Scales of Lewis basicities toward C-centered Lewis acids (Carbocations)

Article

pubs.acs.org/JACS

Scales of Lewis Basicities toward C‑Centered Lewis Acids

(Carbocations)

Herbert Mayr,* Johannes Ammer, Mahiuddin Baidya, Biplab Maji, Tobias A. Nigst, Armin R. Oﬁal,

and Thomas Singer

Department Chemie, Ludwig-Maximilians-Universitat Munchen, Butenandtstraße 5-13, Haus F, 81377 Munchen, Germany

̈

S

* Supporting Information

ABSTRACT: Equilibria for the reactions of benzhydryl cations (Ar₂CH⁺)

with phosphines, tert-amines, pyridines, and related Lewis bases were

determined photometrically in CH₂Cl₂and CH₃CN solution at 20 °C.

The measured equilibrium constants can be expressed by the sum of

two parameters, deﬁned as the Lewis Acidity (LA) of the benzhydrylium

ions and the Lewis basicity (LB) of the phosphines, pyridines, etc. Least-

squares minimization of log K = LA + LB with the deﬁnition LA = 0 for

(4-MeOC₆H₄)₂CH⁺gave a Lewis acidity scale for 18 benzhydrylium

ions covering 18 orders of magnitude in CH₂Cl₂as well as Lewis

basicities (with respect to C-centered Lewis acids) for 56 bases. The Lewis acidities correlated linearly with the quantum chemically

calculated (B3LYP/6-311++G(3df,2pd)//B3LYP/6-31G(d,p) level) methyl anion aﬃnities of the corresponding benzhydrylium

ions, which can be used as reference compounds for characterizing a wide variety of Lewis bases. The equilibrium measurements

were complemented by isothermal titration calorimetry studies. Rates of S_N1 solvolyses of benzhydryl chlorides, bromides, and

tosylates derived from E(13−33)⁺, i.e., from highly reactive carbocations, correlate excellently with the corresponding Lewis

acidities and the quantum chemically calculated methyl anion aﬃnities. This correlation does not hold for solvolyses of derivatives of

the better stabilized amino-substituted benzhydrylium ions E(1−12)⁺. In contrast, the correlation between electrophilic reactivities

and Lewis acidities (or methyl anion aﬃnities) is linear for all donor-substituted benzhydrylium ions E(1−21)⁺, while the acceptor-

substituted benzhydrylium ions E(26−33)⁺react more slowly than expected from their thermodynamic stabilities. The boundaries

of linear rate-equilibrium relationships were thus deﬁned.

rates of the reactions of a series of B⁻with a certain reference

INTRODUCTION

■

electrophile) with the corresponding equilibrium constants and

to use the terms hydrogen basicity, carbon basicity, and sulfur

basicity for comparing the relative aﬃnities of various bases

toward the proton, carbon-centered Lewis acids (e.g.,

carbenium ions), or sulfur-centered Lewis acids, respectively.⁹

As relative carbon basicities should vary at least somewhat with

the nature of the reference carbon acid, for certain purposes a

further subdivision into the more speciﬁc categories methyl

basicity, phenyl basicity, acetyl basicity, etc., may be

appropriate.¹⁰The association constants K for combinations

of carbocations R⁺with Lewis bases B⁻are given by eq 1.

The equilibrium constant K (eq 1) is related to Brønsted

basicity 1/K_awhich describes the aﬃnity of B⁻toward the

Relationships between rate and equilibrium constants are a

key, possibly the most important key, for understanding organic

reactivity.¹⁻⁵In this context, Brønsted correlations,^1,4i.e.,

relationships between rate constants and pK_avalues, play a

central role, because pK_avalues are available for most classes

of organic compounds.^6,7Recently, even a scale of absolute

Brønsted acidities has been proposed.⁸The fundamental

problem of these correlations is obvious, however: The pK_a

(−log K_a) values of the acids HB express the relative aﬃnities

of their conjugate bases (B⁻) toward the proton and, therefore,

the rates of the reactions of nucleophiles B⁻with other classes

of electrophiles cannot be expected to be tightly correlated

with pK_a.

proton (eq 2)^11,12and Deno’s pK_Rvalues, which describe

+

the equilibrium constants for the reactions of R⁺with water

(eq 3).^13,14

In their seminal 1965 paper, titled “Carbon Basicity”,¹⁵Hine

and Weimar pointed out that the basicities of B⁻toward cations

R⁺relative to their Brønsted basicities can be expressed by the

equilibrium constant K^R_H^B_Bfor eq 4,^12,16which is accessible from

compiled thermodynamic data.

In view of this problem, Parker suggested to compare the

Received: November 12, 2014

nucleophilic reactivities of diﬀerent bases B⁻(i.e., the relative

A

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Table 1. Reference Lewis Acids E(1-33)⁺and Their Lewis

Acidities LA_{CH Cl}and LA_{CH CN}, Calculated Methyl Anion

2

3

+

Aﬃnities ΔG_MA, and pK_RValues

Combination of eqs 2−4 gives access to absolute values of

Lewis acid/Lewis base association constants (eq 1).^12,16,17

Kessler and Feigel demonstrated for few systems that

equilibrium constants for combinations of carbocations with

anions B⁻correlate with the pK_Rvalues of the carbocations

+

and the pK_avalues of the conjugate acids HB.¹⁸Takeuchi and

Kitagawa reported analogous relationships for combinations of

carbocations with carbanions.¹⁹

However, the calculation of Lewis acid/Lewis base

association constants K from eq 1 has not frequently been

used in practice, probably because of the lack of a suﬃcient

+

number of suitable pK_Rvalues and the diﬃculties to properly

handle the inﬂuence of solvents on these equilibrium constants.

We now report on an alternative, easily applicable method for

determining Lewis basicities toward C-centered electrophiles

which uses benzhydrylium ions as reference Lewis acids

(Scheme 1). This method is analogous to that which we have

Scheme 1. Benzhydrylium Ions E⁺as Reference Lewis Acids

for the Determination of Lewis Basicities

previously used for the construction of comprehensive

nucleophilicity²⁰⁻²²and nucleofugality²³scales where benzhy-

drylium ions Ar₂CH⁺(E⁺) were employed as reference

electrophiles and reference electrofuges, respectively. As the

Lewis acidities of Ar₂CH⁺(E⁺) can widely be varied by

modifying the substituents at the arene rings, strong Lewis

bases can be characterized by measuring their coordination

equilibria with weakly Lewis-acidic (donor-substituted) benzhy-

drylium ions, while weak Lewis bases can be characterized by

measuring their coordination equilibria with less stabilized

more Lewis-acidic benzhydrylium ions. In order to keep the

steric demand of the electrophilic reaction center constant, only

m- and p-substituted benzhydrylium ions have been employed

for these equilibrium measurements, as for the previous kinetic

investigations (Table 1).²⁰⁻²³

By using the method of overlapping correlation lines, we will

derive a Lewis acidity scale for benzhydrylium ions in CH₂Cl₂

solution, which can be used for the characterization of a large variety

of Lewis bases by photometric measurements of equilibrium con-

stants. We will then show that the Lewis acidities thus obtained

correlate well with quantum chemically calculated methyl anion

aﬃnities in the gas phase. Since the term “carbon basicity”, as

deﬁned by Parker and Hine,^9,15is often misunderstood as

“reactivities of carbon bases”, we will avoid this term and instead

refer to “Lewis basicity with respect to certain Lewis acids”.

Correlating the Lewis acidities and Lewis basicities derived in

this work with the corresponding rate constants will provide

important insights into the role of intrinsic barriers^24,25in polar

organic reactivity. We address this aspect only brieﬂy in this

a

We use the same numbering as in ref 22 and omit the

b

ferrocenyl(phenyl)methylium ion (E12⁺). Lewis acidities LA_{CH Cl}

2

c

and LA_{CH CN}of E⁺as deﬁned by eq 7, this work. Methyl anion

3

aﬃnities of E⁺calculated at the B3LYP/6-311++G(3df,2pd)//B3LYP/

d

6-31G(d,p) level of theory, this work. Unless noted otherwise: data

from ref 26 adjusted to the H_Racidity scale from ref 14; see section S2

e

f

of the Supporting Information for details. Not available. From ref 14.

g

h

Not determined. From ref 27.

article to demonstrate the relevance of the data presented in

this work, and will elaborate this facet in more detail in sub-

sequent publications.

