Isotope Effects

ISOTOPE EFFECTS

Besides the energy of the activated complex, structure and bonding in the acti-vated complex can be probed in several other ways using rate constant data. One very powerful way to investigate bonding in the activated complex is to use kinetic isotope effects. Isotope effects derive from the fact that a heavier isotope of an element has a lower zero-point energy and hence more energy is required to break a bond to a heavier isotope than a bond to a lighter isotope (i.e., the activation energy is greater). At a given temperature this means that the rate of reaction for a compound containing a heavy isotope is slower than the rate of reaction for the compound with a lighter isotope. This is only true if breaking of that bond is involved at the transition state of the rate-determining step. If breaking of this bond occurs prior to or after the rate-determining step, isotopic substitution does not give a large change in the rate. This effect is most pronounced for hydrogen/deuterium, which has the largest mass difference of any isotopic pair and thus the largest difference in zero-point energies. If a bond to hydrogen (or deuterium) is being broken in the rate-determining step, then k_H/ k_D values of 2 – 8 are typical. These are termed primary kinetic deuterium isotope effects.

If the C–H(D) bond is not being broken in the rate-determining step, there are sometimes smaller effects on the rate resulting from isotopic substitution that are termed secondary kinetic deuterium isotope effects. They result from zero-point energy differences in deformation modes but they are small and typically k_H/ k_D values are 1 – 1.3 for these effects. If a kinetic deuterium isotope effect is found to be greater than about 1.5, it is a primary kinetic deuterium isotope effect and C–H(D) bond breaking is occurring in the rate-determining step. If a kinetic deuterium isotope effect is found to be between 1 and 1.5, it is a secondary kinetic deuterium isotope effect and C–H(D) bond breaking is not occurring in the rate-determining step.

The largest values of primary kinetic deuterium isotope effects are found for reactions where the bond to hydrogen is about one-half broken (k_H/ k_D values are 6 – 8). Smaller values are found in reactions in which the bond to hydro-gen is less than or more than one-half broken. Normally, k_H/ k_D values less than maximum correspond to bond cleavage of < 1/2 . 

Primary kinetic deuterium isotope effects thus provide insight into the extent of C–H bond cleavage in the activated complex.

For example, the free-radical bromination of toluene by N -bromosuccinimide (NBS) proceeds with k_H/ k_D = 4.9, while for the same bromination of isopropyl benzene, k_H/ k_D = 1.8 (Figure 5.16). Both are primary kinetic deuterium iso-tope effects, indicating that hydrogen abstraction by a bromine atom is the rate-determining step. The much lower value of the isotope effect for isopropyl-benzene suggests that the transition state is much earlier than for toluene. The lesser extent of hydrogen transfer in isopropylbenzene is due to the more stable radical being produced, resulting in an earlier transition state.

Therefore

The electrophilic nitration of benzene using acetyl nitrate involves the replace-ment of a hydrogen on the benzene ring by a nitro group. The reaction is second order overall, first order in benzene, and first order in the nitrating agent -ν = k[C₆H₆][acetyl nitrate].

Use of fully deuterated benzene gave k_H/ k_D = 1. These data suggest that the nitrating agent attacks the benzene ring in the rate-determining step, but C–H bond breaking is not involved in the rate-determining step. These observations are consistent with an electrophilic attack of the nitrating agent of the π system. The proton is lost in a subsequent fast step, after the rate-determining step.

Thus, even though loss of hydrogen is required for the product to be formed, its removal is not taking place in the rate-determining step of the reaction — it must take place after the rate-determining step.

The base-promoted bromination of ketones is a second-order process, first order in ketone and first order in base; thus ν = k[ketone][base]. The bromine concentration does not appear in the rate law; that is, the reaction is zero order in [Br₂].

Use of deuterated substrates gives k_H/ k_D = 6.5. This is a primary kinetic deu-terium isotope effect, indicating that proton removal is an essential component of the rate-determining step. The lack of rate dependence on bromine requires that bromine is added to the molecule after the rate-determining step. A mechanism consistent with these facts has proton removal and enolate formation rate determining.

If we now take this basic scenario and add our notions of electron movement to the picture, we can construct a detailed picture of electronic change that is consistent with the observed facts.

The activated complex for proton removal, the rate-determining step, can be envisioned as having a partial charge from proton removal delocalized into the carbonyl group (as it is in the product enolate). This also requires that the proton being removed has a dihedral angle of 90^◦ with the plane of the carbonyl group so that the developing charge can overlap with the carbonyl π bond.

Base-promoted elimination in the two β-phenethyltrimethylammonium deriva-tives shown below is found to be second order overall, first order in substrate, and first order in base; that is, ν = k[C₆H ₅CH₂CH₂N⁺ (CH₃)₃][CH₃CH₂O⁻].

This means that both the substrate and the ethoxide base are present in the transition state of the rate-determining step. The rate constants for the deuterated and protio substrates were measured. The magnitudes (k_H/ k_D = 3 – 4) of the kinetic deuterium isotope effects for both substrates are typical primary kinetic deuterium isotope effects, which means that C–H bond breaking is involved at the transition state of the rate-determining step. This suggests that proton removal by a base in the activated complex is an essential element of the rate-determining step and is a key feature in the mechanism of the elimination reaction.

The difference between the k_H/ k_D values, however, means that the extent of C–H bond breaking at the transition state in the second substrate is different from the first. (The transition state of the second substrate is actually earlier in terms of proton removal by the base because in both cases proton transfer is greater than half completed.) Thus a change in structure of the substrate leads to a distinct change in the structure of the activated complex which can be detected and described by kinetic isotope effects.

From the above examples it is clear that kinetic deuterium isotope effects are a powerful way to probe bonding changes in the activated complex. The magnitude of the isotope effect indicates whether bonds to hydrogen are being made or broken in the rate-determining step. Differences in kinetic isotope effects in closely related precursors can also be used to pinpoint whether one transition state is earlier than another — a direct measure of the effect of the substrate structure on the structure of the transition state.

Other elements can be used to measure isotope effects; however, the magni-tudes of these isotope effects are much smaller than primary kinetic deuterium isotope effects. Substitution of ¹³C for ¹²C in a reaction could lead to a maximum kinetic isotope effect of k¹²C/ k¹³C = 1.05 for a reaction in which a bond to carbon is broken in the rate-determining step. (Recall that maximum k_H/ k_D’s are 8 – 10.) Most standard kinetic methods are not capable of distinguishing such small rate differences reproducibly, and so kinetic isotope effects for elements other than hydrogen (deuterium) are not very abundant in the literature. In some instances, isotopic abundances determined by mass spectrometry can be used to measure such differences accurately and isotope effects can be informative. The decarboxylation of malonic acid proceeds with k¹²C/ k¹³C = 1.045. This large primary-isotope effect (for carbon) indicates that C–C bond breaking is well developed in the transition state. This detailed information about the structure of the activated complex permits a shift in focus from a curved-arrow type of mechanism to a real structure of the activated complex.