From Carbodiimides to Carbon Dioxide: Quantification of the Electrophilic Reactivities of Heteroallenes

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From Carbodiimides to Carbon Dioxide: Quantiﬁcation of the

Electrophilic Reactivities of Heteroallenes

Zhen Li, Robert J. Mayer, Armin R. O ﬁ al,* and Herbert Mayr*

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ABSTRACT: Kinetics of the reactions of isocyanates, isothiocya-

nates, carbodiimides, carbon disulﬁde, and carbon dioxide with

carbanions or enamines (reference nucleophiles) have been measured

photometrically in acetonitrile or DMSO solution at 20 °C. The

resulting second-order rate constants and the previously published

reactivity parameters N and s_Nof the reference nucleophiles were

substituted into the correlation log k₂(20 °C) = s_N(N + E) to

determine the electrophilicity parameters of the heteroallenes:

TsNCO (E = −7.69) ≫ PhNCO (E = −15.38) > CS₂(E =

−17.70) ≈ PhNCS (E = −18.15) > PhNCNPh (E = −20.14) ≫

CyNCNCy (E ≈ −30). An approximate value could be derived for

CO₂(−16 < E < − 11). Quantum chemical calculations were

performed at the IEFPCM(DMSO)/B3LYP‑D3/6‑311+G(d,p) level of theory and compared with experimental Gibbs activation

energies. The distortion−interaction model was used to rationalize the diﬀerent reactivities of O- and S-substituted heteroallenes.

Eventually it is demonstrated that the electrophilicity parameters determined in this work can be used as ordering principle for

literature-known reactions of heteroallenes.

electrophiles with π-, σ-, and n-nucleophiles. The linear free-

energy relationship (1) characterizes electrophiles by one

parameter (electrophilicity E) and nucleophiles by two

solvent-dependent parameters (nucleophilicity N and suscept-

ibility s_N).⁸

INTRODUCTION

■

Heteroallenes¹are important reagents in organic synthesis; they

include isocyanates,²isothiocyanates,^2d,3carbodiimides,⁴car-

bon disulﬁde,⁵carbon dioxide,⁶etc. Whereas isocyanates, in

particular those with electron-withdrawing substituents, are

known to be highly reactive electrophiles,^2c,g,hcarbon dioxide is

a rather inert molecule, and many attempts to use it as a

feedstock for organic compounds are presently investigated.⁷It

was the goal of this work to elucidate relationships between

structure and reactivities of heteroallenes (Chart 1) in order to

include these compounds in our comprehensive electrophilicity

scales and in this way describe their applicability in organic

synthesis.

log k₂(20 °C) = s_N(N + E)

(1)

We now report on the kinetics of the reactions of the

heteroallenes 1a−1h with the carbanions 2 and enamines 3

(Table 1)⁹and use the resulting rate constants for determining

the electrophilicity parameters E of 1a−1h.

RESULTS AND DISCUSSION

■

Product Studies. The reactions of the heteroallenes 1 with

the reference nucleophiles 2 or 3 (Table 1)^9,10in DMSO or

acetonitrile proceeded smoothly at 20 °C (Table 2). In some

cases, the products were only identiﬁed by NMR spectroscopic

analysis of the reaction mixture because they decomposed

during workup. Phenyl isocyanate (1a) reacted with the

carbanions 2c,d,i,k (generated by deprotonation of the

In previous work, we had developed scales of nucleophilicity

and electrophilicity on the basis of eq 1, which can be used to

predict scope and selectivities of reactions of a large variety of

Chart 1. Heteroallenes 1a−1h Studied in This Work (Cy =

Cyclohexyl)

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tosyl isocyanate (1b) with other enamines have previously been

reported.¹²

Table 1. Carbanions 2 and Enamines 3 Used for Determining

the Electrophilicities of the Heteroallenes 1

The adduct 4cn⁻Na⁺, formed in the reaction of phenyl

isothiocyanate (1c) with the malononitrile anion (2n), was

1

identiﬁed by the NH resonance in the H NMR spectrum (δ

8.89 ppm in d₆-DMSO) and the molecular anion peak in the

high resolution mass spectrum (Table 2, entry 6). In analogy to

the synthesis of ketene-N,S-acetals by Kirsch and co-workers,¹³

iodomethane was used to methylate 4cn⁻Na⁺to yield 6cn in

80% yield, which conﬁrmed the structure of the initial adduct

4cn⁻(Table 2, entry 9). The additions of carbanions 2o and 2p

to the aryl isothiocyanates 1c (Table 2, entries 7, 8) and 1d

(Table 2, entries 10−12) were carried out in analogy to entry 6

and analyzed by NMR spectroscopic methods without isolation

of the products.

Ketene aminals were isolated in good yields when diphenyl

carbodiimide (1e) was combined with various carbanions 2

(generated from their conjugate acids 2-H and KOtBu) in

DMSO and subsequently treated with aqueous ammonium

acetate solution (Table 2, entries 13−17). Potassium

dithiocarboxylates were formed by the reactions of the

pregenerated potassium salts 2f,g-K with carbon disulﬁde (1g)

in d₆-DMSO and identiﬁed by ¹H (4gf⁻, 4gg⁻) and ¹³C NMR

(4gf⁻) spectroscopy (Table 2, entries 18, 19). Treatment of CS₂

with 2-(4-nitrophenyl)acetonitrile (2i-H) and NaOH in d₆-

DMSO gave an adduct, which tautomerized to give the

enedithiolate anion 4gi⁻(Table 2, entry 20). In order to

match the situation of the kinetic investigations (use of excess

CS₂) indenide (2j) was combined with 2 equiv of CS₂(1g). The

resulting mixture of two adducts was subsequently treated with

iodomethane to give the corresponding methylation products

6gj and 7gj with 30% and 54% yield, respectively (Table 2, entry

21).

The indenide ion 2j (generated in DMSO solution from 2j-H

and KOtBu) reacted with solid CO₂in DMSO to give 1H-

indene-3-carboxylic acid (4hj) in 80% isolated yield after

treatment with 2 M HCl (Table 2, entry 22, and Scheme 1). In

contrast, several other carbanions did not yield a product when

combined with CO₂under similar conditions (Supporting

Information, Chart S1). Only potassium ﬂuorenide (generated

in DMSO solution from ﬂuorene and KOtBu) gave trace

amounts of ﬂuorene-9-carboxylic acid, in accord with a study by

Chiba, Miura, and co-workers who showed that carboxylation of

CH acids with carbon dioxide (1 atm) required the presence of

potassium carbonate and 18-crown-6 in the DMSO solutions.¹⁴

Kinetic Investigations. The kinetic investigations of the

reactions of 1a−h with the carbanions 2a−k and the enamines 3

(reference nucleophiles listed in Table 1) were performed in

DMSO or acetonitrile solution at 20 °C by following the

disappearance of the UV/vis absorptions of the nucleophiles 2

and 3 under pseudo-ﬁrst-order conditions ([1]₀/[2(or 3)]₀>

7). The ﬁrst-order rate constants k_obswere obtained by least-

squares ﬁtting of the exponential function A = A₀exp(−k_obst) +

C to the observed time-dependent absorbances of the reactants

2 or 3 (Figure 1a). The remaining absorbance at 344 nm during

the reaction of 1a with 2c (Figure 1a) is due to the adduct

4ac⁻K⁺, which was conﬁrmed by measuring the UV/vis

spectrum of a solution obtained by treatment of isolated 4ac

with KOtBu. When the carbanions 2l−p were used as reference

nucleophiles, the kinetic investigations were performed by

following the increase of the UV/vis absorbances of the products

under pseudo-ﬁrst-order conditions ([2]₀/[1]₀> 10). The ﬁrst-

order rate constants k_obswere then obtained by least-squares

a

b

With nucleophilicity parameters N and s_Nfrom refs 8b and 9. This

c

work (Supporting Information). Calculated from two rate constants

in ref 9b.

conjugate acids 2-H with KOtBu) to form adducts. After

aqueous workup the amides 4 were isolated (Table 2, entries 1−

4).

