Hammond's postulate

In physical organic chemistry, Hammond's postulate, also referred to as the Hammond–Leffler postulate, is a hypothesis concerning the transition state of organic chemical reactions, proposed by George S. Hammond. The postulate helps chemists by providing information about the structure of transition state, which generally cannot be directly characterized experimentally.^[1] The postulate, first published in a Journal of the American Chemical Society paper in 1955, states that:^[2]

If two states, as, for example, a transition state and an unstable intermediate, occur consecutively during a reaction process and have nearly the same energy content, their interconversion will involve only a small reorganization of the molecular structures.

In other words, species with similar energies along the reaction will also have similar structures. The postulate allows us to accurately predict the shape of a reaction coordinate diagram, and has been used extensively, for example, to explain the effects of aromatic substituents in electrophilic aromatic substitution.^[3]

History

The postulate is named after its creator, George S. Hammond. He first suggested that transition-state theory could be used qualitatively to explain the relationships between reactants, transition states, and products. The postulate was published in 1955 while Hammond was a professor of Chemistry at Iowa State University. In fact, John E. Leffler of Florida State University proposed a similar idea a few years earlier in a Science paper in 1953, two years before Hammond published his version of the postulate.^[4] However, Hammond's version has received a much wider attention from scientific communities due to its qualitative nature while Leffler's version utilizes multiple mathematical equations. Hammond's postulate is sometimes called the Hammond-Leffler postulate to give credit to both scientists.^[5]

Interpreting the postulate

Effectively, the postulate states that the structure of a transition state resembles that of the species nearest to it in free energy. This can be explained with reference to potential energy diagrams:

In case (a), which is an exothermic reaction, the energy of the transition state is closer in energy to that of the reactant than that of the intermediate or the product. Therefore, from the postulate, the structure of the transition state also more closely resembles that of the reactant. In case (b), the energy of the transition state is close to neither the reactant nor the product, making none of them a good structural model for the transition state. Further information would be needed in order to predict the structure or characteristics of the transition state. Case (c) depicts the potential diagram for an endothermic reaction, in which, according to the postulate, the transition state should more closely resemble that of the intermediate or the product.

Another significance of Hammond’s postulate is that it permits us to discuss the structure of the transition state in terms of the reactants, intermediates, or products. In the case where the transition state closely resembles the reactants, the transition state is called “early” while a “late” transition state is the one that closely resembles the intermediate or the product.^[6]

One other useful interpretation of the postulate often found in textbooks of organic chemistry is the following:

Assume that the transition states for reactions involving unstable intermediates can be closely approximated by the intermediates themselves.

This interpretation ignores extremely exothermic and endothermic reactions which are relatively unusual and relates the transition state to the intermediates which are usually the most unstable.

The Transition States for S_N1 Reaction

Energy diagrams showing the transition states for SN1 reactions as related to Hammond's postulate

Hammond postulate can be used to compare structures of various carbocations in an SN1 reactions. It is known that the relative stabilities of carbocations decreases from tertiary > secondary > primary > methyl[6][7]. Therefore, according to Hammond’s Postulate, the reaction coordinate diagrams for heterolysis reactions can be drawn as shown here. The transition state moves toward the reactant as the reaction becomes less endothermic or as the carbocation involved becomes more stable. In other words, the transition state is more stable when the carbocation is relatively more stable, thus explaining why SN1 mechanism is more likely at tertiary alkyl centers.

Applying the postulate

Hammond's postulate is useful for understanding the relationship between the rate of a reaction and the stability of the products. While the rate of a reaction depends just on the activation energy (often represented in organic chemistry as ΔG^‡ “delta G double dagger”), the final ratios of products in chemical equilibrium depends only on the standard free-energy change ΔG (“delta G”). The ratio of the final products at equilibrium corresponds directly with the stability of those products.

Hammond's postulate connects the rate of a reaction process with the structural features of those states that form part of it, by saying that the molecular reorganizations have to be small in those steps that involve two states that are very close in energy. This gave birth to the structural comparison between the starting materials, products, and the possible "stable intermediates" that lead to the understanding that the most stable product is not always the one that is favored in a reaction process.

Explaining seemingly contrary results

Hammond's postulate is especially important when looking at the rate-limiting step of a reaction. However, one must be cautious when examining a multistep reaction or one with the possibility of rearrangements during an intermediate stage. In some cases, the final products appear in skewed ratios in favor of a more unstable product (called the kinetic product) rather than the more stable product (the thermodynamic product). In this case one must examine the rate-limiting step and the intermediates. Often, the rate-limiting step is the initial formation of an unstable species such as a carbocation. Then, once the carbocation is formed, subsequent rearrangements can occur. In these kinds of reactions, especially when run at lower temperatures, the reactants simply react before the rearrangements necessary to form a more stable intermediate have time to occur. At higher temperatures when microscopic reversal is easier, the more stable thermodynamic product is favored because these intermediates have time to rearrange. Whether run at high or low temperatures, the mixture of the kinetic and thermodynamic products eventually reach the same ratio, one in favor of the more stable thermodynamic product, when given time to equilibrate due to microreversal

See also

• Bema Hapothle
• Curtin-Hammett principle
• Microscopic reversibility
• Bell-Evans-Polanyi principle

References

Further reading

• IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version:  (2006–) "Hammond principle (Hammond postulate)".