LEWIS ACIDITY AND BASICITY SCALES

■

Equilibrium Constants in CH₂Cl₂at 20 °C. As

benzhydrylium ions E⁺are colored, the equilibrium constants

K for their reactions with Lewis bases (Scheme 1) can be deter-

mined photometrically. We have previously employed this

method to determine the equilibrium constants K for some

reactions of E⁺with phosphines,²⁸pyridines,²⁹isothioureas,³⁰

guanidines,³¹oxazolines and thiazolines,³²and other Lewis

bases in dichloromethane. For the calibrations in this work, we

selected the most precise published experimental data and

collected them in Table 2. Equilibrium constants, which were

B

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Table 2. Equilibrium Constants K (M⁻¹) for the Reactions of Benzhydrylium Ions E⁺with Lewis Bases N in CH₂Cl₂at 20 °C

and Comparison with Equilibrium Constants K_calc(M⁻¹) Calculated from Eq 7

C

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Table 2. continued

D

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Table 2. continued

a

b

Photometric determination from this work unless indicated otherwise. Calculated from eq 7 using LA_{CH Cl}from Table 1 and LB_{CH Cl}from this

2

c

d

e

f

g

h

table. From ref 31. From ref 30. From ref 28. From ref 29. From ref 32. The ΔΔG⁰(−70 °C) values and ΔΔS⁰≈ 0 have been reported for the

i

34

−

reverse (ionization) reactions E(15−20)-Cl + BCl₃⇌ E(15−20)⁺+ BCl₄. These values were combined with ΔG⁰(−70 °C) and ΔS⁰for the

i

ionization of E20-Cl (see footnote j) to calculate the ionization equilibrium constants 1/K at 20 °C. Only one equilibrium constant was used for the

j

determination of LA_{CH Cl}. 1/K (20 °C) was calculated from the thermodynamic parameters of the ionization reaction E20-Cl + BCl₃⇌ E20⁺+

2

−

BCl₄: ΔH⁰= −32.6 kJ mol⁻¹(ref 34) and ΔG⁰(−70 °C) = −7.0 kJ mol⁻¹(ref 35) (and thus ΔS⁰= −126 J K⁻¹mol⁻¹).

i

less accurate due to the occurrence of slow subsequent

reactions, or which were determined indirectly from the ratio

of rate constants k_forward/k_backward(Scheme 1), are not included

in Table 2.

The ionization entropy of ΔS⁰= −126 J K⁻¹mol⁻¹was then

i

used to convert the ΔG⁰(−70 °C) values to 20 °C and to

i

calculate the equilibrium constants 1/K for the reactions of eq 5

at 20 °C; the inverse values (K) yield the required equilibrium

constants for the combination reactions (Table 2). Due to the

absence of side-reactions at low temperatures (−70 °C), we

could thus extend the experimental Lewis acidity scale in

CH₂Cl₂to benzhydrylium ions as reactive as E20⁺. The more

electrophilic benzhydrylium ions E(21−33)⁺undergo side

reactions so readily (e.g., Friedel−Crafts-type reactions with the

Lewis adducts) that we were not able to ﬁnd conditions which

allowed us to determine equilibrium constants for the reactions

of these carbocations with Lewis bases.

Correlation Analysis of the Equilibrium Constants in

CH₂Cl₂. The equilibrium constants K for the reactions of

benzhydrylium ions with Lewis bases listed in Table 2 can be

described by the two-parameter equation (eq 7), which

characterizes benzhydrylium ions by the parameter LA (Lewis

acidity) and Lewis bases by the parameter LB (Lewis basicity).

In order to link the previously reported equilibrium constants

with each other, we have now employed the same method to

determine further 74 equilibrium constants for the reactions of

benzhydrylium ions with pyridines, pyrimidine, quinoline, and

isoquinoline, as well as with phosphines, sulﬁdes, and dimethyl

selenide in CH₂Cl₂(Table 2; details in section S8 of the

Supporting Information). For these measurements, we likewise

applied the strict requirement that the determination of the

equilibrium constant should not be disturbed by subsequent

reactions. This restriction implies that in CH₂Cl₂at 20 °C only

equilibrium constants for reactions of the benzhydrylium ions

E(1−16)⁺were determined, because at room temperature, the

more reactive benzhydrylium ions E(17−33)⁺react too quickly

with traces of impurities which are present in our highly

puriﬁed CH₂Cl₂.³³

The equilibrium constants K (20 °C) for the reactions of

E(15−20)⁺with BCl₄in CH₂Cl₂(N37), which are listed in

−

log K = LA + LB

(7)

Table 2, were calculated from the previously reported equilib-

rium constants for the ionization reactions (eq 5) at −70 °C.³⁴

The LA parameters of E(1−20)⁺listed in Table 1 and the LB

parameters of N(1−37) in CH₂Cl₂listed in Table 2 were

calculated by a least-squares minimization: For that purpose, we

minimized Δ²speciﬁed by eq 8 using the nonlinear solver

program “What’s Best! 7.0” by Lindo Systems Inc.³⁶In the

following, we will use subscripts to indicate the solvent to

which the LA and LB parameters refer.

ΔG⁰

i

−

E(15−20)‐Cl + BCl₃HooooI E(15−20)⁺+ BCl₄

(5)

For the reaction of E20-Cl with BCl₃, an ionization free

energy of ΔG⁰(−70 °C) = −7.0 kJ mol⁻¹was measured

i

conductometrically in CH₂Cl₂solution at −70 °C.³⁵This value

can be combined with the calorimetrically determined heat

2

Δ =

(log K − log K

(log K − (LA + LB))²

)

calc

of ionization of E20-Cl in CH₂Cl₂/BCl₃at −70 °C (ΔH⁰=

∑

i

−32.6 kJ mol⁻¹)³⁴to calculate the ionization entropy in

=

(8)

CH₂Cl₂as ΔS⁰= −126 J K⁻¹mol⁻¹. As the diﬀerences of

i

the entropies for the ionizations of E(16−18)-Cl are small

(ΔΔS⁰≈ 0),³⁴the value of ΔS⁰= −126 J K⁻¹mol⁻¹was

i

A total of 115 equilibrium constants for the reactions

of 18 benzhydrylium ions with 37 Lewis bases were em-

ployed for this correlation analysis; the LA_{CH Cl}parameter of

assumed to hold also for the ionizations of E(15−19)-Cl

by BCl₃in CH₂Cl₂. The diﬀerences in free energy ΔΔG⁰

i

2

(−70 °C) determined by NMR spectroscopic measurements

the dianisylcarbenium ion (E15⁺) was set to 0.00, as this

carbocation also served as reference point for the correlations

of our kinetic data.²⁰⁻²³Table 2 provides a comparison of

the calculated equilibrium constants K_calcobtained in this

manner with the experimental values of K(CH₂Cl₂). None of

the calculated values deviates from the experimental values

by more than a factor of 1.7, which corroborates the appli-

cability of eq 7.

of ionization equilibria for E(15−20)-Cl (eq 6)³⁴were then

anchored to the directly measured ionization free energy ΔG⁰

i

(−70 °C) for E20-Cl.³⁵

Ar₂CH⁺BCl₄⁻+ Ar′₂CH‐Cl

ΔΔG⁰

i

−

HoooooI Ar CH‐Cl + Ar′₂CH⁺BCl₄

(6)

2

E

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Figure 1. Plot of log K for reactions of benzhydrylium ions E⁺with Lewis bases in CH₂Cl₂against the Lewis acidity parameters LA_{CH Cl}of the

2

benzhydrylium ions. The lines have a slope of unity and were calculated from eq 7. Some correlation lines have been omitted for the sake of clarity

(see Figure S1.1 in section S1 of the Supporting Information).

The quality of the correlations is illustrated by Figure 1,

which plots log K(CH₂Cl₂) for the reactions of the

benzhydrylium ions (E⁺) with Lewis bases against the LA_{CH Cl}

equilibrium constants for the correlation analysis. Therefore,

equilibrium constants for reactions of benzhydrylium ions

which are more reactive than E8⁺are not included in Table 3,

because these benzhydrylium ions were found to undergo slow

reactions with impurities that remain present in highly puriﬁed

CH₃CN.

A comparison of Tables 2 and 3 shows that the equilibrium

constants K are generally 1.3−9 times (reactions of E7⁺, 12−38

times) larger in CH₃CN than in CH₂Cl₂solution, i.e., the

formation of adducts from benzhydrylium ions and neutral

Lewis bases is more favorable in CH₃CN than in CH₂Cl₂. This

diﬀerence indicates that the onium salts generated by the

reaction of the benzhydrylium ions with the neutral Lewis bases

(Scheme 1) are better stabilized by the polar solvent CH₃CN

than the benzhydrylium ions, in which the charge is highly

dispersed. The equilibrium constants for the combinations of

the benzhydrylium ions E⁺with the anions N(45−47) are so

large in CH₂Cl₂that their magnitude could not be measured by

the photometric method employed in this work.

