Article pubs.acs.org/joc
Complexes and Negative Activation Energies in Arylhalocarbene/ Alkene Additions: Activation Parameter Dependence on Alkane Solvent Chain Length Lei Wang, Robert A. Moss,* and Karsten Krogh-Jespersen* Department of Chemistry and Chemical Biology, Rutgers, The State University of New Jersey, New Brunswick, New Jersey 08903, United States S Supporting Information *
ABSTRACT: Activation parameters for the additions of PhCCl, F5-PhCCl, and 3,5dinitro-PhCCl to tetramethylethylene, cyclohexene, and 1-hexene have been determined in decane. With the exception of two carbene/alkene combinations, Arrhenius correlations of ln kaddn vs 1/T were unimodal and linear, affording negative activation energies and entropies. The additions of PhCCl or F5-PhCCl to 1-hexene gave bimodal Arrhenius correlations. Comparisons to the analogous experimental data obtained in pentane and computational studies help to elucidate the observed behavior. Activation entropies decrease in parallel with activation enthalpies going from pentane to decane solvent, suggesting that enthalpy−entropy compensation is operative in these carbene additions. The bimodal Arrhenius behavior is proposed to result from carbene−alkene additions taking place intrinsically or extrinsically to decane solvent cage assemblies.
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contribution of the unfavorable entropic term, −TΔS‡. This hypothesis was supported by numerical model potential functions for additions of CF2, CCl2, and CBr2 to isobutene and TME.7,8 Since these early reports, negative activation energies have been observed in the additions of several other highly reactive and electrophilic transient carbenes to alkenes. Considering only reactions in which TME is the substrate, Ea < 0 has been observed for additions of CCl2,9 ClCCF3,10 (N-methyl-3pyridinium)chlorocarbene 1 (MePyr+CCl),11 pentafluorophenyl-chlorocarbene 2 (F5-PhCCl),12 and 3,5-dinitrophenylchlorocarbene 3 (3,5-DN-PhCCl).12 Pertinent activation parameters appear in Table 1. Significantly negative activation energies of Ea ≈ −3.5 kcal/mol have also been reported for additions of the nucleophilic adamantanylidene13 and dimethylcarbene14 to (e.g.) methyl acrylate. The negative activation energies are therefore associated with carbenic reactivity, not philicity.
INTRODUCTION In 1982, Turro, Moss and co-workers reported the first example of a negative activation energy for the addition of a halocarbene to an alkene: the addition of phenylchlorocarbene (PhCCl) to tetramethylethylene (TME) proceeded with Ea ≈ −1.7 kcal/ mol between 248 and 301 K.1 They suggested that the negative activation energy could be understood in terms of a “reversibly formed dissociable intermediate” (i.e., a carbene/alkene molecular complex), which either continued on to a cyclopropane product or reverted to carbene and alkene.1−3 Similar mechanisms had been offered to rationalize negative activation energies in certain Diels−Alder reactions4 and in exciplex formation between excited aryl ketones and TME.5 Houk and co-workers offered an alternative explanation for the negative activation energies observed in the carbene/alkene additions.6−8 Their ab initio computational studies (MP2/321G) suggested the absence of carbene/alkene π-complexes in the additions of CCl2 to ethene, propene, or isobutene, although a complex was predicted between the more stable carbene CF2 and ethene.6 It was concluded that no stable complexes, other than possible solvent “cage” complexes, formed between the more reactive halocarbenes and alkenes in solution.6,8 In place of a carbene/alkene complex explanation, Houk et al. presented a model in which a free energy maximum in the carbene/alkene addition arose from entropic factors, while the reaction enthalpy decreased all along the reaction coordinate.7,8 Thus, activation enthalpies ΔH‡ and energies Ea (Ea = ΔH‡ + RT for a bimolecular reaction) were negative, whereas the free energy of activation ΔG‡ was positive due to the significant © XXXX American Chemical Society
The activation parameters exhibited in Table 1 show substantial negative entropies of activation (ΔS‡) that lead to Received: January 24, 2017
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DOI: 10.1021/acs.joc.7b00186 J. Org. Chem. XXXX, XXX, XXX−XXX
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The Journal of Organic Chemistry
