microscopic rate
2
constants in Scheme 10 as shown in eqs 6 and 7.
kHkp
kH
kde
¼
¼
ð6Þ
ð7Þ
In addition to calculations for the parent cyclohexadienyl
cation, hydride ion affinities were estimated for a series of
6-substituted cations, including OH and other substituents of
differing hyperconjugating ability, namely CH3, SiH3, F, Cl, SH,
NH2, PH2, and spirocyclopropyl. HIA values for both mono- and
disubstituted ions are shown in Table 3. The calculations were
made at the G3MP2 level and gave values which correlated well
kH O þ kp
1 þ kH O=kp
2
2
kH OkA
2
KH O
¼
2
kHkp
with HIAs calculated at the MP2/6-311+G** level (HIAMP2
=
1.082HIAG3 + 29.62, r2 = 0.998, n = 18).
Combining the values of kde = 6.8 ꢁ 10ꢀ6 Mꢀ1 sꢀ1, KH O
=
2
2.5 ꢁ 10ꢀ4, and kH = 2.6 ꢁ 10ꢀ3 Mꢀ1 sꢀ1 leads to kA = 1.70 ꢁ
The geometries of the ions in Table 3 were also calculated at
the MP2/6-311+G** level. The calculations showed that the
pentadienyl segments of the ions are very nearly planar. For the
6-hydroxycyclohexadienyl ion, the 1,2,3,4 = 2,3,4,5 dihedral angle
is 4.4°, while the cross-ring 1,2,4,5 dihedral is 0.4°. However, the
tetrahedral carbon at the 6-position is 10.5° out of the plane and
allows substituents to occupy either a pseudoaxial or a pseudo-
equatorial position.
10ꢀ9 Mꢀ1 sꢀ1 and kp/kH O = 2.6 ꢁ 10ꢀ3. The consistency of this
2
analysis is confirmed by the finding that the derived value of
kp/kH O shows a good fit to a correlation of log kp/kH O with
2
pKH O for a wide range of carbocations.13 As expec2ted for
2
formation of a nonaromatic alkene, the low value of kp/kH O
2
implies that the deprotonation step is strongly rate-determining
in the dehydration reaction. From the previously determined
value of kH O = 3.0 ꢁ 109 sꢀ1 from the azide trapping measure-
ments, we2 obtain kp = 7.9 ꢁ 106 sꢀ1. This value shows a
satisfactory fit to a plot of log kp against pKa for other
carbocations.13
In the table, the axial substituent is indicated by bold letters,
and the final two columns of the table provide dihedral angles
with respect to the plane of the ring. For the disubstituted cations
the dihedral angles are equal. Where more than one conforma-
tion is identified, HIA is reported for the more stable. An
exception is made for SH where two structures are reported,
one in which the SH is pseudoaxial and one in which it is
symmetrically bridged between adjacent carbon atoms.
The hydride ion affinities are also shown as ΔHIA values
relative to the cyclohexadienyl cation. Positive values of ΔHIA
imply a stabilizing effect of the substituent and negative values
destabilization. Also shown are average carbonꢀcarbon bond
lengths within the cyclohexadienyl ring. Of interest here is the
variation in bond lengths indicated by the average deviation from
the averaged length. Thus electron delocalization leading to
aromaticity (as a consequence of hyperconjugation) might be
expected to lead to equalization of bond lengths around the ring.
The differences between substituents are not large, but as
discussed below, the smallest variation (0.013 Å) and largest
(0.052 Å) are associated with the strongest and weakest hyper-
conjugating substituents, SiH3 and F, respectively (with 0.010 Å
for spirocyclopropyl).
Details of energies of carbocations and neutral compounds
used for the computation of hydride ion affinities shown in
Table 3 or referred to elsewhere in the paper are listed in Table S7.
Geometric coordinates for the cations and the compounds are listed
in Table S8.
Magnetic Ring Currents. A defining characteristic of aro-
matic molecules is the existence of a ring current induced by
application of a perpendicular external magnetic field. Experi-
mentally, this is manifested in measurable magnetic response
quantities such as NMR chemical shifts and magnetic sus-
ceptibility. These second-order quantities can be evaluated by
appropriate integration over the current density distribution,
which is a function that shows the current vector per inducing
field at each point in space and, most importantly for interpreta-
tion, corresponds to the organic chemist’s qualitative idea of a
Computational Results. The measured difference in values of
pKR for cyclohexa- and cycloheptadienyl cations was compared
with a calculated difference in hydride ion affinities (ΔHIA) of
the ions in the gas phase. G3MP2 calculations gave HIA values of
ꢀ215.1 and ꢀ223.3 kcal molꢀ1 for the six- and seven-membered
ring cations, respectively. This corresponds to a difference of
8.2 kcal molꢀ1 compared with the experimental value based on
ΔpKR in aqueous solution of 13 kcal molꢀ1
.
The discrepancy between calculated and experimental values
is perhaps not so large as to deserve comment. However, a
comparison of 2-cyclohexenyl and 2-cycloheptenyl cations gave
HIA values of ꢀ229 and ꢀ226.8 kcal molꢀ1, respectively. This
suggests that 2 kcal molꢀ1 of the reduced difference in stability of
the seven- relative to the six-membered ring in the gas phase
might be attributed to the larger size of the ion. Correction for
this implies a value of ΔHIA closer to 10.4 kcal molꢀ1 for
comparison with the solution value. Little or no contribution is
expected from the difference of alcohol from hydrocarbon
reference molecules for pKR and ΔHIA.9
A formal, if unlikely, possibility is that hyperconjugation in the
cycloheptadienyl cation benefits from a no-bond resonance
structure which includes, if not an aromatic structure, at least
the homoaromatic structure of cycloheptatriene14 (Chart 1).
Greater electron delocalization in the gas phase could then lead
to a smaller difference in stability from the cyclohexadienyl cation
than in solution. In principle, the existence of such stabilization
might be taken to imply “homohyperaromatic” character for the
cycloheptadienyl cation! Alternatively, the ion might be viewed as an
antiaromatic bis-homocyclopentadienyl structure,15 but this would
imply a less rather than more stable structure. The symmetry of the
ion is C2, and the calculations show a nonplanar pentadienyl cation
fragment and no unusual bond distances. Details of the geometry are
provided in the Supporting Information.
