Carbene–Carbanion Equilibria
The most well-known equilibrium in carbene chemistry is arguably the second step of Hine's classic mechanism for the hydrolysis of chloroform, Eq. (2) in the three-step sequence Eqs. (1)-(3) [1].
Although step (2) is shown as a (rate determining) forward process, Hine later demonstrated that dichlorocarbene (CCl_{2}) could react with Cl^{−}, and with other halide ions Br^{−} or I^{−}, so as to either reform the trichloromethide carbanion or afford the new trihalomethide carbanions CBrCl_{2}^{−} or CICl_{2}^{−} [2]. Thus, step (2) should be written as an equilibrium and we can ask what is the equilibrium constant, K.
To determine K for carbene–carbanion equilibria it is necessary to visualize these species for quantitation. A combination of laser flash photolysis (LFP) for carbene generation, coupled with UV–Vis spectroscopy to visualize the resulting short-lived intermediates, enables the quantitative study of carbene–carbanion equilibria, provided that the key species have accessible spectroscopic signatures.
CCl_{2} may be generated by LFP of dichlorodiazirine, Eq. (4) [3]. When this reaction is carried out in 1:1 CH_{2}Cl_{2}–MeCN solution containing
0.9 m tetrabutylammonium (TBA) chloride, a weak absorption appears at 328 nm, assigned to CCl_{3}^{−}; the absorption is calculated (TD-B3LYP/6-311 + G(d)//PBE/6-311 + G(d), in CPCM-simulated MeCN) at 344 nm [4]. The appearance of CCl_{3}^{−} suggests the operation of the reverse of Eq. (2); cf. Eq. (4). However, it is not possible to directly determine K for the Eq. (2)/Eq. (4) equilibrium because the very weak absorption of CCl_{2}, observed at 460–530 nm in an argon matrix [5, 6], cannot be detected under our LFP conditions.
A system that is easier to study is CCl_{2}/CCl_{2}Br^{−}, obtainable by the reaction of CCl_{2} with Br^{−}, Eq. (5) [4].
The bromodichloromethide carbanion absorbs at 388 nm (computed at 376 nm) in 1:1 CH_{2}Cl_{2}–MeCN with 0.6 m TBABr [4]. Although CCl_{2} itself is still not visualized, the strong absorbance of CCl_{2}Br^{−} makes possible an indirect estimation of K for Eq. (5), extracted from the competitive reactions shown in Scheme 1 [4].
Here, LFP of diazirine 1 generates CCl_{2} which is either trapped by Br^{−} to give CCl_{2}Br^{−} (k_{1}) or captured by cyclohexene (k_{2}) to yield 7,7-dichloronorcarane 4. Carbanion CCl_{2}Br^{−} can revert to CCl_{2} and Br^{−} (k_{−1}) or add to acrylonitrile (k_{4}), ultimately affording cyclopropane 3 via Michael intermediate 2. Finally, CCl_{2} itself can add directly to acrylonitrile (k_{3}), yielding cyclopropane 3. All the rate constants of Scheme 1 can be measured, except for k_{−1}. Thus, k_{1} (2.1 × 10^{7} m^{−1} s^{−1}) is obtained from the slope of a correlation of the observed rate constants for the rise of CCl_{2}Br^{−} vs the concentration of Br^{−} [4]. The rate constant k_{2} (6.4 × 10^{7} m^{−1} s^{−1}) for the addition of CCl_{2} to cyclohexene is obtained using pyridine to visualize CCl_{2} as the pyridine ylide [3, 7, 8]. The rate constant for the addition of CCl_{2} to acrylonitrile (k_{3} = 4.9 × 10^{5} m^{−1} s^{−1}) is obtained from competitive CCl_{2} additions to acrylonitrile vs cyclohexene [9]. Finally, k_{4} (4.1 × 10^{6} m^{−1 }s^{−1}) is derived from the slope of a correlation of the observed rate constants for the decay of CCl_{2}Br^{−} absorbance vs the concentration of acrylonitrile [4].
