Ab initio structural studies of cyclobutylmethyl cations: effect of fluoroalkyl groups on the relative stability of the carbocations

Ab initio calculations at MP2/cc-pVTZ level show that the trifluoromethyl group has a strong destabilizing effect on the nonclassical, σ-bridged cyclobutylmethyl cations. The GIAO-MP2 derived 13 C NMR chemical shifts indicate substantial charge delocalization from the neighboring cyclobutyl ring for carbocations with an α -fluorolkyl group as compared to the 1-cyclobutylethyl cation, and this enhanced charge delocalization in case of the α -(trifluoromethyl)cyclobutylmethyl cation would lead to the ring-opening rearrangement to form the relatively more stable nonclassical primary cyclobutylmethyl cation, in which the carbocation center is farthest from the strongly electron-withdrawing trifluoromethyl group

We have also located the transition structure for the interconversion of the nonclassical cyclobutylmethyl cation 6 to the classical C 2 -symmetric cyclopentyl cation, which is the global minimum on the potential energy surface and is 10.3 kcal/mol more stable than the nonclassical structure 6. 9 This transition state is very similar in structure to that of the nonclassical structure 6 and is only 0.7 kcal/mol higher in energy.The GAIO-MP2 calculated 13 C NMR chemical shifts unequivocally show that the positive charge is significantly delocalized among the C 2 and C 5 carbons in carbocations 6-9.
The experimental observation of the destabilized cyclobutylmethyl cations remains challenging, and all attempts of preparing such carbocations, including relatively stabilized secondary cyclobutylmethyl cations have been unsuccessful to date. 8,10,11However, we were able to prepare and characterize the cylobutyldicyclopropylmethyl cation (10) in superacidic media at low temperature.The latter carbocation, although predominantly a classical carbocation, involves significant delocalization into the neighboring cyclobutyl and the cyclopropyl rings. 10e destabilized cyclobutylmethyl cations are expected to involve extensive charge delocalization into the cyclobutyl ring, potentially leading to further rearrangements.Thus, it would be interesting to explore the structural characteristics of the destabilized carbocations, such as cyclobutyl(trifluoromethyl)methyl cation (11), at high level ab initio calculations.We have accordingly calculated structures of the cyclobutyl-(fluoroalkyl)methyl cations at high-level ab initio calculations, at MP2/cc-pVTZ level, which reveal that the αtrifluoromethyl group strongly destabilizes the nonclassical σ-delocalized carbocation, and the optimization resulted in the rearranged carbocation, a primary σ-bridged cyclobutylmethyl cation 12, with the trifluoromethyl group being placed at a distant carbon from the carbocation center.

