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Philicities, Fugalities, and Equilibrium Constants
Herbert Mayr* and Armin R. Ofial
Department Chemie, Ludwig-Maximilians-Universität München, Butenandtstrasse 5-13 (Haus F), 81377 München, Germany
CONSPECTUS: The mechanistic model of Organic Chemistry is based on
relationships between rate and equilibrium constants. Thus, strong bases are
generally considered to be good nucleophiles and poor nucleofuges. Exceptions to
this rule have long been known, and the ability of iodide ions to catalyze nucleophilic
substitutions, because they are good nucleophiles as well as good nucleofuges, is just
a prominent example for exceptions from the general rule.
In a reaction series, the Leffler−Hammond parameter α = δΔG⧧/δΔG° describes
the fraction of the change in the Gibbs energy of reaction, which is reflected in the
change of the Gibbs energy of activation. It has long been considered as a measure
for the position of the transition state; thus, an α value close to 0 was associated with
an early transition state, while an α value close to 1 was considered to be indicative of a late transition state. Bordwell’s
observation in 1969 that substituent variation in phenylnitromethanes has a larger effect on the rates of deprotonation than on
the corresponding equilibrium constants (nitroalkane anomaly) triggered the breakdown of this interpretation. In the past, most
systematic investigations of the relationships between rates and equilibria of organic reactions have dealt with proton transfer
reactions, because only for few other reaction series complementary kinetic and thermodynamic data have been available.
In this Account we report on a more general investigation of the relationships between Lewis basicities, nucleophilicities, and
nucleofugalities as well as between Lewis acidities, electrophilicities, and electrofugalities. Definitions of these terms are
summarized, and it is suggested to replace the hybrid terms “kinetic basicity” and “kinetic acidity” by “protophilicity” and
“protofugality”, respectively; in this way, the terms “acidity” and “basicity” are exclusively assigned to thermodynamic properties,
while “philicity” and “fugality” refer to kinetics.
Benzhydrylium ions (diarylcarbenium ions) with para- and meta-substituents are used as reference compounds for these
investigations, because their Lewis acidities and electrophilicities can be varied by many orders of magnitude, while the steric
surroundings of the reaction centers are kept constant. The rate constants for their reactions with nucleophiles correlate linearly
over a wide range with the Lewis acidities of the benzhydrylium ions: from slow reactions with late transition states to very fast
reactions with early, reactant-like transition states (including reactions which proceed without an enthalpic barrier, ΔH⧧ = 0).
Thus, unequivocal evidence is obtained that even within a series of closely related reactions, the Leffler−Hammond α cannot be a
measure for the position of the transition state.
Differences in intrinsic barriers lead to deviations from the linear rate-equilibrium correlations and give rise to counterintuitive
phenomena. Thus, 1,4-diazabicyclo[2.2.2]octane (DABCO) reacts with lower intrinsic barriers than 4-(dimethylamino)pyridine
(DMAP) and, therefore, is a stronger nucleophile as well as a better nucleofuge than DMAP. Common synthetically used SN2
reactions are presented, in which weak nucleophiles replace stronger ones. Whereas solvolysis rates of alkoxy- and alkylsubstituted benzhydryl derivatives correlate linearly with the Lewis acidities of the resulting carbenium ions, this is not the case
for amino-substituted benzhydrylium ions, where differences in intrinsic barriers play a major role. The common rule that a
structural variation, which increases the electrophilicity of a carbocation at the same time reduces its electrofugality, does not hold
any longer. The need to systematically analyze the role of intrinsic barriers is emphasized.
Hammond’s postulate4 and its quantification by Leffler are
consequences of such considerations.5 Until 1969, it seemed to
be even possible to derive the position of the transition state
from the Leffler−Hammond coefficient α, which defines the
fraction of the change of the Gibbs energy of reaction, which is
reflected by the change of the Gibbs energy of activation.5
As illustrated in Figure 3, an α value close to 0 was
considered to be indicative of an early (reactant-like) transition
state, whereas an α value close to 1 was associated with a late
(product-like) transition state. This interpretation collapsed in
1. INTRODUCTION
Our comprehension of organic reactivities is coined by thinking
in thermodynamic terms. A typical example for this approach is
illustrated by Figure 1, which shows that the rate constants for
the reactions of 1-chlorobutane with different families of anions
correlate linearly with their Brønsted basicities expressed by
pKaH, i.e., the acidity constants of their conjugate acids.1,2 This
behavior has commonly been rationalized by the Bell−Evans−
Polanyi principle (Figure 2), which models the transition states
through the intersection of two correlation lines: one for the
breaking of a bond in the reactant and one for the formation of
the new bond in the product.3
© 2016 American Chemical Society
Received: February 9, 2016
Published: April 25, 2016
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Scheme 1. Nitroalkane Anomaly (Data from ref 6)
sum of α for forward and backward reaction must be 1.00, the
resulting value of α = −0.31 for the backward reaction leads to
the counterintuitive conclusion that less basic nitronate anions
are protonated faster than more basic ones.6
The term “nitroalkane anomaly”, commonly used to describe
this phenomenon, may lead to the assumption that the behavior
of nitroalkanes is unique. However, Leffler−Hammond
coefficients outside the range 0 < α < 1 are just spectacular
cases demonstrating that α cannot be a measure for the
position of the transition state.
