# What exactly is “B-strain”?

On factors that influence the stability of carbocations, I came across this peculiar one:

Bulky groups attached to the positively charged $C$-atom (of the carbocation), stabilize it by B-strain, which prevents the C-atom for returning to the $sp^{3}$ state.

Source: Pearson's Organic Chemistry (7e), Morrison and Boyd

The issue? I've never heard of "B-strain" before. I mean, it's possible that bulky groups stabilize the positive $C$-atom via inductive (and other) effects...but what's with "B-strain"?

I ran a cursory Google search, but I couldn't find any reliable Chemistry-literature that deals with this. In fact, it raised more questions than answers, most notably, the presence of another effect called the "F-strain".

What is the "B-strain", and how does it contribute to stabilization of carbocations?

Additionally, is there such a thing as the "F-strain"? If so, what's it all about?

• B stands for back or behind (Carey, F. A.; Sundberg, R. J. Advanced organic chemistry Part A. Structure and Mechanisms, 5th ed.; Springer: New York, 2007., p. 417). F stands for front (Houghton. Metal Complexes-Organic Chemistry, 1 edition.; Cambridge University Press: Cambridge ; New York, 1979. p. 66). If you have troubles accessing the sources, I can try to provide an answer including the book parts. – andselisk Jul 12 '17 at 7:18
• @andselisk I see! I know for certain that my library doesn't have the books you mentioned, so I'd really appreciate an answer from you. Meanwhile, I'll try looking for the PDF versions ... – paracetamol Jul 12 '17 at 7:21

### B-strain

Both B- and F-strains are the terms I found were originally used to describe steric hindrance in complexes [1, pp. 66-67]:

The concept that steric hindrance in a monodentate ligand can affect the affinity of that ligand for a metal was first introduced by Brown and Bartholomay (1944) who suggested that co-ordination of a tertiary amine with bulky substituents would create strain within the amine. This strain, termed B-strain on account of it occurring behind the ligand atom with respect to the metal, would arise because although in the unco-ordinated amine any steric interaction between the bulky substituents could be relieved to some extent by an increase in the $\ce{C-N-C}$ angles.

Interestingly, further it is pointed out that at the same time there is no other solid evidences that B strain exists. Although modern organic chemistry textbooks are widely using this term for tertiary compounds.

From [2, p. 417]:

Steric effects of another kind become important in highly branched substrates, and ionization can be facilitated by relief of steric crowding in going from the tetrahedral ground state to the TS for ionization. The relative hydrolysis rates in 80% aqueous acetone of $t$-butyl $p$-nitrobenzoate and 2,3,3-trimethyl-2-butyl $p$-nitrobenzoate are 1:4.4.

This effect has been called B-strain (back strain), and in this example only a modest rate enhancement is observed. As the size of the groups is increased, the effect on rate becomes larger. When all three of the groups in the above example are t-butyl, the solvolysis occurs 13,500 times faster than in t-butyl p-nitrobenzoate.

According to [3, p. 350]:

Not all steric effects decrease reaction rates. In the hydrolysis of $\ce{RCl}$ by an $\mathrm{S_N1}$ mechanism ..., the ﬁrst step, which is rate determining, involves ionization of the alkyl chloride to a carbocation:

The central carbon in the alkyl chloride is $\mathrm{sp^3}$ hybridized, with angles of $\sim 109.5^\circ$, but when it is converted to the carbocation, the hybridization becomes $\mathrm{sp^2}$ and the preferred angle is $120^\circ$. If the halide is tertiary and the three alkyl groups are large enough, they will be pushed together by the enforced tetrahedral angle, resulting in strain. This type of strain is called B strain (for back strain), and can be relieved by ionization to the carbocation.

[...]

Substitution of ethyl groups for the methyl groups of tert-butyl chloride does not cause B strain; the increase in rate is relatively small, and the rate smoothly rises with the increasing number of ethyl groups. The increase is caused by normal ﬁeld and resonance (hyperconjugation) effects. Substitution by one isopropyl group is not greatly different. But with the second isopropyl group the crowding is now great enough to cause B strain, and the rate is increased 10-fold. Substitution of a third isopropyl group increases the rate still more.