2

parameters of the benzhydrylium ions. Equation 7 implies that

the correlation lines for all Lewis bases are parallel to each

other. The good agreement between experimental and cal-

culated values shown in Figure 1 for all investigated classes of

compounds conﬁrms that, unlike in the analogous treatment of

the corresponding rate constants,²⁰⁻²³sensitivity parameters

are not needed. Thus, the parameters LA_{CH Cl}and LB_{CH Cl}of

2

the two reaction partners, which adopt the dimension of a²reac-

tion free energy when multiplied with −RT ln(10), combine

additively to describe the Gibbs free energies of the combina-

tion reactions (−RT ln K).

The fact that a sensitivity parameter is not required is due

to the fact that the steric surroundings of the reaction centers

of the benzhydrylium ions are kept constant (only p- and

m-substitutents) and furthermore indicates that the electron

densities in the benzhydrylium fragments of the diﬀerent Lewis

adducts are not signiﬁcantly altered.

Equilibrium Constants in CH₃CN at 20 °C. In order to

study the role of the solvent, we have also investigated the

reactions of E(1−8)⁺with Lewis bases in CH₃CN solution.

Table 3 lists 96 equilibrium constants, 56 of which have been

determined in this work, while the others have previously been

reported.³⁷⁻⁴⁰Again we have employed only the most reliable

A closer look at the data is provided by Figure 2, which plots

log K(CH₃CN) for reactions of benzhydrylium ions E⁺with

pyridines and phosphines in CH₃CN (Table 3) against log K

(CH₂Cl₂) for the same reactions in CH₂Cl₂(Table 2). Two

observations can be made: (a) the equilibrium constants for the

reactions of pyridines (green circles) experience a larger solvent

eﬀect (further remote from the dashed unity line) than those

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Table 3. Equilibrium Constants K (M⁻¹) for the Reactions of the Benzhydrylium Ions E⁺with Lewis Bases N in CH₃CN

at 20 °C and Comparison with the Equilibrium Constants K_calc(M⁻¹) Calculated from Eq 7

G

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Table 3. continued

a

b

c

d

Photometric determination from this work unless indicated otherwise. Calculated from eq 7. From ref 37. ΔH⁰and ΔS⁰were determined from a

van’t Hoﬀ analysis of the photometrically determined equilibrium constants at diﬀerent temperatures ranging from −10 to +20 °C, this work;

e

f

see end of section S8 in the Supporting Information for details. ΔH⁰= −53.5 kJ mol⁻¹and ΔS⁰= −99.2 J K⁻¹mol⁻¹. ΔH⁰= −50.7 kJ mol⁻¹and ΔS⁰=

g

h

i

j

−88.7 J K⁻¹mol⁻¹. ΔH⁰= −40.5 kJ mol⁻¹and ΔS⁰= −101.4 J K⁻¹mol⁻¹. From ref 38. Equilibrium constants at 25 °C, from ref 39. From ref 40.

for the reactions of phosphines (orange triangles), and (b) the

equilibrium constants for reactions of the phenylamino-sub-

stituted benzhydrylium ion E7⁺(open symbols) experience an

unusually large solvent eﬀect. Possibly, n−π* interactions in the

pyridinium fragments account for the fact that Lewis adducts

generated from pyridines are better stabilized by acetonitrile

than other Lewis adducts.

by minimizing Δ²as deﬁned in eq 8. As precise equilibrium

constants for the reactions of E15⁺(LA_{CH Cl}= 0) with Lewis

2

bases could not be determined in CH₃CN (Table 3), we

deﬁned LA_{CH CN}(E1⁺) = −12.76 (i.e., the same value as ob-

3

tained for E1⁺in CH₂Cl₂) as the reference point. The good

agreement between calculated and experimental equilibrium

constants (last column of Table 3) shows that eq 7 also holds in

Correlation Analysis of the Equilibrium Constants in

CH₃CN. Although Figure 2 indicates that the equilibrium con-

stants for the reactions in CH₃CN correlate with those for the

reactions in CH₂Cl₂, we did not make any a priori assumptions

about the eﬀect of the solvent on the Lewis acids and bases.

Instead, we subjected the CH₃CN data to an independent

correlation analysis, and subsequently compared the results.

We thus performed another least-squares optimization

according to eq 7 for the equilibrium constants from Table 3

CH₃CN and allows us to derive the LA

and LB

CH₃CN

parameters for CH₃CN solution which are listed in Table 3. A

graphical illustration of the correlations is given in Figure 3,

which plots log K (CH₃CN) for the reactions of benzhydrylium

ions with Lewis bases in CH₃CN against the LA

param-

CH₃CN

eters of the benzhydrylium ions E⁺in CH₃CN.

Remarkably, also the benzoate anions N(45−47)³⁹and

thiocyanate anion (N48, reaction at N)⁴⁰follow the same

H

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free energies ΔG_MA(eq 9) in the gas phase, were calculated for

32 benzhydrylium ions on the B3LYP/6-311++G(3df,2pd)//

B3LYP/6-31G(d,p) level (see sections S9−S11 in the

Supporting Information).⁴¹

−

E⁺+ CH₃→ E‐CH₃

(9)

Full geometry optimizations and vibrational analyses were

performed at the B3LYP/6-31G(d,p) level of theory. The un-

scaled harmonic vibrational frequencies were used to calculate

the thermal corrections to 298.15 K, which were applied to

single point energies from B3LYP/6-311++G(3df,2pd) level to

give H₂₉₈and G₂₉₈. The Boltzmann distribution was used to

calculate the statistical weights of the individual conformers,

and averaged energies were used for the calculations of the

methyl anion aﬃnities ΔG_MA, which are listed in Table 1.

Zhu et al. have previously calculated the free energies

ΔGg* for hydride transfer from the diarylmethanes E-H to the

benzyl cation in the gas phase (eq 10) on the BLYP/6-311++G

(2df, 2p) level.⁴²The reverse reaction of eq 10 provides the

relative hydride aﬃnities of the benzhydrylium ions E⁺.

Figure 2. Plot of log K(CH₃CN) for reactions of benzhydrylium ions

E⁺with pyridines (green circles) and phosphines (orange triangles) in

CH₃CN against log K(CH₂Cl₂) for the same reactions in CH₂Cl₂.

Pyridines: log K(CH₃CN) = 0.913 log K(CH₂Cl₂) + 0.984, R²= 0.977.

Phosphines: log K(CH₃CN) = 0.872 log K(CH₂Cl₂) + 0.673, R²=

0.990. The data points for E7⁺(empty symbols) were not used for the

correlations.

+

E‐H + PhCH₂⇌ E⁺+ PhCH₂‐H

(10)

Figure 4 shows a linear correlation with unity slope between

the relative hydride anion aﬃnities in the gas phase (−ΔG_g*)

Figure 4. Correlation of the calculated free energies ΔG_g* (kJ mol⁻¹)

for hydride transfer from the diarylmethanes Ar₂CH₂(E-H) to the

benzyl cation in the gas phase (eq 10)⁴²with the calculated methyl anion

aﬃnities ΔG_MA(kJ mol⁻¹) of the benzhydrylium ions E⁺in the gas phase

(eq 9) from this work (ΔG_g* = −1.04ΔG_MA− 971; R²= 0.998).

reported by Zhu⁴²and the methyl anion aﬃnities ΔG_MAin

the gas phase calculated in this work. This correlation implies

that structural variation of the benzhydrylium ions aﬀects their

Figure 3. Plot of log K(CH₃CN) for reactions of benzhydrylium ions

E⁺with Lewis bases in CH₃CN against the Lewis acidity parameters

LA_{CH CN}of the benzhydrylium ions in CH₃CN calculated from eq 7.

Some³correlation lines have been omitted for the sake of clarity (see

Figure S1.2 in section S1 of the Supporting Information).

aﬃnities toward diﬀerent anions (CH₃or H⁻) to equal ex-

−

tents, in line with previous analyses which also included hydrox-

ide aﬃnities.⁴³This behavior reﬂects the fact that variation of

the substituents aﬀects the free energies of the neutral adducts

E-CH₃and E-H almost equally.

correlation as the pyridines and phosphines (Table 3 and

Figure 3).

