Concerted [4 + 2] and Stepwise (2 + 2) Cycloadditions of Tetrafluoroethylene with Butadiene: DFT and DLPNO-UCCSD(T) Explorations

Tetrafluoroethylene and butadiene form the 2 + 2 cycloadduct under kinetic control, but the Diels–Alder cycloadduct is formed under thermodynamic control. Borden and Getty showed that the preference for 2 + 2 cycloaddition is due to the necessity for syn-pyramidalization of the two CF2 groups in the 4 + 2 transition state. We have explored the full potential energy surface for the concerted and stepwise reactions of tetrafluoroethylene and butadiene with density functional theory, DFT (B3LYP and M06-2X), DLPNO-UCCSD(T), and CASSCF-NEVPT2 methods and with the distortion/interaction–activation strain model to explain the energetics of different pathways. The 2 + 2 cycloadduct is formed by an anti-transition state followed by two rotations and a final bond formation transition state. Energetics are compared to the reaction of maleic anhydride and ethylene.

The reaction of 1 and 2 was studied theoretically by Borden and Wang 30 years ago. They sought to quantify the π-bond strength of TFE. 13 Calculations were performed at the HF/6-31G* level with an MP2 correction to account for electron correlation. It was determined that the origin of the weak π-Scheme 1. (a) Reaction between TFE and Butadiene. (b) Cycloaddition Products of the Reaction of Trifluoroethylene and Butadiene at 215°C 9 Figure 1. Experimentally determined product distribution of the cycloadducts of 1 and 2 formed as a function of temperature. The temperature is given in°C. 12 Reprinted with the permission of Elsevier.
bond of 1 was due to the cost of planarizing the two CF 2 groups, highlighting the propensity of fluorine substituents to stabilize the sp 3 geometry (Bent's Rule). 14 Later, but now 28 years ago, Borden and Getty calculated the energies of diradical intermediates and concluded that the Diels−Alder transition state is energetically unfavorable due to the necessity of syn-pyramidalization of the two CF 2 groups. 15 While the results of Borden explain why the usually favored Diels−Alder reaction is disfavored here, there are many details of these reactions, as well as computational comparisons with systems that favor Diels−Alder additions, that attracted us to this reaction once again. We have studied cycloadditions involving concerted and 2 + 2 diradical pathways using contemporary theoretical methods. The details of mechanisms of 2 + 2 and Diels−Alder reactions and analysis of barriers by the distortion/interaction−activation strain model are reported here. The reactions of TFE were also compared to those of ethene and maleic anhydride.