Further in [3, p. 419]:

For some tertiary substrates, the rate of $S_N1$ reactions is greatly increased by the relief of B strain in the formation of the carbocation. Except where B strain is involved, $\beta$ branching has little effect on the $S_N1$ mechanism, except that carbocations with $\beta$ branching undergo rearrangements readily.

There is also a Baeyer strain aka angle strain most noticeable for three-membered rings ($60^\circ$ is far from expected tetrahedral angles), which can also probably be abbreviated alike. [3, p. 193]

It also seems like earlier sources used B-strain as a reference to H. C. Brown [4, p. 291]:

Hammond has proposed a steric "B-strain" (see H. C. Brown, J. Chem. Soc. (London) p. 1248 (1956)) argument to explain the greater stability of primary over secondary or tertiary carbanions. From the viewpoint of hybridization, structure A with $90^\circ$ geometry is preferred in carbanions. But this conformation brings the substituents too close together, and a compromise structure with larger bond angles results. Methide ion, $\ce{^-CH3}$, with the smallest substiuent groups, should be the most stable simple carbanion, since it can more nearly adopt the small angled conformation A preferred on electronic grounds. The more alkyl groups are added, the less able sterically are the anions to adopt the favorable conformations with smaller angles, and the less stable and more reactive the intermediates become.

### F-strain

[1, p. 68] illustrates the origins of the term F-strain:

The boron trifluoride and boron trichloride complexes of diethyl ether are less stable than those of dimethyl ether, and the same order of stability is observed for the complexes of diethyl and dimethyl sulphides. As expected, the steric interaction is decreased as the distance between the metal and ligand atom is increased. Thus it is decreased when the metal atom is changed from boron to aluminium, and when the ligand atom is changed from oxygen to sulphur. It is largely eliminated, of course, if the substituents on the ligand atom are held back away from the metal, and thus very stable complexes are formed by the tertiary amine quinuclidine, while complexes of tetrahydrofuran and tetrahydropyran (and also the analogous sulphur heterocycles) are far more stable than those of their acyclic analogues.

Strain which arises as the result of this type of steric interaction has been termed F-strain by H. C. Brown -- who has carried out extensive investigations in this area -- on the grounds that the interactions responsible for the strain occurs mainly in front of the ligand atom with respect to the metal. For a critical but now rather dated review of H. C. Brown’s work, see Hammond (1956).

### References

1. Houghton, R. P. Metal Complexes-Organic Chemistry, 1st ed.; Cambridge University Press: Cambridge; New York, 1979.
2. Carey, F. A.; Sundberg, R. J. Advanced organic chemistry Part A. Structure and Mechanisms, 5th ed.; Springer: New York, 2007.
3. Smith, M. March’s advanced organic chemistry: reactions, mechanisms, and structure, 7th ed.; Wiley: Hoboken, New Jersey, 2013.
4. Hartley, H.; Karabatsos, G. J. Advances in alicyclic chemistry; 1966; Vol. 1.

The term "B-strain" was coined in the article Acid-Base Studies in Gaseous Systems. II. The Anomalous Base Strength of the Methylamines; A New Manifestation of Steric Strain J. Am. Chem. Soc., 1944, 66 (3), pp 435–442.

The term “B-strain” is proposed for this effect. (The letter B is used to indicate that the interference which causes the strain is localized at the “back” of the molecule-trimethylamine in the case under discussion-away from the entering group; it is thus contrasted to F-strain which results from interference at the “front” of the molecule, at the interface between the two components of the addition compound.)

Now consider an acid (Say Boron trifluoride) forms acid-base adduct with a base with bulky substituents (Say tripropylamine), then there will be steric hinderance between the bulky substituents which results in opening bond angle (Propyl-Nitrogen-Propyl) of the alamine. This opening in bond angle causes more s-character in the N-R (Propyl-Nitrogen) bond more p-character left in the lone pair of nitrogen due to which lone pair is poorly situated for donation. This phenomenon is called B-Strain.

Note:
• F-strain decreases the basicity of the base.
• More s-character results larger bond angle

For more detail Refer Inorganic Chemistry By James E. Huheey, Ellen A. Keiter, Richard L. Keiter and Okhil K. Medhi