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Table 3. Calculated Hydride Ion Affinities (HIA, G3MP2)a and Selected Geometric Features (MP2/6-311+G**) for 6-Substituted
ARTICLE
+
+
+
Cyclohexadienyl Cations: 6-X,6-Y-C6H5 ; ΔHIA Values Calculated as HIA(6-X,6-Y-C6H5 ) ꢀ HIA(C6H7 )
G3MP2b
X, Y
HIA
ΔHIA
average ring bond lengths, Å
ωX,c deg
ωH,d deg
H, He
ꢀ215.1e
ꢀ214.7
ꢀ214.6
ꢀ195.6
ꢀ218.8
ꢀ225.2
ꢀ236.4
ꢀ233.3
ꢀ251.5
ꢀ196.6
ꢀ193.0
ꢀ207.7
ꢀ221.8
ꢀ230.9
0
0.4
1.419 ( 0.032
1.416 ( 0.032
1.419 ( 0.032
1.405 ( 0.010
1.415 ( 0.024
1.417 ( 0.027
1.432 ( 0.052
1.419 ( 0.033
1.433 ( 0.052
1.409 ( 0.013
1.411 ( 0.016
1.412 ( 0.018
1.415 ( 0.016
1.420 ( 0.032
54.6
48.9
58.3
29.2
20.1
21.8
57.9
24.6
58.8
83.5
55.6
83.8
74.3
31.4
54.6
64.0
NA
CH3, H
CH3, CH3
spirocyclopropylf
NH2, H
OH, H
0.5
19.5
NA
ꢀ3.7
ꢀ10.0
ꢀ21.3
ꢀ18.2
ꢀ36.4
18.5
98.7
91.7
NA
OH, OH
F, H
89.9
NA
F, F
SiH3, H
SiH3, SiH3
PH2, H
SH, Hg
17.8
NA
22.1
7.4
23.3
39.2
82.4
ꢀ6.7
ꢀ15.9
Cl, H
a In kcal/mol. The experimental value for the enthalpy of the hydride ion, H = 333.1 kcal/mol, is used. Pseudoaxial substituents for the monosubstituted
σ complexes are indicated in bold. b G3MP2 enthalpies are at 298 K. c The dihedral angle defined by substituent X, C6, C1, and the hydrogen attached to
C1. d The dihedral angle defined by the hydrogen attached to C6, C6, C1, and the hydrogen attached to C1. e The experimental value is ꢀ215.9 kcal/mol,
calculated from data available in Bartmess, J. E. In NIST Standard Reference Database Number 69; Mallard, W. G., Linstrom, P. J., Eds.; National Institute
of Standards and Technology: Gaithersburg, MD, June, 2005; http://webbook.nist.gov. The phenonium cation: spiro[2.5]octa-4,6-dienyl+. g The
f
thio-substituted ion also has a more stable, symmetrically bridged, Cs structure, d(CꢀS) = 1.948 Å. The endo form is more stable than the exo form
by 0.4 kcal/mol, and more stable than the unbridged form by 2.7 kcal/mol
ring current. Circulations around rings can be visualized directly,
and their diatropic (anticlockwise in our convention) or para-
tropic (clockwise) direction can be used to diagnose aromaticity
or antiaromaticity. The quantities that can be calculated from the
full current density function include nucleus-independent chemi-
cal shifts (NICS) of which the most sophisticated variant is
NICS(0)πzz, which is computed at the center of a molecule and
extracts the out-of-plane tensor component of the isotropic
NICS and includes contributions only from π orbitals.16
NICS(0)πzz values are reported in this paper for a number
of potentially hyperaromatic molecules.17
Chart 2
’ DISCUSSION
The technical question of how to calculate and map18 the current
density with ab initio wave functions has been solved by using
“distributed origin” methods developed by Bader and others.19 In
this paper, the continuous transformation of origin of current density
diamagnetic zero (CTOCD-DZ) method (known more informa-
tively as the “ipsocentric” method) is used to display maps of current
density evaluated at 1 bohr above the plane of the potentially
aromatic ring. The key to the ipsocentric approach is that current
density at any point is computed with that point as the origin. This
has the effect of enabling modest basis sets to deliver results of a
quality that would require huge numbers of basis functions in other
approaches. The arrows in the maps indicate the strength and
direction of the induced current, and direct inspection reveals
concerted global ring-current circulations, if any are present. In
delocalized π-monocycles, the current density is dominated by
contributions of HOMO π-orbitals, and the ring current may be
characterized numerically in terms of the maximum magnitude of
current density per unit inducing magnetic field. This gives a standard
unit for estimation of ring currents in aromatic systems. For benzene,
for example, the value of this “jmax” quantity is 0.079 au when
calculated at the level of theory used in this paper for computation of
ring currents of arenium ions (cf. Discussion below).
Cycloheptadienyl Ion. The experiments described above
confirm that, as measured by pKR, the stability of the cyclohep-
tadienyl cation is indeed much less than that of the cyclohex-
adienyl cation (benzenium) ion, a result which is corroborated
by G3MP2 calculations for the gas phase. Comparison between
the ions is complicated, however, by the fact that, although
the ions correspond to single structures, their pKR values
measure stability relative to isomeric alcohols. The carbocations
are characterized by at least two values of pKR, therefore. The
relevant values are shown under the structures of their respective
alcohols in Chart 2.
Values of pKR for the first pair of structures come from direct
experimental measurements,13 while those for the second are
inferred from the relative stabilities of their isomeric alcohols.8,9
In both cases, the implied difference in stabilities of the two ions
is large. For the first pair (13 and 6), the measured values of ꢀ2.3
and ꢀ12.1 imply a difference of nearly 1010-fold in equilibrium
constant or 13 kcal molꢀ1 in free energy. For the second pair (14
and 12), the values of pKR are ꢀ2.6 and ꢀ16.1, and the difference
is more than 13 powers of 10, or 18 kcal molꢀ1. These differences
are certainly consistent with the operation of “hyperconjugative
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Chart 3
Chart 4
aromaticity” as a stabilizing influence for the benzenium ion
which is absent for the cycloheptadienyl cation.20
Chart 5
Two questions arise. First, could the differences represent
instability of the cycloheptadienyl cation arising from ring strain
rather than stabilization of the benzenium ion? And second,
which of the two comparisons of pKR values is the more
appropriate, that for the 2,4-dienols (13 and 6) or that for the
2,5- and 2,6-dienols (14 and 12)?