The fact that the transition state cannot generally be
described by a merger of reactant and product configurations
has meticulously been analyzed by Jencks,7 Williams,8 Shaik,9
Bernasconi,10 and many others as quoted in refs 7−10. Pross
noted that α is ∞ for a series of identity reactions11 because
variation of Y affects ΔG⧧ while ΔG° stays 0 (Scheme 2).
Figure 1. Relationships between S N 2 reactivities toward 1chlorobutane and Brønsted basicities (with data from refs 1 and 2).
Scheme 2. Pross’ Analysis of Identity Reactions11
Figure 2. Illustration of the Bell−Evans−Polanyi principle.3
Prior to a general analysis of rate-equilibrium relationships let
us summarize the definitions of the key terms used in this
Account. According to IUPAC recommendations, Lewis acidity
and basicity are thermodynamic terms, while -philicity and
-fugality refer to kinetics (Chart 1).12 Electron-deficient species,
which may either be ionic or neutral (R+, E), can be regarded as
Lewis acids, electrophiles, or electrofuges, depending on the
properties which are considered. While Lewis acidities refer to
the equilibrium constants of their reactions with electron-surplus
compounds, electrophilicities refer to the rate constants of their
reactions with X− or Nu, and electrofugalities refer to the rate
constants of the corresponding backward reactions. Analogously,
Lewis basicities, nucleophilicities, and nucleofugalities describe
different properties of electron-surplus compounds, and
statements that a certain species X− behaves either as a
nucleophile or a base are obsolete.
When the solvated proton is selected as the reference Lewis
acid, we arrive at the lower part of Chart 1, which shows that
Brønsted basicity is a special case of Lewis basicity, while H−X
can be considered as a special type of Lewis pair. We think that
much confusion in teaching comes from the hybrid terms
“kinetic basicity” and “kinetic acidity”, which intermix kinetics
and thermodynamics. Though everybody understands what
“kinetic acidity” means, use of this term suggests that the
complementary term should be “thermodynamic acidity” and
thus obscures the generally accepted convention that “acidity”
by itself represents a thermodynamic property. For that reason,
Figure 3. Hammond−Leffler’s α as an alleged measure for the position
of the transition state.
1969, when Bordwell observed α = 1.31 for the deprotonation
of substituted 1-nitro-1-phenylethanes, indicating that variation
of the substituents X affects the energies of the transition states
more than the energies of the products (Scheme 1).6 As the
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Chart 1. Relationships Between Kinetic and Thermodynamic Terms
we recommend to replace the terms “kinetic basicity” and
“kinetic acidity” by “protophilicity” and “protofugality”,
respectively; “protophilicity” has previously been employed
nonuniformly to describe rate as well as equilibrium constants
of proton transfer reactions. With the definitions in Chart 1,
philicity and fugality refer consistently to kinetic properties,
while acidity and basicity are exclusively associated with
equilibrium constants and not with kinetics.
Please note that Lewis acidity and basicity as well as the
corresponding philicities and fugalities refer to a certain
reference compound. As there is an infinite number of potential
reference compounds, there is also an infinite number of Lewis
acidity and basicity scales as well as of philicity and fugality
scales. This Account will be restricted to reactions with carboncentered Lewis acids.
expressed by KA (eq 2), Hine suggested to derive carbon
basicities relative to OH− (KAR, eq 4) by multiplication of the
tabulated Brønsted basicities KA with the equilibrium constants
KHARA defined by eq 3.