While the reactions of phenyl isocyanate (1a) with isobutyr-

aldehyde-derived enamines have been reported to give [2+2]

cycloadducts,^11azwitterionic intermediates were characterized

in reactions of p-tosyl isocyanate (1b) with β,β-dialkyl

enamines.^11bNucleophilic addition of enamine 3a to p-tosyl

isocyanate (1b) and subsequent proton shift yielded a mixture of

E-/Z-isomeric β-pyrrolidino-α,β-unsaturated enamides 4ba

1

(identiﬁed by two sets of pyrrolidino protons in the H NMR

spectrum, Supporting Information). As these enamides were

diﬃcult to separate and isolate, they were treated with 2%

aqueous HCl to give the hydrolysis product 5ba, which was

isolated in 70% yield (Table 2, entry 5). Analogous reactions of

B

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Table 2. Product Studies of Heteroallenes 1 with Carbanions 2 and Enamines 3

a

Yield of isolated product after chromatographic puriﬁcation.

acetonitrile have been determined in this work using our

standard methods (Table 1 and section 5 in the Supporting

Information). Reactivity parameters for these carbanions have

previously been reported for DMSO solution (Table 1).

The preparation of DMSO solutions with diﬀerent concen-

trations of carbon dioxide (1h) by diluting saturated solutions of

CO₂in DMSO and applying available data on the pressure-

dependent solubility of CO₂in DMSO¹⁵is explicitly described

in the Supporting Information, section 7.

Figure 2 shows that the correlations of (log k₂)/s_Nfor the

reactions of heteroallenes 1 with carbanions 2 and enamines 3

versus the corresponding nucleophilicity parameters N are linear

with a slope of roughly 1 as required by eq 1. The reactions of

these C_sp-centered electrophiles with enamines and carbanions

thus follow the linear free-energy relationship eq 1 like the

corresponding reactions of C(sp²)-centered electrophiles.^8,9

Scheme 1. Carboxylation of Indenide 2j

ﬁtting of the exponential function A = A_∞[1 − exp(−k_obst)] + C

to the observed time-dependent absorbances of the products.

The slopes of the linear correlations between k_obsand the

variable concentrations of the excess components (Figure 1b)

correspond to the second-order rate constants k₂

Table 3. Since the isocyanates 1a and 1b are not persistent in

DMSO solution, kinetic experiments with these compounds

were carried out in acetonitrile solution. The reactivity

parameters N and s_Nof carbanions 2b, 2c, 2d, 2i, and 2k in

exptl

listed in

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pyramidalization of the malononitrile anion, which accounts for

the low intrinsic barriers for its reactions with Michael

acceptors.¹⁸Thus, the major contribution to the distortion

energy comes from the heteroallene. Figure 5 (left) shows that

before reaching the transition state, distortion of the SCS

fragment generally requires more energy than distortion of the

OCO part. Since the interaction energy is similar for the

reactions with CO₂and CS₂(Figure 5, right, green lines), the

reaction with CS₂proceeds via an earlier, higher energy

transition state than the reaction with CO₂(Figure 5, right,

black lines).

Due to the lower symmetry, the situation is more complex for

the reactions with phenyl isocyanate (1a) and phenyl

isothiocyanate (1c). As illustrated in Figure 6 for the reaction

of the malononitrile anion (2n) with 1a, variation of the dihedral

angle C_Ar−N−C−C_Nuat a constrained length of the new CC

bond (2.30 Å) results in two discrete minima at 180° and 25°,

which indicate that the nucleophile 2n does not attack from top

or bottom of the molecular plane, which would be expected if

the reaction would be controlled by interaction with LUMO-

(1a), but from two directions (anti and syn) in or close to the

molecular plane of 1a.

Intrinsic reaction coordinate (IRC) calculations show that the

anti attack proceeds perfectly in the molecular plane and is

controlled by interaction with π*(CO), i.e., LUMO+2 of phenyl

isocyanate (1a). In the corresponding transition state TS(B),

depicted in Figure 7, all atoms of phenyl isocyanate and the

methine carbon of the attacking carbanion are perfectly

coplanar.

The alternative trajectory (syn attack) is controlled by

interaction of the HOMO(2n) with both, LUMO and

LUMO+2, of 1a and begins with a gauche approach of 2n at

1a (dihedral angle C_Ar−N−C−C_Nuis 44° at a distance of 3.24

Å). As the nucleophile gets closer, it moves more and more into

the molecular plane of 1a as indicated by the dihedral angle of

25° at 2.30 Å distance (Figure 6) and of 15.5° at the transition

state TS(A) in Figure 7. The diﬀerent views of the transition

states in Figure 7 furthermore show that in the syn transition

state TS(A), the phenyl ring is strongly twisted toward the plane

of the developing heteroallyl anion (C_Ar−C_Ar−N−C = 127°)

and thus gives up conjugation.

The energetics of the entire reaction cascades are shown in

Figure 8a. The larger lobe of LUMO+2 on the syn side and the

additional interaction with LUMO can explain why the syn

pathway proceeds via a lower barrier than the anti pathway (57.8

vs 70.9 kJ mol⁻¹). In the initially formed adducts (IA), the

relative energies are inverted, however, and the product arising

from anti attack, IA(B), is more stable than IA(A) by 10 kJ

mol⁻¹. Both initially formed adducts IA undergo a proton

transfer to the more stable tautomers (E)-TA and (Z)-TA.

Rapid rotation around the C−N single bond transforms (E)-TA

into (Z)-TA, the most stable reaction product. The tautome-

rization step reﬂects the fact that malononitrile is a stronger

Brønsted acid than aniline.

Figure 1. (a) Monoexponential decay of the absorbance A (at 344 nm)

of 2c during the reaction of 1a (1.07 × 10⁻³M) with 2c (5.00 × 10⁻⁵

M) in acetonitrile at 20 °C. (b) Plot of k_obsfor the reaction of 1a with 2c

versus the concentration of 1a.

exptl

Least-squares optimization [minimization of Δ²= ∑(log k₂

− log k₂^{eq 1})²] = ∑(log k₂

− s_N(N + E))²] of the rate

exptl

constants of the reactions of 1a−e and 1g with carbanions 2 and

enamines 3 gave the electrophilicity parameters E for the

heteroallenes 1 in the second column of Table 3. Since the

kinetics of nucleophilic additions to CO₂could only be

measured for one carbanion, the listed E value for CO₂could

not be conﬁrmed independently. Due to the low intrinsic

barriers, the reactions of CO₂with carbanions of higher basicity

can be expected to approach diﬀusion control, and therefore,

cannot be used to derive a more reliable electrophilicity

parameter E for CO₂.

