Quantitative Treatments of the Effect of Structure on Reactivity - Effects of Structure and Medium on Reactivity - Introduction - March's Advanced Organic Chemistry: Reactions, Mechanisms, and Structure, 7th Edition (2013)

March's Advanced Organic Chemistry: Reactions, Mechanisms, and Structure, 7th Edition (2013)

Part I. Introduction

Chapter 9. Effects of Structure and Medium on Reactivity

9.C. Quantitative Treatments of the Effect of Structure on Reactivity16

Suppose a reaction is performed on a substrate molecule that can be represented as XGY, where Y is the site of the reaction, X a variable substituent, and G is a skeleton group to which X and Y are attached. In such a molecule, changing X from H to CH3 results in a rate increase by a factor, of say, 10. What part of the increase is due to each of the effects previously mentioned? The obvious way to approach such a problem is to try to find compounds in which one or two of the factors are absent or at least negligible. This is difficult because factors that seem negligible to one investigator do not always appear so to another. The first attempt to give numerical values was that of Hammett.17 For the cases of m- and p-XC6H4Y, Hammett set up the equation

equation

where k0 is the rate constant or equilibrium constant for X = H, k is the constant for the group X, ρ is a constant for a given reaction under a given set of conditions, and σ is a constant characteristic of the group X. The equation is called the Hammett equation.

The value of ρ was set at 1.00 for ionization of XC6H4COOH in water at 25°C. The values of σm and σp were then calculated for each group (for a group X, σ is different for the meta and para positions). Once a set of σ values was obtained, ρ values could be obtained for other reactions from the rates of just two X-substituted compounds, if the s values of the X groups were known (in practice, at least four well-spaced values are used to calculate ρ because of experimental error and because the treatment is not exact). With the ρ value calculated and the known s values for other groups, rates can be predicted for reactions that have not yet been run.

The σ values are numbers that sum up the total electrical effects (resonance plus field) of a group X when attached to a benzene ring. The treatment usually fails for the ortho position. The Hammett treatment has been applied to many reactions and to many functional groups. It correlates an enormous amount of data quite well. Jaffé's review article17 listed ρ values for 204 reactions,18 many of which have different ρ values for different conditions. Among them are reactions as disparate as the following reactions.

Rate constants for the following:

equation

Equilibrium constants for

equation

The Hammett equation also has been shown to apply to many physical measurements, including IR frequencies and NMR chemical shifts.19 The treatment is reasonably successful whether the substrates are attacked by electrophilic, nucleophilic, or free radical reagents, the important thing being that the mechanism be the same within a given reaction series.

However, there are many reactions that do not fit the treatment. These are mostly reactions where the attack is directly on the ring and where the X group can enter into direct resonance interaction with the reaction site in the transition state (i.e., the substrate is XY rather than XGY). For these cases, two new sets of σ values have been devised: σ+ values (proposed by H.C. Brown) for cases in which an electron-donating group interacts with a developing positive charge in the transition state (this includes the important case of electrophilic aromatic substitutions; see Chapter 11), and σ values, where electron-withdrawing groups interact with a developing negative charge. Table 9.4gives σ, σ+, and σ values for some common X groups.20 As shown in the table, σ is not very different from σ+ for most electron-withdrawing groups. The values of img are not shown in the table, since they are essentially the same as the σm values.

Table 9.4 The σ, σ+, and σ Values for Some Common Groupsa

img

img

A positive value of σ indicates an electron-withdrawing group and a negative value an electron-donating group.21 The constant ρ measures the susceptibility of the reaction to electrical effects.22 Reactions with a positive ρ are helped by electron-withdrawing groups and vice versa. The following ρ values for the ionization of some carboxylic acids illustrate this:23

equation

This example shows that the insertion of a CH2 or a CH=CH group diminishes electrical effects to about the same extent, while a CH2CH2 group diminishes them much more. A ρ > 1 would mean that the reaction is more sensitive to electrical effects than is the ionization of XC6H4COOH (ρ = 1.00).