KA R
R−OH + A− HoooI R−A + OH−
(1)
KA
H−OH + A− ⇌ H−A + OH−
KHA RA
(2)
R−OH + H−A HoooooI R−A + H−OH
(3)
KA R = KAKHA RA
(4)
However, when using the term “carbon basicity” in several of
our recent papers, we have realized that it was often
misinterpreted as “basicities of carbon-centered Lewis bases”
(i.e., basicities of carbanions). For that reason, we decided not
to use this term any longer and instead employ the less
ambiguous expression “Lewis basicities toward carbon-centered
Lewis acids”.14
Of course, there are thousands of carbon-centered Lewis
acids which might be selected as reference acids for a Lewis
basicity scale. The choice is limited by the fact, however, that
direct experimental determinations of the equilibrium constants
K, as described by eq 5, are only possible when the reactants LA
or LB coexist in comparable concentrations with the Lewis
adducts LA←LB.
2. LEWIS ACIDITIES AND BASICITIES
Most investigated rate-equilibrium relationships for organic
reactions are Brønsted correlations, i.e., correlations of rate
constants for certain reaction series with the pKa or pKaH values
of the corresponding reactants. The interpretation of these
correlations is not straightforward, however, when the rate
constants refer to reactions with C-, N-, Si-, or B-centered
electrophiles, while the equilibrium constants (pKa or pKaH)
refer to reactions with the proton.
Given that reactions with carbon-centered electrophiles are
of particular importance in organic chemistry, Hine introduced
the term “carbon basicity” for characterizing relative Lewis
basicities with respect to carbon centered Lewis acids.13 The
equilibrium constants KAR for the (hypothetical) reaction 1
reflect the relative basicities of A− and HO− toward R+. As the
relative Brønsted basicities of A− and HO− toward H+ are
K
LA + LB ⇌ LA←LB
(5)
To directly compare Lewis bases of widely differing
strengths, we selected a series of benzhydrylium ions Ar2CH+
as reference Lewis acids (Table 1), whose strengths are varied
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by substituents in para- and meta-position, while the steric
shielding of the reaction center is kept constant.
It was found that these equilibrium constants can be
described by the sum of a base-independent Lewis acidity
parameter LA and an acid-independent Lewis basicity
parameter LB (eq 6), which were obtained by subjecting 115
equilibrium constants (log K) for the reactions of the
benzhydrylium ions E1+−E20+ with 37 Lewis bases in
CH2Cl2 at 20 °C to least-squares minimization with the
definition LA[(4-MeOC6H4)2CH+] = 0.0. The resulting Lewis
acidity parameters LACH2Cl2 are listed in Table 1 and the
corresponding Lewis basicities LB have been reported in ref 14.
Table 1. Reference Lewis Acids E1+−E33+, Their Lewis
Acidities LACH2Cl2 and LAMeCN, and Calculated Methyl Anion
Affinities ΔGMA (for 20 °C, data from ref 14)
log K = LA + LB
(6)
The good fit of the experimental equilibrium constants to the
correlation lines in Figure 5 shows that the relative strengths of
the Lewis bases are independent of the nature of the
benzhydrylium ions and justifies enforcing a slope of unity in
the least-squares minimization according to eq 6.
When the Lewis bases are ordered according to increasing
LB from left to right and Lewis acids are ordered according to
increasing LA from top to bottom, as depicted in Figure 6,
Lewis adducts, which are located on the diagonal from bottom
left to top right, are formed with an equilibrium constant of K =
1 at 20 °C. The multicolor corridor in Figure 6 refers to
equilibrium constants in the range 1 < K (M−1) < 106, i.e.,
equilibrium constants which can easily be measured in
millimolar solutions. While Lewis acids and bases in the blue
sector do not coordinate in millimolar solution, Lewis adducts
in the red corridor are formed almost quantitatively.
Similar presentations can analogously be constructed for
other solvents. Only small changes of the relative Lewis
basicities can be expected when benzhydrylium ions are
replaced by other types of carbocations as references, but
significant changes of the ranking of the Lewis basicities will
occur when charges are generated or destroyed during Lewis
acid−Lewis base coordination. Lewis basicities determined with
respect to benzhydrylium ions furthermore do not apply for
interactions with very bulky reference acids (frustrated Lewis
pairs)15 or when the Lewis adducts are stabilized or destabilized
by anomeric16 or inverse anomeric effects,17 respectively.
Multiplication of the Lewis acidities LA listed in Table 1 with
−2.303RT yields standard Gibbs energies (20 °C) ΔG° for the
reactions of the corresponding Lewis acids with a Lewis base of
LB = 0. Figure 7 shows that these Gibbs energies correlate
linearly with quantum chemically calculated methyl anion
affinities ΔGMA of the corresponding benzhydrylium ions in the
gas phase. Since the calculated methyl anion affinities ΔGMA
correlate linearly with the corresponding H−, H2N−, and HO−
affinities with a slope of 1.0,18,19 the abscissa of Figure 7 can be
replaced by the affinity toward other anions. The linearity of
this correlation indicates the absence of differential solvation of
these benzhydrylium ions in dichloromethane. By this
correlation calculated gas phase data can be transferred into
equilibrium constants in solution without employing quantum
chemical solvent models.
