The Hammond Postulate

The rate of an SnI reaction depends on the rate of formation of the carbocation (the product of the rate-determining step) via heterolysis of the C-X bond. 

the rate of an SnI reaction increases as the stability of the carbocation increases. 

The reaction is faster with a more stable carbocation. 

The rate of a reaction depends on the magnirnde of E, and the stability of a product depends on AG°. The Hammond postulate, first proposed in 1955, relates rate to stability. 

The Hammond postulate provides a qualitative estimate of the energy of a transition state. 

Even where the goal, a well-defined singular mechanism, is not yet attained for a given reaction, observations can be used to make predictions. For example, using the Hammett equation (Section 4.3.7), we can predict from measured rates of some cases of a reaction how fast a new case with different substitution will occur. 

In a reaction coordinate diagram, it is obvious that the potential energy content at a transition state is closer to that in the starting materials in an exothermal step and closer to the products in an endothermal step. Since potential energy is required to distort a molecule, the structure of the transition state will more closely resemble those molecules to which it is closer in potential energy that is, a small vertical difference in a reaction coordinate diagram corresponds to a small horizontal difference. Transition states are late in endothermal steps and early in exothermal steps. This is the Hammond postulate [4] and it is useful for predicting products where there is potentially close competition between two alternative steps. 

Comparisons can be made for less extreme cases as well. Comparing two endothermal reactions, we can predict that the more endothermal one will be the more selective. For example, hydrogen atom abstraction from propane by bromine atoms is more endothermal and more selective than by chlorine atoms. 

FIGURE 7.9 In the ethyl carhocation, CH3CH2 , there is a stabilizing interaction between the carhocation p orbital and adjacent C-H r bonds on the methyl substituent, as indicated by this molecular orbital. The more substituents there are, the greater the stabilization of the cation. Only the C-H bonds that are roughly parallel to the neighboring p orbital are oriented properly to take part in hyperconjugation. 

Show the structures of the carhocation intermediates you would expect in the following reactions  

Draw a skeletal structure of the following carhocation. Identify it as primary, secondary, or tertiary, and identify the hydrogen atoms that have the proper orientation for hyperconjugation in the conformation shown. 

Let s summarize our knowledge of electrophilic addition reactions to this point  

What we have not yet seen is how these two points are related. Why does the stability of the carbocation intermediate affect the rate at which it s formed and thereby determine the structure of the final product After all, carbocation stability is determined by the free-energy change AG°, but reaction rate is determined by the activation energy AG. The two quantities aren t directly related. 

The Hammond postulate is likely the most widely used principle for estimating the structures of activated complexes. In fact, it is so useful that all introductory organic chemistry textbooks cover it, and many chemists use it intuitively. The value of the Hammond postulate stems from the fact that transition states are transient in nature and generally cannot 

Various energy surfaces and their two-dimensional projections that obey the Hammond postulate. 

Several reaction coordinate diagrams that obey Hammond s postulate and where the activation energy has a direct correlation with the energy change of the reaction. 

I Electrophilic addition to an unsymmetrically substituted alkene gives the more highly substituted carbocation intermediate. A more highly substituted carbocation forms faster than a less highly substituted one and, once formed, rapidly goes on to give the final product. 

I A more highly substituted carbocation is more stable than a less highly substituted one. T hat is, the stability order of carbocations is tertiary secondary primary methyl. 

Reaction-energy diagram for the first propagation step in the bromination of propane. The energy difference in the transition states is nearly as large as the energy difference in the products. 

Energy required to break the CH3—CH H bond Energy released in forming the H-j-Br bond Total energy for reaction at the secondary position  

The energy differences between chlorination and bromination result from the difference in the bond-dissociation enthalpies of H—Cl (431 kJ) and H—Br (368 kJ). The HBr bond is weaker, and abstraction of a hydrogen atom by Br- is endothermic. This endothermic step explains why bromination is much slower than chlorination, but it still does not explain the enhanced selectivity observed with bromination. 

Two impotant differences are apparent in the reaction-energy diagrams for the first propagation steps of chlorination and bromination  

The first propagation step is endothermic for bromination but exothermic for chlorination. 

George Simms Hammond (1921- ) was born in Auburn, Maine, the son of a farmer. He received his Ph.D. at Harvard University in 1947 and served as professor of chemistry at Iowa State University, California Institute of Technology (1958-1972), and the University of California at Santa Cruz (1972-1978). He is known for his exploratory work on organic photochemistry— the use of light to bring about organic reactions. 

Reaction energy diagrams for two similar competing reactions, in (a), the faster reaction yields the more stable intermediate. In (b). the slower reaction yields the more stable intermediate. The curve shown in (a) represents the typical situation. 

An explanation of the relationship between reaction rate and intermediate stability was first advanced in 1955. Known as the Hammond postulate, this explanation intuitively links reaction rate and intermediate stability by looking at the energy level and structure of the transition state. 

