Inductive effect in carbocations/radicals

[sludger13]

Let's have primary, secondary and terciary carbo radical/cation.
C(./+)H2R
C(./+)HR2
C(./+)R3

1) The central carbon has lesser shielded nucleus (one electron from a group is missing or both its and groups's electrons are missing). So the nucleus electrostatic force increases.

2) Primary carbo radical/cation attracts electrons from two hydrogens and from one carbon. Also the two hydrogens gets larger effective charge, but this effect on carbon (on its hydrogens) is weaker (btw. why is it weaker?). In primary carbo the hydrogens have the largest effective charge and so that is the reason of its unstablility.

3) Terciary carbo radical/cation attracts electrons from only three carbons, and again the inductive effect on their hydrogens is weaker, so the hydrogens there have the slightest effective charge and so that is the reason of terciary carbo relative stability.

Please tell me whether this thesis is true (if the carbo stability is the reason of the degree of its hydrogens effective charge). I'm interested only in the inductive effect (not in hyperconjugation as the other stabilising factor).

 

[Yanick]

I've never heard of the inductive effect being described by the induction of partial charges on the neighboring groups. It has always been an electron 'push' of R groups or electron pull of electronegative groups (O, F etc).

I'm not exactly sure you're description is correct. Did you actually read this, or something like this, somewhere? I've always considered the physical basis of the inductive effect a bit hand-wavy and have come to just accept that it allows us to develop trends and make quick qualitative predictions without resorting to ab initio QM calculations. It would be extremely impractical for a synthetic organic chemist to spend a vast majority of their time setting up models and running calculations for a multi-step synthesis. Most times it is cheaper and more efficient to just mix some stuff together, reflux overnight and characterize the products after making an educated guess about the electronics, but I digress.

Try posting up where you read such a description of the inductive effect and we can try to examine it together.

 

[sludger13]

Did you actually read this, or something like this, somewhere?

No, I figured it out as I read the only explanations that didn't physically explain the whole thing (the inductive effect doesn't occur on hydrogens, because...).

I've never heard of the inductive effect being described by the induction of partial charges on the neighboring groups.

The primary result of the inductive effect is a partial charge, as I know.

The partial charges in carbo cation molecules are on the picture below:

SOURCE

From that I guess the positive partial charge in primary ion is the highest (because only one carbon is donating electrons). That causes primary ion unstability.
The positive partial charges in terciary ion are the lowest (because three carbons are donating electrons, so every carbon donates just a little, and their partial charges do not add up). That causes terciary ion stability.

Though I have never found (and probably will not ever find (definitely not from a chemist )), why the hydrogens do not participate. If so, there must be a reason (why the carbons induct and hydrogens don't, as is shown on the picture). A carbon has higher electronegativity than a hydrogen, so positive partial charges would anyway end up on the hydrogens - that is my thought written above.

Try posting up where you read such a description of the inductive effect and we can try to examine it together.

If you get over I devised the thought, you can either disprove it or examine the chemguide source...

 

[abitslow]

March Adv Org Chem 2nd Ed (sorry, don't have more recent) pg 20-21:
This polarization effect is actually the sum of two effects. ... This polarization of one bond caused by the polarization of an adjacent bond is called the *inductive effect*. The effect is greatest for adjacent bonds but may also be felt farther away... The other effect operates directly through space or through solvent molecules, and is called the *field effect*. It is often very difficult to separate the two kinds of effect... the field effect depends the geometry of the molecule but the inductive effect depends only on the nature [and connectivity] of the bonds.
<now here we get to the important part (pg 21) >
The evidence ...is overwhelming that field effects are much more important than inductive effects. In most cases the two types of effect are considered together... ← < note! its likely what you are reading is misleading, conflating the two effects and using the term "inductive" to mean both>
<Finally> Functional groups can be classified as electron-withdrawing (-I) or electron-donating (+I) groups RELATIVE TO HYDROGEN. <emphasis mine> this answers your question about hydrogen, its defined as the zero-point. (which makes sense in organic chemistry, less sense in physical/quantum chemistry)
Also note that δ± is meant in the sense of "very small". Meaning 0 ±δ or +1 ±δ are still very close to 0 or +1 respectively, like the δ of calculus, f(x+δ) as δ → 0, So +1 + 3(δ+) is still close to +1. Quantum mechanically speaking, the more ways we can distribute the (unstable) + charge density, the less unstable will be the resulting species.

 

[Yanick]

I should've been more clear in my response, it was late and my brain was tired.

I couldn't piece together your description of the hydrogen participation. By that I mean I (mis)understood your post as implying that the hydrogens connected to the alkyl groups neighboring the carbocation play a role in the charge distribution.

abitslow gave a pretty good reply so I'll leave it at that for now.

 

[sludger13]

<Finally> Functional groups can be classified as electron-withdrawing (-I) or electron-donating (+I) groups RELATIVE TO HYDROGEN. <emphasis mine> this answers your question about hydrogen, its defined as the zero-point. (which makes sense in organic chemistry, less sense in physical/quantum chemistry)

Doesn't make a sense. If hydrogen is defined as the zero-point, then all the carbons should have (-δ).
I don't understand how electron "transfer" can be relative to one special atom - electron is transfering from one atom (electron-donating atom (+I)) to another atom (electron-withdrawing atom (-I)).

 

[Yanick]

Because it is all a bit hand wavy, like I tried to say above. Maybe you are confused because you are assuming a saturated sp3 carbon has an equivalent electronegativity to a carbocation which is better described as an sp2 carbon. The latter can be considered a bit more electronegative as well as acidic. To convince yourself of this, look up the pKa's of ethane, ethene and ethyne for example which are sp3, sp2 and sp.

Once again I want to reiterate that all of these explanations are pretty hand wavy. Even electronegativity scales are defined in many different ways, the most common being Pauling's scale. These are all empirical rules of thumb developed by chemists to explain trends found through experiment and really were developed because people already knew, for example, that HF become H⁺ and F^-.

Consider acetic acid with a pKa of 4.75. When we replace one hydrogen with a fluorine atom (fluoroacetic acid) the pKa becomes ~2.66, for trifluoroacetic acid the pKa become ~0. This trend is very well explained by the inductive effect. You can do something similar with chloroacetic acid but notice that the effect won't be as large since chlorine is not as electronegative as fluorine. [ref: http://openmopac.net/pKa_table.html]

I hope this might clear some things up for you.

 

[sludger13]

The latter can be considered a bit more electronegative as well as acidic. To convince yourself of this, look up the pKa's of ethane, ethene and ethyne for example which are sp3, sp2 and sp.

This trend seems logic. It results not only in rising acidity of (ethane, ethene, ethyne), but in the largest reactivity of alkane carbons with only one hydrogen (C-C(CH3)H-C) (for example in radical substitution).
You correctly mentioned acidity as the partial positive charge on hydrogens as the least electronegative elements in the molecule. It is sure (+δ) moves to hydrogens also in carbo cation/radical.