Analogous correlations with slopes of ΔΔG° CH 2 Cl 2 /
ΔΔG°gas phase = 0.84−0.95 have been found for reactions with
neutral Lewis bases (pyridine, NH3, PH3, H2CCH−NH2),
indicating that the differences of the Lewis acidities of
benzhydrylium ions toward neutral Lewis bases are only
slightly smaller in the CH2Cl2 solution than in the gas phase.19
a
As reliable equilibrium constants in MeCN could only be determined
with highly stabilized benzhydrylium ions, the Lewis acidity scale in
MeCN was fixed at LA(E1+) = −12.76, the LA for E1+ in CH2Cl2
solution. bBenzhydrylium ions with p-phenoxy or p-phenylamino
groups deviate from the correlation used to calculate LAMeCN (see ref
14). cFrom LAMeCN = 0.878LACH2Cl2 − 1.60 (ref 14). dCalculated from
ΔGMA by the correlation equation shown in Figure 7. eHighly reactive
carbocations undergo Ritter reactions with MeCN.
In this way, we characterized strong Lewis bases through
photometric determination of the equilibrium constants K for
their reactions with highly stabilized benzhydrylium ions,
whereas weak Lewis bases were calibrated through their
reactions with less stabilized benzhydrylium ions (Figure 4).14
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Figure 4. Benzhydrylium ions as reference Lewis acids for the determination of Lewis basicities.14
Figure 5. Plot of log K for reactions of benzhydrylium ions E+ with Lewis bases in CH2Cl2 at 20 °C against the Lewis acidity parameters LACH2Cl2 of
the benzhydrylium ions (with data from ref 14).
with α values between 0.48 and 0.73 again shows that α cannot
be related to the position of the transition state.
If α were a measure of the position of the transition state,
one had to postulate that variation of the carbocations in each
of the depicted reaction series does not affect the transition
structures, i.e., that the positions of the transition states for slow
reactions with highly stabilized carbocations (bottom left) and
for the fast reactions with highly reactive carbocations (top
right) would be identical. This scenario is totally unrealistic
because some of these reaction series include also reactions
with rate constants of >(1−10) × 106 M−1 s−1, i.e., reactions
3. CORRELATIONS BETWEEN PHILICITIES AND
EQUILIBRIUM CONSTANTS
3.1. Electrophilicity vs Lewis Acidity
Figure 8 shows that the rate constants for the reactions of
different types of nucleophiles with benzhydrylium ions
correlate linearly with the corresponding Lewis acidities.14
Unlike in many Brønsted correlations (correlations with pKa
values), rate and equilibrium constants now refer to the same
reactions. The amazingly long linearity of these correlations
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Figure 6. When do Lewis acids and bases coordinate? (Reproduced with permission from ref 14 Copyright 2015 American Chemical Society).
of reaction ΔG° and the intrinsic barrier ΔG0⧧, which
corresponds to ΔG⧧ for a reaction with ΔG° = 0. Differentiation of eq 7 gives eq 8, which simplifies to eq 9 (see Chart
2) for |ΔG°| ≪ ΔG0⧧, which applies for the reactions under
consideration.
According to eq 9 (see Chart 2), a linear correlation between
ΔG⧧ and ΔG° can only exist if ΔG0⧧ remains constant
throughout the reaction series (α = 1/2) or varies proportionally with ΔG°. Values of α > 1/2, as observed for most reaction
series of Figure 8, imply that ΔG0⧧ decreases with increasing
exergonicity, which might be explained by an increasing
contribution of the HOMO−LUMO interaction, corresponding to increasing importance of inner-sphere electron transfer.
3.2. Nucleophilicity vs Lewis Basicity
Since rate constants (log k) and equilibrium constants (log K)
in Figure 9 refer to the same reactions, one of the problems
which hamper the straightforward interpretation of many
Brønsted correlations (rate constants for reactions with R−X vs
equilibrium constants for interaction with H+, see Figure 1) has
been eliminated.
As shown in Figure 9, rate constants correlate very poorly
with equilibrium constants even when reactions of nucleophiles
with the same central atom are compared. Thus, DABCO (1,4diazabicyclo[2.2.2]octane) is a much stronger nucleophile (i.e.,
reacts much faster) than NMI (N-methylimidazole) though
being a slightly weaker Lewis base. One has to conclude,
therefore, that the slightly higher Lewis basicity (ΔG°) of NMI
compared to DABCO is overcompensated by the significantly
higher intrinsic barrier (ΔG0⧧) for the reaction of NMI.