PhCCl to TME, cyclohexene, and 1-hexene (nine reactions). Our methodology was identical to that employed previously.12 Absolute rate constants for the carbene/alkene additions were measured by laser flash photolysis (LFP) using a xenon fluoride excimer laser emitting at 351 nm. The carbene precursors were the appropriate diazirines.20−22 Rate constants for the carbene/ alkene additions in decane were determined exactly as described for the analogous reactions in pentane.12 Control experiments with PhCCl showed that C−H insertion into decane did not compete with addition to TME.16 Similar experiments with F5-PhCCl afford analogous results with either TME or 1-hexene. Alkene addition is the sole pathway observed in both pentane and decane. Given the much larger (computed) activation energy for C−H insertion relative to the (observed and computed) activation energies for CC additions (see below), the disparity between addition and insertion would increase as the reaction temperature decreases. Activation parameters were derived from measured carbene/ alkene rate constants at five temperatures (±0.1 K) between 275 and 324 K. With the exception of two carbene/alkene combinations (discussed below), Arrhenius correlations of ln kaddn vs 1/T were distinctly unimodal and linear (r ≥ 0.99). Hence, determinations of the activation energies for seven of the nine carbene/alkene additions were straightforward. For example, the addition of 3,5-DN-PhCCl to cyclohexene afforded a nicely linear Arrhenius correlation over the temperature range 275 to 316 K with a slope of 2.92, a Yintercept of 8.34, and a correlation coefficient r = 0.993; cf. Figure 1. These results lead to Ea = −5.78 ± 0.39 kcal/mol, ΔS‡
Table 1. Measured Activation Parameters for Carbene Additions to TMEa Carbene
Ea
ΔH‡
ΔS‡
−TΔS‡
ΔG‡
ref.
CCl2 ClCCF3 MePyr+CCl PhCCl F5-PhCCl 3,5-DN-PhCCl
−1.2 −2.1 −3.1 −1.8 −1.8 −4.7
−1.8 −2.6 −3.7 −2.4 −2.4 −5.3
−20 −25 −28 −28 −26 −36
6.0 7.4 8.5 8.3 7.8 11.
4.2 4.8 4.8 6.0 5.4 5.5
b c d e f f
Units are kcal/mol for Ea, ΔH‡, −TΔS‡, and ΔG‡; and cal-deg/mol for ΔS‡. Ea = ΔH‡ + RT. ΔH‡ is calculated at 286 K; ΔG‡ is calculated at 298 K. Errors are 0.2−0.3 kcal/mol or less in Ea; errors in ΔS‡ are ∼1 e.u. Solvent is 1,2-dichloroethane for MePyr+CCl and pentane for the other carbenes. bReference 9. cReference 10. dReference 11. e References 1 and 12. fReference 12. a
small positive values of ΔG‡ despite the negative values of ΔH‡ that accompany these carbene/alkene additions. These results are in accord with Houk’s model6−8 and the earlier analysis of Skell and Cholod.15 Nevertheless, the continued observation of negative activation energies in these reactions (Table 1) suggested to us that renewed experimental and computational studies of the carbene/alkene addition reaction might be fruitful at this time, given that more than 30 years have passed since the Turro-Moss1−3 and Houk6−8 analyses. We are particularly interested in Houk’s suggestion that solvent “cage” complexes might intervene in reactions between alkenes and the more reactive carbenes in solution,6,8 because this idea provides a potential intersection between the two mechanistic models. We therefore determined the activation parameters for additions of PhCCl to TME in a series of alkane solvents of varied chain length from pentane to n-hepta-decane.16 We found that Ea for this carbene/alkene addition decreased from −1.8 kcal/mol, to −3.3 kcal/mol, and to −5.2 kcal/mol as the solvent changed from pentane, through octane, to decane. Simultaneously, ΔS‡ decreased from −28 eu to −40 eu.16 Elongation of the solvent alkyl chain beyond decane to pentadecane or heptadecane led to insignificant additional decreases in the activation parameters. We concluded that the reactions in decane (and higher alkanes) involved solvent “cages” by which reactant diffusion was constrained, leading to the likely “formation of PhCCl + TME “proximity pairs” or even complexes”.16 Note that, by solvent “cages”,17 we imply enthalpy driven assemblies of (one or more) solvent molecules preferentially solvating a carbene, alkene, or carbene/alkene pair (as an encounter complex or transition state), with mutual cohesion provided by long-range electrostatic forces.18,19 More recently, we examined carbene additions to tetramethoxyethylene, observing analogous significant decane solvent effects.18 Presently, we have determined the activation parameters for the carbene/alkene additions of three reactive, electrophilic halocarbenes to three alkenes of varying reactivity, in both pentane and decane solvents. The new experimental results, coupled with new extended computational studies and analysis, foster a more detailed mechanistic model for these iconic reactions.
