Stability of carbocations: CF3+ vs CH3+

Is $\ce{CF\_3+}$ more stable than $\ce{CH\_3+}$?


In $\ce{CF\_3+}$, there is $\ce{C-F}$ back bonding that increases stability of the carbocations. But -I effect of $\ce{F}$ dominates +R effect and this decreases the carbocation stability. How can I compare these two competing effects to find the more stable carbocation?


Also, is $\ce{CF\_3+}$ more stable than $\ce{CH3-CH+-CH\_3}$ and tert-butyl carbocation?




$\ce{CF3+}$ is more stable than $\ce{CH3+}$. The comparison between -I and +R effect is made while talking about activation or deactivation of halogens when substituted on benzene. Fluorine always stabilises a carbocation to a large extent because of a very good overlap of $\ce{2p -~2p}$ orbitals.


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Despite the strong $\sigma$-electron withdrawing effect of fluorine, $\ce{CF3+}$ has been stabilized relative to that of $\ce{CH3+}$. For example, the reaction:
$$\ce{CH3+ + CHF3 -> CF3+ + CH4}$$ is exothermic by $\pu{13.2 kcal mol-1}$ (Ref.1). It was also found that hydrogen abstraction in following reaction is even more exothermic than previous one:
$$\ce{CH3+ + CH2F2 -> CHF2+ + CH4} \qquad \Delta H = \pu{-28.3 kcal mol-1}$$


According to authors, the only order which can be constructed that is consistent with all observations gives the relative hydride affinities as $\ce{CH3+ \gt CF3+ \gt CH2F+ \gt CHF2+}$. It is also noteworthy that within the references in Ref.1 has given that $\Delta H\_f (\ce{CH3+}) = \pu{276.1 kcal mol-1}$ while that of $\Delta H\_f (\ce{CF3+}) = \pu{99.3 kcal mol-1}$.


**References:**


1. R. J. Blint, T. B. McMahon, and J. L. Beauchamp, "Gas-phase ion chemistry of fluoromethanes by ion cyclotron resonance spectroscopy. New techniques for the determination of carbonium ion stabilities," *J. Am. Chem. Soc.* **1974**, *96(5)*, 1269–1278 (DOI: <https://doi.org/10.1021/ja00812a001>).


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