As the intrinsic barriers are related to the reorganization
energies λ (= 4ΔG0⧧),21,22 the low nucleophilic reactivities of
the imidazoles indicate that more structural reorganization,
Figure 7. Correlation of ΔG° (= −2.303RT·LACH2Cl2) for the reactions
with a Lewis base (LB = 0) with calculated methyl anion affinities
ΔGMA of E1+−E20+ (20 °C, with data from Table 1).
with activation enthalpies of ΔH⧧ = 0, where electrophiles and
nucleophiles combine without crossing an enthalpic barrier.20 A
theoretical rationalization for this behavior is missing.
According to Marcus theory (eq 7 (see Chart 2)),21,22 the
Gibbs energy of activation ΔG⧧ depends on the Gibbs energy
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Figure 8. Correlation of log k2 for the reactions of benzhydrylium ions E1+−E20+ with different nucleophiles in CH2Cl2 versus the corresponding
Lewis acidities LACH2Cl2 (from Table 1).14
Chart 2. Marcus Equation for Group Transfer Reactions
including solvent reorganization, is required when imidazolium
ions are generated from imidazoles than when quaternary
ammonium ions are generated from tertiary amines. A
rationalization for this behavior may be achieved by the
activation strain model.24
The different ranking of nucleophilicity and Lewis basicity
has previously been illustrated by the comparison of DABCO
and DMAP.25 Though DABCO reacts 103 times faster (i. e., is
more nucleophilic) with benzhydrylium ions than DMAP, the
low Lewis basicity of DABCO accounts for the fact that it does
not give a Lewis adduct with highly stabilized benzhydrylium
ions despite of extrapolated rate constants between 106 to 107
M−1 s−1, corresponding to reactions on the millisecond time
scale in millimolar solutions (Figure 10). This example
rationalizes why one cannot find carbenium ions, which react
slowly with tertiary amines. Because of the low intrinsic
barriers, reactions of carbocations with tertiary amines are
either extremely fast or do not occur at all.26 This point is
furthermore illustrated by Figure 9: Though eq 10 predicts fast
reactions between E2+ and all nucleophiles depicted there, the
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Figure 9. Correlation of log k for the reactions of nucleophiles with E2+ and E8+ (in MeCN at 20 °C) with the corresponding equilibrium
constants14 (closed circles, experimental rate constants from references quoted in ref 23; open symbols, log k extrapolated by using eq 10).
Figure 10. Differentiation of nucleophilicity and Lewis basicity for DABCO and DMAP (in MeCN, 20 °C, data from ref 25). aExtrapolated value
from this graph. bFrom eq 6 using data from ref 14.
open red circles indicate electrophile-nucleophile combinations
which do not give adducts in millimolar solutions because of
the high reversibility.
Figure 9 shows that Cl− is a much stronger nucleophile in
acetonitrile than N-methylimidazole (NMI). Scheme 3 thus
illustrates that in the synthesis of 1,3-dialkylated imidazolium
ions27 the weak nucleophile NMI replaces the strong
nucleophile Cl−. The reaction works, because imidazole is a
stronger Lewis base than chloride.
Analogously the formation of carboxylic esters from
carboxylate anions and benzyl bromide (Scheme 3)28 is
possible because carboxylate anions are stronger Lewis bases
than bromide anions. It should be noted, however, that the
relative Lewis basicities of anionic and neutral Lewis bases
Scheme 3. Substitutions of strong nucleophiles by weak
nucleophiles
depend on the nature of the solvent, and the ordering shown in
Figure 9 will be different in other solvents.
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Large differences in intrinsic barriers also account for the fact
that in many reactions of ambident nucleophiles, the products
of kinetic control differ from those formed under thermodynamically controlled conditions. The thiocyanate anion, for
example, gives thiocyanates with C-centered electrophiles
under conditions of kinetic control, and isothiocyanates
under conditions of thermodynamic control (Scheme 4).29
Earlier attempts to explain ambident reactivities by the ‘hard−
soft acid−base principle’ or the Klopman-Salem concept have
been discredited.30
Figure 12. Gibbs energy profiles for the deprotonation of nitromethane (left) and 2-nitropropane (right) by HO− (H2O, 25 °C).32
Scheme 4. Thiocyanate Anion as a Typical Example for an
Ambident Nucleophile
analogous for different carboxylate leaving groups in different
solvents. In all series, the benzhydrylium ions E1+ and E3+ with
annelated 5-membered heterocycles are generated more slowly
than benzhydrylium ions E2+ and E4+of similar Lewis acidity,
but with annelated 6-membered rings.