Quantum Chemical Calculations. As illustrated in

Scheme 2, attack of a carbanion at the central carbon of

heteroallenes initially yields the heteroallyl anion IA, which may

tautomerize to TA with an equilibrium constant depending

predominantly on the nature of R, Y, R¹, and R², whereas X and

R′ play a minor role (X-R′ is part of the heteroallyl anion system

in IA and TA).

Activation and reaction Gibbs energies for the reactions of the

symmetrical (CS₂, CO₂) and unsymmetrical (1a, 1c) hetero-

allenes with the carbanion 2n were calculated at the IEFPCM-

(DMSO)/B3LYP‑D3/6‑311+G(d,p) level of theory.^16a−cAs

illustrated in Figure 3, the nucleophilic attack at CO₂is faster,

but thermodynamically less favorable than attack at CS₂. Proton

shift converts the initially formed adducts IA into the tautomers

TA, which are 22 (4hn⁻) and 37 kJ mol⁻¹(4gn⁻) more stable.

Figure 4 shows that the formation of the new CC bond is

further advanced in the transition state of the reaction with CO₂

(2.17 Å) than in the reaction with CS₂(2.25 Å). In other words,

the reaction with CO₂proceeds via a later transition state.

Distortion interaction analysis¹⁷shows that deformation of

the nucleophile (NC)₂CH⁻(2n) requires very little energy

(Figure 5, left), in line with the well-known ﬂat energy surface for

A similar pattern of relative Gibbs energies of transition states

and adducts IA and TA was calculated for the reaction of 2n with

the sulfur analog 1c (Figure 8b).

Figure 9 illustrates the distortion interaction analysis for the

reaction of malononitrile anion (2n) with phenyl isocyanate

(1a). As described above for the reactions with CO₂and CS₂

(Figure 5), the distortion energies of the anion 2n are very small

for both reaction pathways (Figure 9, left) and the distortion

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Table 3. Experimental (k₂^exptl) and Calculated (k₂^{eq 1}) Second-Order Rate Constants for the Reactions of Heteroallenes 1 with

Nucleophiles 2 and 3 at 20 °C

a

b

c

Calculated by using eq 1, N and s_Nfrom Table 1, and E from this table. E value is derived by quantum chemical calculation. Too slow to be

measured.

energy of the isocyanate 1a is much greater for the anti attack

than for the syn attack.

Comparison of the origin of the diﬀerent reactivities of phenyl

isocyanate (1a) and phenyl isothiocyanate (1c) shows

analogous phenomena as the comparison of CO₂and CS₂.

Figure 8 already indicates that nucleophilic attack at the sulfur

derivative 1c is more exergonic (for the formation of IA) than

attack at the oxygen analogue 1a. Figure 8 also shows that the

kinetic preference of nucleophilic attack at phenyl isocyanate

(1a) compared to phenyl isothiocyanate (1c) (18.2 kJ mol⁻¹for

the syn path) is slightly smaller than the kinetic preference of

CO₂over CS₂. Figure 11 reveals the reason: It is again the larger

distortion energy of the sulfur-containing compound 1c which

accounts for its lower reactivity compared to the oxygen-

containing analog 1a.

Consistency of Data: Comparison of Calculated and

Experimental Activation Energies. As illustrated in Figure

12a, the DFT-calculated Gibbs activation energies ΔG^⧧_calcdfor

the reactions of the heteroallenes 1a−h with the nucleophiles 2a

and 2n correlate with high quality, conﬁrming the consistency of

the calculated numbers. On the other hand, the analogous

The right part of Figure 9 shows that the interaction energies

(green) for the two pathways are almost identical in the ﬁrst part

of the reaction coordinate (C−C > 2 Å). For that reason, the

transition state of the anti attack TS(B) is reached earlier (C−C

= 2.30 Å) than TS(A) of the syn attack (C−C = 2.17 Å). The

smaller activation energy for the syn attack is thus due to the fact

that the distortion energies at the transition states of both

pathways are almost the same, while the interaction energy is

much larger at the later transition state TS(A) of the syn attack.

Figure 10 compares the geometry of phenyl isocyanate with

those of the distorted phenyl isocyanate fragments in the two

reaction pathways. At a distance of 2.45 Å between the two

reaction centers, the O−C−N angle is slightly more distorted in

the syn pathway than in the anti pathway. The larger distortion

energy of the anti attack must, therefore, be due to the distortion

of the C−N−C_Arangle, which is strongly reduced from 141.9° to

121.1° in the anti pathway and only to 136.4° in the syn pathway.

E

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Figure 4. Geometries of the transition states^16dfor the reactions of 1g

and 1h with 2n at the IEFPCM(DMSO)/B3LYP‑D3/6‑311+G(d,p)

level of theory.

behaves diﬀerently from the other nucleophiles and may,

therefore, not be a suitable reference nucleophile for the

parametrization of electrophilic reactivities. This insight is

unfortunate as 2j was the only nucleophile which we could use

for determining the electrophilicity of CO₂.

Table 4 shows that all quantum chemically calculated Gibbs

activation energies ΔG^⧧

agree with the directly measured

calcd

values (printed in parentheses in Table 4) within 13 kJ mol⁻¹. If

one excludes the reaction of carbanion 2a with CO₂(1h), the

standard deviation between experimental ΔG^⧧(i.e., ΔG^⧧

exptl

Figure 2. Plots of (log k₂)/s_Nvs N for the reactions of heteroallenes 1

with carbanions 2 and enamines 3 in DMSO or acetonitrile at 20 °C

(the slope of the depicted correlation lines is enforced to 1). For the

sake of clarity, the correlation lines for 1a and 1c are shown only in the

Supporting Information (Figure S13).

directly measured or derived from eq 1) and DFT calculated

Gibbs activation energies ΔG^⧧_calcdis 12 kJ mol⁻¹.

The Gibbs activation energies ΔG^⧧_exptlfor the reactions of the

heteroallenes 1 with 2n derived by eq 1 using N and s_Nfrom

Table 1 and E from Table 3 correlate well with the DFT

calculated values (exception 1h, Figure 13a). If the insecure

entry for CO₂(1h) is neglected, a correlation between

experiment and theory with a slope of 1.02 is obtained. The

intercept of this correlation implies that the experimental

activation energies are in average 6 kJ mol⁻¹smaller than the

theoretical values. An analogous correlation for the reactions of

carbanion 2a with the heteroallenes 1 is of slightly lower quality

(R²= 0.92, Supporting Information, Figure S29A). As a

consequence of these linear correlations, there is also a linear

correlation between the empirical electrophilicity parameters E

of the heteroallenes 1 with the calculated Gibbs activation

energies ΔG^⧧_calcdfor their reactions with carbanion 2n (Figure

13b). From the correlation in Figure 13b one would expect an

electrophilicity parameter E = −11.4 for CO₂.

Scheme 2. Mechanism of the Reactions of Heteroallenes with

Carbanions

What is the reason for the strikingly unique position of CO₂in

these correlations? We assume that the origin for the deviation of

CO₂in the correlations in Figure 13 is due to the fact that the

indenide ion 2j, which was used as reference for the calculation

correlations between the barriers for the indenide ion (2j) and

2n (Figure 12b) or 2a (Supporting Information, Figure S26C)

show a higher scatter, indicating that the indenide ion (2j)

Figure 3. Gibbs energy proﬁles for the reactions of malononitrile anion 2n with CS₂(1g, black pathway) and CO₂(1h, blue pathway) at the

IEFPCM(DMSO)/B3LYP‑D3/6‑311+G(d,p) level of theory.

