Secondary a-deuterium KIEs

Using secondary a-deuterium KIEs to determine the symmetry of SN2 transition states 164... 

The effect of a change in substituent on the secondary a-deuterium KIEs 171... 

The effect of a change in solvent on the secondary a-deuterium KIEs 195 Secondary a-deuterium KIEs and the effect of ionic strength on transition state structure 197... 

A secondary deuterium kinetic isotope effect is observed when substitution of a deuterium atom(s) for a hydrogen atom(s) in the substrate changes the rate constant but the bond to the deuterium atom is neither broken nor formed in the transition state of the rate-determining step of the reaction. Several types of secondary hydrogen-deuterium (deuterium) KIEs are found. They are characterized by the position of the deuterium relative to the reaction centre. Thus, a secondary a-deuterium KIE is observed when an a-hydrogen(s) is replaced by deuterium [equations (1) and (2)], where L is either hydrogen or deuterium. 

It is worth noting that Murr and Donnelly (1970a,b) have demonstrated that the secondary a-deuterium KIE is only approximately 75% of the theoretical maximum kinetic isotope effect when the ionization (ki) step of the reaction (Scheme 1) is fully rate determining, i.e. when the reaction occurs via a limiting SN1 mechanism (Shiner, 1970b Westaway, 1987c). 

Table 1 The maximum secondary a-deuterium KIEs expected for SN1 reactions with various leaving groups at 25°C.a...

Recently, this view of secondary a-deuterium KIEs has had to be modified in the light of results obtained from several different theoretical calculations which showed that the Ca—H(D) stretching vibration contribution to the isotope effect was much more important than previously thought. The first indication that the original description of secondary a-deuterium KIEs was incorrect was published by Williams (1984), who used the degenerate displacement of methylammonium ion by ammonia (equation (4)) to model the compression effects in enzymatic methyl transfer (SN2) reactions. 

The secondary a-deuterium KIEs calculated for the uncatalysed reaction were in the range found experimentally for other SN2 methyl transfers. The calculated KIE was also analysed in terms of the zero-point energy (ZPE), the molecular mass-moment of inertia (MMI) and the excitation (EXC) contributions to the total isotope effect. The inverse KIE was found to arise from an... 

Table 3 The contribution to the observed secondary a-deuterium KIEs for the SN2 reactions between microhydrated chloride ion and methyl chloride at 300 K. ...

Hu and Truhlar (1995) also found the same source and temperature dependence for the secondary a-deuterium KIE in a theoretical investigation of the secondary a-deuterium KIEs for three halide ion-methyl halide SN2 reactions (7). 

Table 5 The experimental and theoretical secondary a-deuterium KIEs and the components of the vibrational contribution to these KIEs for three SN2 reactions between halide ion and methyl halides at 300 K."...

Fig. 2 The temperature dependence of the vibrational contributions to the secondary a-deuterium KIE for the SN2 reaction between chloride ion and methyl bromide by (a) the high energy C —H(D) stretching vibrations, (b) the Ca—H(D) bending vibrations and (c) the low-energy transition state vibrations. Modified, with permission, from Hu...

Wolfe and Kim (1991) also reported that the magnitude of a secondary a-deuterium KIE is primarily determined by the changes that occur in the Ca—H(D) stretching vibrations when the reactant is converted into the transition state. Wolfe and Kim calculated the transition state structures and the secondary a-deuterium KIEs for a series of identity SN2 reactions of methyl substrates [reaction (8)] at various levels of theory ranging from 4-31G to MP4/6-31 + G //6-31 + G. The KIEs were partitioned into two contributions, those from the Ca—H(D) stretching vibrations and those from the Ca—H(D) bending vibrations. 

Table 6 The secondary a-deuterium KIEs for seven identity SN2 reactions at 298 K."...

Another surprising result of these calculations was that they suggested the relationship between the magnitude of the secondary a-deuterium KIE and transition state structure that had been based on experimental results (Streitwieser et al., 1958 Bartell, 1961 Kaplan and Thornton, 1967) was incorrect. Wolfe and Kim plotted the calculated secondary a-deuterium KIE at various levels of theory versus a looseness parameter, L, for the transition state. The L parameter was defined as the sum of the percentage extension of the C—X and the C—X bonds on going from the reactant (product) to... 

Fig. 3 The calculated secondary a-deuterium KIEs versus the looseness parameter L for seven identity SN2 reactions. Calculations 4-31G, 6-31+ G, A MP2/ 6-31 + G. Data from Table 6. Modified, with permission, from Wolfe and Kim...

Finally, because (i) it was concluded that the secondary a-deuterium KIE was determined primarily by the Ca—H(D) stretching vibrations and (ii) the lengths (strengths) of the C —H bonds were effectively the same in all of the identity SN 2 transition states, Wolfe and Kim concluded that the magnitude of the isotope effect was determined by the length of the Ca—H bonds in the substrate. This was an unusual conclusion because it meant that all the secondary a-deuterium isotope effects for the SN2 reactions of a particular substrate should be the same for example, it meant that the KIE should be... 

Wolfe and Kim s view of the origin of secondary a-deuterium KIEs has been challenged by two different groups. Barnes and Williams (1993) calculated the transition state structures and the secondary a-deuterium KIEs for the identity SN2 reactions between chloride ion and several substituted methyl chlorides (reaction (11)). 

The calculations were performed at the semiempirical level using AMI parametrization. The results for the methyl chloride reaction (Table 8) supported Williams earlier findings for the methylammonium ion-ammonia reaction (p. 147) and the results by Wolfe and Kim in that the inverse secondary a-deuterium KIE arose from an increase in the C —H stretching force constants which accompanied the change from sp3 hybridization at the a-carbon in the reactant to the spMike hybridization in the transition state. More important, however, were the observations that (i) the total KIE is dominated by the vibrational (ZPE) component of the KIE with which it correlates linearly, and (ii) that the inverse contribution from the C —H(D) stretching vibrations is almost constant for all the reactions. Ibis suggests that the contribution from the other vibrations, i.e. the rest in Table 8, determines the magnitude of the KIE. In fact, Barnes and Williams stated that the... 

Table 8 The AMI calculated semiclassical secondary a-deuterium KIEs, the stretching and other contribution to the KIEs and the C—Cl transition state bond lengths for the identity SN2 reactions between chloride ion and substituted methyl chlorides.0...

Poirier, Wang and Westaway (1994) also investigated the relationship between transition state structure and the magnitude of the secondary a-deuterium KIE in a theoretical study of the SN2 reactions between methyl and ethyl chlorides and fluorides with several different nucleophiles (reaction (12)). 

Table 9 The HF/6-31 + G secondary a-deuterium KIEs and vibrational contributions to the KIEs for the SN2 reactions between methyl fluorides and chlorides with different nucleophiles at 25°C. ...

Fig. 5 The total secondary a-deuterium KIE versus rs for the Sn2 reactions of methyl fluorides and chlorides with different nucleophiles at 25°C The open circles are for the methyl chloride reactions and the solid circles are for the methyl fluoride reactions. Data from Poirier et al. (1994), with permission.

The most recent contribution to this controversy is Glad and Jensen s (1997) theoretical investigation at the MP2/6-31 + + G(d, p) ab initio level of the secondary a-deuterium KIEs for the identity SN2 reactions of three methyl halides (reaction (15)). The KIEs were calculated for various x where AR%-x = (Rc-x Rc-x) and Re x and R°cx represent the length of the C—X bond in the transition state and the reactant, respectively. 

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