Since we were unable to measure equilibrium constants with
carbenium ions which are less stabilized than E20+, we cannot
extend Figure 13 to the right. To include also the less stabilized
carbenium ions E21+-E33+ in the electrofugality-Lewis acidity
correlations, we plotted the solvolysis rate constants log ks
against the calculated gas phase methyl anion affinities ΔGMA.
Figure 14 shows the same pattern as Figure 13, which was to be
expected because of the linear correlation between LACH2Cl2
and ΔGMA shown in Figure 7.
Why are there good correlations between rate and
equilibrium constants for weakly stabilized and destabilized
benzhydrylium ions on the right of Figures 13 and 14, but poor
correlations for stabilized benzhydrylium ions on the left?
From the laser-flash photolytically measured rate constants of
the reactions of chloride and bromide ions with weakly
stabilized and nonstabilized benzhydrylium ions, we know that
all reactions of chloride and bromide ions with the carbocations
are diffusion-controlled in the solvents used for the solvolyses,
i.e., these reactions do not have a barrier or their barrier is lower
than that due to diffusion.33 According to the principle of
microscopic reversibility, there also cannot be a barrier for the
reverse reaction, i.e., the transition states of the heterolytic
cleavages of (E20−E33)−X correspond to the ion-pairs
(Figure 15a).
Since the benzhydryl halides (E1−E13)+Cl− are ionic in the
common solvolytic media, the covalent benzhydryl carboxylates
(E1−E13)−O2CR were employed to investigate the rates of
solvolytic generation of the amino-substituted benzhydrylium
ions E1+−E13+. Direct rate measurements of the reactions of
these carbocations with carboxylate ions in the corresponding
solvents showed that these ion combinations proceed via
significant barriers,34 as illustrated in Figure 15b, which implies
that also the transition states of the heterolytic cleavages of
(E1−E13)−O2CR do not correspond to the carbocations.
Thus, the scatter in the left part of the correlations in Figures
13 and 14 is due to the fact that the barrier for the ionization
step does not only depend on the “stabilities” of the resulting
carbocations but also on the different magnitudes of the
intrinsic barriers.
In conclusion, these analyses show that only solvolysis rates
of substrates leading to highly reactive carbenium ions give
accurate information about their Lewis acidities (thermodynamic stabilities), whereas solvolysis rates of substrates, which
give rise to highly stabilized carbenium ions, cannot directly be
associated with “carbocation stabilities”. Detailed investigations
of trityl solvolyses confirmed this interpretation.35
4. CORRELATIONS BETWEEN FUGALITIES AND
EQUILIBRIUM CONSTANTS
4.1. Nucleofugality vs Lewis Basicity
Various reference reactions for establishing nucleofugality
rankings have previously been discussed.31 In heterolytic
bond fissions, the change in nucleofugality usually reflects a
fraction of the change in Lewis basicity. However, structural
modification may also have a greater effect on nucleofugality
than on Lewis basicity. As K = k→/k←, the 103-times faster
reaction of DABCO compared to DMAP (despite the 340times higher Lewis basicity of DMAP, Figure 10) implies that
the stronger nucleophile DABCO is also a 230 000-times better
nucleofuge than DMAP. The low reorganization energies for
the reactions of trialkylamines account for the high
nucleophilicity and nucleofugality of DABCO (Figure 11).
Figure 11. Gibbs energy profiles for the reactions of DABCO and
DMAP with E2+ (MeCN, 20 °C, with data from Figure 10, structure
for −CH(jul)2, see Table 1).
This situation is similar to that for the deprotonation of
nitroalkanes: Nitromethide is a stronger Brønsted base
(nitromethane is less acidic than 2-nitropropane) and a better
protofuge than 2-nitropropan-2-ide, i.e., the thermodynamically
less stable nitromethyl anion is formed faster (Figure 12).6,32
4.2. Electrofugality vs Lewis Acidity
Plots of solvolysis rate constants for benzhydrylium derivatives
Ar2 CH-X against the Lewis acidities of the resulting
benzhydrylium ions are linear in the right part of Figure 13,
but show a poor correlation on the left.14 The deviations from
the correlation lines are not random, however, but are
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Figure 13. Correlation of solvolysis rate constants log kS (25 °C) for (E1-E20)-X with the Lewis acidities LACH2Cl2 of benzhydrylium ions E1+-E20+
(PNB = p-nitrobenzoate, DNB = 3,5-dinitrobenzoate, 80A = 80/20 acetone/water; 90A = 90/10 acetone/water; 80AN = 80/20 acetonitrile/water;
data from ref 14).