F

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Figure 5. Distortion interaction analysis of the transition states for the reaction of 2n with the heteroallenes 1g and 1h calculated at the

IEFPCM(DMSO)/B3LYP‑D3/6‑311+G(d,p) level of theory (electronic energies E_totin kJ mol⁻¹). Inset: Geometries at a C−C distance of 2.60 Å.^16d

Figure 6. (a) Dependence of E_totfor a complex of PhNCO (1a) with the carbanion 2n on the dihedral angle C_Ar−N−C−C_Nuat a constrained length

(2.30 Å) of the new CC bond (at the IEFPCM(DMSO)/B3LYP‑D3/6‑311+G(d,p) level of theory). (b) Unoccupied frontier orbitals of phenyl

isocyanate (1a)^16ecalculated at the IEFPCM(DMSO)/B3LYP‑D3/Def2TZVP//IEFPCM(DMSO)/B3LYP‑D3/6‑311+G(d,p) level of theory.

of E(CO₂), is not a well-behaved nucleophile as shown above

(see discussion of Figure 12b). A further examination of this

hypothesis was not possible because of our failure to determine

kinetics of the reaction of CO₂with other carbanions.

Rate Equilibrium Relationships. Relationships between

rate constants and the corresponding Gibbs reaction energies

are among the most important tools for elucidating the origin of

activation barriers. Brønsted correlations, Bell−Evans−Polanyi

relationships, and Leﬄer−Hammond analyses are the best

known treatments.¹⁹Since in most reactions investigated in this

work, the initially formed adducts IA undergo fast proton shifts

with formation of TA (Scheme 2), it is very diﬃcult, if not

impossible, to determine the reaction energy for the formation

of IA experimentally. For that reason, we calculated the Gibbs

G

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Previous studies revealed good correlations between the

experimental electrophilicity parameters E of Michael acceptors

and ketones and the quantum chemically calculated methyl

anion aﬃnities (MAAs), which are deﬁned analogously as the

MAAs of heteroallenes in eq 2.²⁰The two classes of compounds

followed separate correlations, however, and ketones (CO)

were found to be much more electrophilic than Michael

acceptors (CC) of comparable MAA (Figure 16).^20b

In view of the large structural variety of the heteroallenes

under investigation it is, therefore, not surprising that there is no

good correlation between the electrophilicities E of the

heteroallenes 1 and their MAAs. It is noteworthy, however,

that heteroallenes are much less electrophilic than structurally

related ketones and Michael acceptors of comparable MAA,

indicating that cumulated double bonds react over higher

intrinsic barriers than ordinary double bonds.

Structure−Reactivity Relationships. After establishing

the agreement between experimental and quantum chemically

derived Gibbs activation energies for nucleophilic additions to

heteroallenes 1, let us now consider the inﬂuence of structural

changes in 1 on electrophilicity and Lewis acidity (Figure 17).

The excellent correlation between Gibbs activation energies for

the reactions of the heteroallenes 1 with 2a and 2n (Figure 12a)

implies that reactivities toward either of these carbanions can be

used for this comparison.

Figure 7. Geometries of the syn and anti transition states^16dfor the

reaction of PhNCO (1a) with the carbanion 2n at the IEFPCM-

(DMSO)/B3LYP‑D3/6‑311+G(d,p) level of theory.

reaction energies Δ_rG⁰for the reactions of heteroallenes 1a−h

with the carbanions 2a, 2n, and 2j by DFT methods (Table 5).

The linear correlation between the calculated Gibbs energies

Δ_rG⁰_calcd(IA) for the reaction of 1 with 2a versus the

corresponding Gibbs energies for the reaction of 1 with 2n

shows the consistency of the calculated Δ_rG⁰_calcdfor reactions of

1 with diﬀerent nucleophiles (Figure 14). The analogous

correlation for 2j vs 2n is depicted in the Supporting

Information (Figure S23B, R²= 0.975). Figure 15 shows that

The values of Δ_rG⁰_calcd(IA) in Figure 17b indicate that tosyl

isocyanate (1b) is the only heteroallene in this series, which

yields the initial adduct IA with the malononitrile anion 2n by an

exergonic process. The other reactions of 2n proceed with

endergonic formation of the initial adducts IA, which

subsequently undergo a proton shift to give the thermodynami-

cally more stable tautomers TA (Tables 2 and 5). Only the

reaction of 2n with CO₂remains endergonic even after

tautomerization (Table 5).

Diphenylcarbodiimide (1e), marked by the blue background

color in Figure 17, is the least electrophilic compound of this

series, for which calculated and experimental activation energies

are available. Replacement of the phenyl groups by cyclohexyl

(1e → 1f) increases the Gibbs activation energy of the reaction

with 2n by 39 kJ mol⁻¹. Figure 12a implies that similar eﬀects

can be expected for reactions of 1 with other nucleophiles. With

an estimated electrophilicity E ≈ −30 (from ΔG^⧧_calcdin Table 4

using the correlation in Figure 13b) the reactivity of N,N′-

dicyclohexylcarbodiimide (DCC, 1f) is so low that we did not

ﬁnd any reference nucleophile suitable for kinetic measure-

ments. This observation is in line with the generally accepted

reaction mechanism for DCC-mediated peptide-forming

reactions, which proceed via initial protonation of DCC to

generate a more electrophilic species that subsequently reacts

with carboxylate anions.²¹

the quantum chemically calculated activation barriers ΔG^⧧

calcd

for the reactions of the carbanions 2a, 2n, and 2j with the

heteroallenes 1b−g correlate linearly with the corresponding

Gibbs reaction energies Δ_rG⁰(IA). The slopes of these Leﬄer−

Hammond-type correlations (0.49 ≤ α ≤ 0.63) indicate that

approximately half of the changes of the Gibbs reaction energies

are reﬂected by the Gibbs activation energies. However, phenyl

isocyanate (1a) and CO₂(1h) are signiﬁcantly below the

correlation lines in all three correlations, indicating that 1a and

1h react with signiﬁcantly lower intrinsic barriers than the other

heteroallenes.

What makes the heteroallenes 1a and 1h special? Since the

quantum-chemically calculated ΔG^⧧values in Figure 15 do not

suﬀer from the uncertainty of the experimental value for CO₂, we

assume that it is the presence of a CO double bond. Earlier

work has already shown that carbonyl groups react much faster

with nucleophiles than electron-deﬁcient CC double bonds of

equal Lewis acidity (expressed by methyl anion aﬃnities, i.e., the

negative of the Gibbs reaction energies, Figure 16).^20bThe fact

that p-tosyl isocyanate (1b), which also bears a carbonyl group,

does not show deviating behavior in Figure 15 may be due to the

fact that the tosylamido group is a stronger electron-accepting

group than the carbonyl group with the consequence that charge

delocalization into the carbonyl group is less important than in

the reactions with phenyl isocyanate (1a) and carbon dioxide

(1h).