With rate constants k_{1} − k_{4}, and an apparent value of k_{3}/k_{2} = 0.18 in the presence of 0.28 m Br^{−}, we can extract K = k_{1}/k_{−1} ~ 10 m^{−1} from Scheme 1 [4]. Therefore, k_{−1} ~ 2.1 × 10^{6} s^{−1} for the reversion of CCl_{2}Br^{−} to CCl_{2} and Br^{−}. A computational study at the PBE/6-311 + G(d) level in simulated acetonitrile gives ΔH° = −7.7 kcal mol^{−1} and ΔG° = −2.5 kcal mol^{−1}, leading to K ~ 66 m^{−1} for the CCl_{2} + Br^{−} CCl_{2}Br^{−} equilibrium at 25°C [4].
Although CCl_{2} lacks a useful UV absorbance in our LFP experiments, its phenyl derivative phenylchlorocarbene (PhCCl) exhibits a strong π→p absorption at ~300 nm, together with a weak σ→p absorption at long wavelengths [10]. The UV–Vis spectrum of phenylbromocarbene (PhCBr) is analogous. Accordingly, PhCCl and PhCBr support equilibria with halide ions and reactions with acrylonitrile that parallel CCl_{2} in Scheme 1 [11]. This is illustrated for PhCBr in Scheme 2.
Here, PhCBr is generated by LFP of phenylbromodiazirine 5 in the presence of bromide ion (TBABr), setting up an equilibrium between PhCBr and PhCBr_{2}^{−}. The carbanion absorbs strongly at 430 nm. Analogously to Scheme 1, a competition ensues between PhCBr additions to tetramethylethylene (k_{2}) or acrylonitrile (k_{3}), and the addition of PhCBr_{2}^{−} to acrylonitrile (k_{4}). From the measured rate constants k_{1} − k_{4}, and the product ratio for 7/8 as a function of bromide concentration, we derive K = k_{1}/k_{−1} = 2.8 m^{−1} and k_{−1} = 7.9 × 10^{7} s^{−1}, where k_{1} = 2.2 × 10^{8} m^{−1 }s^{−1} [11]. As we show below, a subsequent direct determination of K is in excellent agreement with the value extracted from Scheme 2.
An important practical aspect of the reactions in Scheme 2 is bromide ion catalysis of the addition of PhCBr to acrylonitrile. Thus, PhCBr is an electrophilic carbene that adds well to an electron-rich alkene like tetramethylethylene (k_{2} = 3.9 × 10^{7} m^{−1} s^{−1}), but poorly to an electron-poor alkene like acrylonitrile (k_{3} = 1.7 × 10^{6} m^{−1 }s^{−1}) [12]. Therefore, the rapid conversion of PhCBr to PhCBr_{2}^{−} (k_{1} = 2.2 × 10^{8} m^{−1 }s^{−1}) and the efficient capture of PhCBr_{2}^{−} by acrylonitrile (k_{4} = 2.9 × 10^{7} m^{−1 }s^{−1}), result in enhanced conversion of PhCBr to cyclopropane 7 via Michael addition intermediate 6.
For example, in the absence of Br^{−}, the relative rate of addition of PhCBr to acrylonitrile vs tetramethylethylene (k_{3}/k_{2}) is 0.042. In the presence of 0.58 m TBABr, k_{rel} increases 28-fold to 1.19 due to operation of the k_{1}/k_{4} pathway [11]. There is an effective umpolung of PhCBr from an electrophilic to a nucleophilic reagent via PhCBr_{2}^{−}. Similar results are obtained with the PhCCl/PhCCl_{2}^{−} system where k_{rel} for addition to acrylonitrile vs tetramethylethylene increases from 0.045 in the absence of Cl^{−} to 0.62 in the presence of 0.54 m TBACl, corresponding to a 13.8-fold enhancement via PhCCl_{2}^{−} [11].
A similar catalysis operates in the addition of phenylfluorocarbene (PhCF) to acrylonitrile. The relative rate of addition of electrophilic PhCF to acrylonitrile vs tetramethylethylene is 0.080 in a 1 m MeCN–THF solvent. In the presence of 0.49 m TBABr, however, k_{rel} increases to 1.40, a 17.5-fold increase [13]. Bromide ion catalysis operates through conversion of PhCF to PhCFBr^{−}, which adds rapidly to acrylonitrile. The mechanism is analogous to that shown for PhCBr in Scheme 2. In the case of PhCF, generated by LFP of phenylfluorodiazirine, measurements of the corresponding rate constants lead to an estimate of K ~ 27 m^{−1} for the equilibrium of Eq. (6), where k_{1} = 2.46 × 10^{7} m^{−1 }s^{−1} and k_{−}_{ 1} = 9.12 × 10^{5} s^{−1} [13].