It seems unlikely that the cycloheptadienyl cation is subject to
substantially greater strain than its dienol reactant. Although
cycloheptane has a strain energy of 6 kcal molꢀ1 relative to a
formally strainless cyclohexane,21 Turner’s studies of heats of
hydrogenation of cycloheptene, 1,3- and 1,4-cycloheptadienes,
and cycloheptatriene offer little evidence that the conjugation in
the latter molecules is impaired.7 Thus, the 1,3-diene is more
stable than the 1,4-diene by 6 kcal molꢀ1, whereas cyclohepta-
triene shows appreciable stabilization by homoconjugation.14
Consistently, G3 computations show a 5.1 kcal molꢀ1 difference
between the 2,4- and 2,6-cycloheptadienols. Greater strain for
the 1,4-cycloheptadiene may supplement resonance stabilization
of the 1,3-isomer as a contribution to this difference in energies,
but the importance of resonance is confirmed by computations
and experimental measurements which favor a Cs structure with
planar double bonds as the most stable conformation of the 1,3-
isomer.22 Although a role for ring strain cannot be excluded, it
seems unlikely that this could amount to more than 2ꢀ3 kcal
Schleyer, and Gauss from their MP2 computational study that the
“aromatic” stabilization energy of the benzenium ion20 is close to half
that for benzene itself, estimated as 30ꢀ36 kcal molꢀ1 23
.
A further, and less obvious, comparison may be made with the
pKR values for the cyclohexadienyl and cycloheptadienyl cations
coordinated by an iron tricarbonyl group (15 and 16, Chart 3).
Following coordination, the difference in stabilities of the parent
ions is lost, and the coordinated ions are found to have practically
the same values of pKR, i.e., 4.6 and 4.4.24,25 This is certainly
consistent with, if it does not require, loss of aromaticity through
coordination of Fe(CO)3. Computations indeed confirm a loss
of aromaticity for coordination of Fe(CO)3 to benzene or the
tropylium ion.25 If strain in the cations is unaffected by coordina-
tion, the similar pKR values for the coordinated ions supports
assignment of the difference in stabilities of the parent ions to
aromaticity of the benzenium ion.
molꢀ1
.
More significant indeed is that the difference in energy of 1,3-
and 1,4-cyclohexadienes is only 0.3 kcal molꢀ1 (0.1 kcal molꢀ1
by G3 computation), compared with the 6 kcal molꢀ1 for the
cycloheptadienes.7,8 This is consistent with the known distortion
of the 1,3-cyclohexadiene from a planar structure which limits
stabilization arising from conjugation of the double bonds.21 In
answer to the second question, therefore, it is clear that the first
comparison in Chart 1 is distorted by a lack of conjugation
between the π-bonds in the case of 2,4-cyclohexadienol, which
partially compensates for the greater stability of the cyclohex-
adienyl cation. The comparison which more directly reflects the
relative stabilities of the two cations is thus almost certainly that
shown for the second pair of structures, for which the π-bonds
are unconjugated. This indeed is confirmed by the similar heats
of hydrogenation of 1,4-cyclohexadiene and 1,4-cycloheptadiene
to form the saturated hydrocarbon, namely 53.9 compared with
55.9 kcal molꢀ1 (in acetic acid at 25 °C).7,8
If the pKR values for the carbocations reacting to form 2,5- and
2,6-dienols (14 and 12) are taken as a guide, the implied
stabilization of the cyclohexadienyl cation attributable to hyper-
conjugation is 18 kcal molꢀ1. This value may indeed be moder-
ated by a contribution from strain energy for the cyclohept-
adienyl cation. However, it is hard to imagine that the increase in
strain between dienol and cation is greater for the seven- than the
six-membered ring. Qualitatively the evidence offered by this
comparison is consistent with the conclusion reached by Sieber,
Benzannelation. Further evidence of aromatic stabilization of
the benzenium ion comes from the effect of benzannelation.
Solvolysis measurements indicate that normally benzylic cations
are more stable than allylic cations.26,27 One might have expected
therefore that the cyclohexadienyl cation would be stabilized by
benzannelation. That this is not the case is indicated by the
comparison below of values of pKR = ꢀ2.6, ꢀ3.5, and ꢀ6.0,
respectively, for the benzenium (6), 1-naphthalenium (17), and
9-anthracenium (18) ions in Chart 4.13,28
This behavior is characteristic of aromatic ions, as is illustrated
in Chart 5 for benzannelation of the tropylium ion29,30 and
pyrilium ion.31,32 Olah has measured 13C chemical shifts of 178.1,
180.9, and 183.4 ppm at the formal charge centers of the
benzenium, 1H-naphthalenium, and 9H-anthracenium ions
shown in Chart 4. He notes that if these represent relative
magnitudes of charge, benzannelation is associated with localiza-
tion rather than delocalization of charge.33 This is consistent
with a significant influence of hyperconjugation on delocaliza-
tion. From an IR study of the same ions,34 Koptyug’s group
observed an increase in stretching frequencies and CꢀH
force constants for the CH2 group on going from the benzenium
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Journal of the American Chemical Society
ARTICLE
to 1H-naphthalenium to 9H-anthracenium.35 In an article sum-
marizing the extensive work of Koptyug’s group, Shubin and
Borodkin note that Koptyug concluded that, while protonation
led to loss of aromaticity of the neutral molecule, “some
compensation effect was borne by hyperconjugation of the
ring CH2 fragment with the electron-deficient part of the
arenium ion”.36
It is more difficult to find examples of benzannelation of
nonaromatic ions for comparison. However, as shown in Chart 6,
an approximate pKR = ꢀ8.7 for the dibenzocycloheptadienyl
cation 19 may be inferred from equilibrium measurements in
aqueous trifluoroacetic acid,37 which indicates that the phenyl
groups confer substantial stabilization relative to the parent
cycloheptadienyl cation, with pKR = ꢀ16.1. With respect to
13C chemical shifts, Olah has shown from measurements for
methyl-substituted and dibenzo cyclooctadienyl dications (20)
that, in the absence of aromatic hyperconjugation, and in contrast
to the ions of Chart 5, benzannelation leads to delocalization
rather than localization of charge.38
Arene Oxides. The combination of aromaticity and the
striking difference in hyperconjugative capacity of CꢀH and
CꢀO bonds offers a plausible explanation for an anomalous
pattern of reactivity of arene oxides toward acid-catalyzed ring-
opening. This is apparent from comparisons between the re-
activity of epoxides and of alcohols yielding a common carboca-
tion intermediate save for the presence of a β-hydroxy group in
the case of formation from the epoxide. As illustrated in
Scheme 11 for styrene oxide 2139 and α-phenethyl alcohol
22,40 for which rate constants of 27 and 3.0 ꢁ 10ꢀ6 Mꢀ1 sꢀ1
respectively at 25 °C in aqueous solution are shown, the epoxide
is characteristically 106ꢀ107 times more reactive than the
alcohol. This provides a remarkable contrast to benzene oxide
23 and the corresponding alcohol, benzene hydrate 24, for which
the reactivity of the alcohol is significantly greater than that of the
epoxide (for which the rate constant was measured at the higher
temperature of 30 °C).41
A clue to the origin of this behavior is provided by the
dependence of the ratio of rate constants for arene oxides and
corresponding alcohols (arene hydrates) upon the stability
of the aromatic molecule from which they are derived.26 As
shown in Chart 7, this is reminiscent of the similar depen-
dence of ratios of rate constants for carbocation-forming
reactions of cis- and trans-dihydrodiols.1 In the chart, the
arrows indicate the direction of ring-opening for unsymme-
trical oxides. The temperatures of measurement were 30 and
25 °C respectively for the arene oxides and alcohols (and
epoxide of dihydronaphthalene).