Results and Discussion
We have optimized the structures of the secondary cyclobutylmethyl carbocations -cyclobutyl(fluoromethyl)methyl cation (16), cyclobutyl(difluoromethyl)methyl cation (15), cyclobutyl(trifluoromethyl)methyl cation (11)-initially at MP2/6-311G(d,p) level and then re-optimized at the MP2/cc-pVTZ level.The zero-point energies (ZPE) were then calculated using the optimized geometries, which also revealed them as true minima by not having any imaginary (negative) frequencies.The 13 C NMR chemical shifts were calculated at the GIAOMP2/cc-pVTZ level using the final geometries of the MP2/cc-pVTZ calculations (Table 1).We have calculated the structure and δ 13 C of 7 earlier at the same level of calculations using Gaussian 03 for structure optimization and ACES II program for NMR. 9 In order to be consistent with the present NMR calculations using Gaussian 09, we have recalculated the structure and the 13 C NMR chemical shifts, and also obtained the zeropoint energy at the MP2/cc-pVTZ level (the earlier reported ZPE value corresponds to MP2/6-31G* level).The extent of σ-delocalization from the strained cyclobutyl group in these carbocations is analyzed in terms of the C 1 -C 2 and C 2 -C 5 bond lengths and 13 C NMR chemical shifts of the carbocationic centers.Selected bond lengths of the carbocations 7 and 12-17, along with their MP2/cc-pVTZ optimized structures are shown in Figures 1  and 2. The MP2-derived 13 C NMR chemical shifts are better correlated with the experimental values than those of the SCF-derived ones in the case of the parent cyclopentyl cation in our earlier calculations, 10 so we have focused on the GIAO-MP2/cc-pVTZ//MP2/cc-pVTZ values (Table 1) in analyzing the structural details of the carbocations studied here.showing relatively lower C 1 -C 2 σ-bond participation in case of the carbocation 12.In agreement with this hypothesis, δ 13 C of the carbocationic center C 1 in 12 (174.9ppm; Table 1) is also relatively shielded as compared to that of the unsubstituted primary cyclobutylmethyl cation (δ 13 C (C1) = 196.6). 9 The carbocation 12 can also be considered as unsymmetrically delocalized 2-(trifluoromethyl)cyclopentyl carbocation, where the C 2 -C 5 bond is stabilizing the carbocation center C 1 through the σ-delocalization.The MP2-derived 13 C NMR chemical shifts for the carbocation 12 show extensive charge delocalization among the C 1 and C 5 carbons, with a significant amount of residing on the methine carbon C 1 , as shown by its relatively highly deshielded absorption, δ 13 C = 174.9.The methylene carbon C 5 , although relatively less deshielded (δ 13 C 94.9) than that of the C 1, indicates substantial positive charge at C 5 .The relatively strong electron-withdrawing field effect of the trifluoromethyl group thus disfavors extensive C 1 -C 2 charge delocalization, even when it relatively farther from the carbocationic center.
The unexpected spontaneous rearrangement of cation 11 during its optimization indicates the much lower relative stability of 11-nonclassical structure over the structure 12, in which the trifluoromethyl group is relatively much farther than in 11-nonclassical.We have then calculated the structures of the relatively lightly fluorinated versions of carbocations, the α-difluoromethyl substituted carbocation 15 and α-fluoromethylsubstituted carbocation 16, starting from the corresponding classical structures, and also calculated the structures, energies, and δ 13 C of the 13 and 14, the rearrangement products of the latter carbocations, in order to probe their relative stabilities.Unlike the trifluoromethyl-substituted cation, the nonclassical structures 15 and 16 did not spontaneously rearrange to the carbocations 13 and 14 during structural optimization, reflecting their enhanced stabilities as compared to 12.
As can be seen from Table 1, it is evident that the secondary nonclassical structures 7, 16, and 15 are relatively more stable than the corresponding isomeric primary nonclassical structures 17, 14, and 13, by 3.6, 2.6, and 0.1 kcal/mol, respectively, and thus there is no driving force for their spontaneous rearrangements during their structural optimization, unlike that for 11.Thus, the nonclassical structures are increasingly destabilized as the α-substituent in the carbocations is varied from methyl to trifluoromethyl.These relative stability differences are also in accordance with the δ 13 C(C 1 ) values; the δ 13 C(C 1 ) of 7, 16, and 15 are 133.3,162.0 and 168.5, respectively (Table 1) indicating the gradual increase of the positive charge density at the C 1 carbon for carbocations when the α-substituents are varied with progressively electron-withdrawing groups, methyl, fluoromethyl, and difluoromethyl.

Conclusions
In summary, we have carried out high-level ab initio calculations (MP2/cc-pVTZ and GIAO-MP2/cc-pVTZ at the same basis set) on the cyclobutylmethyl cations, and investigated the effect of the fluoroalkyl groups on the σdelocalization from the strained cyclobutyl ring.Whereas the α-methyl, α-fluoromethyl-, α,α-difluoromethylcyclobutylmethyl cations converged into the corresponding nonclassical, σ-delocalized structures, without any attendant rearrangements during the structure optimization, the strongly destabilized α−trifluoromethylcyclobutylmethyl cation spontaneously rearranges during optimization to give the nonclassical 2-(trifluoromethyl)cyclobutylmethyl cation.The σ-bond participation from the strained cyclobutyl ring, as shown by the calculated 13 C NMR chemical shifts and the bond distances, is correlated with the electron-withdrawing effects of the substituents on the carbocationic center: the higher the electron demand, the greater the σ-bond participation.