Thus far, our determinations of the equilibrium constants for carbene–carbanion equilibria have been indirect. However, when both species exhibit strong UV–Vis absorptions, K can be determined directly. Let us revisit the PhCBr–PhCBr_{2}^{−} system of Scheme 2. LFP of phenylbromodiazirine 5 in the presence of 0.1 m TBABr in dichloroethane (DCE) gives the calibrated spectrum shown in Fig. 1 [14].
Here, the π→p absorption of PhCBr appears at 316 nm and its σ→p absorption falls at 620 nm. The PhCBr_{2}^{−} carbanion absorbs at 428 nm. From measurements of the absorbance ratio, A_{316}/A_{428} as a function of bromide concentration, we obtain K = 3.0 m^{−1} for the equilibrium of Eq. (7), in excellent agreement with the “indirect” value (K = 2.8 m^{−1}) derived from Scheme 2 [11, 14]. We also measured k_{1} = 3.55 × 10^{7} m^{−1 }s^{−1}, so that k_{−1} = 1.18 × 10^{7} s^{−1}.
Three qualifications should be noted. (1) Carbene–carbanion equilibria are not stable on the ms time scale; both species are reactive and the equilibrium will be drained from both ends. However, the A_{316}/A_{428} absorbance ratio is relatively constant from 200 to 300 ns after the laser flash so that an average value of the ratio can be determined over the 200–250 ns postflash time interval [14]. (2) The extinction coefficients of the carbene and carbanion, necessary to transform the absorbance ratio into a concentration ratio, are unknown. Instead, we used the computed oscillator strengths (f) of PhCBr and PhCBr_{2}^{−} at the appropriate wavelengths (f = 0.4326 and f = 0.1370, respectively; TD-B3LYP/6-311 + G(d)//M06-2X/6-311 + G(d) in simulated DCE solvent). We estimate that the f ratio reproduces the desired ratio of extinction coefficients to within a factor of 2 [14]. It should be emphasized that computational studies were crucial throughout our studies, providing anticipated absorption wavelengths and structures for the various transient species, as well as computed f values. [3] The determination of K ignores possible cation–anion interactions between TBA^{+} and Br^{−} or TBA^{+} and PhCBr_{2}^{−}. Potential aggregation of cation–anion pairs is also not considered. Factors (2) and (3) introduce some uncertainty into the calculation of K, so that the agreement between the “indirect” value (2.8 m^{−1}) and “direct” value (3.0 m^{−1}) is comforting.
An analogous determination of K for Eq. (8), based on absorptions of PhCCl at 292 nm and PhCCl_{2}^{−} at 404 nm, gave K = 4.01 m^{−1} [14]. The value of k_{1} was independently measured as 1.97 × 10^{8} m^{−1}s^{−1}, so that k_{−1} = 4.91 × 10^{7} s^{−1} [14].
Determination of K as a function of temperature (260–309 K) permitted the extraction of the thermodynamic parameters governing Eqs. (7) and (8). For PhCBr/PhCBr_{2}^{−}, we found ΔH° = −1.9 kcal mol^{−1}, ΔS° = −4.3 eu and ΔG° = −0.62 ± 0.03 kcal mol^{−1} at 298 K. For PhCCl/PhCCl_{2}^{−}, the analogous values were ΔH° = −5.7 kcal mol^{−1}, ΔS° = −17 eu and ΔG° = −0.71 kcal mol^{−1} [14]. Computed values of the thermodynamic parameters for Eqs. (7) and (8) are more negative than the experimental values. At the M06-2X/6-311 + G(d) level, for example, ΔH° = −10.4 (PhCCl) or −8.4 (PhCBr) kcal mol^{−1}, while ΔG° = −3.7 or −2.0 kcal mol^{−1}, respectively. ΔS° ~ −21 eu in both systems [14]. Differences between the experimental and computed values may stem from neglect in the calculations of halide and halocarbanion interactions with the ammonium cations.
