Distortion/interaction analysis of the reactivities and selectivities of halo– and methoxy–substituted carbenes with alkenes

The transition structures for the (2+1) cycloadditions of dichlorocarbene, chlorofluorocarbene, and difluorocarbene to cyclohexene, 1–hexene, ethylene, and α–chloroacrylonitrile were located using quantum mechanical methods (M06–2X). In addition, transition structures for the (2+1) cycloadditions of chloromethoxycarbene, fluoromethoxycarbene, and dimethoxycarbene to ethylene and α–chloroacrylonitrile were computed. Except for the reactions with ethylene, these cycloadditions were studied experimentally and computationally by Moss and Krogh–Jespersen (Zhang, M.; Moss, R. A.; Thompson, J.; Krogh–Jespersen, K. J. Org. Chem. 2012, 77 , 843–850). As a complement to the work of those groups, we have utilized the distortion/interaction model to understand reactivities and selectivities. Gas–phase calculations were carried out at the M06– 2X/6–31+G(d,p) level of theory.


Introduction
The cycloadditions of carbenes to alkenes constitute a general method for synthesis of cyclopropane ring structures.These cycloadditions have excited widespread interest in the mechanistic details of this reaction.Hoffmann predicted that a C2v cyclic four-electron transition state in which both C-C bonds form simultaneously is orbital-symmetry forbidden; 1,2 therefore, non-least motion approach was proposed by Hoffmann 2 and Moore 3 in which there is initial interaction of the electrophilic empty p-orbital (LUMO) of the carbene with the nucleophilic filled π-orbital (HOMO) of the alkene. 1 This prediction was subsequently verified many times with semiempirical [4][5][6] and ab initio methods 7,8 and was shown to be influenced by a second pair of orbital interactions between the lone pair (HOMO) of the carbene with the π* antibonding orbital (LUMO) of the alkene, which becomes dominant for electron-donor substituted carbenes. 80][11][12] They combined laser flash photolysis and density functional theory calculations to determine activation parameters for a series of carbene cycloadditions. 13They found that trends in ∆E ‡ parallel expectations based on considerations of carbene stability and nucleophilicity.As a complement to the work of those groups, we have computationally investigated the (2+1) cycloadditions of dihalocarbenes 1a-c to cyclohexene (2a) and 1-hexene (2b), as well as the cycloadditions of 1a-c and methoxycarbenes 1d-f to ethylene (2c) and α-chloroacrylonitrile (2d) in the context of the distortion/interaction model of reactivity developed by our group 14 (or the activation-strain model developed independently by Bickelhaupt).

Computational Methodology
Gas phase reactant, product, and transition state geometry optimizations as well as analytical frequencies were computed using the hybrid meta-GGA functional M06-2X 16 with the 6-31+G(d,p) basis set in the Gaussian 09 suite of programs. 17Tight convergence criteria and an ultrafine integration grid were used in all optimizations.All reactants have positive definite Hessian matrices and all transition structures have only one negative eigenvalue in their diagonalized force constant matrices.Intrinsic reaction coordinate (IRC) 18,19 calculations were performed to obtain a potential energy surface for distortion/interaction analysis and to ensure that all optimized transition structures connect the appropriate reactants and products.