One explanation offered for this behavior is that arene oxides
are stabilized by homoconjugation.26 This possibility was inves-
tigated by thermochemical measurements and computations for
benzene oxide and naphthalene oxide by Thibblin, who con-
cluded that stabilization of benzene oxide could account for a
fraction of the reactivity difference but that there must be another
factor involved.42 This is consistent with a recent assessment that
the stabilization of norcaradiene43 is smaller than that of cyclo-
heptatriene and probably does not represent a contribution from
homoaromaticity.14
What that factor might be is suggested by Sayer’s proposal that
the epoxide ring opens initially to a conformation in which the
OH group is close to pseudoaxial with respect to the carbocation
center, as in 25.44 Formation of such a conformation would
prevent stabilization of the carbocation by “aromatic” hypercon-
jugation of a CꢀH bond, which of course would be possible in
the initially formed conformation from reactions of the alcohols.
As expected, the difference from the “normal” reactivity ratio for
hyperconjugatively nonaromatic cations (such as the tetralyl
cation 26) is maximized when the aromaticity of the cation
formed from the alcohol (hydrate) is greatest, as in the case
of benzene oxide and benzene hydrate. Strictly speaking, the
results do not require that 25 exists in a conformational energy
Chart 6
Scheme 11
Chart 7
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Journal of the American Chemical Society
ARTICLE
minimum, only that its instability is reflected in the transition
state for reactions of the arene oxides.
observations suggest that the disilyl cation 27 is intermediate in
character between the aromatic benzene on the one hand and
classical (sic) arenium ions such as the benzenium ion on the
other.
Electrophilic Aromatic Substitution. Protonated aromatic
molecules such as the benzenium ion correspond to the simplest
of Wheland intermediates of electrophilic aromatic substitution,
and specifically aromatic hydrogen isotope exchange.45 In principle,
structure 25 corresponds to a Wheland intermediate formed from
attack of HO+ on a benzene ring in an electrophilic hydroxylation
reaction.
Aromatic Hyperconjugation. Muller’s characterization of
the benzenium ion as a classical structure is symptomatic of a
reluctance to take up Mulliken’s suggestion that hyperconjuga-
tion may be particularly pronounced as a consequence of extra
stabilization arising from its aromatic character.49,50 Two reasons
for this have been (a) that until recently there has been a lack of
unambiguous experimental support for the concept and (b) that
in 1953 calculations were not sufficiently accurate to establish the
magnitude of the effect. Moreover, in the late 1950s and 1960s,
hyperconjugation was subjected to an extended and unfavorable
critique by Dewar.54,55
Nevertheless, the wide scope of σ-bond interactions was early
indicated by the pronounced negative hyperconjugation of
fluorine atoms56 and further illustrated by the σ-delocalization
of silicon and other Group 14 elements.57 In the 1990s, improve-
ment in the effectiveness of computations allowed better assess-
ment of the magnitude of CꢀH and CꢀC hyperconjugation.
In 1993, Sieber, Schleyer, and Gauss reported calculations for
the phenonium ion and benzenium ions, supporting enhanced
hyperconjugative interaction with the cyclopropane and methyl-
ene group conferring aromatic stabilization on the ions.20 Olah58
and Suraya Prakesh59 queried the aromatic character of this
delocalization, but it is confirmed in principle by Muller’s results
for disilylbenzenium ions53 and the experimental work and
calculations of the present papers.1ꢀ3
There can be little doubt that hyperconjugation facilitates
electrophilic aromatic substitution. However, most substitutions
involve displacement of or by a proton, and in those cases one
may suppose that the intermediates are consistently stabilized by
CꢀH hyperconjugation. Where the influence of hyperconjuga-
tion most obviously appears is in the displacement of leaving
groups which are more strongly hyperconjugating than hydro-
gen, namely silicon, germanium, tin, and lead. These were
studied in the 1960s by Eaborn and co-workers,45ꢀ47 who found
indeed that proto-desilylation and corresponding displacements
of other group 14 elements by acids occur with exceptional
ease. Thus, trimethylsilyl benzene is 104 times as reactive as
benzene itself despite the protonation step being rate-
determining.46 Moreover, relative reactivities of ArMR3 with
HClO4 in ethanol are 1.0:36:3.5 ꢁ 105:2 ꢁ 108 for M = Si, Ge,
Sn, and Pb, respectively, an order opposite to that of decreasing
bond strength. However, while the importance of hyperconjuga-
tion in stabilizing the Wheland intermediates was recognized at
the time,45,46,48 there was no reference to its aromatic character
or to the papers by Mulliken49,50 in which this was discussed.
X-ray Structures of Wheland Intermediates. Apart from
measurements of their stabilities and of NMR and IR spectra,
crystal structures of benzenium ions have been determined by
X-ray crystallography and might have been expected to yield
direct evidence of hyperconjugation. The earliest studies were
of hexa or heptamethyl benzenium ions, and these have been
further intensively investigated by Koptyug’s group36 and by
Hubig and Kochi51 for structures corresponding to attack of
different electrophiles on methyl-substituted benzenes. More
recently, with the choice of a sufficiently non-nucleophilic
carborane anion, Reed succeeded in isolating and determining
structures for the parent benzenium ions with attachment of
Thus, despite its long antecedents,20,48ꢀ50 there has been little
recognition of or effort to develop a concept of hyperconjuga-
tive aromaticity. As an exception, Nyulaszi and Schleyer have
reported calculations for cyclopentadienes indicating hyper-
conjugative delocalization when the methylene group is substi-
tuted with electropositive elements SiH3, GeH3, or SnH3 or a
cyclopropane ring and found stabilization energies of up to
10 kcal molꢀ1 based on the isodesmic reaction shown in
eq 9.60 Although Stanger61 has criticized Schleyer’s analysis, we
found it convincing. Of interest in connection with the present
paper is an inference that electronegative substituents Cl and F
are destabilizing, suggesting an antiaromatic character for inter-
actions with bonds to these atoms.60
electrophilic groups H+, CH3 , Cl+, Br+, Et3Si+, and Ag+.52
+
Of interest are electrophiles showing angles between the bond
to the electrophile and the plane of the ring larger than normal for
a tetrahedral carbon. It has been suggested that variations in this
angle might represent a continuity of structures and bonding
between σ- and π-complexes. However, in the case of Et3Si+, for
which the angle is particularly large, there can be little doubt of
the σ-character of the complex. Muller has determined a crystal
structure of the disilylated benzenium ion 27 and demonstrated
the presence of bond length alternations characteristic of a
σ complex as well as tell-tale 1H and 13C NMR spectra. His results
are supported by MP2 and B3LYP calculations for both 27 and
the parent benzenium ion.53 Moreover, NICS(1)zz values would
place 27, with a value of ꢀ26.0, much closer to benzene (ꢀ29.6)
than to a benzenium ion (ꢀ14.6). Muller comments that these
Computational Analysis: Stabilization Energies. A key
feature in the interpretation of hyperconjugative stabilization of
arenium ions presented so far is the contribution of a strongly
stabilizing aromatic structure within a simple valence no-bond
resonance representation of the hyperconjugation (2a T 2b)
shown in Scheme 1. However, such a description can hardly be
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Journal of the American Chemical Society
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sustained without the support of a more rigorous assessment of
the magnitudes of the stabilization energies involved. A series of
G3MP2 or MP2/6-311+G** calculations have been undertaken
therefore, (a) to assess relative stabilizations arising from differ-
ent substituents at the methylene group of a benzenium ion,
especially H and OH, (b) to determine the dependence of any
stabilization on the stereochemical relationship between hyper-
conjugating group and charge center, and (c) to evaluate the
magnitude of the stabilization as a function of the aromaticity of
the arenium ion (especially benzenium compared with naphtha-
lenium and phenanthrenium).
