# Charge distributions in the transition state of the SN2 reaction

I understand that a similar question has been posed here. However, the scope of my question is framed differently. I will present analysis of two different sources of information and I would like to question if there is a contradiction between the two.

Perspective by Carey & Sundberg (2007)

Carey & Sundberg (2007) provides the following perspective on the effect of substituents on the rates of $$\ce {S_N2}$$ reactions, on p. 418-419:

The extent of the rate enhancement of adjacent substituents is dependent on the nature of the TS. The most important factor is the nature of the $$\pi$$-type orbital that develops at the trigonal bipyramidal carbon in the TS. If the carbon is cationic in character, electron donation from adjacent substituents becomes stabilizing. If bond formation at the TS is advanced, resulting in charge buildup at carbon, electron withdrawal is more stabilizing.

It is accompanied by the following diagram:

What I would like to point out is that the authors claim that it is possible for the carbon atom involved in an $$\ce {S_N2}$$ reaction to develop a slight positive charge when the cleavage of the $$\ce {C-LG}$$ bond is more advanced than the $$\ce {C-Nu}$$ bond. Perhaps, we can see this as more electron density is leaving the carbon atom via the transfer onto the leaving group, compared to the electron density transfer from the nucleophile onto the carbon atom.

Computational study by Pross & Shaik (1982)

Pross & Shaik (1982) seeked to dispel the commonly-held belief that:

the extent of charge development in a transition state is dependent on the earliness or lateness of that transition state. For example, in the $$\ce {S_N2}$$ reaction of an anionic nucleophile with a neutral substrate, most of the negative charge would be expected to be localised on the nucleophile for an early transition state ... while for a late transition state most of the charge would be localised on the leaving group ...

They used a method they referred to as the "linear combination of valence-bond configurations". They write that the wavefunction describing the transition state will reflect the fact that both configurations shown below are of equal energy at the crossing point of the diagram (Fig. 1) below by having equal weights, where the two configurations refer to $$\ce {Nu^- + R-X}$$ and $$\ce {Nu-R + X^-}$$. This would mean that the transition state would have around $$\ce {-0.5}$$ of the charge localised on $$\ce {Nu}$$ and the other $$\ce {-0.5}$$ localised on $$\ce {X}$$. Does this suggest that the carbon atom is roughly electrically neutral?

Does research presented by Pross & Shaik (1982) contradict what is mentioned by Carey & Sundberg (2007)? And is the theory presented by the textbook in that paragraph incorrect? Personally, I have never seen such an effect described in this way in other texts on the $$\ce {S_N2}$$ reaction.

References

1. Carey, F. A.; Sundberg, R. J. Advanced Organic Chemistry Part A. Structure and Mechanisms (5th ed.). Springer, 2007.
2. Pross, A.; Shaik, S. S. Is Charge Development a Measure of SN2 Transition State Structure? Tetrahedron Lett. 1982, 23 (51), 5467–5470. doi:10.1016/0040-4039(82)80159-7