Figure 14. Correlation for log ks for the solvolysis reactions of (E1−E33)−X with the methyl anion affinities ΔGMA(gas phase) of E1+−E33+ (with
data from ref 14, DCM = dichloromethane, for further abbreviations see Figure 13).
5. RELATIONSHIPS BETWEEN PHILICITIES AND
FUGALITIES
correlations. For that purpose, the kinetics of reactions of stable
carbocations and Michael acceptors with π-, n-, and σnucleophiles were determined, and it was found that the
resulting second-order rate constants at 20 °C can be described
by eq 10, which characterizes electrophiles by one solventindependent electrophilicity parameter E and nucleophiles by
two solvent-dependent parameters, nucleophilicity N and
susceptibility sN.
The calculation of absolute rate constants by the Marcus
equation (eq 7 (see Chart 2)) does not only require knowledge
of the Gibbs energies of reaction ΔG° but also of the intrinsic
barriers ΔG0⧧. As the latter are not easily accessible, we have
developed an empirical method to predict rate constants for the
reactions of electrophiles with nucleophiles from rate−rate
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benzhydrylium ions and structurally related Michael acceptors
(reference electrophiles) with an accuracy of better than a
factor of 2. Rate constants with other carbocations, Michael
acceptors, and electron-deficient arenes are predicted with an
accuracy of better than a factor of 10−100, which is considered
satisfactory in view of the reactivity range of 40 orders of
magnitude. Additional electrophile-specific susceptibilities are
needed to correlate SN2 reactions.37
Analogously, electrofugality and nucleofugality scales38 were
constructed by subjecting 628 solvolysis rate constants k25 °C for
different benzhydryl derivatives to a least-squares minimization
on the basis of eq 11. Electrofugality parameters Ef for 39
benzhydrylium ions and nucleofuge-specific parameters Nf and
sf for 101 common leaving groups in different solvents
(definition, Ef = 0 for (4-MeOC6H4)2CH+ and sf = 1 for Cl−
in ethanol) were thus obtained. Many additional parameters
have recently been reported by Kronja and co-workers.39
Figure 15. SN1 Reactions with diffusion-controlled (a) and activationcontrolled (b) ion recombination.
log k 20 ° C = s N(E + N )
(10)
log k 25 ° C = sf (Nf + Ef )
These parameters were obtained by subjecting a large
number of experimental rate constants to a least-squares
minimization on the basis of eq 10, with the definitions E[(4MeOC6H4)2CH+] = 0 and sN(2-methyl-pent-1-ene in CH2Cl2)
= 1.06 (formerly 1.00).20,36 While the definition of solventindependent electrophilicity parameters E, which shifts all
solvent effects into the nucleophile-specific parameters N and
sN, works well for reactions with carbocations and quinone
methides (reference electrophiles), consideration of electrophile-specific solvent effects will become necessary when
electrophiles as aldehydes or SN2 substrates are considered.
As illustrated in Figure 16 for the reactions of C-nucleophiles
with benzhydrylium ions, the rate−rate correlations remain
linear up to rate constants of 108 M−1 s−1 and only bend when
the diffusion limit is approached. So far, 1033 nucleophiles and
272 electrophiles have been characterized, and the data are
collected in a freely accessible database.23 Equation 10, which
covers a reactivity range of 40 orders of magnitude, predicts
absolute rate constants for the reactions of nucleophiles with
(11)
The excellent correlations shown in Figure 17 justify the
treatment of the electrofugalities Ef of benzhydrylium ions as
solvent-independent parameters, which shifts all solvent effects
into the nucleofuge-specific parameters Nf and sf. The
underlying assumption that carbocation solvation changes
proportionally with Ef does not generally hold for other types
of carbocations with the consequence that application of eq 11
to such systems leads to aberrations up to factors 50.
When one plots electrofugality vs electrophilicity, one
observes a linear correlation for benzhydrylium ions with E >
−2 and a large scatter for those with E < −2 (Figure 18).38 This
result is not surprising, because linear correlations between
philicities and fugalities can only exist if rate constants are
linearly related to equilibrium constants (eq 12), and it was
shown above that the linear relationship between electrofugalities and Lewis acidities (Figures 13 and 14) and between
electrophilicities and Lewis acidities (Figure 8) only hold for
alkoxy- and less stabilized benzhydrylium ions but not for
Figure 16. Plot of log k2 versus E for the reactions of benzhydryl cations with π-nucleophiles (CH2Cl2, 20 °C). Open symbols indicate rate constants
k2 > 108 M−1 s−1, which were not used for the correlation analysis. (Reproduced with permission from ref 20 Copyright 2012 American Chemical
Society).