Results and Discussion
The distortion/interaction model developed by our group has recently been applied to explain the reactivities and selectivities of (3+2) cycloadditions. 14This model dissects activation barriers (∆E ‡ ) of bimolecular reactions into distortion energies (∆Ed ‡ ) and interaction energies (∆Ei ‡ ).The distortion energy is the amount of energy required to distort the carbenes and alkenes into their transition state geometries without allowing the cycloaddition partners to interact.The interaction energy arises from a combination of closed-shell repulsion, charge transfer involving occupied and vacant orbital interactions, electrostatic interactions, and polarization effects.By definition, ∆E ‡ = ∆Ed ‡ + ∆Ei ‡ , and the position of the transition state occurs at the point along the reaction coordinate, ζ, where the derivatives of the distortion and interaction energies are equal and opposite (∆Ed(ζ)/ζ = -∆Ei(ζ)/ζ).Figure 2 shows the transition structures for the cycloadditions of 1a-c with 2a and 2b and 1a-f with 2c and 2d computed with M06-2X/6-31+G(d,p).Table 1 shows the activation and total distortion energies, the contributions to the distortion energies of the carbene and the alkene, and the interaction energies for reactions of 1ac with 2a and 2b and 1a-f with 2c and 2d.   2. As shown in Table 1, the cycloadditions of CCl2 (1a) and CClF (1b) to cyclohexene (2a) and 1hexene (2b) have negative activation energies, which are controlled by ∆Ei ‡ .1][22][23][24][25][26][27][28][29] We have confirmed πcomplexes for cycloadditions to 2a, 2b, and 2d that are stabilized by 0-5 kcal mol -1 (∆Hº = ∆Hfree ‡ -∆Hcomplex ‡ ) relative to infinitely separated reactants; however, they are not minima on the free energy surface and thus are not expected to be experimentally stable.These computed activation energies are 6-8 kcal/mol too low when compared to activation energies determined experimentally by Moss and Krogh-Jespersen; 13 therefore, conclusions from these results should be taken with caution.An increase of 6-7 kcal mol -1 in the distortion energies and a decrease of 4-5 kcal mol -1 in the favorable (negative) interaction energies results in a substantial increase of the activation energies along the series 1a1b1c.The carbene and alkene contributions to the total distortion energies for 1a and 1b are within ~1 kcal mol -1 .As for reactions of CF2 (1c), distortion of the alkene is the primary cause of the increase in ∆Ed ‡ , as seen in an average ∆∆Ed,carbene ‡ of 1.1 kcal mol -1 and ∆∆Ed,alkene ‡ of 5.1 kcal mol -1 relative to 1a.Distortion of cyclohexene and 1-hexene comprises 42-72% and 40-73%, respectively, of the total distortion energy.In Table 2, the alkene bond distances, r13, increase by a mere 0.02-0.03Å from 1a1b1c; therefore, C1-C3 bond elongation is not a significant contributor to ∆∆Ed ‡ .We use angles α and  to quantify the degree of pyramidalization of the terminal alkene carbons.As shown in Table 2, α increases by 17º and  increases by 6º along the series 1a1b1c.A greater extent of pyramidalization at C3 of the alkene occurs as a result of non-least motion approach in which the C2-C3 bond forms before the C2-C1 bond.We conclude that pyramidalization of the alkene carbons is the major distortion occurring at the transition state, and the change in C1-C3 bond length occurs mainly after the transition state.An increase in the values of α and  indicates progressively later transition states and greater nucleophilic character of the carbene.The distance between C2 and the midpoint of the alkene (d) as well as the forming bond distances (r12 and r23) become shorter along the same series 1a1b1c, which also supports later transition states and increasing ∆Ed ‡ .
Based on the values of the carbene tilt angle  in Table 2, 8 1a-c react as electrophilic carbenes toward electron-rich alkenes 2a and 2b.Increasing carbene LUMO energies (CCl2: -3.74 eV; CClF: -3.39 eV; CF2: -2.83 eV) 13 lead to decreased interaction with the π-orbitals of 2a and 2b, which is likely one factor that attributes to a higher ∆Ei ‡ for 1c.However, since ∆Ei ‡ for 1a and 1b are essentially identical, there must be a complex interplay of factors that render this analysis of ∆∆Ei ‡ incomplete.An energy decomposition analysis would be required for any greater insight into the physical origins of ∆Ei ‡ .

Cycloadditions to ethylene
In addition to the distortion/interaction analyses for the TS that are collected in Table 1, the reaction profiles together with their decomposition into ∆Ed and ∆Ei for cycloadditions of dihalocarbenes 1a-c and methoxycarbenes 1d-f to ethylene (2c) are shown in Figure 3. Plots of ∆Ed and ∆Ei for all cycloadditions to 2c are shown in Figures 4 and 5   Activation energies for cycloadditions of 1a-c and 1d-f to 2c increase from 0-10 and 8-16 kcal mol -1 , respectively.Changes in ∆Ed ‡ and ∆Ei ‡ are comparable in magnitude, and both contribute to an increase in ∆E ‡ from 1a1b1c and from 1d1e1f.The distortion of ethylene comprises 51-74% of the total distortion energy.Carbene tilt angles in Table 2 indicate that 1a-c are predominantly electrophilic and 1d-f are predominantly nucleophilic in cycloadditions to 2c.All interaction energies for the reactions with 2c are positive except for that of 1a, resulting in activation barriers greater than the inherent distortion in the transition structures.This result differs from those seen for example in 1,3-dipolar and Diels-Alder cycloadditions, where the interaction energies at the transition states are negative, i.e., favorable, in all cases such that the activation barrier is decreased relative to the distortion energy. 30The alkyl substituents of 2a and 2b raise the HOMO of ethylene while the -Cl and -CN substituents of 2d lower the LUMO of ethylene.Both of these perturbations decrease the frontier molecular orbital gaps between the carbene and alkene and lead to favorable interaction energies with respect to ethylene.Previously reported trends in HOMO and LUMO energies for these alkenes support this conclusion. 132][33][34][35] Houk and Ess examined cycloadditions of hydrazoic acid, an ambiphilic 1,3-dipole, to a series of substituted alkenes and found that electron-rich and electron-deficient alkenes lower the activation barriers ~2 kcal mol -1 compared to ethylene. 30rom the distortion/interaction analyses in Figure 3, medium-range (d ~ 3 Å) attractive interactions exist while there is yet no distortion between the carbene and ethylene.This results in a negative ∆E relative to infinitely separated reactants and indicates formation of π-complexes, as mentioned earlier.In all cycloadditions to ethylene, there is no substantial increase in ∆Ed while d > 2.4 Å (Figure 3); therefore, the rise in ∆E along the reaction coordinate is primarily due to an increasingly destabilizing interaction between the carbene and the alkene.The early inversion of ∆Ei from destabilizing to stabilizing in 1a is responsible for a particularly early transition state.This behavior seems to be general to pericyclic reactions as it has been observed by Bickelhaupt in (3+2) cycloadditions, 36 Alder-ene reactions, 37 and double group-transfer reactions. 38Bickelhaupt has also pointed out that the initially destabilizing ∆Ei observed in pericyclic reactions contrasts those seen in other bimolecular reactions such as SN2 substitution 39 and E2 elimination. 40

