Nonlinearity Hammett equation

the plot of hammett equation typically seen being linear, either positive or negative slope correlating value of rho. however, nonlinearity emerges in hammett plot when substituent affects rate of reaction or changes rate-determining step or reaction mechanism of reaction. reason of former case, new sigma constants have been introduced accommodate deviation linearity otherwise seen resulting effect of substituent. σ+ takes account positive charge buildup occurring in transition state of reaction. therefore, electron donating group (edg) accelerate rate of reaction resonance stabilization , give following sigma plot negative rho value.

σ- designated in case negative charge buildup in transition state occurs, , rate of reaction consequently accelerated electron withdrawing groups (ewg). ewg withdraws electron density resonance , stabilizes negative charge generated. corresponding plot show positive rho value.

in case of nucleophilic acyl substitution effect of substituent, x, of non-leaving group can in fact accelerate rate of nucleophilic addition reaction when x ewg. attributed resonance contribution of ewg withdraw electron density thereby increasing susceptibility nucleophilic attack on carbonyl carbon. change in rate occurs when x edg, evidenced when comparing rates between x = me , x = ome, , nonlinearity observed in hammett plot.

the effect of substituent may change rate-determining step (rds) in mechanism of reaction. electronic effect may accelerate step no longer rds.

a change in mechanism of reaction results in nonlinearity in hammett plot. typically, model used measuring changes in rate in instance of sn2 reaction. however, has been observed in cases of sn2 reaction ewg not accelerate reaction expected , rate varies substituent. in fact, sign of charge , degree develops affected substituent in case of benzylic system.

for example, substituent may determine mechanism sn1 type reaction on sn2 type reaction, in case resulting hammett plot indicate rate acceleration due edg, elucidating mechanism of reaction.

another deviation regular hammett equation explained charge of nucleophile. despite nonlinearity in benzylic sn2 reactions, electron withdrawing groups either accelerate or retard reaction. if nucleophile negatively charged (e.g. cyanide) electron withdrawing group increase rate due stabilization of charge put on carbon in transition state. on other hand, if nucleophile not charged (e.g. triphenylphosphine), electron withdrawing group going slow down reaction decreasing electron density in anti bonding orbital of leaving group in transition state.