Table 4. Bond Lengths of Methylene-Substituted Benzenium
Ions Computed at the MP2/6-311+G** Level
C3ꢀC4
C2ꢀC3
C1ꢀC2
1.479
1.350
1.497
1.467
1.379
1.412
1.420
1.390
1.405
1.435
1.393
1.404
1.511
1.365
1.423
The importance of hyperconjugative interactions of differently
substituted methylene groups (point a, above) was explored
through calculations at the G3MP2 level of relative hydride ion
affinities (ΔHIA, eq 10) of the doubly substituted ions 28. In
addition to CX2 = CH2 and C(OH)2 in 28, calculations were
carried out for C(SiH3)2, CMe2, and CF2, and with CH2 replaced
by cyclopropyl to provide a comparison with a wider range of
potentially hyperconjugating groups than studied experimen-
tally. The effects are summarized under eq 10 as stabilization
energies of CX2 relative to CH2 (ΔHIA) and are abstracted from
the more comprehensive Table 3. It can be seen that the order
found, i.e. SiH3 > cyclopropyl > Me ∼ H > HO > F, is a
reasonable one for hyperconjugative stabilization of a positive
charge. The slightly more favorable hyperconjugation of CH3
than H contrasts with normal behavior in solution and may
represent the greater importance of polarizability (size) for the
ions in the gas phase. The CF2 and C(OH)2 groups are quite
strongly destabilizing relative to CH2. It is not clear if this represents
weaker “favorable” hyperconjugation than CH2 or, as Nyulaszi and
cyclohexadienyl ring are listed as a concise indication of the
degree of equalization of bond lengths.
The main conclusion to be drawn from the geometries is that
the C3ꢀC4 bond length shows a small but significant variation
with changes in substituent. While this is not unambiguous
evidence of hyperconjugative delocalization, it is apparent that
it is associated with a tendency to equalization of all three CꢀC
bond lengths consistent with aromatic character, especially for
the most strongly interacting substitutents, silyl and cyclopropyl.
This contrasts with fluorine substituents for which bond alter-
nation is accentuated rather than reduced. The degree of equal-
ization of bond lengths can be expressed, e.g., by Julg53,62 or
HOMA63 parameters but is apparent from inspection of the bond
lengths themselves and, in principle (in the case of CF2 and
presumably C(OH)2), can be associated with antiaromaticity as
well as aromaticity. However, it should also be noted that
available evidence suggests that “aromatic” delocalization of
electrons is not greatly impaired by disparities in bond lengths.64
The stereochemical dependence of this conjugative interac-
tion, i.e., point b above, was examined by looking at a benzenium
ion with a singly substituted methylene group. For the di-X-
substituted ions the methylene group (CX2) is close to tetra-
hedral, and the CꢀX bonds are symmetrically located above and
below the plane of the ring. For the benzenium ion with a single
OH substituent, the preferred conformation places the CꢀH
bond in a pseudoaxial location with respect to the charge center,
while the OH group adopts a pseudoequatorial position.
In Table 3, geometries at the methylene group for a series of
substituents X are compared. These are expressed in terms of the
dihedral angles ωX and ωH between the CꢀX or CꢀH bond of
the methylene group and a β-sp2 CꢀH bond of the benzenium
ion (29) as in 30. It can be seen that whether CꢀX or CꢀH
bonds adopt a pseudoaxial position depends on the relative
hyperconjugating ability of the X and H substitutents. The
pseudoaxial dihedral angles range from 82 to 99° and the
pseudoequatorial from 20 to 31°. Only for the CH3 group, which
in the gas-phase calculations has a hyperconjugating capacity very
similar to that of hydrogen, are intermediate values of dihedral
angles, ωH = 64° and ωMe = 49°, observed. A fuller characteriza-
tion of these geometries is shown in Table S7.
Schleyer’s results for substituted cyclopentadienes suggest,70
a
manifestation of antiaromatic character for the ions.
With respect to aromatic (or antiaromatic) character of
arenium ions some indication might be sought in changes in
geometry. Thus, Olah and Suraya Prakesh have suggested that
stabilization of the benzenium ion or phenonium ion arises from
delocalization within the cyclopentadienyl cation fragment of the
ions and does not extend importantly to hyperconjugative
interactions with the CH2 or cyclopropyl group.58,59 In principle,
this might be assessed from comparisons of crystal structures.