We see that although the formation of PhCX_{2}^{−} from PhCX + X^{−} is favorable (ΔH < 0), it is opposed by the unfavorable entropy associated with converting two reactants into one product. As a result, ΔG° is only slightly negative and K for Eqs. (7) and (8) is only 3–4 m^{−1}. Put another way, k_{1} for the formation of PhCX_{2}^{−} is very rapid when X = Cl or Br, but the reversion of the carbanion to the carbene is similarly fast.
Following the direct measurement of K for the PhCCl/PhCCl_{2}^{−} system, we studied the equilibria between a series of ring-substituted ArCCl [9] and ArCCl_{2}^{−} [10]; cf. Eq. (10) [15].
All the carbenes and carbanions of Eq. (10) were readily observed, and values of K, k_{1} and k_{−1} were obtained. These constants are collected in Table 1, together with analogous data for the previously discussed carbene–carbanion equilibria.
Carbene | Carbanion | K (m^{−1}) | k_{1} (m^{−1 }s^{−1}) | k_{−}_{1} (s^{−1}) | References |
---|---|---|---|---|---|
| |||||
CCl_{2} | CCl_{2}Br^{−} | 10^{a}* | 2.1 × 10^{7} | 2.1 × 10^{6}* | [4] |
PhCF | PhCFBr^{−} | 27^{a}* | 2.5 × 10^{7} | 9.1 × 10^{5}* | [13] |
PhCCl | PhCCl_{2}^{−} | 4.0 | 2.0 × 10^{8} | 4.9 × 10^{7} | [14] |
PhCBr | PhCBr_{2}^{−} | 3.0 | 3.6 × 10^{7} | 1.2 × 10^{7} | [14] |
9b | 10b | 31 | 3.2 × 10^{8} | 1.0 × 10^{7} | [15] |
9c | 10c | 240 | 5.2 × 10^{8} | 2.2 × 10^{6} | [15] |
9d | 10d | 3.0 | 1.0 × 10^{8} | 3.4 × 10^{7} | [15] |
9e | 10e | 56 | 3.8 × 10^{8} | 6.9 × 10^{6} | [15] |
For Eq. (10), equilibrium constants are a sensitive function of the aryl substituent: K ranges from a low of 3.0 m^{−1} with a p-fluoro substituent to a high of 240 m^{−1} with a p-trifluoromethyl substituent [15]. The substituent dependence of K is nicely illustrated by a Hammett correlation of K vs σ_{p} where ρ = +3.18 (using σ_{p}^{+} for p-F and σ_{m} for m-Cl) [15]. The positive ρ value indicates that electron-withdrawing substituents stabilize the carbanion and destabilize the carbene, shifting the equilibrium toward the carbanion and increasing K.
A Hammett correlation of computed values of K (wB97XD/6-311 + G(d) in simulated DCE) vs σ_{p} gave ρ = +12.0 [15]. The sign and significance of ρ are analogous to that proffered for correlation of the experimental K values. However, the huge value of ρ for the computed K values reflects a full unit negative charge on the carbanions. In the experimental systems, cation–anion interactions between Bu_{4}N^{+} and carbanion 10 will reduce the effective negative charge and decrease ρ. Also, aggregation of Bu_{4}N^{+}ArCCl_{2}^{−} might lead to further dispersal of the carbanion negative charge and an additional decrease in ρ [15].
The forward reaction of Eq. (10) also exhibits ρ > 0 for Hammett correlation of k_{1}. Values of +1.05 in DCE [15] or +0.86 in MeCN–THF and CCl_{4} [16] are observed. Electron-withdrawing groups that stabilize the carbanion and destabilize the carbene accelerate carbanion formation and increase k_{1}. However, because there is only a partial negative charge on the carbanionic carbon in the transition state for k_{1} of Eq. (10), the magnitude of ρ is only about a third of ρ for the correlation of K, where the negative charge on the carbanionic carbon must be considerably greater [15].
For the reverse reaction of Eq. (10), correlation of k_{−1} vs σ_{p} gives ρ = −2.63 [15]. The change in the sign of ρ, from positive for k_{1} to negative for k_{−1}, signifies that in the reverse direction electron donating groups destabilize the carbanion, stabilize the carbene and accelerate the reaction [16]. The Hammett correlations of K, k_{1} and k_{−1} elucidate the sense and magnitude of the electronic effects that modulate the equilibria of Eq. (10).