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Inductive effect is the partial shifting of the sigma-bonding electrons towards more EN (take as electronegativity or electronegative in this text) atom so why we will say that alkyl groups will always show +I effect.

For the case of boron (EN 2.05) and carbon (EN 2.55), will the alkyl group show +I or -I effect?

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You are right, if we attach a low electronegativity element (such as boron) to carbon, the alkyl group does show -I effect, withdrawing electrons from the less electronegative element.

However, we usually say that less electronegative element ($\ce{B}$, in this case) is showing +I effect because the alkyl moiety is treated as the primary and the other groups are treated as secondary or substituents. Thus, these effects are calculated with respect to the alkyl moiety.

From Literature

Regarding inductive effect Poon and Mayer (2002)$^\text{1}$ said:

The degree of p-donation decreases across the first row from NH2 to F while the inductive effect due to the difference in electronegativity of the atoms increases in the same order.

Although no direct statement has been made regarding inductive effect of methyl group, the same arguement maybe extended to say that methyl group shows a (weak) -I effect.

Regarding the statement about hyperconjugation, the authors said:

The pseudo p-orbital on the methyl group in $\ce{H2BCH3}$ is involved in a weaker hyperconjugation interaction with the vacant p-orbital on B.

Ab-initio

Since, inductive effect has not been directly mentioned and charge analysis is absent from the referenced study, I performed some calculations on my own at B3LYP level theory on the molecule methylborane $\ce{H2BCH3}$. The calculations provide some insights into the properties of the molecule.

Remark Corresponding Molecular Orbital
Sigma bond between boron and carbon is polarized towards carbon showing -I effect of methyl group. methylborane sigma bond between boron and carbon
Methyl group is involved in hyperconjugation with boron showing +H effect of methyl group. hyperconjugation in methylborane
Element Mulliken Charge
$\ce{B}$ -0.35
$\ce{C}$ 0.00
$\ce{H}$s positive

Thus, +H effect of methyl group is compensating for its -I effect fulfilling the electron-deficiency on boron.

Reference

  1. Poon, C. and Mayer, P. M (2002). Electron-spin conservation and methyl-substitution effects on bonds in closed- and open-shell systems — A G3 ab initio study of small boron-containing molecules and radicals. Canadian Journal of Chemistry, 80. 10.1139/v01-185
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  • $\begingroup$ Then BH3 should be more stable than BR3 where R is an alkyl group. But in Hydroboration of an alkene, B is breaking bond from H and forms with R, that should mean that B which is electron deficient is getting relatively more electron density. And if we consider that alkyl groups show +I effect then this fits the logic but we have discussed about their EN values suggesting -I effect of Alkyl groups here. $\endgroup$
    – D13G
    May 11 at 12:36
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    $\begingroup$ We also need to consider hyperconjugation for $\ce{BR3}$, for example, $\ce{B(CH3)3}$ has 9 hyperconjugative structures involving the empty $\mathrm{p}$ orbital of $\ce{B}$. $\endgroup$
    – ananta
    May 11 at 12:41
  • $\begingroup$ If you could attach some sources then I can mark your answer as accepted. $\endgroup$
    – D13G
    Jun 19 at 4:04
  • $\begingroup$ @D13G do the latest edits address your comment? $\endgroup$
    – ananta
    Jun 19 at 5:06
  • $\begingroup$ I will try to understand it within few days and then I will give you the feedback. And Thanks for your update. $\endgroup$
    – D13G
    Jun 22 at 10:29

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