Methyl Anion Aﬃnities of the Benzhydrylium Ions in

the Gas Phase. In order to investigate the eﬀect of solvation

on the relative Lewis acidities of benzhydrylium ions and to

extend the Lewis acidity scale, we performed quantum chemical

calculations. The methyl anion aﬃnities, deﬁned as the Gibbs

Quantum Chemical Calculations and Solvation Ef-

fects. Figure 5 illustrates that the Lewis acidity parameters

LA_{CH Cl}of the benzhydrylium ions E(1−20)⁺, which were

2

derived ²from equilibrium constants in CH₂Cl₂, correlate linearly

with the methyl anion aﬃnities ΔG_MAof these benzhydrylium

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Figure 5. Correlation of the Lewis acidities LA

of the

CH₂Cl₂

Figure 6. Plot of the LA_{CH CN}parameters for benzhydrylium ions in

3

benzhydrylium ions E⁺(eq 7) with calculated methyl anion aﬃnities

CH₃CN versus their LA_{CH Cl}parameters in CH₂Cl₂. The point for

2

ΔG_MA(eq 9) of E⁺(−RT ln(10)LA

= 0.652ΔG_MA+ 487; R²=

CH₂Cl₂

E7⁺(open blue circle) was not used for the correlation: LA_{CH CN}

=

3

0.878LA_{CH Cl}− 1.60; R²= 0.999.

0.987). Blue symbols: p-phenylamino- and p-phenoxy-substituted

2

benzhydrylium ions.

The LB_{CH CN}parameters derived from the equilibrium

3

constants in CH₃CN (Table 3) also correlate linearly with

the corresponding LB_{CH Cl}parameters in CH₂Cl₂(Table 2). In

Figure 7, which spans almost 10 orders of magnitude in

ions in the gas phase. This correlation implies that there is

generally no diﬀerential solvation of the benzhydrylium ions

E(1−20)⁺; i.e., the solvation energies change linearly with the

thermodynamic stabilities of the carbocations, in line with

previous conclusions.⁴²⁻⁴⁵

2

The slope of the correlation in Figure 5 (0.65 at 20 °C)

shows that substituent variation aﬀects the Lewis acidities of the

benzhydrylium ions in CH₂Cl₂by approximately 65% of the

anion aﬃnities in the gas phase. This value is in agreement with

earlier results for a smaller series of carbenium ions.⁴³

As mentioned above (Figure 2), the equilibrium constants

for the reactions of E7⁺with pyridines and phosphines show an

unusual solvent dependence. The deviating behavior of E7⁺is

also evident in Figure 5: Although E6⁺and E7⁺have similar

methyl anion aﬃnities ΔG_MA, the p-N(Me)(Ph)-substituted

benzhydrylium ion E7⁺has a considerably higher Lewis acidity

LA_{CH Cl}than the p-NMe₂-substituted analogue E6⁺. Similarly,

2

the o²ther p-phenylamino- and p-phenoxy-substituted benzhy-

drylium ions (blue symbols in Figure 5) also have LA_{CH Cl}

2

values which are about one unit larger than those of

carbocations with comparable ΔG_MAhaving only p-alkylamino

or p-alkoxy substituents (compare E9⁺/E8⁺, E11⁺/E10⁺, E16⁺/

E15⁺, E19⁺/E18⁺).⁴⁶

Figure 7. Plot of the LB_{CH CN}parameters for pyridines (green circles)

3

and phosphines (orange triangles) in CH₃CN versus their LB_{CH Cl}

2

parameters in CH₂Cl₂: LB_{CH CN}= 0.828LB_{CH Cl}+ 3.22; R²= 0.991.²

3

2

Figure 6 correlates the LA_{CH CN}parameters for E(1−8)⁺

3

obtained from the equilibrium constants in CH₃CN (Table 3)

with the LA_{CH Cl}parameters obtained from the equilibrium

reactivity, the small diﬀerences of solvation on the reactions of

pyridines and phosphines, which have been displayed in Figure 2,

are hardly noticeable. Figure 7 shows that the order of Lewis

basicities is more or less the same for neutral Lewis bases in

CH₃CN and in CH₂Cl₂. The observation that, in contrast

to the behavior in CH₃CN (Figure 3), all benzhydrylium

ions E⁺investigated in this work combine quantitatively

with the carboxylate anions N(45−47) in CH₂Cl₂to give

covalent esters⁴⁸indicates, however, that anionic Lewis bases

generally cannot be expected to follow the correlation shown

in Figure 7.

2

constants in CH₂Cl₂(Table 2). Again an excellent linear

correlation with a slope of 0.88 is observed, indicating that

variation of the substituents aﬀects the Lewis acidities LA

of the benzhydrylium ions E(1−8)⁺in the better solvating

solvent CH₃CN slightly less than in CH₂Cl₂. Only E7⁺shows

a noticeable upward deviation in Figure 6, consistent with a

less eﬃcient solvation of this benzhydrylium ion in CH₃CN

compared to the other benzhydrylium ions (see above). The

linear correlations shown in Figures 5 and 6 imply that there

is also a linear correlation of the Lewis acidities LA_{CH CN}with

3

the methyl anion aﬃnities in the gas phase (Figure S1.3

in section S1 of the Supporting Information), the slope of

which shows that solvation by CH₃CN attenuates the sub-

stituent eﬀects to 60% of the anion aﬃnities observed in the

gas phase.

The slopes in Figures 6 and 7 are diﬃcult to interpret, as the

eﬀects of the solvent on the Lewis acids and Lewis bases cannot

be separated unambiguously. However, by setting LA_{CH CN}(E1⁺) =

3

LA_{CH Cl}(E1⁺), the bulk of the solvent eﬀects is shifted into the

2

LB_{CH CN}terms. The larger equilibrium constants observed in

3

J

DOI: 10.1021/ja511639b

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Article

Table 4. Equilibrium Constants K (M⁻¹) for the Reactions of Benzhydrylium Ions E⁺with the Lewis Bases N48 (S-Terminus)

and N(49-55) in CH₃CN at 20 °C (Laser Flash Photolysis) and LB_{CH CN}Parameters Determined from Eq 7

3

a

b

c

Photometric determination from laser ﬂash photolysis experiments in CH₃CN unless noted otherwise. Calculated from eq 7. From ref 40.

d

e

f

Extrapolated from LA_{CH Cl}parameters using the correlation given in Figure 6. From ref 49. The LA_{CH Cl}parameter of E14⁺has not been

2

determined, but the experimentally determined equilibrium constants K (CH₃CN) are given for comparison with the other experimental values.

g

h

i

j

Solvent: CH₂Cl₂. From ref 51. K = K_calcbecause the LB_{CH CN}parameter was calculated from only one equilibrium constant. LB_{CH CN}parameters

3

k

calculated from the equilibrium constants in this table. For independent examination see below. From ref 52, conventional photometric titration.

l

Data from ref 52 re-evaluated for this work; see end of section S8 in the Supporting Information.

CH₃CN (see Figure 2) are, therefore, predominantly reﬂected by

E(9−11)⁺or E11⁺, respectively, since benzhydrylium ions of

lower Lewis acidity do not show suﬃcient conversion (adduct

formation) whereas the more acidic E13⁺reacts almost

quantitatively. Since the N-phenylamino-substituted benzhy-

drylium ions E9⁺and E11⁺show untypical solvation eﬀects, as

the higher LB_{CH CN}values in CH₃CN.

3

Further Lewis Basicities in CH₃CN. As already mentioned,

in CH₃CN only equilibrium constants for reactions of E(1−8)⁺

have been measured directly, because the K values for the

reactions with these carbenium ions are not aﬀected by

uncontrolled side-reactions. Yet, less precise equilibrium

constants for reactions of more reactive benzhydrylium ions

have been obtained by fast measurement techniques. Thus,

benzhydrylium ions have been generated laser-ﬂash-photolyti-

cally in the presence of variable concentrations of Lewis bases,

and the equilibrium constants K listed in Table 4 have been

derived from the absorbances of the carbocations immediately

after irradiation with a 7 ns laser pulse and the stationary

absorbances which were measured as soon as the equilibrium

for the reaction of interest was established.^40,49−51

described above, the LB_{CH CN}values determined in this way are

3

not very reliable. Because of the great importance of the Lewis

basicities of halide ions we sought further conﬁrmation of the

data for Cl⁻and Br⁻listed in Table 4 by relating the Lewis

basicity of Br⁻(N55) to the strengths of neutral Lewis bases.

For that purpose, we investigated the equilibria for the

reactions of benzhydryl halides with Lewis bases in CD₃CN

solution (eq 11) by NMR spectroscopy.

E

‐Br + N ⇌ E−N⁺+ Br⁻

(11)

A major problem of these investigations was the identi-

ﬁcation of systems which do not show side reactions while

having suitable equilibrium constants (see section S5 of the

Supporting Information for details). We were able to determine

the equilibrium constants K for the reaction of E17-Br with

pyrimidine (N30) at diﬀerent temperatures from −20 °C to

+20 °C, from which we obtained the thermodynamic param-

eters ΔH⁰= −62.7 kJ mol⁻¹and ΔS⁰= −210.2 J mol⁻¹K⁻¹

(see section S5 of the Supporting Information). The large nega-

tive reaction entropy is explained by the increased solvation

of the generated ions, which requires strong organization of

the solvent. The equilibrium constant K = 1.6 shows that the

bromide ion (N55) is slightly less Lewis basic than pyrimidine

Subjecting the equilibrium constants thus obtained to a least-

squares optimization according to eq 7 yielded the LB_{CH CN}param-

3

eters for the S-terminus of the thiocyanate ion (N48),⁴⁰for

trimethylamine (N49),⁴⁹the hydrazines N(50,51),⁴⁹and the

hydrazones N(52,53).⁵¹The equilibrium constants calculated

by substituting LA_{CH CN}(Table 1) and LB_{CH CN}(Table 4) into eq

3

7 show a good agreement with the experimental values (Table 4).