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Figure 17. Plots of solvolysis rate constants log k (at 25 °C) for benzhydryl halides and various esters vs the electrofugality parameters Ef of
benzhydrylium ions. Mixtures of solvents are given as (v/v); A = acetone, E = ethanol, TFE = 2,2,2-trifluoroethanol. (Reproduced with permission
from ref 38 Copyright 2010 American Chemical Society).
J. P. Richard has shown that α-CF3-substituted benzyl cations
react with nucleophiles with similar rates as their CH3substituted analogues though they are 107 times more slowly
generated in solvolysis reactions (Scheme 5).40
Scheme 5. Comparison of Rates of Generation (as SN1
Intermediates) and Electrophilic Reactivities of α-Methyl
and α-Trifluoromethyl Substituted Benzyl Cations (Data
from ref 40, TFE = 2,2,2-trifluoroethanol)
Figure 18. Correlation of electrofugality Ef and electrophilicity E of
benzhydrylium ions (with data from ref 38).
highly stabilized amino-substituted analogues. Though the
deviations of the amino-substituted benzhydrylium ions from
the correlation lines in Figure 8 are small, they are not random
and show the same pattern for reactions with different
nucleophiles.
log k = α log K + c
(12)
While most chemists are well aware of the fact that the
intuitive expectation that strong nucleophiles are weak
nucleofuges (based on the Bell−Evans−Polanyi principle)
does not always hold (iodide ions are good nucleophiles and
good nucleofuges), the left part of Figure 18 illustrates that also
the inverse relationship between electrofugalities and electrophilicities does not generally hold.
Because of the low SN1 reactivities of vinyl halides, vinyl
cations have long been considered to be highly unstable
intermediates.41 However, the almost identical gas phase
hydride affinities of the benzyl (1002 kJ/mol) and αphenylvinyl cation (1004 kJ/mol)42 indicate that vinyl cations
do not have very low thermodynamic stabilities and that the
low rates of their formation are due to the high intrinsic
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barriers. Scheme 6 illustrates the fact that the triaryl substituted
vinyl cation, which is generated 108 times more slowly than the
to the LMU München in 1996. He is a member of the Bavarian
Academy of Sciences and the German National Academy of Sciences.
His work focuses on the quantification of organic reactivity.
Scheme 6. Comparison of SN1 Rates and Electrophilic
Reactivities of Vinyl and Benzhydryl Derivatives
Armin R. Ofial studied chemistry at the TU Darmstadt (doctoral
degree 1996). Since 1997 he has been a Research Associate at the
LMU München where he habilitated in 2013. His research interests
include reactions of iminium ions, chemical kinetics, and C−H bond
functionalizations.
■
ACKNOWLEDGMENTS
Dedicated to Professor George A. Olah. We thank all associates
who have contributed to the development of this concept and
Professor Reinhard Brückner (Freiburg) for helpful comments.
■
Extrapolated from measurements at 120 °C, ref 43. bCalculated from
data in ref 38. cFrom ref 44. dFrom ref 45.
a
bis(p-tolyl)methylium ion, reacts even slightly slower with
trifluoroethanol than the rapidly generated bis(p-tolyl)methylium ion.
6. CONCLUSION
The Bell−Evans−Polanyi principle, commonly used to rationalize relationships between rate and equilibrium constants
within reaction series, remains to be the first guide for
predicting the influence of structural variation on the rates of
polar organic reactions. However, changes in intrinsic barriers
often disturb the linear relationships between nucleophilicity
and Lewis basicity on one side and between electrophilicity and
Lewis acidity on the other. As a consequence, structural
variations, which are associated with a change of intrinsic
barriers, may lead to the counterintuitive observation that
structural variations in nucleophiles may simultaneously
increase nucleophilicity and nucleofugality. Analogously,
structural variations in electrophiles may simultaneously
increase (or reduce) electrophilicity and electrofugality. We
hope that this Account will stimulate theoretical chemists to
systematically analyze the origin of intrinsic barriers and thus
arrive at a deeper understanding of organic reactivity.
■
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AUTHOR INFORMATION
Corresponding Author
*E-mail: [email protected].
Funding
Financial support by the Deutsche Forschungsgemeinschaft
(SFB 749, Project B1) is gratefully acknowledged.
Notes
The authors declare no competing financial interest.
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