Figure 1. Arrhenius correlation for the addition of 3,5-DN-PhCCl to cyclohexene with carbene visualized as the pyridine ylide; see text and Table 2 for details.
= −44 ± 1.3 eu, and hence ΔH‡ = −6.4 kcal/mol and ΔG‡ = ΔH‡ − TΔS‡ = 6.7 kcal/mol at 298 K.23 Activation parameters determined this way for carbene/alkene additions in decane are collected in Table 2; graphical displays of all rate constant determinations and Arrhenius correlations appear in the Supporting Information. Following the experimental procedure described above, the additions of PhCCl or F5-PhCCl to 1-hexene in decane unmistakably showed bimodal Arrhenius correlations (cf.
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RESULTS AND DISCUSSION Experimental Studies. For comparison to the analogous data in pentane,12 we determined the activation parameters in decane for the additions of PhCCl, F5-PhCCl, and 3,5-DNB
DOI: 10.1021/acs.joc.7b00186 J. Org. Chem. XXXX, XXX, XXX−XXX
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The Journal of Organic Chemistry Table 2. Measured Activation Parameters for Carbene/ Alkene Additions in Decanea Carbene
Alkeneb
Ea
ΔH‡
ΔS‡
−TΔS‡
ΔG‡
3,5-DN-PhCCl PhCCl F5-PhCCl 3,5-DN-PhCCl PhCCl F5-PhCCl 3,5-DN-PhCCl PhCCl (low T)c PhCCl (high T)c F5-PhCCl (low T)c F5-PhCCl (high T)c
TME TME TME cyclohex cyclohex cyclohex 1-hex 1-hex 1-hex 1-hex 1-hex
−8.0 −5.2 −5.5 −5.8 −2.6 −2.2 −2.2 −2.0 0.8 −1.7 1.0
−8.6 −5.8 −6.1 −6.4 −3.2 −2.8 −2.8 −2.6 0.2 −2.3 0.4
−46 −40 −38 −44 −39 −34 −34 −38 −29 −33 −24
13.7 11.9 11.3 13.1 11.6 10.1 10.1 11.4 8.6 9.8 7.1
5.1 6.1 5.2 6.7 8.4 7.3 7.3 8.8 8.4 7.5 7.5
Units are kcal/mol for Ea, ΔH‡, −TΔS‡, and ΔG‡; and cal-deg/mol for ΔS‡. Ea = ΔH‡ + RT. ΔH‡ is calculated at 286 K; ΔG‡ is calculated at 298 K. Errors are 0.2−0.3 kcal/mol or less in Ea; errors in ΔS‡ are ∼1 e.u. bTME = tetramethylethylene, cyclohex = cyclohexene, 1-hex = 1-hexene. cBimodal in decane, see text. a
Figure 2. Bimodal Arrhenius correlation for the addition of PhCCl to 1-hexene in decane with PhCCl observed at 292 nm. For quantitative details, see the text and Table 2.