Again, the relatively large deviation between experimental and

calculated values for the series including the N-phenylamino-

substituted benzhydrylium ions (E9⁺, E11⁺) can be explained by

the diﬀerent solvation of these benzhydrylium ions (see previous

section).

The direct determination of equilibrium constants for the

reactions of chloride (N54) and bromide (N55) ions with

benzhydrylium ions (Table 4) was only possible with

1

(N30, LB_{CH CN}= 8.59) in acetonitrile at 20 °C. Further H

3

NMR (CD₃CN) measurements for the reactions of E17-Br

with the pyridines N26 and N29 at 20 °C (Table 5) conﬁrm

K

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Article

with the Lewis bases N in CH₃CN at 20 °C with the cor-

Table 5. Equilibrium Constants K (Dimensionless) for the

Reactions of the Benzhydryl Halides E17-Br and E14-Cl with

Azines in CD₃CN at 20 °C

responding LB_{CH CN}parameters from Table 3 (Figure 8).

3

There is a diﬀerence of 10 kJ mol⁻¹, however, between the

calorimetrically determined value (ΔH⁰= −52.7 kJ mol⁻¹) for

the reaction of E15-Br with N30 (Table 6) and the value of

ΔH⁰= −62.7 kJ mol⁻¹obtained from the temperature-dependent

NMR measurements of equilibrium constants for the reaction of

E17-Br with N30 (see above), showing a discrepancy between the

two methods, the origin of which is not yet clear.

Lewis base

LB_{CH CN}of halide

benzhydryl

halide

equilibrium

b

3

a

c

formula LB_{CH CN}

constant K

ion

3

E17-Br

N26

N29

N30

9.44

9.00

8.59

1.0 × 10²

7.4

7.8

8.4

16

d

1.6

Equilibrium constants K(CH₃CN) for the reactions of

benzhydrylium ions E⁺with 1,8-diazabicycloundec-7-ene

(DBU, N56) could not be determined with the photometric

method because even the least reactive benzhydrylium ions E1⁺

and E2⁺react quantitatively with DBU (N56).⁵⁴We can use

E14-Cl

N21

11.82

10.49

1.5 × 10³

∼9

9.8

N24

4.8

a

b

1

From Table 3. Determined from H NMR (200 MHz, 23 °C).

c

d

1

LB_{CH CN}(halide) = −log K + LB_{CH CN}(N). Determined from H

NMR ³(400 MHz, 20 °C); a van’t Hoﬀ plot shows good linearity and

yields the thermodynamic parameters ΔH⁰= −62.7 kJ mol⁻¹and ΔS⁰=

−210.2 J mol⁻¹K⁻¹(see section S5 of the Supporting Information).

3

the correlation given in Figure 8, however, to calculate LB_{CH CN}

=

19.7 for DBU (N56) from the heat of the reaction of DBU³with

E15-Br in CH₃CN (Table 6).

The ITC method was also used to study ΔH⁰for the

reactions of N56 with the benzhydrylium tetraﬂuoroborates

E(1−8)⁺BF₄⁻in CH₃CN (eq 13), which are listed in Table 7.

the value of LB

ﬂash photolysis experiment (Table 4).

≈ 8 for Br⁻(N55) derived from the laser

CH₃CN

E⁺BF ⁻+ N56 ⇌ E−N56⁺BF ⁻

Analogous NMR experiments were performed to study the

equilibria of the reactions of E14-Cl with N21 and N24 in

CD₃CN at 20 °C (Table 5). From these data, one can derive

LB_{CH CN}≈ 9 for Cl⁻(N54), again in fair agreement with the

value³from the laser ﬂash photolysis experiments (Table 4).

Thus, the chloride ion is about 20 times more Lewis basic than

the bromide ion in acetonitrile.

Calorimetric Data. An independent access to relative

strengths of Lewis bases is provided by isothermal titration

calorimetry (ITC). For that purpose, we investigated the heats

of the reactions of the dimethoxybenzhydryl bromide E15-Br

with various Lewis bases in CH₃CN (eq 12) by adding small

amounts (10 μL of a 2 × 10⁻³M solution) of the Lewis bases N

to a large excess (1.4 mL of a 2 × 10⁻³M solution) of E15-Br.

The sample cell and a reference cell ﬁlled with CH₃CN were

both thermostated to 20 °C, and the diﬀerences in the heat

energies required for maintaining the temperature constant in

both cells were recorded in order to determine the reaction

enthalpies ΔH⁰, which are listed in Table 6.

(13)

4

Subtracting ΔH⁰for the reaction of a covalent benzhydryl

bromide with DBU (eq 12, N = N56, last entry of Table 6)

from the values for ΔH⁰for the reaction of a benzhydryl cation

with DBU (eq 13, Table 7) provides ΔH⁰for the combinations

of E(1−8)⁺with Br⁻, from which we can also estimate the

corresponding reaction entropies, as elaborated in section S7 of

the Supporting Information. Figure 9 shows that the LA_{CH CN}

3

parameters of E⁺correlate linearly with the enthalpies ΔH⁰for

the reactions of E⁺with N56 in CH₃CN at 20 °C which are

listed in Table 7.

As the terms −RT ln(10)LA and −RT ln(10)LB correspond

to the fractions of ΔG⁰for the Lewis acid−Lewis base co-

ordinations which are allotted to the Lewis acid or Lewis base,

respectively, the deviations of the slopes of the correlations in

Figures 8 and 9 from −RT ln(10) reveal the contributions of

the reaction entropy ΔS⁰to the Lewis acidity and Lewis basicity

parameters.

Since the equilibrium constant for eq 12 does not depend on

the substitution pattern of the benzhydryl fragment,⁵³the value

of K = 1.6, which was measured for the reaction of E17-Br

with pyrimidine N30 (Table 5) should also hold for the

reaction of E15-Br with N30. As a consequence, this reaction

proceeds almost quantitatively at the concentrations em-

ployed in the ITC experiment (>99% for the ﬁrst addition,

>95% for the 10th addition), and the heats measured in the

calorimetric experiments with N30 and stronger Lewis bases

correspond to the reaction enthalpies ΔH⁰for the reactions

with E15-Br.

Though the slope of the correlation in Figure 9 should be

considered with caution because of the moderate quality of

this correlation, it is interesting to note that multiplication of

LA_{CH CN}with −RT ln(10) yields a value of 1.18; i.e., the

3

increasing negative value of ΔH⁰with increasing Lewis acidity

is enhanced by the entropy term. As the benzhydrylium ions’

need for solvation increases when the positive charge of the

benzhydrylium ions is less delocalized (e.g., E1⁺is less solvated

than E8⁺), less ordering of the solvent molecules is given up in

the combination of a Lewis base with a better stabilized

benzhydrylium ion (e.g., E1⁺), and the formation of the Lewis

adduct proceeds with a more negative reaction entropy than an

analogous reaction with a less stabilized benzhydrylium ion

(e.g., E8⁺). As a result, substituent variation in Figure 9 aﬀects

ΔG⁰more than ΔH⁰. The same line of arguments was used to

rationalize why the equilibrium constants for the reactions of

benzhydrylium ions with neutral Lewis bases are larger in the

more polar solvent CH₃CN than in CH₂Cl₂(Figure 2).

The reaction (eq 12) can be split up into two steps (eqs 12a

and 12b), and ΔH⁰(eq 12) can be expressed by eq 12c.

E15‐Br + N ⇌ E15−N⁺+ Br⁻

(12)

E15‐Br ⇌ E15⁺+ Br⁻

(12a)

E15⁺+ N ⇌ E15−N⁺

(12b)

When LB_{CH CN}is expressed in units of kJ mol⁻¹(by

ΔH⁰(eq 12) = ΔH⁰(eq 12a) + ΔH⁰(eq 12b)

3

(12c)

multiplication with −RT ln(10)), the slope of the correlation in

Figure 8 is 0.83; i.e., the substituent eﬀect on reaction enthalpy

ΔH⁰is attenuated by a compensating entropy eﬀect. More

speciﬁcally: As the enthalpy term ΔH⁰becomes more negative,

As ΔH⁰(eq 12a) is a constant term for all calorimetrically

investigated reactions of Table 6, one obtains a linear correla-

tion between the enthalpies ΔH⁰for the reactions of E15-Br

L

DOI: 10.1021/ja511639b

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Table 6. Reaction Enthalpies ΔH⁰(kJ mol⁻¹) for the Reactions of E15-Br with Diﬀerent Lewis Bases N (Eq 12) in CH₃CN at 20 °C

a

b

c

From Table 2. From Tables 3 and 4. Isothermal titration calorimetry, this work (see section S6 of the Supporting Information). Average values

d

e

from 3−4 individual runs; values in parentheses are standard deviations. Not available. Calculated from ΔH⁰in this table and the correlation

shown in Figure 8.