However, Muller has shown that for silicon-substituted benze-
nium ions there is good agreement between crystallographically
determined geometries and those from MP2 or B3LYP calcula-
tions for the gas phase.53 Moreover, the consistency of the
calculations lends itself to identification of systematic trends. In
Table 4, variations in the length of the σ-bonds to the methylene
group (C3ꢀC4) and π-bonds of the formal cyclohexadienyl
cation (C2ꢀC3 and C1ꢀC2) are compared for the different
substituents X. For a reference structure exhibiting little deloca-
lization, we have followed Sieber, Schleyer, and Gauss in choos-
ing cyclohexa-2,5-dienone.20 More substituents are included in
Table 3, in which variations in average bond lengths within the
That neighboring group interactions are encompassed by the
calculations is shown by an SH substituent for which, in addition
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Journal of the American Chemical Society
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to the hyperconjugating structure, a structure of similar energy in
which the sulfur atom symmetrically bridges α- and β-carbon
atoms is identified. For OH, the bridged ion, protonated
benzene oxide, is significantly less stable than the unbridged
β-hydroxy cyclohexadienyl cation. A difference between un-
bridged SH and OH monosubstituted ions is that the OH
occupies a pseudoequatorial position relative to a pseudoaxial
hydrogen atom while the SH occupiesa pseudoaxialposition, with
hydrogen pseudoequatorial. The pseudoaxial orientation of the
CꢀS bond might seem surprising insofar as the substituted ion is
less stable than the parent cyclohexadienyl cation. Presumably this
is because, although CꢀS hyperconjugation is more favorable
than CꢀH, the stabilizing effect is overridden by an unfavorable
inductive effect. In Table 3 it is noticeable that all the second-
row elements except chlorine occupy pseudoaxial positions.
Indeed, a crystal structure of ipso-protonated chlorobenzene
shows even chlorine in a pseudoaxial position.52
Table 5. Dihedral Angles and Energy Differences between
Conformations for β-Hydroxy Arenium Ionsa
31 32 33 34 35
dihedral angle ωOH for stable conformer (deg) 22 37 29 53 27
constrained dihedral angle ωOH (deg)
ΔE (kcal molꢀ1
80 80 80 55b 82b
)
8.8 6.0 4.3 0.8 0.8
a Calculated at MP2/6-311+G** for cyclohexadienyl and cyclohexenyl
cations and at MP2/6-31G* for the larger ions. b Stable but higher energy
conformer.
For the gas-phase calculations, the structures of monosubsti-
tuted cyclohexadienyl cations shown in Table 3 correspond to
stable conformations. Generally they represent a single minimum
energy structure. This may differ from the situation in solution
where the difference in reactivities of cis- and trans-arene
dihydrodiols1 or 2-substituted dihydro-1-naphthols2 found ex-
perimentally suggests formation of distinct conformers of carbo-
cations with β-CꢀH and β-CꢀX bonds respectively in
pseudoaxial positions. A difference in energy between conforma-
tions in the gas phase nevertheless may be calculated by
constraining the dihedral angle ωX (in 30) to a reasonable
value for the less stable conformer. Thus in the case of an HO-
substituted benzenium ion, if the dihedral angle ωOH is
increased to 80°, the energy of the ion increases by 8.8 kcal
molꢀ1. This may be taken as a guide to the difference in energies
of two “stable” conformations existing in solution or, alterna-
tively, of different transition states for carbocation formation
originating respectively from cis- and trans-dihydrodiol
precursors.
At this point we return to the question of whether the
unfavorable influence of OH reflects more importantly absence
of activation by CꢀH or “positive” deactivation by CꢀOH (over
and above the expected influence of an inductive effect).1 So far it
has been supposed that the presence or absence of CꢀH
hyperconjugation controls reactivity. However, Nyulaszi and
Schleyer’s demonstration of antiaromaticity for cyclopentadienes
with electronegative substituents raises the possibility that for-
mation of a carbocation with CꢀOH in a pseudoaxial position
may be intrinsically unfavorable, and that this factor may be more
important in determining the difference in reactivities between
cis- and trans-dihydrodiols than stabilization of the cis isomer by
CꢀH hyperconjugation (eq 9).
NICS(0)πzz calculations for C6H6OH+ (+7.8 ppm) and
C6H6F+ (ꢀ0.4 ppm) reveal no special (hyper)aromaticity com-
pared to the benzenium ion (ꢀ18.0 ppm). The value for the
latter ion is approximately half that for benzene (ꢀ35.9 ppm). In
+
contrast, the disubstituted C6H5(SiH2)2 (ꢀ27.9 ppm) and
+
C6H5F2 (12.1 ppm) show enhanced “hyperaromaticity” and
“hyperantiaromatcity” (as in Nyulaszi and Schleyer’s cyclopen-
tadiene analogues).17,60
A further important feature of the experimental results is the
dependence of the cis/trans rate ratio for reaction of arenedihy-
drodiols on the extent of hyperconjugative aromatic stabilization
of the arenium ion intermediate formed from them (point c
above). This too could be tested by calculation, by comparing the
difference in energies of stable and constrained conformations of
arenium ions bearing a β-hydroxy group for benzenium (31),
naphthalenium (32), and phenanthrenium (33) ions and for the
nonaromatic acenaphthenium (34) and cyclohexenyl (35) ca-
tions shown in Table 5. The comparison represents a progression
from the potentially strongly aromatic ring of the benzenium ion
to the two nonaromatic rings, with intermediate degrees of
aromaticity for the rings formally bearing the positive charge of
the naphthalenium and phenanthrenium ions. This too is
expressed as a difference in energies between stable conforma-
tions and conformations in which the CꢀOH rather than the
CꢀH bond is constrained to be axial. The differences (ΔE)
are listed in Table 5 under the relevant structures together with
the constrained dihedral angle ωOH between the CβꢀOH and
+
Cα ꢀH bonds for the arenium ions. For the “nonaromatic”
cations 34 and 35, both conformations are accessible and no
constraint was necessary. Because of the size of the phen-
anthrenium, naphthalenium, and acenaphthenium ions, the
calculations for these ions are at a lower level (MP2-6-31G*)
than the G3MP2 calculations which have been cited hitherto.
Further details are provided in Table S8.
Evidence on this point is conflicting. The correlation of rates of
reaction of cis 2-OH or 2-OMe substituents by a Taft relationship
in the acid-catalyzed dehydration of 2-substituted 1,2-dihydro-1-
naphthols described in a previous paper2 suggests that the
influence of these (cis) substituents on the stability of the parent
naphthalenium ion is mainly inductive. This implies that stabi-
lization of the parent naphthalenium ion by hyperconjugative
resonance is substantially retained in the β-HO substituted ion,
provided that a β-CꢀH bond occupies a pseudoaxial position.