The equation of Bell-Evans—Polanyi (see eq. (7.18)) implies that exothermic reactions will have lower barriers than the endothermic ones. The view that a transition state has structural and energy features that are intermediate between those of starting materials and products is due to George Hammond [9], who resurrected the view implied by those three authors in 1955. The aim of Hanunond was that of mechanistic interpretations, postulating that the changes in structure of the TS are affected by the manner in which the substituents affect the energies of intermediates on alternate pathways from reactants to products. Since then this assumption has been known as the Hammond postulate. 

Conversely, if a 1 then AA G AGp and the transition state responds to changes in snbstitnents in a similar fashion to the products, a characteristic of highly endoenergetic elementary reaction. The transition state is closer to the products and its structural features are similar to those of the final materials. Large structural rearrangements are required to attain the transition state and the activation barrier is high. 

These considerations are essentially vahd when the force constants of reactants and products are similar. However, when there is a general tendency for the transition state to be closer to reactants, even for endothermic reactions. The inverse is vaUd, that is when the transition state has a tendency to be closer to the product configuration. 

In many series of analogous reactions a second proportionality is found experimentally, namely, between the free energy change (AGr a thermodynamic quantity) and the free energy of activation (AG, a kinetic quantity). In a series of analogous reactions, a third parameter besides AH and AG no doubt also depends on the AG and AGr values, namely, the structure of the transition state. This relationship is generally assumed or postulated, and only in a few cases has it been supported by calculations (albeit usually only in the form of the so-called transition structures they are likely to resemble the structures of the transition state, however). This relationship is therefore not stated as a law or a principle but as a postulate, the so-called Hammond postulate. 

The Hammond Postulate The Hammond postulate can be stated in several different ways. For individual reactions 

The form of the Hammond postulate just presented is very important in the analysis of the selectivity of many of the reactions we will discuss in this book in connection with chemoselec-tivity (Section 1.7.2 also see Section 3.2.2), stereoselectivity (Section 3.2.2), diastereoselec-tivity (Section 3.2.2), enantioselectivity (Section 3.2.2), and regioselectivity (Section 1.7.2). 

Selectivity Selectivity means that one of several reaction products is formed preferentially or exclusively. In the simplest case, for example, reaction product 1 is formed at the expense of reaction product 2. Selectivities of this type are usually the result of a kinetically controlled reaction process, or kinetic control. This means that they are usually not the consequence of an equilibrium being established under the reaction conditions between the alternative reaction products 1 and 2. In this latter case one would have a thermodynamically controlled reaction process, or thermodynamic control.  

For reactions under kinetic control, the Hammond postulate now states that  

VVfiat we have not yel seen is how these two points arc related. Why does 

Tire structure of a transition state resembles the structure of lire nearest stable species. Transition states for endergonic steps structurally resemble products, and transition states for exergonic steps structurally resemble reactants. 

Electrophilic addition to an unsymmetrically substituted alkene gives the more highly substituted carbocation intermediate. A 

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Many programs allow the user to input a weighting factor (i.e., to give a structure that is 70% of the way from reactants to products). This allows the application of the Hammond postulate that the transition structure will look more like the reactants for an exothermic reaction and more like the products for an endothermic reaction. 

The substituent effects in aromatic electrophilic substitution are dominated by resonance effects. In other systems, stereoelectronic effects or steric effects might be more important. Whatever the nature of the substituent effects, the Hammond postulate insists diat structural discussion of transition states in terms of reactants, intermediates, or products is valid only when their structures and energies are similar. 

Figure S-13 Demonstration of the Hammond postulate with harmonic potential wells.

The Hammond postulate is a valuable criterion of mechanism, because it allows a reasonable transition state structure to be drawn on the basis of knowledge of the reactants and products and of energy differences between the states (i.e., AG and AG°). Throughout this chapter we have located transition states in accordance with the Hammond postulate. 

Figure S-14. (A) A parabolic potential barrier and a linear perturbation. (B) Sum of the parabolic and linear functions, showing shift in maximum in accord with the Hammond postulate. (C) Two parabolic potential wells aa and bb are equivalent to the parabolic barrier cc .

It would be desirable to achieve a quantitative version of the Hammond postulate. For this purpose we need a measure of progress along the reaction coordinate. Several authors have used the bond order for this measure.The chemical significance of bond order is that it is the number of covalent bonds between two atoms thus the bond orders of the C—C, C==C, bonds are 1, 2, and 3,... 

According to this very simple derivation and result, the position of the transition state along the reaction coordinate is determined solely by AG° (a thermodynamic quantity) and AG (a kinetic quantity). Of course, the potential energy profile of Fig. 5-15, upon which Eq. (5-60) is based, is very unrealistic, but, quite remarkably, it is found that the precise nature of the profile is not important to the result provided certain criteria are met, and Miller " obtained Eq. (5-60) using an arc length minimization criterion. Murdoch has analyzed Eq. (5-60) in detail. Equation (5-60) can be considered a quantitative formulation of the Hammond postulate. The transition state in Fig. 5-9 was located with the aid of Eq. (5-60). 

