C-F bond lengths of octafluoropropane using Bent's rule I was trying to predict different $\ce{C-F}$ bond lengths of octafluoropropane,  $\ce{CF3-CF2-CF3}$ :



Applying Bent's rule here, we see that 


For $\ce{C^2}$, we have $\ce{C^3}$ and $\ce{C^1}$ towards which s-character of $\ce{sp^3}$ orbitals is richer. Hence $\ce{sp^3}$ orbital of $\ce{C^2}$ has lesser s-character directed towards $\ce{F}$.
For $\ce{C^1}$ (or $\ce{C^3}$), we have only  $\ce{C^2}$ toward which  s-character of $\ce{sp^3}$ orbitals is richer. Hence $\ce{sp^3}$ orbital of $\ce{C^1}$ has greater s-character directed towards $\ce{F}$.


Using this I think $\ce{C^2 - F}$ bond length is greater than $\ce{C^1 - F}$. 

Q. Is this explanation reasonable?

Q. Can we use Bent's rule to predict bond-lengths here or we should consider steric effects of $\ce{CF3}$ (trifluoromethyl) groups ? (here both lead to same result)

I mean in general on which rule should we rely on? On wikipedia article on Bent's rule its written that often times Bent's rule prediction would contradict predictions based on other classical effects alone (steric effects etc). In such cases how can we justify any prediction? 

(Wikipedia) Bent's Rule - Bond lengths


  A prediction based on sterics alone would lead to the opposite trend, as the large chlorine substituents would be more favorable far apart. As the steric explanation contradicts the experimental result, Bent’s rule is likely playing a primary role in structure determination.
It is very much non-trivial to attempt estimations on a perfluorated alkane using Bent’s rule. In Bent’s rule, one should not only consider the effects of the electronegative substituents on the substituted atom itself, but also onto the next atom. Consider for example the following table taken from Bent’s review article:[1]

\begin{array}{lr}\hline
\text{Compound} &amp; \angle(\ce{R^1-O-R^2}) \\ \hline
\ce{Me-O-Me} &amp; 111^\circ \\
\ce{Me-O-H} &amp; 107{-}109^\circ \\
\ce{H-O-H} &amp; 104.5^\circ \\
\ce{F-O-F} &amp; 103.8^\circ \\ \hline\end{array}

This very nicely corresponds to increasing group (!) electronegativities[2] in the series $\ce{Me} &gt; \ce{H} &gt; \ce{F}$. $\ce{CF3}$ should have a higher electronegativity than both $\ce{Me}$ and $\ce{H}$ (compare the acidities of formic acid, acetic acid and trifluoroacetic acid). Yet $\angle(\ce{C-O-C}) = 120^\circ$ in $\ce{F3C-O-CF3}$.[3] This corresponds to a higher $\mathrm s$ contribution than for the previous groups indicating other, more important contributions (here the anomeric effect of oxygen acting on the $\ce{CF3}$ group).[4]

Luckily, there are no such secondary effects in perfluoropropane. However, if you want to estimate all bond lengths compared to propane or 2,2-difluoropropane, these must be considered. Specifically, going from propane to 2,2-difluoropropane should not only reduce the $\ce{C-C}$ bond lengths due to increased $\mathrm s$ contribution but also due to partial double bond character due to a gauche-type effect which can be rationalised in Lewis formalism by the following resonance structure:

$$\ce{H-C-C-F &lt;-&gt; \overset{+}{H}\bond{...}C=C\bond{...}\overset{-}{F}}$$

Of course, the partial $\ce{C-C}$ double bond and the less-than-single $\ce{C-F}$ bonds also mess with the observed bond angles in 2,2-difluoropropane; they don’t only influence bond lengths.



So to attempt an estimation of the differences in bond length of the two $\ce{C-F}$ bonds in perfluoropropane, we would need to know how the group electronegativites of the $\ce{CF3}$ and $\ce{C2F5}$ groups compare to the electronegativity of fluorine and to each other. I don’t see any simple way to do this.

Mack et al. have published gas phase structures of 2,2-difluoropropane and perfluoropropane. These are their results (all values in picometres):[5]

\begin{array}{lcc}\hline
\text{compound} &amp; d(\ce{C-C}) &amp; d(\ce{F2RC-F}) &amp; d(\ce{R2FC-F}) \\ \hline
\ce{Me2CF2} &amp; 151.2 &amp; \text{–/–} &amp; 137.0 \\
\ce{(CF3)2CF2} &amp; 154.6 &amp; 132 &amp; 134 \\ 
\ce{Me2CH2} &amp; 153.1 &amp; \text{–/–} &amp; \text{–/–} \\ \hline \end{array}

As you can see, the experimental values just confirm your prediction of the central $\ce{CF2}$ having longer bond lengths than the terminal $\ce{CF3}$ groups. As expected, all $\ce{C-F}$ bonds in perfluoropropane are shorter than the bond lengths of 2,2-difluoropropane. And the $\ce{C-C}$ bond lengths increase from 2,2-difluoropropane to propane to perfluoropropane.

The conclusion is that indeed $\ce{CF3}$ is slightly less electronegative than fluorine, but the effect seems minimal.

References and Notes:

[1]: H. A. Bent, Chem. Rev. 1961, 61, 275–311. DOI: 10.1021/cr60211a005.

[2]: Bent explicitly considers group electronegativities. Only by that is the group electronegativity of a methyl group lower than the electronegativity of hydrogen.

[3]: A. H. Lowrey, C. George, P. D'Antanio, J. Karle, J. Mol. Struct. 1980, 63, 243–248. DOI: 10.1016/0022-2860(80)80330-9.

[4]: F. R. Leroux, B. Manteau, J.-P. Vors, S. Pazenok, Beilstein J. Org. Chem. 2008, 4, 13. DOI: 10.3762/bjoc.4.13.

[5]: H.-G. Mack, M. Dakkouri, H. Oberhammer, J. Phys. Chem. 1991, 95, 3136–3138. DOI: 10.1021/j100161a034.