Figures S-18a and S-18b for PhCCl/1-hexene; Figure S-36 for F5-PhCCl/1-hexene). In contrast, these additions yielded unremarkable unimodal and linear Arrhenius correlations in pentane.12 Bimodal, or “curved”, ln k vs 1/T plots are typically interpreted in terms of two “mechanisms” or “processes” operating concurrently. The coexisting processes must necessarily exhibit different temperature dependences in their respective kinetics parameters, yet be governed overall by comparable free energies of activation in the temperature range under consideration. We determined “best” activation parameters for the PhCCl/ 1-hexene and F5-PhCCl/1-hexene addition processes as follows. For the PhCCl/1-hexene pair, three separate series of experiments were executed: two runs generated five (T, kaddn) points each, covering the entire available temperature range of 275−324 K, while a third run produced additional points at low and at high temperatures. From the accumulated total of 12 rate constant vs temperature determinations, we used the three points obtained at the highest (T > 308 K) and the three points obtained at the lowest (T < 281 K) temperatures, respectively, to construct two linear Arrhenius correlation lines of ln kaddn vs 1/T. Six points were considered to be in the intermediate temperature range and were not used in fitting (cf. Figure 2). For the process dominant at higher temperatures, the leastsquares correlation treatment led to Ea = 0.79 ± 0.59 kcal/mol and ΔS‡ = −28.7 ± 1.9 eu. By extrapolation, ΔH‡ = 0.2 kcal/ mol and ΔG‡ = 8.4 kcal/mol at 298 K for the “high T” process (Table 2). Similarly, for the process dominant at lower temperatures, we obtained Ea = −2.0 ± 0.60 kcal/mol and ΔS‡ = −38.3 ± 2.2 eu; consequently, at 298 K, ΔH‡ = −2.6 kcal/mol and ΔG‡ = 8.8 kcal/mol for the “low T” process (Table 2). However, the activation parameters determined for the PhCCl/1-hexene addition by this approach (six data points selected from a total of 12) do not deviate statistically from activation parameters extracted from the two individual fivepoint runs (Figures S-18a and S-18b). Thus, the more approximate approach of fitting to five (T, kaddn) points was taken for the F5-PhCCl/1-hexene pair (Figure 3). For the F5PhCCl/1-hexene addition, the process dominant at higher temperatures shows Ea = 0.98 ± 0.09 kcal/mol and ΔS‡ = −24.3 ± 1.9 eu; therefore, ΔH‡ = 0.4 kcal/mol and ΔG‡ = 7.5
Figure 3. Bimodal Arrhenius correlation for the addition of F5-PhCCl to 1-hexene in decane with F5-PhCCl observed at 300 nm. For quantitative details, see the text and Table 2.
kcal/mol at 298 K. Similarly, for the process dominant at lower temperatures, the correlation treatment leads to Ea = −1.7 ± 0.11 kcal/mol and ΔS‡ = −33.4 ± 0.4 eu; thus, at 298 K, ΔH‡ = −2.3 kcal/mol and ΔG‡ = 7.5 kcal/mol (Table 2). Table 3 compares values of Ea and ΔS‡ determined in pentane12 with analogous data in decane (this work). Focusing briefly on the seven unimodal correlations in decane, we observe that the change in solvent from pentane to decane on average lowers ΔH‡ (Ea) by 3.3 ± 0.5 kcal/mol and lowers ΔS‡ by an average of 11 ± 2 eu. The similar reductions in activation energies and entropies across these varied carbene/alkene additions suggest a similar cause in each instance. In two cases (cyclohexene plus either PhCCl or F5PhCCl), solvent alteration induces a positive to negative change in the activation energies for the carbene additions. The decreases in ΔH‡ accompanying the pentane to decane solvent change are paid for by decreases in entropy, presumably C
DOI: 10.1021/acs.joc.7b00186 J. Org. Chem. XXXX, XXX, XXX−XXX
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The Journal of Organic Chemistry Table 3. Comparative Activation Parameters Measured in Pentane and in Decanea
a
Data obtained in pentane solvent in black; data obtained in decane solvent in red. bTME = tetramethylethylene, cyclohex = cyclohexene, 1-hex = 1hexene. cBimodal in decane for PhCCl and F5-PhCCl; see text.