On the other hand, NICS calculations for benzenium ions with
the methylene group substituted by OH or a halogen (and CꢀH
occupying a pseudoaxial position) imply that by this criterion
there is no ring current associated with these ions. Thus,
Computational Analysis: Ring Currents. Further insight
into the aromaticity of arenium ions is provided by an evalua-
tion of ring currents.18 A “current-density map” based on the
distributed-gauge (“ipsocentric”) method CTOCD-DZ19,65 at
the RHF/6-31G** level of theory, calculated at 1ao above the
median plane using the SYSMO and GAMESS packages66,67 for
the structure optimized at the B3LYP/6-31G** level with
GAUSSIAN 09,68 has been obtained for the benzenium ion
and is shown in Chart 8 (36). The map shows the summed
contribution of all occupied orbitals of π symmetry, which in
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Journal of the American Chemical Society
ARTICLE
Chart 8
Chart 9
qualitative terms should capture all the contributions from the
conventional π system of the ring, plus any contribution that may
arise from the antisymmetric combination of CH bonds of the
methylene group. There is a clear indication of a global ring
current passing above and below all carbon centers, including
that of the CH2 group, which is thus consistent with aromatic
character deriving from hyperconjugative participation of these
hydrogens. The π current in 36 is roughly half as strong as in
benzene in the 1 bohr plotting plane; the maximum magnitude of
current density per unit inducing field is 0.046 au, compared to
0.079 au for benzene calculated at the same level of theory. If the
CH2 group is replaced by C(SiH3)2, or by a spirocyclopropyl
ring, calculations at the same level of theory show that the ring
current persists, and indeed becomes stronger, as indicated by
the respective maps (37 and 38).
In contrast to structures 36ꢀ38, for the cycloheptadienyl
cation 39 there is no evidence of an appreciable π ring current of
the conventional type. Structure 39 is nonplanar, and π-orbital
symmetries are therefore approximate; the map also contains
some distracting large local currents where the plotting plane
intersects CC/CH σ bonds, but the significant feature of the map
is what is missing, i.e., a global circulation concentrated on the
carbon centers of the seven-membered ring. This negative result
is of interest insofar as this ion is potentially homoaromatic (or
perhaps more properly “homohyperaromatic”!) in analogy with
cycloheptatriene. The lack of current is consistent with the large
energy difference between the cyclohexadienyl and 2,4-cyclo-
heptadienyl cations that is implied by the pKR values for the two
cations (ΔpKR = 13.5), as discussed above.
the parent hydrocarbons. The uniform global perimeter circula-
tion of naphthalene, for example, gains a short-circuiting cross
current in the less symmetrical environment of the C10H9
cation, where the conventional aromatic ring current in the
unsubstituted benzene ring (diminished by <10% from the value
for benzene itself) is appreciably stronger than the hyperaromatic
current in the protonated ring. A fuller account of currents and
their orbital analysis for Wheland intermediate systems is in
preparation.
+
’ SUMMARY
In conclusion, comparison of pKR values for cyclohexadienyl
(benzenium) and cycloheptadienyl cations reinforces evidence
from the difference in reactivity of cis- and trans-benzenedi-
hydrodiols toward acid that the arenium ions they give rise to are
“hyperaromatic”, with stabilization energies as large as 18 kcal
molꢀ1. Further evidence is provided by the structure dependence
of relative reactivities of arene oxides and arene hydrates,
reactivity patterns in electrophilic aromatic substitution
(especially ipso displacement of Group 14-substituted benzenes
by protons), and the effect of benzannelation on the stability of
the benzenium ion. The behavior is most simply interpreted as
arising from the contribution of an aromatic no-bond resonance
structure within a valence bond representation of hyperconjuga-
tive stabilization of the ions. The interpretation is endorsed by
G3 calculations of ion stabilities and by current density maps
pointing to cyclic delocalization of cyclohexadienyl π electrons
with involvement of electrons from the CH bonds of a methylene
group. The term “hyperaromaticity” is suggested as an extension
of the term “hyperconjugation”,69 in analogy with homoconjuga-
tion and homoaromaticity.1,70
’ EXPERIMENTAL SECTION
Analytical Methods and Synthesis. NMR spectra were mea-
sured on a Varian 300 MHz spectrometer. UVꢀvis spectra were
measured with a Cary 50 spectrophotometer which was also used to
monitor acid-catalyzed dehydration of cycloheptadienol to cyclohepta-
triene. HPLC measurements were made with a Waters 600 HPLC
system equipped with dual-wavelength absorbance detection and a
HiChrom-5 (4.6 ꢁ 250 mm) C-18 reverse-phase column. Cyclohepta-
dienol was preparedfromtheepoxideofcycloheptatrieneandwastreatedwith
dichloroacetyl chloride to furnish the dichloroacetate ester as described below.
Cycloheptadiene-1,2-oxide. To an ice-cold solution of m-chloro-
perbenzoic acid (0.38 g, 5.1 mmol) in dichloromethane (20 mL) was
added 1,3-cycloheptadiene (0.50 g, 5.3 mmol) over 10 min. The mixture
was stirred overnight at room temperature and the precipitated
m-chlorobenzoic acid removed by filtration. The filtrate was poured into
Of particular interest is the result for the benzenium ion in
which the methylene group is replaced by CF2 (40, Chart 9). It
can be seen that the ring current is lost and that the behavior here
is consistent with antiaromatic character for this ion, and
presumably also for the corresponding ion in which the fluorine
atoms are replaced by OH groups. Finally, structures 41 and 42
indicate that the hyperconjugative ring current persists in the
magnetic maps for naphthalenium and phenanthrenium cations,
where the maps correspond to perturbed versions of the maps for
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ice-cold saturated aqueous sodium bicarbonate (20 mL) and quickly
extracted with chloroform (25 mL). The organic layer was separated and
washed with 5% sodium thiosulfate solution (20 mL) followed by saturated
sodium bicarbonate (20 mL) and water (20 mL). Drying over sodium
sulfate, filtration, and removal of the solvent under reduced pressure gave
1,3-cycloheptadiene 1,2-oxide (0.32 g, 56%): 1H NMR (300 MHz, CDCl3)
δ 3.23 (t, 2H, J = 4.5 Hz), 3.43 (s, 2H), 5.76ꢀ5.93 (m, 4H).71
The reactions at 1 M HClO4 were too fast for the determination of
reliable rate constants. Kinetic analyses were carried out therefore using
the equilibrium concentration of trifluoroethyl ether obtained at the higher
acid concentration to evaluate rate constants from measurements at 0.1 M
HClO4. To correct for the loss of ether at longer reaction times, the
percentages of trifluoromethyl measured as a function of time (t) werefitted
to the modified first-order kinetic expression a(1 ꢀ ct)(1 ꢀ eꢀkt), where
a is the limiting percentage of ether at 1 M HClO4 and 1 ꢀ ct is a
correction term based on the supposition that loss through evaporation
increases linearly with the concentration of trifluoroethyl ether and the
time of reaction. The value of c was chosen to give a best fit of calculated
to experimental data.
The quality of fit for the measurements in 70% TFEꢀ30% water is
shown in Figure 1. The fit here is substantially better than for measure-
ments at 50% and 30% TFE, for which the reaction was significantly
slower and the extent of loss of trifluoroethyl ether correspondingly
greater. This is apparent from the poor quality of the plot of log k at the
2,4-Cycloheptadienol (6)72. To a stirred solution of 1,3-cyclo-
heptadiene-1,2-oxide (0.32 g, 2.9 mmol) in anhydrous diethyl ether
(10 mL) was added 3 mL (4.8 mmol) of 1.6 M methyllithium in hexane.