Successive replacement of the PhN groups of carbodiimide 1e

by oxygen to give phenyl isocyanate 1a and carbon dioxide 1h,

reduces the activation Gibbs energies by 17 and 11 kJ mol⁻¹,

respectively. The analogous substitution of PhN by sulfur (1e →

1c → 1g) has no or very little inﬂuence on reaction rates (Figure

17a). The diﬀerences between the O- and S-series are due to

diﬀerent intrinsic barriers in the two series since Figure 17b

shows that in the ﬁrst series (replacement of NPh by O, 1e → 1a

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Figure 8. Energy proﬁles (ΔG, in kJ mol⁻¹) for the syn and anti pathways of the reactions of the malononitrile anion (2n) with 1a (a) and 1c (b) at the

IEFPCM(DMSO)/B3LYP‑D3/6‑311+G(d,p) level of theory. Energies refer to the energetically lowest lying conformer for the depicted mode of

attack.

Figure 9. Distortion interaction analysis on the IRC pathways for the syn and anti pathways of the reaction of the malononitrile anion (2n) with phenyl

isocyanate (1a).

→ 1h) the Gibbs reaction energy decreases only marginally,

while replacement of NPh by S (1e → 1c → 1g) reduces

Δ_rG⁰_calcd(IA) by 15 and 4 kJ mol⁻¹. PhNCO (1a) is thus a

signiﬁcantly stronger electrophile than PhNCS (1c) while the

I

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Figure 10. Comparison of the geometries of the relaxed and distorted phenyl isocyanate fragments at a C−C distance of 2.45 Å.^16d

relative thermodynamic driving forces are vice versa, i.e., the

stronger electrophile is the weaker Lewis acid. An analogous

relationship is found for CS₂and CO₂: Nucleophilic additions to

CO₂proceed faster, but have lower thermodynamic driving

forces.

Electrophilicity Parameters E as Ordering Principle for

Heteroallene Reactivities. The electrophilicity parameters E

of the carbonyl derivatives and Michael acceptors shown in the

left part of Figure 18 have previously been derived from the

kinetics of their reactions with C-centered nucleophiles, like

those for the heteroallenes in this work (Table 3). Figure 18

illustrates that tosyl isocyanate (1b), the most reactive

heteroallene of this series, has an electrophilicity comparable

to that of 1,1-bisphenylsulfonyl-ethylene, the most reactive

Michael acceptor we have parametrized so far. Phenyl isocyanate

(1a), which is 8 orders of magnitude less reactive than 1b

(toward nucleophiles with s_N= 1), has an electrophilicity

comparable to that of trans-1,2-dicyanoethylene, and the

electrophilicity of diphenylcarbodiimide (1e) is slightly lower

than that of diethyl maleate. The calculated electrophilicity of

Figure 11. Distortion interaction analysis of the kinetically favored syn

pathways of the reactions of 2n with phenyl isocyanate (1a) and phenyl

isothiocyanate (1c) calculated at the IEFPCM(DMSO)/B3LYP‑D3/

6‑311+G(d,p) level of theory.

Figure 12. Correlation between Gibbs activation energies ΔG^⧧

(kJ mol⁻¹) for the reactions of heteroallenes 1a−h with diﬀerent carbanions

calcd

calculated at the IEFPCM(DMSO)/B3LYP‑D3/6‑311+G(d,p) level of theory.

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Table 4. Experimental and Quantum Chemically Calculated Gibbs Energies of Activation (kJ mol⁻¹) for the Reactions of

Heteroallenes 1 with Carbanions 2a, 2n, and 2j (in DMSO)

a

b

Calculated at the IEFPCM(DMSO)/B3LYP‑D3/6‑311+G(d,p) level of theory for 25 °C (Supporting Information). Derived from the

c

d

electrophilicity E and the nucleophile-speciﬁc parameters N and s_Nbased on eq 1 for 20 °C. In acetonitrile. Diﬀusion-controlled reaction.

e

Directly measured at 20 °C.

Figure 13. (a) Correlation of experimental Gibbs activation energies ΔG^⧧_exptlfor the reactions of 2n with 1a-h (from eq 1 using N and s_Nfrom Table 1

and E from Table 3; data for CO₂not used for the correlation) against ΔG^⧧_calcdcalculated at the IEFPCM(DMSO)/B3LYP‑D3/6‑311+G(d,p) level of

theory. (b) Analogous correlation between electrophilicities E and the calculated Gibbs activation energies ΔG^⧧_calcdfor the reactions of 1 with 2n.

dicyclohexylcarbodiimide (1f) is signiﬁcantly lower than that of

all Michael acceptors we have parametrized so far.

s_Nparameters are typically in the range of 0.7 < s_N< 1.0, second-

order rate constants from 10⁻⁴to 10⁻³M⁻¹s⁻¹at 20 °C can be

expected for reactions of electrophiles with nucleophiles if (E +

N) = −4. These rate constants correspond to a half reaction

times of 1 h to half a day for 0.2 M solutions. Reactions with the

highly nucleophilic alkyllithium and alkylmagnesium com-

pounds with heteroallenes are well-known and will not explicitly

be considered in the following discussion.

Tosyl Isocyanate (1b, E = −7.69). According to the Rule of

Thumb, tosyl isocyanate (1b), the most reactive electrophile of

this series, should undergo noncatalyzed reactions at room

temperature with nucleophiles of E > 4. Thus, 1b should react

with all types of carbanions, as exempliﬁed by the reaction of 1b

with the anion of diethyl 2-phenylmalonate (2q, N = 15.93) in

THF (Table 6, entry 1).^22aProducts of the reactions of 1b with

enamines, which were used for the kinetic studies in this work

(Tables 2 and 3) as illustrated for the reaction with 1-(N-

It should be noted, however, that this comparison refers

explicitly to kinetics. From the relative MAAs depicted in Figure

16, one can derive that nucleophilic additions to heteroallenes 1

without CO group are more exergonic than the correspond-

ing reactions with ketones and Michael acceptors of similar

electrophilicity, which can be explained by release of strain of the

cumulated double bonds. Though we were not able to derive a

reliable value for the electrophilicity of CO₂, Figure 18 shows

that it is comparable to that of benzaldehyde or fairly strong

Michael acceptors. Carbon dioxide (1h), thus, is not a weak

electrophile, and it is the low thermodynamic driving force

which accounts for its failure to react with a large variety of

nucleophiles.

Rule of Thumb. Let us now use the reactivity parameters of

eq 1 to summarize the synthetic potential of heteroallenes 1. As

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Table 5. Quantum Chemically Calculated Gibbs Reaction

a

Energies Δ_rG⁰(kJ mol⁻¹) for the Reactions of Heteroallenes

1 with Carbanions 2a, 2n, and 2j (298 K, DMSO)

2a

2n

2j

Δ_rG⁰

calcd

c

calcd

(IA)

calcd

(TA)

calcd

(IA)

calcd

(TA)

calcd

(IA)

b

c

b

c

b

(TA)

1a

1b

1c

1d

1e

1f

−7

−78

−26

−48

−9

52

−24

−2

−36

−63

−27

−43

−36

−24

3

34

−27

25

6

40

93

21

35

−53

−69

−40

−54

−45

−25

−16

14

−21

−105

−44

−71

−21

39

−74

−98

−68

−93

−72

−41

−59

−13

1g

1h

−56

−19

37

a

Calculated at the IEFPCM(DMSO)/B3LYP‑D3/6‑311+G(d,p)

b

level of theory. Δ_rG⁰_calcd(IA) is the Gibbs reaction energy for

c

formation of the initial adducts IA. Δ_rG⁰_calcd(TA) is the Gibbs

reaction energy for formation of the tautomeric adducts TA.