17% of the decrease of ΔH⁰is compensated by an increase of

the −TΔS⁰term, so that only 83% of the change in ΔH⁰is

reﬂected by changes of ΔG⁰. This means that the formation of

Lewis adducts from stronger Lewis bases (more negative ΔH⁰)

is associated with a more negative value of ΔS⁰, i.e., a larger

increase of ordering during the reaction. This implies a weaker

solvation of the stronger Lewis bases and/or that stronger

Lewis bases form Lewis adducts which have higher need for

solvation. Overall, we thus observe a linear correlation between

enthalpy and entropy eﬀects (compensation eﬀect⁵⁵) for the

combinations of Lewis acids and Lewis bases.

pK_Rvalues of the less stabilized carbocations refer to sulfuric

acid solutions of variable concentration, i.e., a change of the

solvent (from water to concentrated Brønsted acids) is un-

+

avoidable when determining pK_Rvalues of carbocations with

widely diﬀering reactivities. Because of this ambiguity and the

nonavailability of pK_Rvalues for E(7−14)⁺, we refrain from

+

discussing the correlations of LA_{CH Cl}(eq 14) and ΔG_MA(eq 15)

2

+

with pK_R; see Figure S1.4 in section S1 of the Supporting

Information.

+

pK_R= −1.15LA

− 5.28; R²= 0.998

CH₂Cl₂

(14)

(15)

+

Correlation of LA and ΔG_MAwith pK_Rof the

pK_R= 0.112ΔG_MA+ 79.0; R²= 0.968

+

Benzhydrylium Ions. Deno’s pK_Rvalues,^13,14which reﬂect

+

the equilibrium constants for the reactions of carbocations with

water (eq 3), are a well-known measure for the stabilities of

carbocations. Figure S1.4 in section S1 of the Supporting

Correlation of the Lewis Basicities with pK_aValues.

Figure 10a illustrates that the LB_{CH CN}parameters of the Lewis

3

bases in CH₃CN do not follow a common correlation with

their pK_avalues in CH₃CN. Instead, we observe separate

correlation lines for Lewis bases belonging to diﬀerent

classes of compounds, such as pyridines, tertiary amines,

phosphines, or benzoates. From the fact that the slopes of

the individual correlations are close to 1.0, one can conclude

+

Information plots the available log K_Rversus the LA_{CH Cl}

2

parameters of the benzhydrylium ions, as well as versus th²eir

methyl anion aﬃnities ΔG_MAin the gas phase.

The interpretation of the slopes of these correlations is

not unambiguous due to the fact that the highly negative

M

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Article

Figure 8. Plot of LB_{CH CN}parameters of Lewis bases N versus the

3

enthalpies ΔH⁰for their reactions with E15-Br in CH₃CN at 20 °C

(LB_{CH CN}= −0.148ΔH⁰+ 0.317; R²= 0.970).

3

Table 7. Reaction Enthalpies ΔH⁰(kJ mol⁻¹) for the

Reactions of the Benzhydrylium Tetraﬂuoroborates

E(1−8)⁺BF₄with 1,8-Diazabicycloundec-7-ene (DBU,

−

N56) in CH₃CN at 20 °C

Lewis acid

a

E⁺

abbreviation

ΔH⁰/kJ mol⁻¹

E1⁺

E2⁺

E3⁺

E4⁺

E5⁺

E6⁺

E8⁺

(lil)₂CH⁺

−73.2 ( 0.6)

−73.3 ( 0.3)

−77.1 ( 0.3)

−81.4 ( 0.5)

−89.9 ( 0.3)

−95.3 ( 0.5)

(jul)₂CH⁺

(ind)₂CH⁺

(thq)₂CH⁺

(pyr)₂CH⁺

(dma)₂CH⁺

(mor)₂CH⁺

a

Isothermal titration calorimetry, this work (see section S6 of the

Supporting Information). Average values from 3−4 individual runs;

values in parentheses are standard deviations.

Figure 10. Plot of Lewis basicities LB_{CH CN}in CH₃CN versus pK_a

3

values of the Lewis bases in CH₃CN (a) and H₂O (b). The pK_avalues

were taken from refs 7 and 59.

One factor which accounts for the occurrence of separate

correlation lines in Figure 10a is the diﬀerence in bond

dissociation energies.^56,57Since the average N−H vs N−C

bond energies diﬀer by ∼86 kJ mol⁻¹while the P−H and P−C

bond energies diﬀer by only ∼58 kJ mol⁻¹,⁵⁸one can already

explain why phosphines are stronger bases toward Ar₂CH⁺than

amines of comparable pK_a(the diﬀerence of 28 kJ mol⁻¹

corresponds to ca. 5 units of LB_{CH CN}in Figure 10a). Similarly,

3

the O−H and O−C bond energies diﬀer by ∼104 kJ mol⁻¹,⁵⁸

which is an even larger diﬀerence than that between N−H vs

N−C bonds. However, bond energies vary widely depending

on the exact structure of the compound,^56,57and this may

Figure 9. Plot of the LA_{CH CN}parameters of the benzhydrylium ions

3

−

E(1−8)⁺versus the enthalpies ΔH⁰for the reactions of E(1−8)⁺BF₄

with 1,8-diazabicycloundec-7-ene (DBU, N56) in CH₃CN at 20 °C

(LA_{CH CN}= −0.211ΔH⁰− 28.1; R²= 0.951).

3

contribute to the large gap (several units of LB_{CH CN}) between

3

that structural variation within one class of compounds has

the same eﬀect on Brønsted basicity and on Lewis basicity

toward C-centered Lewis acids. Similar plots with near-unity

slopes were previously observed between Lewis basicity and

Brønsted basicity for diﬀerent classes of anions in the gas

phase.⁴

the correlation lines for pyridines and tertiary amines.

As pK_avalues are strongly solvent-dependent, it is clear that the

more readily available pK_avalues in water cannot be used for esti-

mating Lewis basicities in acetonitrile. Still, we observe correlations of

LB_{CH CN}with pK_a(H₂O) within some series of related compounds

3

such as pyridines, phosphines, and benzoates (Figure 10b).

N

DOI: 10.1021/ja511639b

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Article

RELATIONSHIPS BETWEEN KINETIC AND

THERMODYNAMIC PARAMETERS

■

Heterolysis Rate Constants (S_N1 Solvolyses). In

previous work, we have compiled rate constants k_s(corre-

sponding to k_backwardin Scheme 1) for solvolysis reactions of

benzhydryl derivatives E(1−33)-X (X = Br, Cl, OAc, OBz, 3,5-

dinitrobenzoyl, p-nitrobenzoyl, OCO₂Me, etc.) in hydroxylic

solvents.²³Rate constants k_sfor heterolysis reactions of

benzhydryl halides in aprotic solvents like CH₂Cl₂and

CH₃CN have subsequently been determined by conductimetry

in the presence of amines or triphenylphosphine, which trap the

intermediate ion pairs and suppress ion recombination.^60,61

Figure 11a plots log k_sfor representative examples of

solvolysis reactions of E(13−20)-X versus the Lewis acidities

LA_{CH Cl}of E⁺and illustrates excellent linear correlations

2

between kinetic and thermodynamic data for this limited set of

systems. Lewis acidities LA_{CH Cl}of benzhydrylium ions less

2

stabilized than E20⁺are not avai²lable, but the thermodynamic

stabilities of these species can be derived from the calculated

methyl anion aﬃnities. Figure 11b shows excellent linear

correlations between solvolysis rate constants k_sfor the

benzhydrylium ions E(13−33)⁺and the calculated methyl

anion aﬃnities ΔG_MA(eq 9) of E⁺;⁶²data for the p-phenoxy-

substituted benzhydrylium ions E16⁺and E19⁺are not

included in Figure 11b, because of the diﬀerent solvation of

these systems (see above).

