Kinetic isotope effects for gas phase S_N2 methyl transfer: A computational study of anionic and cationic identity reactions

The relationship between energy barriers, transition-state looseness and 2° α-deuterium kinetic isotope effects (KIEs) has been re-evaluated for a range of identity S_N2 methyl transfer reactions that extends to "exploded" transition structures (TSs). Ab initio MP2/6-311+G* molecular orbital calculations have been performed for reactions involving the neutral nucleophiles X = CO, N₂, NH₃, N(CH₃)₃, OH₂, Kr, Ar, Ne and He, along with anionic nucleophiles X^- = F, Cl, Br, CN, NC, CCH, and OH. The behaviour previously noted by Wolfe and co-workers, from MP2/6-31+G* studies of identity and non-identity methyl transfers with anionic nucleophiles and neutral electrophiles only, does not apply to the broader range which also includes neutral nucleophiles and cationic electrophiles: a looser TS is not associated with a higher energy barrier and a more inverse 2° α-D KIE. Moreover, when the interaction of the nucleophile with the electrophile in the reactant complex (RC) is considered, no simple relationships between "looseness" or "tightness" and either energy barriers or KIEs are found. The variation in energy barriers may be understood by means of a simple model involving the distance travelled by the methyl group within the encounter complex from RC to the product complex (PC) and the force constant for stretching the bond to the leaving group in RC. There is a fair linear correlation between the 2° α-D KIE and the change in this same stretching force constant, from RC to TS. The methyl group in the S_N2 TS does not resemble an isolated methyl cation, even for systems showing "S_N1-like" properties, owing to the significant influence of the nucleophile and leaving group. Consideration of the unusual range of nucleophiles X = Kr, Ar, Ne and He in identity reactions with CH₃X⁺ shows a mechanistic changeover from a double-well potential with a true S_N2 TS to a single-well potential with a symmetric intermediate corresponding to a solvated methyl cation.