Similar calculations have been made for compounds with two groups X and X′ on one ring, where the σ values are sometimes additive and sometimes not,36 for other ring systems, (e.g., naphthalene)37 and heterocyclic rings,38 and for ethylenic and acetylenic systems.39

The Hammett equation is a linear free energy relationship (LFER). This relationship can be demonstrated as follows for the case of equilibrium constants (for rate constants a similar demonstration can be made with ΔG instead of ΔG). For each reaction, where X is any group,

equation

The Hammett equation can be rewritten

equation

so that

equation

and

equation

For a given reaction under a given set of conditions, σ, R, T, and ΔG0 are all constant, so that σ is linear with ΔG.

The Hammett equation is not the only LFER.40 Some, like the Hammett equation, correlate structural changes in reactants, but the Grunwald–Winstein relationship (see Sec. 10.G.iv) correlates changes in solvent and the Brimgnsted relation (see Sec. 8.D) relates acidity to catalysis. The Taft equation is a structure–reactivity equation that correlates only field effects.41

Taft, following Ingold,42 assumed that for the hydrolysis of carboxylic esters, steric and resonance effects will be the same whether the hydrolysis is catalyzed by acid or base (see the discussion of ester-hydrolysis mechanisms, Reaction 16-59). Rate differences would therefore be caused only by the field effects of R and R′ in RCOOR′. This system is presumably good to use for this purpose because the transition state for acid-catalyzed hydrolysis (8) has a greater positive charge (and is hence destabilized by −I and stabilized by +I substituents) than the starting ester, while the transition state for base-catalyzed hydrolysis (9) has a greater negative charge than the starting ester. Field effects of substituents X could therefore be determined by measuring the rates of acid- and base-catalyzed hydrolysis of a series XCH2COOR′,43 where R′ is held constant.38 From these rate constants, a value σI could be determined by the equation44

img

equation

In this equation, (k/k0)B is the rate constant for basic hydrolysis of XCH2COOR′ divided by the rate constant for basic hydrolysis of CH3COOR′, (k/k0)A is the similar rate-constant ratio for acid catalysis, and 0.181 is an arbitrary constant. The substituent constant σI is for a group X, substituted at a saturated carbon, which reflects only field effects.45 Once a set of σI values was obtained, it was found that the equation holds for a number of reactions, among them:46

equation

equation

As with the Hammett equation, σI is constant for a given reaction under a given set of conditions. For very large groups, the relationship may fail because of the presence of steric effects, which are not constant. The equation also fails when X enters into resonance with the reaction center to different extents in the initial and transition states. A list of some σI values is given in Table 9.5.47 The σI values are4849 about what is expected for pure field-effect values (see Sec. 1.I) and are additive, as field effects (but not resonance or steric effects) would be expected to be. Thus, in moving a group one carbon down the chain, there is a decrease by a factor of 2.8 ± 0.5 (cf. the values of R in Table 9.5 for R = Ph and CH3CO). An inspection of Table 9.5 shows that σI values for most groups are fairly close to the σm values (Table 9.4) for the same groups. This result is not surprising, since σm values would be expected to arise almost entirely from field effects, with little contribution from resonance.

Table 9.5 The σI and img Values for Some Groupsa

img

Since σp values represent the sum of resonance and field effects, these values can be divided into resonance and field contributions if σI is taken to represent the field-effect portion.50 The resonance contribution σR51 is defined as:

equation

As it stands, however, this equation is not very useful because the σR value for a given group, which should be constant if the equation is to have any meaning, is actually not constant, but depends on the nature of the reaction.52 In this respect, the σI values are much better. Although they vary with solvent in some cases, σI values are essentially invariant throughout a wide variety of reaction series. However, it is possible to overcome53 the problem of varying σR values by using a special set of σR values, called img,54 that measure the ability to delocalize π electrons into or out of an unperturbed or “neutral” benzene ring. Several img scales have been reported; the most satisfactory values are obtained from img chemical shifts of substituted benzenes.55 Table 9.5 lists some values of img, most of which were obtained in this way.56

An equation, for example,

equation

which treats resonance and field effects separately, is known as a dual substituent parameter equation.57

The only groups in Table 9.5 with negative values of σI are the alkyl groups methyl and tert-butyl. There has been some controversy on this point.58 One opinion is that σI values decrease in the series methyl, ethyl, isopropyl, tert-butyl (respectively, −0.046, −0.057, −0.065, −0.074).59 Other evidence, however, has led to the belief that all alkyl groups have approximately the same field effect and that the σI values are invalid as a measure of the intrinsic field effects of alkyl groups.60