In contrast, the rate constants of solvolyses that proceed via

the highly stabilized amino-substituted benzhydrylium ions

E(1−11)⁺correlate poorly with LA_{CH Cl}of E⁺(Figure 12),

2

indicating that the rates of these heterolysis reactions are not

predominantly controlled by the relative thermodynamic

stabilities of the carbocations but are largely aﬀected by the

diﬀerent intrinsic barriers.^23,39,63

The excellent linear correlations (Figure 11) with slopes

close to −1 for leaving groups such as Cl⁻/CH₂Cl₂and

Cl⁻/CH₃CN in Figure 11a are explained by the fact that these

heterolyses have small or negligible barriers for the recombina-

tion reaction of the carbocation with the leaving group.

The slightly smaller slopes for 90A10W and 80AN20W in

Figure 11a indicate that the relative Lewis acidities of E⁺are

more attenuated in these more polar solvents than in CH₂Cl₂.

(cf. Figure 6). Thus, ΔG^⧧corresponds to ΔG⁰for these

reactions, as illustrated by the free energy diagram for the

solvolysis of E18-Cl in aqueous acetonitrile (Figure 13a). The

reaction of E18⁺with Cl⁻in this solvent proceeds with a rate

constant of 1.02 × 10⁹M⁻¹s⁻¹;⁶⁴i.e., there is only a small free

energy barrier for the combination of the ions (Figure 13a,

Figure 11. Correlation of log k_sfor solvolysis reactions (25 °C) of

E(13−33)-X^23,60versus the Lewis acidities LA_{CH Cl}(a) and calculated

2

methyl anion aﬃnities ΔG_MA(b) of the benzhydrylium ions E⁺. The

slopes of the correlation lines are given in parentheses; data for E16⁺

and E19⁺are not shown and were not used for the correlations.

Abbreviations: DNB⁻= 3,5-dinitrobenzoate; mixtures of solvents are

given as (v/v), A = acetone, AN = acetonitrile, W = water.

E1-OAc ⇌ E1⁺+ AcO⁻, i.e., there is a signiﬁcant intrinsic

barrier, and the solvolysis rates are not predominantly

controlled by the relative free energies of the ionization step

(LA_{CH Cl}of E⁺, Figure 12).

reaction from right to left). The energy barrier ΔG^⧧for the

i

ionization reaction (Figure 13a, from left to right) thus more or

less corresponds to the free ionization energy ΔG⁰for the

i

reaction E18-Cl ⇌ E18⁺+ Cl⁻and for all substrates yielding

less stabilized carbenium ions. This conclusion has previously

been drawn from Arnett’s observation that the diﬀerences in

activation free enthalpies of ethanolysis reactions of alkyl

chlorides reﬂected 89% of the heats of ionization of the same

substrates in superacidic media.⁶⁵

2

Solvolysis experiments thus provide information about the

thermodynamic stabilities of carbocations if the recombination

reaction of the carbocation with the leaving group occurs with-

out barrier. In our previous work, we have measured diﬀusion-

controlled or almost diﬀusion-controlled (>10⁸M⁻¹s⁻¹) rate

constants for many combination reactions of E(13−33)⁺with Cl⁻

and Br⁻in solvolytic media.⁶⁴In these cases, the Lewis acidities

of E⁺can thus be derived indirectly from their solvolysis rate

constants k_s. On the other hand, the smaller slopes for X = OTs

in Figure 11b might indicate that there is a barrier for the

combinations of E⁺with the very weak nucleophile TsO⁻so

Figure 13b, on the other hand, shows the free energy diagram

for the solvolysis of E1-OAc in 80% aqueous acetone. As the

combination of E⁺with AcO⁻proceeds with a considerable

barrier in this solvent (Figure 13b, reaction from right to left),³⁹

ΔG^⧧for the ionization (Figure 13b, from left to right) is much

i

larger than the ionization free energy ΔG⁰for the reaction

i

O

DOI: 10.1021/ja511639b

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Journal of the American Chemical Society

Article

Figure 14. Correlation of log k₂for the reactions of E⁺with diﬀerent

nucleophiles^{20,22,28,29,31}in CH₂Cl₂versus the Lewis acidities LA_{CH Cl}

2

of E⁺(this work).

Figure 12. Plot of log k_sfor solvolysis reactions (25 °C) of E(1−13)-

X²³versus the Lewis acidities LA_{CH Cl}of the benzhydrylium ions E⁺.

2

Abbreviations: PNB⁻= p-nitrobenzoat²e; mixtures of solvents are given

as (v/v), A = acetone, AN = acetonitrile, W = water.

Figure 15. Plots of log k₂for the reactions of E(3−30)⁺with diﬀerent

nucleophiles^20,22in CH₂Cl₂(a) and log k₁for the reactions of

E(15−31)⁺with triﬂuoroethanol^33,72and with 95% aqueous

hexaﬂuoroisopropanol (w/w)⁷⁴(b) versus the calculated methyl

anion aﬃnities ΔG_MA(eq 9) of E⁺. Data for the acceptor-substituted

benzhydrylium ions E(25−29)⁺(empty symbols) and second-order

rate constants >10⁸M⁻¹s⁻¹(shaded area in panel a) were not used for

the correlations.⁷⁵

Figure 13. Free energy diagrams for the ionization steps in the

solvolyses of E18-Cl in 80% aqueous acetonitrile (80AN20W)⁶⁶(a)

and E1-OAc in 80% aqueous acetone (80A20W)⁶⁷(b). The

subsequent reaction of E⁺with the solvent has been omitted for

clarity (this reaction is much faster than the ionization in most S_N1

solvolyses⁶⁸).

Rate Constants for Combinations of Carbocations

with Nucleophiles. Figure 14 illustrates that the rate con-

stants log k₂for the reactions of E⁺with diﬀerent nucleophiles

that the carbocation character is not fully developed in the

transition states of the tosylate solvolyses.

P

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Journal of the American Chemical Society

Article

decrease with increasing electrophilicity of the benzhydrylium

ions has now obtained a quantitative basis, because Figure 14

1

shows that all π-nucleophiles are characterized by α > /₂. In

these series, the Hammond eﬀect, which reduces δΔG^⧧/δΔ_rG⁰

as the transition state is shifted toward reactants in more

exergonic reactions, must be compensated by a decrease of the

intrinsic barriers with increasing exergonicity.

2

(ΔG^⧧

)

1

2

0

ΔG^⧧= ΔG^⧧

+

ΔG^⧧

+

0

16ΔG^⧧

(16)

0

As LA_{CH Cl}parameters for the highly reactive benzhydrylium

2

ions E(21−33)⁺are not available, we also plotted log k₂versus

the calculated methyl anion aﬃnities ΔG_MA(eq 9) of E⁺. While

the donor-substituted benzhydrylium ions E(1−21)⁺show

good linear correlations (Figure 15), a linear extrapolation of

this correlation overestimates the rate constants for the acceptor-

substituted benzhydrylium ions E(26−29)⁺considerably

(Figure 15), although several of these rate constants are still

below the limit of 10⁸M⁻¹s⁻¹where the rate-limiting eﬀect of

diﬀusion begins to play a role (yellow-shaded area in Figure 15).²²

Moreover, the same behavior is found for the ﬁrst-order decay

reactions with solvents such as triﬂuoroethanol (Figure 15b),^33,72

acetonitrile,^33,73or hexaﬂuoroisopropanol−water mixtures,⁷⁴in

which diﬀusion does not have any limiting eﬀect at all.

The deviation of the highly reactive carbocations from the

correlation line cannot result from a ground state solvation

eﬀect, since the plots of log k_sfor the heterolysis reactions

versus the calculated methyl anion aﬃnities ΔG_MAof E(13−33)⁺

are perfectly linear (Figure 11b). The bends in Figure 15,

panels a and b, thus indicate that the intrinsic barriers of the

combination reactions vary in a diﬀerent way for donor- and

acceptor-substituted benzhydrylium ions. A detailed inves-

tigation of these relationships is in progress.

Figure 16. Plot of log k₂for the reactions of E6⁺with diﬀerent

nucleophiles N in CH₃CN²⁸⁻³⁰versus the Lewis basicities LB_{CH CN}of N

3

(this work). Empty symbols: log k₂calculated from eq 17 and the reac-

tivity parameters published in refs 29−32. The line shows the correlation

for all data points (log k₂= 0.38LB_{CH Cl}− 0.74; R²= 0.814).

2

20,22,28,29,31

in CH₂Cl₂

correlate linearly with the Lewis acidities

LA_{CH Cl}of E⁺from this work.