The resulting mixture was allowed to warm to room temperature, and
unreacted methyllithium was hydrolyzed with 5% aqueous sodium
hydroxide (5 mL). The aqueous layer was separated and extracted with
3 ꢁ 10 mL of diethyl ether. The combined organic solutions were
washed with saturated aqueous sodium chloride (10 mL), dried over
anhydrous sodium sulfate, and filtered, and the solvent was removed
under reduced pressure. The crude product was purified by column
chromatography (70:30 cyclohexane:ethyl acetate) to give 2,4-cyclo-
heptadienol (0.30 g, 94%): 1H NMR (300 MHz, CDCl3) δ 1.82
(m, 1H), 2.08 (m, 1H), 2.32 (m, 2H), 4.43 (s, 1H), 5.80ꢀ6.00 (m, 4H).
1-Dichloroacetoxy-2,4-cycloheptadiene (8). To a stirred ice-
cold solution of 2,4-cycloheptadienol 6 (0.10 g 0.92 mmol) in anhydrous
dichloromethane (5 mL) was added 0.1 mL of anhydrous pyridine (1.26
mmol). The resulting mixture was allowed to come to room temperature and
stirred for 2 h. The reaction was quenched by the addition of 5 mL of saturated
sodium bicarbonate solution, and the organic layer was separated and washed
with water (3 ꢁ 10 mL) and saturated sodium chloride solution (10 mL). The
solution was dried over anhydrous sodium sulfate and filtered, and the solvent
was removed under reduced pressure. The crude product was purified by
column chromatography (70:30 cyclohexane:ethyl acetate) to give 1-dichlor-
oacetoxy-2,4-cycloheptadiene (0.10 g, 49%): 1H NMR (300 MHz, CDCl3) δ
1.86ꢀ2.02(m, 1H), 2.11ꢀ2.26(m, 1H), 2.39(dd, J= 11.5, 5.5 Hz, 2H), 5.59
(s, 1H), 5.82 (ddd, J= 16.3, 11.6, 5.8 Hz, 2H), 5.95 (s, 1H), 6.01 (ddd, J= 15.5,
11.5, 6.2 Hz, 2H); 13C NMR (101 MHz, CDCl3) δ 25.1, 30.2, 64.5, 76.1,
124.3, 127.8, 128.7, 136.1, 163.7; m/z (ES) 95.1 [MꢀOCOCHCl2+H+]+.
Kinetic Measurements and Product Analyses. Acid-catalyzed
dehydration of 2,4-cycloheptadienol was monitored by UVꢀvis spectro-
photometry at 240 nm in the concentration range 2.0ꢀ6.0 M HClO4.
Reactions were initiated by injection of 20 μL of a 1.8 ꢁ 10ꢀ2 M solution
of substrate in acetonitrile into 2 mL of acid in a cuvette thermostatted at
25 °C. Measured first-order rate constants determined at different acid
concentrations are shown in Table S1. Logs of second-order rate
constants were plotted against the acidity parameter Xo, and a value
for dilute aqueous solution was extrapolated at Xo = 0 (Figure S1).73
Equilibration of 2,4-cycloheptadienol with its trifluoroethyl ether in
aqueous trifluoroethanol containing 30, 50, and 70% (v:v) TFE in the
presence of HClO4 was monitored by HPLC. Typically 50 μL of a 10ꢀ2
M solution of cycloheptadienol was injected into 500 μL of TFEꢀH2O,
0.1 M in HClO4. Samples of 25 μL were quenched at various times in
three drops of saturated sodium bicarbonate solution, followed by
addition of 200 μL of acetonitrile to minimize broadening of HPLC
peaks. The analysis involved isocratic elution of samples with a 70:30
(v/v) acetonitrileꢀwater mixture at a flow rate of 1 mL/min.
three solvent compositions against values of log k/kH O for the dehydra-
2
tion of benzothiophene (Figure S2). However, uncertainty in the
extrapolated rate constant has a relatively mild effect on derived rate
and equilibrium constants. Thus omission of the point for 30% TFE
modifies the value in water from 2.6 to 1.7 ꢁ 10ꢀ3 Mꢀ1 sꢀ1 and pKR for
2,4-cycloheptadienol from ꢀ12.1 to ꢀ12.25.
Rate constants for solvolysis of the dichloroacetate ester of cyclo-
heptadienol in water were also determined by HPLC. The reaction
was initiated by injection of 50 μL of a stock solution in acetonitrile
(10ꢀ2 M) into 2 mL of water. Samples of 25 μL were withdrawn every
few minutes and quenched in 250 μL of MeCN, in which the
dichloroacetate ester showed no further reaction in 24 h. The HPLC
analysis was performed with the detector set at a wavelength of 250 nm
using a solvent mixture of 30:70 (v:v) aqueous acetonitrile.
’ ASSOCIATED CONTENT
S
Supporting Information. Reactions of cycloheptadienol
b
and its dichloroacetate ester in water and aqueous TFE (Tables
S1ꢀS5); free energies of formation of seven-membered ring
hydrocarbons (Table S6); plots of kinetic data and products from
solvolysis of cycloheptadienyl dichloroacetate in azide buffers
(Figures S1ꢀS4); computational data (Tables S7 and S8); NMR
spectra; and complete ref 68. This material is available free of
charge via the Internet at http://pubs.acs.org.
’ AUTHOR INFORMATION
Corresponding Author
rmof@ucd.ie
’ ACKNOWLEDGMENT
This work was supported by the Science Foundation Ireland
(Grant No. 04/IN3/B581). Financial support for D.E.B. from
EPSRC and the University of Sheffield (UK) is also gratefully
acknowledged, as is a Royal Society Conference Travel Grant for
P.W.F. The authors thank Yitzhak Appeloig, Herbert Mayr, and Paul
Schleyer for helpful discussions and suggestions, and Judy Wu and
Paul Schleyer for communicating results in advance of publication.
In the course of the reaction, it was noticeable that, as expected, the
concentration of the trifluoroethyl ether at first increased. However,
instead of reaching a constant value, at long reaction times it began to
decrease (Figure 1). As there was no sign of reaction to form a new
product, the most plausible explanation seemed to be that the ether is
sufficiently volatile to be lost through evaporation. The behavior was
confirmed insofar as if the reaction was carried out at a substantially
higher concentration of acid (1 M HClO4 instead of 0.1 M), so that it
was complete in a much shorter time, a larger amount of the trifluoro-
methyl ether was obtained than in the slower reactions.
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