Branch and Calvin

The reasonable extension of these ideas is to express o- as a sum of contributions from the inductive and resonance effects. Branch and Calvin suggested this, and much of the research on LFER of the past three decades has been concerned with... 

Oae found that for both base- and acid-catalyzed hydrolysis of phenyl benzenesul-fonate, there was no incorporation of 0 from solvent into the sulfonate ester after partial hydrolysis. This was interpreted as ruling out a stepwise mechanism, but in fact it could be stepwise with slow pseudorotation. In fact this nonexchange can be explained by Westheimer s rules for pseudorotation, assuming the same rules apply to pentacoordinate sulfur. For the acid-catalyzed reaction, the likely intermediate would be 8 for which pseudorotation would be disfavored because it would put a carbon at an apical position. Further protonation to the cationic intermediate is unlikely even in lOM HCl (the medium for Oae s experiments) because of the high acidity of this species a Branch and Calvin calculation (See Appendix), supplemented by allowance for the effect of the phenyl groups (taken as the difference in between sulfuric acid and benzenesulfonic acid ), leads to a pA, of -7 for the first pisTa of this cation about -2 for the second p/sTa. and about 3 for the third Thus, protonation by aqueous HCl to give the neutral intermediate is likely but further protonation to give cation 9 would be very unlikely. 

For species 12, we hrst estimate the pA a of HO-S02 using the method of Branch and Calvin (see Appendix), knowing full well that this will not be accurate because the central atom is highly charged, the estimate for sulfuric acid with is too acidic, and resonance will also make a contribution, so that the crude estimate will not be acidic enough. However, the errors may partly cancel. 

Numbers used in this cycle AG° for hydroxide plus monomethyl sulfate, assumed to be the same as for dimethyl sulfate estimated above AG° for ionization of monomethyl sulfate AG° for tautomerization of the anionic adduct, based on pK values estimated by the method of Branch and Calvin AG° for ionization of the apically protonated adduct, based on a pK estimated by the method of Branch and Calvin.)... 

Numbers used in the cycle AG° for addition of hydroxide to p-nitrophenyl sulfate, see above AG° for proton transfer from p-nitrophenyl sulfate to hydroxide, based on pA a values AG° for ionization of the monoanionic adduct of p-nitrophenyl sulfate, estimated by the method of Branch and Calvin, supplemented by the difference in pATa between sulfuric acid and p-nitrophenyl sulfate.)... 

By analogy with the proposal of Branch and Calvin, we can calculate the p Ta of an oxonium ion X-OH2 by the related equation... 

Branch and Calvin, The Theory of Organic Chemistry, p. 122, Prentice-Hall, New York, 1945. 

Since no pK values are available for hydroxyphosphoranes, the pK of pentahydroxyphosphorane is estimated by the method of Branch and Calvin (1941) as 8.5. The application of the free-energy change for reaction (4) to... 

Branch and Calvin, Theory of Organic Chemistryy Prentice-Hall, 1941, p. 466. 

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