Another attempt to divide σ values into resonance and field contributions61 is that of Swain and Lupton, who show that the large number of sets of σ values (σm, σp, σp, σp+, σI, img, etc., as well as others we have not mentioned) are not entirely independent and that linear combinations of two sets of new values F (which expresses the field-effect contribution) and R (the resonance contribution) satisfactorily express 43 sets of values.62 Each set is expressed as:

equation

where f and r are weighting factors. Some F and R values for common groups are given in Table 9.6.63 From the calculated values of f and r, Swain and Lupton63 calculated that the importance of resonance, %R, is 20% for σm, 38% for σp, and 62% for img.64 This is another dual substituent parameter approach.

Table 9.6 The F and R Values for Some Groupsa

Reprinted with permission Swain, C.G.; Unger, S.H.; Rosenquist, N.R.; Swain, M.S. J. Am. Chem. Soc. 1983, 105, 492. Copyright © 1983 American Chemical Society.

img

a. See Ref. 63.

Taft and co-workers63 were also able to isolate steric effects.65 For the acid-catalyzed hydrolysis of esters in aqueous acetone, long (k/k0) was shown to be insensitive to polar effects.66 In cases where resonance interaction was absent, this value was proportional only to steric effects (and any others67 that are not field or resonance). The equation is

equation

Some Es values are given in Table 9.7,68 where hydrogen is taken as standard, with a value of 0.69 This treatment is more restricted than those previously discussed, since it requires more assumptions, but the Es values are approximately in order of the size of the groups. Charton70 show that Es values for substituents of types CH2X, CHX2, and CX3 are linear functions of the van der Waals radii for these groups.

Table 9.7 The Es, υ, and Va Values for Some Groupsa

Reprinted with permission from Gallo, R.; Roussel, C.; Berg, U. Adv. Heterocycl. Chem. 1988, 43, 173, Copyright © 1988, with permission from Elsevier Science.

img

a. See Ref. 68.

Two other steric parameters are independent of any kinetic data. Charton's υ values are derived from van der Waals radii,71 and Meyer's Va values from the volume of the portion of the substituent that is within 0.3 nm of the reaction center.72 The Va values are obtained by molecular mechanics calculations based on the structure of the molecule. Table 9.7 gives υ and Va values for some groups.73 As can be seen in the table, there is a fair, but not perfect, correlation among the Es, υ, and Va values. Other sets of steric values (e.g., img,74 img,75 Ωs76 and δf,77 have also been proposed.73

Since the Hammett equation has been so successful in the treatment of the effects of groups in the meta and para positions, it is not surprising that attempts have been made to apply it to ortho positions also.78 The effect on a reaction rate or equilibrium constant of a group in the ortho position is called the ortho effect.79 Despite the many attempts made to quantify ortho effects, no set of values has so far commanded general agreement. However, the Hammett treatment is successful for ortho compounds when the group Y in o-XC6H4Y is separated from the ring; for example, ionization constants of o-XC6H4OCH2CO2H can be successfully correlated.80

Linear free energy relationships can have mechanistic implications. If log k/k0 is linear with the appropriate σ, it is likely that the same mechanism operates throughout the series. If not, a smooth curve usually indicates a gradual change in mechanism, while a pair of intersecting straight lines indicates an abrupt change,81 although nonlinear plots can also be due to other causes (e.g., complications arising from side reactions). If a reaction series follows σ+ or σ better than σ it generally means that there is extensive resonance interaction in the transition state.82

Information can also be obtained from the magnitude and sign of ρ. For example, a strongly negative ρ value indicates a large electron demand at the reaction center, from which it may be concluded that a highly electron-deficient center, perhaps an incipient carbocation, is involved. Conversely, a positive ρ value is associated with a developing negative charge in the transition state.83 The σρ relationship even applies to free radical reactions, because free radicals can have some polar character (Sec. 14.A.ii), though ρ values here are usually small (less than ~1.5) whether positive or negative. Reactions involving cyclic transition states (Sec. 6.B) also exhibit very small ρ values.