2

The linearity of these correlations over a wide rangefrom

slow reactions with late transition states at the lower end of the

correlation lines to very fast, almost diﬀusion-controlled

reactions with early transition states at the topagain show

that the Leﬄer−Hammond α = Δ(log k)/Δ(log K) cannot be

a measure for the position of the transition state.^25,69,70

According to Marcus theory (eq 16),^{3,24,25,70,71}rate-

equilibrium relationships, i.e., log k vs log K correlations

(≙ΔG^⧧vs ΔG⁰correlations) can only be linear if (a) the

⧧

intrinsic barrier ΔG₀is very high compared with the reaction

free enthalpy Δ_rG⁰or if (b) the intrinsic barriers ΔG₀change

In the discussion so far we have neglected the fact that the

quality of the correlations on the left-hand side of Figure 14 is

slightly worse than that of those on the right-hand side; the

⧧

proportionally with Δ_rG⁰. Our previous conclusion⁴³that in the

reactions of E(1−20)⁺with π-nucleophiles the intrinsic barriers

Figure 17. Semiquantitative schemes to estimate equilibria for reactions of Lewis acids (vertical axis) and Lewis bases (horizontal axis) in CH₂Cl₂(a)

and CH₃CN⁷⁸(b) at 20 °C. Combinations located in the red area of the ﬁgures form Lewis adducts, while combinations located in the blue area do not.

Q

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Journal of the American Chemical Society

Article

deviations show a similar pattern as in Figure 12. For example,

for Lewis acidities, but was not observed in this work as we only

considered benzhydrylium ions, i.e., Lewis acids with similar

structures.

while having very similar LA_{CH Cl}parameters, E2⁺is generated

2

faster in S_N1 reactions but also²reacts faster in combination

reactions than E1⁺. Similarly, both E4⁺and E5⁺are generated

and consumed faster than E3⁺, and E10⁺is generated and

consumed faster than E9⁺. These discrepancies show that our

thermodynamics-coined intuitionthe better stabilized a

cation, the faster it is formed and the slower it reactshas to

be reﬁned. From the rate-equilibrium relationships in Figures 12

and 14, one can clearly see that diﬀerences in intrinsic barriers

are responsible for the fact that ionization and combination

reactions of certain systems deviate from the correlation lines in

the same direction.⁷⁶

Whereas the electrofugalities of all acceptor-substituted and

weakly donor-substituted benzhydrylium ions E(13−33)⁺(S_N1

solvolysis rates) show excellent linear correlations with the

corresponding Lewis acidities (from equilibrium measure-

ments) or methyl anion aﬃnities (from quantum chemical

calculations), these correlations break down for the amino-

substituted benzhydrylium ions E(1−12)⁺. The rates of

heterolysis of E(1−12)−O₂CR are only weakly correlated

with the corresponding Lewis acidities (i.e., thermodynamic

stabilities) of the resulting benzhydrylium ions, while the

relative magnitudes of the intrinsic barriers play an important

role.^76,77As a consequence, it is now clear that rates of solvolyses

of substrates yielding carbocations with LA_{CH Cl}≥ −1 usually

As mentioned in the Introduction, the interpretation of

Brønsted correlationsi.e., relationships between nucleophilic

reactivities and Brønsted basicitiesis hampered by the fact

that rate and equilibrium constants refer to interactions with

diﬀerent reaction centers. Using the Lewis basicities derived in

this work, one can now correlate nucleophilic reactivities

toward C-centered electrophiles with equilibrium constants for

reactions with C-centered Lewis acids (benzhydrylium ions).⁷⁷

Figure 16 shows that the rate constants for the reactions of

various P- and N-centered Lewis bases with E6⁺(used as the

reference electrophile) correlate only poorly with the

2

provide direct information about the thermodynamic stabilities

of the resulting carbocationsor vice versacalculated methyl

anion aﬃnities of carbocations with ΔG_MA< −720 kJ mol⁻¹

provide direct information about the corresponding solvolysis

rates of R-Cl and R-Br, because the ion recombinations of such

systems are diﬀusion-controlled.

In contrast, the electrophilic reactivities of all donor-

substituted benzhydrylium ions E(1−20)⁺correlate excellently

with the corresponding Lewis acidities, while now the highly

acidic, nonstabilized or destabilized benzhydrylium ions

E(21−33)⁺deviate from the linear correlation between rate

and equilibrium constants. These ﬁndings explain our previous

observation that only for the narrow group of alkoxy- and alkyl-

substituted benzhydrylium ions E(13−20)⁺electrophilicities

(i.e., relative rates of reactions with nucleophiles) are the

inverse of electrofugalities (i.e., relative rates of formation in

S_N1 reactions).²³

corresponding Lewis basicities LB_{CH Cl}. Unlike in Brønsted

2

correlations, where various reasons ma²y account for the scatter,

the poor quality of the correlation in Figure 16 must be due to

diﬀerences in intrinsic barriers because rate (log k₂) and

equilibrium constants log K = LB_{CH Cl}+ LA_{CH Cl}(E6⁺) now

2

correspond to the same reaction. As rate consta²nts for the

reactions of nucleophiles with benzhydrylium ions can very

reliably be calculated from eq 17,²⁰⁻²²it is now possible to

systematically analyze the relationships between structure and

intrinsic barriers.

In summary, we have created the thermodynamic counter-

part to our previously published kinetic scales: nucleophilicity

and electrophilicity on one side,²⁰⁻²²and nucleofugality and

electrofugality on the other.²³By employing the wide-ranging

Lewis acidity scale for benzhydrylium ions reported in this work

it is now possible to determine the Lewis basicity (toward C-

centered acids) for a wide variety of Lewis bases. Combination

of the resulting equilibrium constants with the corresponding

rate constants gives access to a systematic evaluation of intrinsic

barriersa basis for the understanding of chemical reactivity.

log k₂(20 °C) = s_N(N + E)

(17)

CONCLUSION

■

It was demonstrated that the equilibrium constants for the

reactions of Lewis acids with Lewis bases in CH₂Cl₂and

CH₃CN can be expressed by log K (20 °C) = LA + LB (eq 7),

where LA is a Lewis acidity and LB is a Lewis basicity param-

eter. By arranging Lewis bases with increasing LB from left to

right and carbocations with increasing Lewis acidity from top to

bottom, one arrives at Figure 17, where the diagonals in panels

a and b correspond to Lewis adducts which form with K = 1.

As the equilibrium constants have the dimension liters per

mole, K > 10²L mol⁻¹is needed to obtain predominantly

covalent adducts in 10⁻²M solutions, corresponding to the red

sectors in panels a and b of Figure 17, while the blue sectors

indicate separated Lewis acids and Lewis bases.

ASSOCIATED CONTENT

■

S

* Supporting Information

Additional tables and ﬁgures (section S1) as well as

miscellaneous information mentioned in the text (sections

S2−S4 and S7); experimental details for the NMR equilibrium

measurements (section S5), isothermal titration calorimetry

experiments (section S6), and photometric measurements

(section S8); and details of the quantum chemical calculations

(sections S9 and S10). This material is available free of charge

via the Internet at http://pubs.acs.org.

From the excellent linear correlation of Lewis acidities LA of

benzhydrylium ions with calculated methyl anion aﬃnities

ΔG_MAone can derive that the diﬀerences of the Lewis acidities

in the gas phase are attenuated to 65% in CH₂Cl₂solution and

to 60% in CH₃CN. The Lewis acidities and Lewis basicities

reported in this work can, therefore, be used as a quantitative

basis for calibrating semiempirical quantum chemical methods.⁷⁹

As expected, the Lewis acidities LA are tightly correlated with

AUTHOR INFORMATION

■

Corresponding Author

*herbert.mayr@cup.uni-muenchen.de

+

pK_R, while the Lewis basicities LB only correlate with the

Notes

corresponding Brønsted basicities within groups of structurally

closely related compounds. A similar situation can be expected

The authors declare no competing ﬁnancial interest.

R

DOI: 10.1021/ja511639b

J. Am. Chem. Soc. XXXX, XXX, XXX−XXX

Journal of the American Chemical Society

Article

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ACKNOWLEDGMENTS

■

Dedicated to Professor Rolf Saalfrank on the occasion of

his 75^thbirthday. We thank Dr. David Stephenson for

assistance with the NMR experiments and the Deutsche

Forschungsgemeinschaft (SFB 749, Project B1) for ﬁnancial

support.

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(46) Analogous solvent eﬀects were previously noted in our kinetic

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treating the electrophilicity parameters E as solvent-independent

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solvent-dependent nucleophile-speciﬁc parameters N and s_N.²⁰⁻²²

Though this method worked well for the majority of benzhydrylium

ions, phenylamino- and phenoxy-substituted benzhydrylium ions,

particularly E7⁺and E9⁺, always react faster in acetonitrile than

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T

DOI: 10.1021/ja511639b

J. Am. Chem. Soc. XXXX, XXX, XXX−XXX

Article Doi

Scales of Lewis basicities toward C-centered Lewis acids (Carbocations)

DOI: 10.1021/ja511639b

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