A simple harmonic oscillator model of the intrinsic barrier to group transfer

Abstract

The intrinsic barrier in group-transfer reactions has been shown to correspond to the coupling energy of two identical harmonic oscillators. It has also been shown that the barrier, ΔG_XX^‡, can be represented as ΔG_XX^‡=½f(r_X–r₀)²+ΔG₀₀^‡ where r_X is the distance to the crossing point of the two oscillators and r₀ is the distance to the energy minimum. In considering a series of related reactions, the force constant, f, can be regarded as constant within a particular series and the intrinsic barriers of the series are shown to correlate with either approximate linearity of positive gradient in the E region and negative gradient in the C region; or as a parabolic curve in the B region centred on the minimum.

Examples of reactions belonging to each region are given and the following two relations are shown to hold in all cases of the intrinsic, controlled reaction series: r_X=λσ+r₀λ < 0 Δ log|ρ_XY|=kσ_zk > 0 where ρ_XY is the cross-interaction constant between substituents in the nucleophile (X) and substrate (Y), σ_Z is the substituent constant for the leaving group, and λ and k are constants. Thus these two relations constitute important criteria for intrinsic-barrier controlled reaction series. For thermodynamically controlled reaction series, the sign of the two constants is reversed, i.e.λ > 0 and k < 0.