Figure 16. Correlation between electrophilicities E and MAA values

(eq 2) calculated at SMD(DMSO)/B3LYP/6-311++G(3df,2pd)//

B3LYP/6-31G(d,p) level of theory for ketones, Michael acceptors, and

heteroallenes.

pyrroles (Table 6, entries 3 and 7) and the donor substituted

fulvene 3h (Table 6, entry 5), in line with Watt’s report on

uncatalyzed reactions of 1b with N-alkylindoles (N ≈ 5.75,

Table 6, entry 8).^22cNo reaction was observed, however, when

1b was combined with less nucleophilic arenes, such as 2-

methylfuran (3l, N = 3.61) or 1,3-dimethoxybenzene (3m, N =

2.48) at 20 °C (Table 6, entries 9 and 10).

Apart from enamines also siloxy- and alkoxy-substituted

ethylenes undergo noncatalyzed reactions with 1b, as reported

for the reactions with 3i (N = 6.57, Table 6, entry 6), 1-

(trimethylsiloxy)cyclohexene (N = 5.21),^22dand 1,1-diethox-

yethene (3g, N = 9.81, Table 6, entry 4).^22eNo reaction at

ambient temperature was observed with the less nucleophilic α-

methylstyrene (3n, N = 2.35, Table 6, entry 11), and the same is

expected for other alkyl-substituted ethylenes.

Figure 14. Correlation between Gibbs reaction energies Δ_rG⁰_calcd(IA)

(kJ mol⁻¹) for the reactions of heteroallenes 1 with carbanions 2a and

2n calculated at the IEFPCM(DMSO)/B3LYP‑D3/6‑311+G(d,p)

level of theory.

morpholino)cyclohexene (3e, N = 11.40) (Table 6, entry 2),

have been reported previously.^12c,22bWe have found that 1b

undergoes electrophilic aromatic or vinylic substitutions with

Reactions of p-tosyl isocyanate (1b) with enol ethers have

extensively been studied by Eﬀenberger et al.²⁴From stereo-

chemical and kinetic investigations of the reactions of 1b with

Figure 15. Correlations of Gibbs activation energies ΔG^⧧with Gibbs reaction energies Δ_rG⁰(IA) for the reactions of heteroallenes 1 with 2n (a), 2a

(b), and 2j (c) calculated at the IEFPCM(DMSO)/B3LYP‑D3/6‑311+G(d,p) level of theory. Data for 1a and 1h were excluded when calculating the

linear correlations.

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Figure 17. Structural eﬀects on the Gibbs activation energies ΔG^⧧_calcd(a) and reaction energies Δ_rG⁰_calcd(IA) (b) for the reactions of heteroallenes 1

with the malononitrile anion (2n). The positive Gibbs reaction energies Δ_rG⁰_calcd(IA) imply that the thermodynamic driving force for many of these

observable reactions comes from tautomerization of the initial adducts IA into TA.

ones with the donor substituents in 4-position were formed, as

reported for 3o and related enol ethers by Eﬀenberger.^24a,b

Kinetic investigations by ¹H NMR spectroscopy showed that the

reactions proceeded 5 times faster in CD₃CN than in CD₂Cl₂,

indicating a moderate increase of polarity from reactants to the

transition state (Table 7).

With the assumption that these reactions proceed stepwise

with rate-determining formation of zwitterions, i.e., with

formation of only one new σ-bond in the rate-determining

step (Scheme 4), their rates should be predictable by eq 1. Table

7 shows that the rate constants k₂^{eq 1}calculated by eq 1 are 4 to 8

times smaller than k₂^exptl, indicating a transition state which

closely resembles the zwitterion depicted in Scheme 4.

Since the ratio k₂^exptl/k₂^{eq 1}is within the uncertainty limits of

eq 1, this small ratio does not allow to diﬀerentiate between a

stepwise process and a concerted cycloaddition with a highly

unsymmetrical transition state. Anyway, the small diﬀerence

exptl

eq 1

between k₂

and k₂

in Table 7 indicates that the

electrophilicity parameter E for 1b determined in this work

can be used to predict absolute rate constants for [2+2]

cycloadditions of 1b with highly nucleophilic ethylene

derivatives. Quantum chemical calculations support these

conclusions and indicate initial formation of the CC-bond

followed by a barrier-less subsequent ring closure (Supporting

Information, Figure S31).

Phenyl Isocyanate (1a, E = −15.38). From the Rule of

Thumb presented at the beginning of this section, one can derive

that 1a will react with nucleophiles of N > 11 at 20 °C. In line

with this prediction numerous stabilized carbanions have been

reported to react with 1a at room temperature in diﬀerent

solvents, e.g., 2m,^25a2n,^25bthe anion of ethyl cyanoacetate (N =

19.62 in DMSO),^25c−fthe anion of diethyl 2-phenylmalonate

(2q, N = 15.93),^25gand the anion of ethyl 2-cyano-2-

phenylacetate (N = 15.85).^25e

Figure 18. Comparison of electrophilicities of heteroallenes 1, Michael

acceptors, and carbonyl derivatives (E parameters from Table 3 and ref

10).

There are several reports on the reactions of 1a with

enamines: 1-(N-morpholino)cyclohexene (3e, N = 11.40)

reacted with 1a at room temperature in benzene^26a,band

under reﬂux in chloroform.^26c1-(N-Morpholino)cyclopentene

(N = 13.41) smoothly underwent a reaction with 1a at room

temperature in acetone.^22bThe less nucleophilic α-(N-

cis-/trans-isomeric enol ethers they concluded that the resulting

azetidin-2-ones were formed via concerted [2+2] cycloadditions

with partially charged transition states.^24d

We have now investigated the reactions of 1b with the enol

ethers 3o and 3p, for which nucleophilicity parameters have

previously been reported.^8aAs shown in Scheme 3, azetidin-2-

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Table 6. Reactions of p-Tosyl Isocyanate (1b) with Nucleophiles

a

b

Calculated according to eq 1 with N and s_Nparameters from this table and E(1b) from Table 3. Calculated for 95% conversion with [1b] = [3] =

c

d

e

f

g

0.2 M. In DMSO, from ref 23a. In dichloromethane, from ref 8a. In MeCN, from ref 23b. In dichloromethane, from ref 23c. In MeCN, from

ref 23d. The reaction furnished a 4:1 mixture of 4bh and an unknown product (approximate yield refers to 4bh). For R = Me, in

dichloromethane, from ref 23e. In dichloromethane, from ref 8c. This work.

h

i

j

k

Scheme 3. [2+2] Cycloadditions of 1b with Enol Ethers 3

Table 7. Experimental and Calculated Second-Order

Constants k₂(in M⁻¹s⁻¹) of Reactions of p-Tosyl Isocyanate

(1b) with Enol Ethers 3o and 3p in CD₂Cl₂and CD₃CN (20

°C)

exptl

enol

N/s_N(in

k₂

/

a

b

exptl

eq 1

ether

CH₂Cl₂)

solvent

k₂

3.9

3o

3.92/0.90

CD₂Cl₂

CD₃CN

1.6 × 10⁻³

8.0 × 10⁻³

4.1 × 10⁻⁴

morpholino)styrene (N = 10.30) reacted with 1a in cyclohexane

at 80 °C within 30 min^22bor in Et₂O at 5 °C within 24 h.^26d

On the other hand, nucleophiles with N < 11 have been

reported not to undergo uncatalyzed reactions with 1a at room

temperature. Eﬀenberger, for example, mentioned that ordinary

enol ethers do not react with phenyl isocyanate (1a) while 1,1-

diethoxyethene (3g, N = 9.81) reacted with 1a (neat) within 7 h

3p

3.94/1.00

CD₂Cl₂

CD₃CN

1.5 × 10⁻³

7.0 × 10⁻³

1.8 × 10⁻⁴

8.3

a

b

From ref 8a Calculated by using eq 1, N and s_N, and E(1b) = −7.69

(from Table 3).