Cycloadditions to α-chloroacrylonitrile
The same general increase in ∆E ‡ from 1a1b1c is observed with α-chloroacrylonitrile as in additions to 2a-c due to increased stabilization of the carbene by fluorine substituents.The distortion of α-chloroacrylonitrile (2d) is the dominant factor of ∆Ed ‡ , comprising 71-100% of the total distortion energy in the transition state.The activation energy of 1a addition to 2d is negative due to a favorable interaction energy of 4.5 kcal mol -1 that compensates for the 1 kcal mol -1 distortion energy of 2d in the transition state.The computed activation barrier of -3.2 kcal/mol for the cycloaddition of 1a to 2d is substantially lower than the experimentally determined value of 5.4 kcal/mol. 13There is a dramatic increase in reactivity of 1d-f toward 2d as compared to 2c (∆∆E ‡ ranges from 8-15 kcal mol -1 ).These differences are caused by large favorable changes in interaction energy and relatively small unfavorable changes in distortion energy of the 2d series relative to 2c: average values of ∆∆Ed ‡ and ∆∆Ei ‡ for cycloadditions of 1d-f to 2c and 2d are +2.4 and -8.7 kcal mol -1 respectively.Cycloadditions of 1c and 1d to 2d have the same amount of distortion in the TS; thus, the higher reactivity of 1d relative to 1c is a result of a 5 kcal mol -1 difference in ∆Ei ‡ .
Houk and Ess discovered a linear correlation between activation energy and distortion energy in the transition states for 18 1,3-dipolar cycloadditions. 30Houk and co-workers also observed a similar correlation for 1,4-dihydrogenations and Diels-Alder cycloadditions of aromatic molecules. 41Figure 6 shows a plot of ∆E ‡ versus ∆Ed ‡ for the cycloadditions to ethylene and α-chloroacrylonitrile.The observed correlation (r 2 = 0.95) for cycloadditions to 2c indicates that the increasing activation barrier is a direct result of increasing distortion energy in the transition state.The cooperative increase in ∆Ei ‡ as shown in Table 1 results in the same correlation (r 2 = 0.95) between ∆E ‡ and ∆Ei ‡ for additions to 2c (Figure S-1).Therefore, activation energies for cycloadditions of 1a-f to 2c are equally controlled by both ∆Ed ‡ and ∆Ei ‡ .Similarly, ∆Ed ‡ and ∆Ei ‡ exert equal control of ∆E ‡ for cycloadditions of 1a-c to 2a and 2b with r 2 ~ 0.95-0.99(not shown).For cycloadditions to 2d, there is essentially no correlation (r 2 = 0.38) between ∆E ‡ and ∆Ed ‡ for the complete carbene set; however, a correlation does exist for the dihalocarbenes 1a-c (r 2 = 1).Generally, it is observed that pyramidalization of the alkene carbons is the primary contributor to ∆Ed ‡ in carbene cycloadditions.When compared to dihalocarbenes 1a and 1b, cycloadditions of 1c to all four alkenes show anomalously unfavorable interaction energies in the transition state.
Cycloadditions of 1b and 1c with 2c have essentially the same distortion energy profile, as seen in Figure 4; therefore, the higher ∆E ‡ of the latter is the result of a later transition state originating from more destabilizing ∆Ei throughout the reaction.∆Ed ‡ is constant for the reactions of 1c and 1d to 2d, so a more favorable ∆Ei ‡ relative to 1c is responsible for the higher reactivity of 1d.The cycloaddition of C(OMe)2 to α-chloroacrylonitrile shows a ∆Ei ‡ that is more favorable than expected (1f + 2d; Table 1) and contributes to a breakdown in the correlation between ∆E ‡ and ∆Ed ‡ /∆Ei ‡ observed for 2a-c.These results suggest that (2+1) cycloadditions are not only distortion-controlled as are other pericyclic reactions.As represented in Figures 4 and 5, small differences in distortion energies but large differences in interaction energies control the position of the transition state and the reaction rate.

Table 2 .
Geometrical parameters of the cycloaddition transition structures computed at the M06-2X/6-31+G(d,p) level.Distances are in Å and angles are in degrees