■ COMPUTATIONAL METHODS
All stationary points were fully optimized at both UB3LYP/6-311+ +G(d,p) and UM06-2X/6-311++G(d,p) levels of theory and verified as minima or first-order saddle points with frequency calculations using Gaussian 09. 16 Diradicals were optimized as open-shell singlets. One should be aware of possible shortcomings of density functional theory (DFT) in this regard. 17 Intrinsic reaction coordinate (IRC) calculations were also performed to link transition states to their respective minima. Calculations were performed in the gas phase at 1 atm and 635.15 K. Additionally, DLPNO-UCCSD(T) 18 single-point energy calculations were performed using ORCA 4.0.1 19 and the cc-pVTZ 20 basis set on UB3LYP/6-311++G(d,p) geometries. While UCCSD(T) calculations have been employed in investigations of diradicals, 21 it has been noted that DLPNO-UCCSD(T) can lead to unphysical behavior in case of preceding broken symmetry selfconsistent field (SCF) calculations. 22−24 Therefore, the barriers of the rate-determining steps and the electronic nature of intermediate 5 were also investigated using a second-order perturbative treatment of CASSCF wave functions in the form of NEVPT2 calculations as implemented in ORCA. The (2,2) and (4,4) active space was chosen for reactants 1 and 2, respectively, while (6,6) was used for TS1−TS7 and 5. Relative energies calculated at the NEVPT2 and DLPNO-UCCSD(T) level are in excellent agreement (Supporting Information, Figure S1). Detailed information about the computational methods is provided in the Supporting Information.
Once intermediate 6 is formed, inversion of the radical center at C1 is necessary to align the two radicals on C1 and C4, making ring closure facile. This can be accomplished by inversion through a planar high-energy transition state TS12 or by rotation around the C1−C2 bond through TS9 (Figure 4). This rotation avoids the unfavorable planarization of the radical on C1. The rotational barrier for the conversion of 6 to 7 is 2.6 kcal/mol. The minimum energy reaction paths (MERPs) for the formation of 3 and the concerted [4 + 2] cycloaddition pathway to form 4 are shown in Figure 5.
The MERP leading to the 2 + 2 adduct includes a flat, entropically controlled energy surface after the initial formation of a diradical. Similar energy surfaces have been described for other diradicals such as the tetramethylene species. 25 The antidiradical-forming transition state on s-trans-butadiene is the rate-limiting step for the formation of 3. For 5 to form 3, a vibrational mode corresponding to rotation around the C2− C3 bond must be activated in addition to the inversion of the radical at C1 by rotation through TS9 or inversion (TS12). The ring closure proceeds through a near barrierless reaction step (TS10). In accordance with experimental results, the concerted [4 + 2] pathway to form 4 is kinetically disfavored by 4(E) to 6(G) kcal/mol over the diradical pathway forming the (2 + 2) product 3, but product 4 is thermodynamically favored over 3 by about 30 kcal/mol.
No direct pathway from s-cis-or s-trans-butadiene derived diradical species to the [4 + 2] product 4 could be found.
Distortion/Interaction−Activation Strain Analysis. The preference for the kinetically controlled formation of 3 can be explained using the distortion/interaction−activation strain analysis, 26−33 which was conducted using autoDIAS. 34 In this analysis, the activation energy, ΔE ‡ , is divided into two components. The first component, ΔE dist ‡ , gives the energy required to distort the reactants to their transition state geometries without interactions. The second component, ΔE int ‡ , is the interaction energy between distorted reactants, usually a stabilizing effect. The sum of ΔE dist ‡ and ΔE int ‡ equals the energy of activation, ΔE ‡ . This analysis has been successfully applied to explain the reactivity in various   The Journal of Organic Chemistry pubs.acs.org/joc Article cycloaddition reactions. 35−44 We compared the reactions of butadiene with ethylene 9 and maleic anhydride 10, which both yield exclusively Diels−Alder adducts, and butadiene with tetrafluoroethylene 1, which gives the 2 + 2 adduct through diradical 5. UB3LYP/6-311++G(d,p) structures were used for the distortion/interaction−activation strain analysis shown in Figure 6. The high distortion energy of the dienophile TFE (18.2 kcal/mol) in the Diels−Alder transition state TS7 provides an explanation for the high energy of the concerted pathway in contrast to similar 4 + 2 cycloadditions. In the two prototypical Diels−Alder reactions with dienophiles 9 and 10, the dienophile distortion energy is much lower (8.6 and 10.2 kcal/mol, respectively). The high dienophile distortion energy in TS7 is attributed to syn-pyramidalization, which distorts the relatively negative fluorine substituents into proximity. This is Getty and Borden's conclusion. 15 By contrast, the stepwise 2 + 2 cycloaddition with tetrafluoroethylene has a low diene distortion energy (6.3 kcal/mol) in TS1, thus leading to an overall decreased energy of activation and preference for this pathway. The distortion energy of tetrafluoroethylene in the diradical pathway, 17.9 kcal/mol, is similar to the value found for the concerted [4 + 2] cycloaddition (18.2 kcal/mol). This can be explained by the fact that in TS7, the out of plane bending of the fluorides in TFE is only 15°and the forming bond distance is 2.30 Å while in TS1, the bending is much stronger with 22°and the forming bond distance is shorter with 1.97 Å. However, in TS1, the second CF 2 unit is free to adopt any conformation, which allows for better stabilization through anti-pyramidalization, while in TS7, unfavorable syn-pyramidalization is enforced leading to similar distortion energy at lower geometric distortion. Figure 7 shows the TFE distortion energies along intrinsic reaction coordinates calculated for the [4 + 2] cycloaddition proceeding through TS7 and the diradicalforming reaction going through TS1. As shown, for a given angle, the distortion energy is higher in the case of the [2 + 4] reaction due to the forced syn-pyramidalization. The preference of alkenes and alkynes for anti-pyramidalization in both radical and ionic cases is well established. 13,45−47 Compared to the 2 + 2 diradical pathways of ethylene (9) and maleic anhydride (10), the forming C2−C3 bond length in TS1 is significantly longer than those in TS15 and TS16.   Thus, the diene in TS1 does not need to distort much to achieve the transition structure geometry resulting in the low diene distortion energy of only 6.3 kcal/mol. The earlier TS1 can be attributed to the better stabilization of the forming diradical. The Diels−Alder transition state with maleic anhydride (TS14) is stabilized largely by the interaction energy (-12.1 kcal/mol), while maleic anhydride fails to stabilize the radical center formed in TS16, leading to a later transition state. In TS15, a positive (energetically destabilizing) interaction energy of 8.4 kcal/mol is observed due to the inability of hydrogen to stabilize radicals, making the 2 + 2 pathway not feasible. Energy of Concert. The energy by which the activation energy of the concerted reaction is favored over stepwise reaction is the energy of concert. 48 Figure 8 shows energy of concert analyses for the three reactions described earlier. The reaction of 2 with 1 has negative energy of concert. The stepwise reaction is preferred in this case by 4.2 kcal/mol. Reactions of 2 with 9 or 10 have positive energies of concert. The concerted mechanism is favored with similar energy of concert values, 9.6 and 9.5 kcal/mol, respectively. Previous calculations for butadiene and ethylene predicted energies of concert of 2−7 kcal/mol. 49 The stepwise reaction is preferred in the TFE case because the diradical intermediates and the transition states leading to them are stabilized. By contrast, the maleic anhydride dienophile stabilizes the concerted pathway to a large extent and the stepwise pathway less, although it does stabilize that also. The interaction energy in TS14 plays a large role in the stabilization of the [4 + 2] cycloaddition pathway for maleic anhydride; this arises from the well-known charge transfer interactions resulting from the small highest occupied molecular orbital−lowest unoccupied molecular orbital (HOMO−LUMO) gap. The absence of energetically unfavorable syn-pyramidalization of CF 2 centers in the dienophile of TS13 versus TS7 lowers the electronic energy of this transition state.

■ CONCLUSIONS
The stepwise (2 + 2) cycloaddition is kinetically preferred over the concerted Diels−Alder reaction for the butadiene−TFE reaction. The syn-pyramidalization penalty identified by Borden and Getty for the concerted reaction is consistent with this model. In addition, we identified the low diene distortion in the stepwise (2 + 2) cycloaddition as an important factor for the preference of this pathway.
Diradical transition structures TS1−TS6 are all lower in energy than the Diels−Alder transition state, TS7. These six transition states can all form the (2 + 2) cycloaddition product. The MERP in Figure 5 shows that a preference for antidiradical formation dominates, and subsequent rotation around the C2−C3 bond followed by radical inversion along a flat PES eventually affords the kinetic (2 + 2) cycloaddition product.