consideration here are presented in Table 5, along with corresponding experimental data obtained in pentane.12 A representative TS involving F5-PhCCl adding to TME is illustrated in Figure 4b. The computed Ea’s are consistently lower than the experimental values. Additions to TME, in particular, have computed Ea’s much lower than experimental values; also, addition of F5-PhCCl appears notably favored by the calculations. For all three carbenes, the calculations find that Ea’s for alkene addition follow the rank order TME < cyclohexene < 1-hexene, in agreement with experiment. As customarily observed for bimolecular reactions, the computed (essentially gas phase) entropies of activation are more negative than indicated by (solution phase) experimental values.31,32 Somewhat fortuitously therefore, computed free energies of activation (ΔG‡) differ relatively little (1−2 kcal/mol) from the experimental values and agree well with the observed rank order. Overall, we consider the agreement between computational and experimental results to be acceptable, especially considering the atypical activation parameters pertaining to the carbene/alkene pairs under consideration. Computed thermodynamic parameters for carbene/alkene πcomplex and product cyclopropane formation in pentane are shown in Table 6. For all nine carbene/alkene pairs, a π-type complex could be located as a potential energy minimum along the reaction coordinate, in the vicinity of the corresponding TS for cycloaddition, with an enthalpy of formation (ΔH) value in the −4 to −9 kcal/mol range (relative to separated reactants). The minimum energy π-complex located for the F5-PhCCl/ TME pair is illustrated in Figure 4a. Of course, cyclopropane formation is a highly exothermic process as evidenced by computed ΔH values in the −65 to −75 kcal/mol range. For all π-complex/TS pairs, the enthalpy is lower for the TS than the
originating in increased translational and rotational restriction of the reactant pairs or complexes in the decane solvent assemblies. Moreover, the solvent change evokes strict compensation in the ΔH‡ and ΔS‡ responses (3.3 kcal/mol are equivalent to 11 eu at T = 298 K); both decrease in tandem (Table 3) in such a manner that the ΔG‡ values for these carbene/alkene additions hardly change as the solvent changes (cf. Table 4). Table 4. Comparison of Experimental ΔG‡ Measured in Pentane and in Decanea PhCCl alkene
b
TME cyclohex 1-hex
ΔG
‡
pent
6.0 8.3 8.6
F5-PhCCl
ΔG‡dec 6.1 8.4 8.6c
ΔG
‡
pent
5.4 7.4 7.6
3,5-DN-PhCCl
ΔG‡dec
ΔG‡pent
ΔG‡dec
5.2 7.3 7.5c
5.5 6.9 7.1
5.1 6.7 7.3
Units are kcal/mol for ΔG‡, which is calculated at 298 K. bTME = tetramethylethylene, cyclohex = cyclohexene, 1-hex = 1-hexene. c Average value, calculated from activation parameters for the bimodal Arrhenius correlations; see text and Table 2. a
Computational Studies. We have carried out electronic structure calculations at the DFT level using the MN12-SX exchange-correlation functional24 and 6-311+G(d) basis sets25−29 (MN12-SX/6-311+G(d)); general bulk solvent effects were included using a standard continuum dielectric model (CPCM;30 cf. Computational Details in the Experimental Section). We have used this or comparable levels of theory successfully in previous computational studies of carbene− alkene additions with low activation barriers.13,14,16,18 The computed activation parameters in the pentane model solvent for the nine carbene−alkene combinations under
Table 5. Calculated and Measured Activation Parameters for Carbene/Alkene Additions in Pentanea,b
Computed values in black; experimental values in red from ref 12. bUnits are kcal/mol for Ea, ΔH‡, −TΔS‡, and ΔG‡; and cal-deg/mol for ΔS‡. TME = tetramethylethylene, cyclohex = cyclohexene, 1-hex = 1-hexene. dValue of vibrational frequency characteristic of the curvature of the potential energy surface at the TS structure; units of cm−1. eEa = ΔH‡ + RT. fValues calculated from electronic structure theory are referenced to T = 298.15 K and concentrations of 1 M. a c
D
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Figure 4. (a) Computed (MN12-SX/6-311+G(d)) F5-PhCCl/TME π-complex. Some illustrative distances (Å) and angles (degrees) are C1−C19 = 2.82; C2−C19 = 2.97; C1−C2 = 1.35; C1−C2−C19 = 70.7; C2−C1−C19 = 82.4; and C2−C1−C19−C24 = −39.9. (b) Computed (MN12-SX/6311+G(d)) TS for F5-PhCCl/TME cycloaddition. Some illustrative distances (Å) and angles (degrees) are C1−C19 = 2.68; C2−C19 = 2.91; C1− C2 = 1.36; C1−C2−C19 = 66.6; C2−C1−C19 = 85.7; and C2−C1−C19−C24 = −60.4.
Table 6. Computed Energetic Parameters for π-Complex and Cyclopropane Formation in Model Pentane Solutiona
formation (Table 6), there should be many TSs available for carbene/alkene pairs to transit on the free energy surfaces, effectively avoiding the shallow wells corresponding to the πcomplexes. Given that the free energies of π-complex formation are distinctly positive, we do not expect the π-complexes to influence the rates of addition in any consequential manner at ambient temperatures, and it is probably prudent to consider the carbene/alkene π-complexes to be transitory “collision” or “encounter” complexes in nature.8 The π-complexes evidently represent minima on the potential energy surfaces, but their status on the free energy surfaces for cycloaddition, and hence general significance, remains undetermined.