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Scheme 4. Hypothetical Stepwise [2+2] Cycloaddition of 1b

with Enol Ethers

Scheme 5. Piperidine-Catalyzed Reaction of Meldrum’s Acid

with 1f (as Reported in Ref 32)

at 100 °C.^22eWhereas the reactions of silyl enol ethers with p-

tosyl isocyanate (1b) proceeded smoothly at room temper-

ature²⁴(Scheme 3), heating at 130−160 °C in the presence of a

catalytic amount of tertiary amine was required to achieve the

reactions of 1a with 3i (N = 6.57) and 1-(trimethylsiloxy)-

cyclohexene (N = 5.21).^22dFurthermore, the reaction of 1a with

N-methylindole (N = 5.75) was reported to require Me₂AlCl as

catalyst,^27aand Ni(0) catalysis was used to enable the reaction of

1a with cyclopentene (N = −1.55).^27b

Phenyl Isothiocyanate (1c, E = −18.15). Because of its lower

electrophilicity, compared with its O-analog 1a, phenyl

isothiocyanate reacts only with stronger nucleophiles (N >

14). At room temperature, reactions of 1c with the anion of

phenylacetonitrile (N ≈ 29),^28athe anions of methyl phenyl-

acetate (N ≈ 27.5),^28bof alkyl cyanoacetate (N ≈ 19.6),^28c−eof

1-phenylbutane-1,3-dione (N = 16.03),^28f,gof diethyl cyanome-

thylphosphonate (N = 18.57), and of triethyl phosphonoacetate

(N = 19.23) in diethyl ether have previously been reported.^28h

Furthermore, mixtures of 1c with anionic C-nucleophiles such as

2m−p (generated from the corresponding CH acids and

potassium carbonate in DMF) and iodomethane have been

described to yield ketene-N,S-acetals at room temperature.¹³

Moderately reactive enamines were reported to react with 1c

at elevated temperature. Thus, 1-(N-morpholino)cyclopentene

(N = 13.41) reacted with 1c in chloroform under reﬂux,^26cand

the weakly nucleophilic α-(N-morpholino)styrene (N = 10.30)

reacted with 1c in EtOAc under reﬂux for 1 h.^22bHarsh reaction

conditions were needed for the reactions of ketene acetals (N ≈

10) with 1c.²⁹Thus, the [2+2] cycloaddition of 1,1-dimethoxy-

2-methylprop-1-ene across the CN bond of 1c was reported

to take place when equimolar amounts of the two reactants were

heated without a solvent for 3 days at 100 °C.²⁹

As expected from their low nucleophilicities, toluene (N =

−4.36), furan (N = 1.33), and pyrrole (N = 4.63) do not

undergo uncatalyzed reactions with 1c.³⁰These arenes can be

converted into the corresponding aromatic thioamides,

however, by heating them with phenyl isothiocyanate (1c) in

cyclohexane solution with stoichiometric amounts of AlCl₃.³⁰

Diphenylcarbodiimide (1e, E = −20.14). In line with the

predictions of the linear free-energy relationship (eq 1),

reactions of 1e with various carbanions have been reported

previously,^31a,bincluding reactions with 2m (N = 20.22),^31c2n

(N = 19.36),^31dthe anion of ethyl cyanoacetate (N = 19.62),^31b,d

the anion of 1,3-diphenylpropane-1,3-dione (N = 17.46),^31dand

the anion of ethyl 3-oxo-3-phenylpropanoate (N = 17.52),^31d

while trimethylsulfoxonium ylide (N = 21.29)^31ewas the only

neutral C-nucleophile which was reported to undergo

uncatalyzed reactions with 1e.

Dicyclohexylcarbodiimide (1f, E ≈ −30). As mentioned in

Table 3, the electrophilicity of 1f is so low that it did not even

react with the highly nucleophilic carbanion 2e (N = 27.54)

when generated by deprotonation of ethyl phenylacetate with

KOtBu in DMSO. In view of this observation, the report by

Stephen³²that 1f reacted with the much less nucleophilic anion

of Meldrum’s acid (N = 13.91) appears surprising (Scheme 5).

However, in line with the observations described in Table 3,

no reaction was observed within 12 days at ambient temperature

when we treated 1f with 1.1 equiv of an equimolar mixture of

Meldrum’s acid and KOtBu in d₆-DMSO. On the other hand,

following the conditions of Stephen, i.e., when we treated an

equimolar mixture of Meldrum’s acid and 1f with a few drops of

piperidine in CDCl₃(Scheme 5) we observed the quantitative

formation of an adduct within 4 days at room temperature. Thus,

the nucleophilic attack of the anion of Meldrum’s acid at 1f is

possible when a proton source (piperidinium ion) is available. In

contrast, the acidity of tert-butanol (formed from Meldrum’s

acid and KOtBu) is obviously not suﬃcient to assist the

nucleophilic attack at 1f. In line with these ﬁndings, the

formation of peptide bonds by 1f-promoted coupling of

carboxylic acids with amines proceeds via initial protonation

of 1f followed by nucleophilic attack of the carboxylate anion at

the protonated carbodiimide.²¹

Carbon Disulﬁde (1g, E = −17.70). CS₂is a stronger Lewis

acid but a weaker electrophile than CO₂(Figure 17) and can be

attacked by nucleophiles with N > 14. It was reported to react

with N-heterocyclic carbenes, e.g., 1,3-dimesitylimidazolylidene

(N = 21.72) in THF at room temperature to form the

zwitterionic dithiocarboxylates.³³Several pyridinium ylides (N

> 18)¹⁰were also reported to react with CS₂in EtOH at room

temperature.³⁴The sodium salts of diethyl cyanomethyl-

phosphonate (N = 18.57) and of triethyl phosphonoacetate

(N = 19.23) were reported to react with 1g in THF at room

temperature.³⁵Cyclic enamines (N > 14) were found to react

with CS₂at −30 °C yielding 1,4-dipoles that can be stored for 1

day at 0 °C in the absence of moisture.³⁶

Carbon Dioxide (1h). The prediction of reactions of CO₂on

the basis of eq 1 is problematic for two reasons. First, the

experimentally derived electrophilicity E(1h) = −16.3 is based

on the rate of reaction of CO₂with only one nucleophile (2j).