The Hammond Postulate implies that the transition stah of a fast exothermic reaction resembles the reactants (se( reaction energy diagram at left). This means that it wil be hard to predict the selectivity of competing exothermi( reactions both barriers may be small and similar even i one reaction is more exothermic than the other. 

Obtain the partial CH and HF bond distances in eacl transition state, and compare them to the CH and HF bon( distances in propane and hydrogen fluoride, respectively Does the Hammond Postulate correctly predict whicl bond distances will be most similar Explain. 

Use of the Hammond Postulate requires that the reverse reactions both be fast. Obtain energies for the transition states leading to 1-propyl and 2-propyl radicals ipropane+Br end and propane+Br center), and draw a reaction energy diagram for each (place the diagrams on the same axes). Is use of the Hammond Postulate justified Compare the partial CH and HBr bond distances in each transition state to the corresponding distances in propane and hydrogen bromide, respectively. Does the Hammond Postulate correctly predict which bond distances will be most similar Explain. 

Obtain the energies of propene, dimethylborane, and 1-propyldimethyl borane, and calculate AH n for dimethylborane addition. Is this reaction exothermic or endothermic Use this result and the Hammond Postulate to predict whether the transition state will be more reactant like or more product like . Compare the geometry of the transition state to that of the reactants and products. Does the Hammond Postulate correctly anticipate the structure of the transition state Explain. 

Electrophilic nitration of a substituted benzene may lead to ortho, meta or para products, depending on the substituent. According to the Hammond Postulate, the kinetic product will be that which follows from the most stable intermediate benzenium ion, i.e. 

Examine the structures of the two transition states (chlorine atom+methane and chlorine+methyI radical). For each, characterize the transition state as early (close to the geometry of the reactants) or as late (close to the geometry of the products) In Ught of the thermodynamics of the individual steps, are your results anticipated by the Hammond Postulate Explain. 

Would you describe the transition state for the Claisen rearrangement as early (like reactants), late (like products) or in between Given the overall thermodynamics of reaction, do you conclude that the Hammond Postulate applies Explain. 

How does the Hammond postulate apply to electrophilic addition reactions The formation of a catbocation by protonation of an alkene is an endergonic step. Thus, the transition state for alkene protonation structurally resembles the... 

Markovnikov s rule can be restated by saying that, in the addition of HX to an aikene, the more stable carbocation intermediate is formed. This result is explained by the Hammond postulate, which says that the transition state of an exergonic reaction step structurally resembles the reactant, whereas the transition state of an endergonic reaction step structurally resembles the product. Since an aikene protonation step is endergonic, the stability of the more highly substituted carbocation is reflected in the stability of the transition state leading to its formation. 

The isobutyl cation spontaneously rearranges to the tart-butyl cation by a hydride shift. Is the rearrangement exergonic or endergonic Draw what you think the transition state for the hydride shift might look like according to the Hammond postulate. 

The enhanced selectivity of alkane bromination over chlorination can be explained by turning once again to the Hammond postulate. In comparing the abstractions of an alkane hydrogen by Cl- and Br- radicals, reaction with Br- is less exergonic. As a result, the transition state for bromination resembles the alkyl radical more closely than does the transition state for chlorination, and the stability of that radical is therefore more important for bromination than for chlorination. 

According to the Hammond postulate (Section 6.10), any factor that stabilizes a high-energy intermediate also stabilizes the transition state leading to that inlermediate. Since the rate-limiting step in an S l reaction is the spontaneous, unimolecLilar dissociation of the substrate to yield a carbocation, the reaction is favored whenever a stabilized carbocation intermediate is formed. The more stable the carbocation intermediate, the faster the S l reaction. 

The Hammond postulate says that any factor stabilizing the intermediate carbocation should increase the rate of an S l reaction. Solvation of the carbocation—the interaction of the ion with solvent molecules—has just such an effect. Solvent molecules orient around the carbocation so that the electron-rich ends of the solvent dipoles face the positive charge (Figure 11.14), thereby lowering the energy of the ion and favoring its formation. 

Radical additions are typically highly exothermic and activation energies are small for carbon30-31 and oxygen centered32,33 radicals of the types most often encountered in radical polymerization, Thus, according to the Hammond postulate, these reactions are expected to have early reactant-like transition states in which there is little localization of the free spin on C(J. However, for steric factors to be important at all, there must be significant bond deformation and movement towards. sp hybridization at Cn. 

For the SnI mechanism, a branching increases the rate, as shown in Table 10.4. We can explain this by the stability order of alkyl cations (tertiary > secondary > primary). Of course, the rates are not actually dependent on the stability of the ions, but on the difference in free energy between the starting compounds and the transition states. We use the Hammond postulate (p. 284) to make the assumption that the transition states resemble the cations and that anything (such as a branching) that lowers the free energy... 

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