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DISCUSSION This section will focus on the unexpected results of our present studies, namely the distinct solvent dependence of the activation parameters (cf. Table 3) and the bimodal Arrhenius correlations observed in decane only (cf. Figures 2 and 3; Table 2). The bimodal correlations observed for the additions of PhCCl and F5-PhCCl to 1-hexene in decane solvent argue for two simultaneous and energetically competitive processes, which are most readily conceived of as reactions differing in their specific involvement of decane solvent. We suggest that the simultaneously occurring processes may, in the limit, be considered as carbene/alkene additions extrinsic and intrinsic to decane solvent assemblies. Specifically, in Figures 2 and 3 we assign the limbs with Ea > 0 to extrinsic reactions, dominant at higher temperatures, and the limbs with Ea < 0 to intrinsic reactions which control the carbene/alkene additions at lower temperatures. In support of these assignments, we note that the higher temperature limbs reflect activation parameters for PhCCl and F5-PhCCl additions to 1-hexene of Ea = 0.8 and 1.0 kcal/mol, and ΔS‡ = −29 eu and −24 eu, respectively. These values are quite similar to the corresponding activation parameters measured in pentane (Ea = 1.2 and 2.7 kcal/mol; ΔS‡ = −27 eu and −18 eu for PhCCl and F5-PhCCl, respectively), where we hypothesize no significant solvent cage formation, and hence the dominance of extrinsic reactions (cf. Table 3 and ref 16). Accepting this primary assignment, we find that the intrinsic reactions (dominant at lower temperature) have the lower activation energies for PhCCl and F5-PhCCl additions to 1-hexene (Ea = −2.0 kcal/mol and −1.7 kcal/mol, respectively)
a Values for π-complex formation in black; values for cyclopropane formation in red. Units are kcal/mol for ΔH, −TΔS, and ΔG; and caldeg/mol for ΔS. bTME = tetramethylethylene, cyclohex = cyclohexene, 1-hex = 1-hexene. cValues referenced to T = 298.15 K and concentrations of 1 M.
corresponding π-complex. Indeed, the enthalpy appears to decrease uninterruptedly upon exit from the π-complex well, with the TS positioned on the leg descending toward the cyclopropane product. Occurring later on the reaction coordinate, however, the TS accrues a larger entropic penalty than the π-complex so that the free energy of activation for cycloaddition is several kcal/mol larger than the free energy of the π-complex. The situation is very much akin to that described by Houk et al;6−8 accordingly, the free energy of the TS reaches a maximum due to the entropic factor. The free energies for formation of the π-complexes (ΔG) occupy a relatively narrow range, 2−4 kcal/mol above the isolated reactants (Table 6). A carbene/alkene π-complex and its corresponding TS for cycloaddition are always structurally very similar (cf. Figure 4; also refs 12 and 16). Furthermore, the “imaginary” frequency of the TS is always modest in magnitude (at most 250i cm−1; Table 5), indicating that the potential energy surface is quite flat in the region of the TS, and the πcomplexes most likely occupy shallow basins at best. Ensembles of molecules in solution at ambient temperature span wide ranges in kinetic energies and geometrical orientations. Considering the highly “attractive” nature of the enthalpy surface engendered by the large exothermicity for cyclopropane E
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Figure 5. Views of the minimum energy PhCCl/pentane and PhCCl/decane complexes in perspective, and with fading background.