Second, the questionable transferability of this number has been

discussed above. However, since quantum chemical calculations

indicate an even higher electrophilicity of CO₂(E = −11), the

value derived from the rate of its reaction with 2j can be

considered as the lower limit with the consequence that

nucleophiles with N > 12 should generally be able to attack at

CO₂. The failure to obtain products with a variety of highly

nucleophilic carbanions (Supporting Information, Chart S1),

may therefore be caused by the unfavorable thermodynamics of

these reactions. The thermodynamic driving force is suﬃcient,

however, for reactions with the highly reactive alkyllithium and

alkylmagnesium compounds.^6bIn line with its nucleophilicity

parameter, the N-heterocyclic carbene 1,3-dimesityl-

imidazolylidene (N = 21.72) reacted with 1 atm CO₂in THF

at room temperature to give a zwitterionic adduct.³⁷N-

Methylindole (N = 5.75) and N-methyl pyrrole (3j, N = 5.85)

are not suﬃciently nucleophilic to attack CO₂, but their Lewis

acid-catalyzed reactions have been reported.^27a,38Though the

intensively investigated reactions of carbon dioxide with amines

may proceed via diﬀerent catalyzed and uncatalyzed mecha-

nisms to give ammonium carbamates,³⁹most secondary amines

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Figure 19. Graphical summary of the synthetic potential of heteroallenes 1.

are able to undergo uncatalyzed reactions with CO₂due to their

large variety of suﬃciently strong nucleophiles is due to a lack of

thermodynamic driving force.

N-values in the range 14 < N < 18.¹⁰

The reactivities of CO₂and CS₂as well as those of phenyl

isocyanate and phenyl isothiocyanate toward nucleophiles were

investigated by quantum-chemical methods applying the

distortion interaction analysis. The higher demand of distortion

energy for the CS₂fragment explains the lower reactivity of CS₂

compared with CO₂in analogous reactions though nucleophiles

form the more stable adducts with CS₂. Nucleophiles approach

the heteroallenes PhNCO and PhNCS by anti or syn pathways,

with the lower calculated Gibbs energies of activation for the syn

attack. In analogy to the relative reactivities of CO₂/CS₂, it is the

lower distortion energy of PhNCO which makes it the stronger

electrophile though PhNCS reacts more exergonically with

nucleophiles.

The satisfactory agreement between quantum chemically

calculated Gibbs activation energies and experimental values

conﬁrms the internal consistency of our data and allowed us to

investigate rate-equilibrium relationships. Earlier studies

showed fair correlations between the electrophilicities of

acceptor-substituted ethylenes and ketones with calculated

methyl anion aﬃnities (MAAs).²⁰The analogous E vs MAA

correlation for the heteroallenes is very poor, due to the large

structural diversity of the investigated heteroallenes. The fact

that heteroallenes are generally less electrophilic than ketones

CONCLUSION

■

The photometrically determined second-order rate constants

for the reactions of heteroallenes 1 with the carbanions 2 and

enamines 3 in DMSO or acetonitrile follow the linear free-

energy relationship eq 1, which allowed us to determine the

electrophilicity parameters E of heteroallenes. As depicted in

Figure 18, tosyl isocyanate (1b, E = −7.69), the most reactive

heteroallene of this series, is 8 orders of magnitude more reactive

than phenyl isocyanate (1a, E = −15.38), which has an

electrophilicity comparable to trans-1,2-dicyanoethylene. Phe-

nyl isothiocyanate (1c, E = −18.15) and carbon disulﬁde (1f, E =

−17.70) are more than 2 orders of magnitude less reactive, and

there is another hundred-fold decrease of electrophilicity to

diphenylcarbodiimide (1e, E = −20.14). The electrophilicity of

dicyclohexylcarbodiimide (1f) is so low that we do not have

suitable reference nucleophiles for measuring its reactivity, and

its approximate electrophilicity E ≈ − 30 was derived by

quantum chemical calculations. The electrophilicity of CO₂

could not unambiguously be quantiﬁed, but the accessible

experimental data and quantum chemical calculations agree that

CO₂is not a weak electrophile. Its reactivity is comparable to

that of benzaldehyde. The failure of CO₂to give products with a

P

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J. Am. Chem. Soc. XXXX, XXX, XXX−XXX

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Article

and Michael acceptors of comparable MAA implies that

cumulated double bonds react over higher intrinsic barriers

than ordinary double bonds.

ACKNOWLEDGMENTS

■

Dedicated to Professor Reinhard Bru

his 65th birthday. We thank the China Scholarship Council

(fellowship to Z.L.) and the Fonds der Chemischen Industrie

̈

ckner on the occasion of

The reactivity parameters in eq 1 have been derived from

reactions of electrophiles with nucleophiles, in which one, and

only one, new bond is formed in the rate-determining step. For

that reason, eq 1 is generally not applicable to multi-bond

reactions. However, when the one-bond electrophilicity E of p-

tosyl isocyanate (1b) and the one-bond nucleophilicity

parameters N and s_Nof enol ethers are applied in eq 1,

second-order rate constants are calculated which closely

resemble those which have been measured for the [2+2]

cycloadditions of these reactants. Hence, this work adds another

example to the observation that the one-bond reactivity

parameters E, N and s_Ncan also be used for predicting absolute

rate constants for stepwise or highly unsymmetrical concerted

cycloadditions.⁴⁰

As s_Nparameters of C-nucleophiles are typically in the range

of 0.7 < s_N< 1.0, second-order rate constants from 10⁻⁴to 10⁻³

M⁻¹s⁻¹at 20 °C can be expected for reactions of electrophiles

with C-nucleophiles if (E + N) = −4. Since these rate constants

correspond to a half reaction times of 1 h to half a day for 0.2 M

solutions, one can summarize the synthetic potential of

heteroallenes semiquantitatively as shown in Figure 19:

Heteroallenes 1 will undergo uncatalyzed reactions at 20 °C

with those nucleophiles which are positioned below themselves

in Figure 19, provided there is suﬃcient thermodynamic driving

force.

́

(Kekule fellowship to R.J.M.) for ﬁnancial support.

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ASSOCIATED CONTENT

■

sı

* Supporting Information

The Supporting Information is available free of charge at

https://pubs.acs.org/doi/10.1021/jacs.0c01960.

Synthetic procedures, details of kinetic measurements,

procedure for the preparation of CO₂solutions in DMSO,

details of quantum-chemical calculations, and NMR

spectra of all characterized compounds (PDF)

Coordinates of optimized structures (ZIP)

AUTHOR INFORMATION

■

Corresponding Authors

Armin R. Oﬁal − Department Chemie, Ludwig-Maximilians-

̈

Universitat Munchen, 81377 Munchen, Germany; orcid.org/

0000-0002-9600-2793; Email: o ﬁ al@lmu.de

̀

Systems; Societa Chimica Italiana, 2018; Vol. 22, pp 298−317

(f) Eschliman, K.; Bossmann, S. H. Synthesis of Isothiocyanates: An

Update. Synthesis 2019, 51, 1746−1752.

Herbert Mayr − Department Chemie, Ludwig-Maximilians-

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(c) Rudorf, W. D. Reactions of carbon disulfide with N-nucleophiles. J.

̈

Universitat Munchen, 81377 Munchen, Germany; orcid.org/

0000-0003-0768-5199; Email: herbert.mayr@cup.uni-

muenchen.de

Authors

Zhen Li − Department Chemie, Ludwig-Maximilians-Universitat

Munchen, 81377 Munchen, Germany

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Robert J. Mayer − Department Chemie, Ludwig-Maximilians-

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Universitat Munchen, 81377 Munchen, Germany

Complete contact information is available at:

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From Carbodiimides to Carbon Dioxide: Quantification of the Electrophilic Reactivities of Heteroallenes

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