with increasing viscosity as the solvent changes from pentane to octane to decane, while further change to even longer alkane chains and higher viscosities (pentadecane, heptadecane) brings about little additional change. Given that the static dielectric constants of pentane and decane are small and quite similar (εpentane = 1.84 and εdecane = 1.98, a difference of less than 10%),35 only minor energy differences and hence effects could conceivably be associated with the differential change in dielectric constant from pentane to decane. Overall, these observations argue strongly against an explanation based on a macroscopic homogeneous property, in particular solvent viscosity, as the primary cause for the observed behavior. Rather, we seek an explanation more closely associated with a microscopic perspective. Potentially, cohesive carbene/alkene interactions lead to πcomplex formation in alkane solvent prior to cycloaddition (Table 6, Figure 4). Are carbene/alkane interactions viable and, if so, does their strength aid us in rationalizing the observed bimodal Arrhenius behavior? If carbene/alkane complexes do form, how might such complexes affect reactivity? We turn (again) to conventional computational electronic structure methods (DFT) in an attempt to gain additional insight, with the expressed caveat that obtaining convincing answers to such questions would undoubtedly require the extended use of advanced molecular dynamics methodologies. Development and application of such techniques are, however, well beyond the scope of the present work. In Tables S4−S6 (Supporting Information) we show computational data, equivalent to the data presented above in Tables 5 and 6 (which are reproduced in Tables S1−S3 for convenience) but employing decane as the model solvent. With almost no exceptions, parameters for both thermodynamics and kinetics computed for carbene/alkene complexes, transition states for addition, and product cyclopropanes in model decane solvent differ by less than 0.3 kcal/mol from values obtained with model pentane solvent. The CPCM solvation model applied30 is strictly a dielectric continuum model, and the primary solvent parameter determining the magnitudes of the computed solvation energies is hence the dielectric constant of
but correspondingly more unfavorable entropies of activation (ΔS‡ = −38 eu and −33 eu, respectively). This supports our notion that longer alkane chain solvent assemblies stabilize all species, including π-complexes and TSs for addition, and lower activation enthalpies as well as entropies.18 Moreover, the pentane to decane activation parameter changes for PhCCl and F5-PhCCl reacting with 1-hexene intrinsic to the decane assemblies are ΔEa = −3.2 kcal/mol and −4.4 kcal/mol, and ΔΔS‡ = −11 eu and −15 eu, respectively (low T, Table 3). These changes are nearly identical to the average activation parameter modifications found for the seven unimodal carbene/alkene Arrhenius correlations accompanying the change of reaction locus from pentane solution to the postulated decane solvent assemblies (ΔEa = −3.3 kcal/mol and ΔΔS‡ = −11 eu, respectively; see above and Table 3). We also note that ΔG‡ measured for additions of PhCCl and F5PhCCl to 1-hexene extrinsic or intrinsic to the decane assemblies are experimentally identical to ΔG‡ for these additions in pentane (see text and Table 4), again highlighting the operation of strict enthalpy−entropy compensation. The experimental results do not reveal the nature of the interactions causing the observed behavior. For example, are the observed effects defined by a homogeneous property of the alkane solvent such as dynamic viscosity or dielectric constant, or is an explanation more closely identified with heterogeneity preferable? The temperature range experimentally employed is approximately 275−324 K. The viscosity (η) of pentane (units of mPa·s) is 0.273 at 273 K and 0.173 at 323 K;33 similarly, for decane η = 1.29 at 273 K and 0.612 at 323 K.34 Thus, the viscosity of decane is not only considerably larger than that of pentane, but it also changes more with varying temperature, in both relative and absolute terms. We might anticipate, naively perhaps, that Ea for a bimolecular process would tend to be larger in a more viscous solvent (i.e., decane). However, this is opposite to what is observed (Table 3): changing the solvent from pentane to decane on average lowers Ea by 3.3 ± 0.5 kcal/ mol. Furthermore, as mentioned in the Introduction, we have demonstrated16 that, for PhCCl/TME addition, Ea decreases F
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respectively). The π-electron “rich” carbenes, F5-PhCCl and 3,5-DN-PhCCl, have the stronger complex forming interactions and also the lower barriers for alkane C−H insertion. Importantly, however, the activation energies for C−H insertion are much larger than the barriers for alkene addition (cf. Tables 3 and 5, or Tables S2, S5, and S7). Moreover, in ref 16, we showed that C−H insertion of PhCCl into decane did not occur in competition with addition to tetramethylethylene (TME). Additional experiments have now given analogous results for F5-PhCCl with either TME or 1-hexene. Thus, according to both experiment and computations, C−H insertion is unlikely to occur to any appreciable extent in either solvent (despite the very large number of C−H bonds potentially available in decane). Our previous studies of the PhCCl/TME addition reaction led us to suggest that the reductions observed in activation energies with increasing alkane solvent chain length did not result from general solvent−solute interactions; more likely, the diminished activation energies reflected specific stabilizing interactions of carbene/alkene encounter or molecular complexes in solvent cages formed by longer aliphatic chains.16 As noted above, within a continuum dielectric solvent model, minimal changes from bulk solvation are computed in ΔH‡ (
