Theory of the SCOTCH experiment for reactions involving radical pairs

Abstract

SCOTCH (spin coherence transfer in chemical reactions) is a 2D NMR experiment in which cross peaks connect the chemical shifts of nuclei in starting compound and reaction product. If a reaction proceeds via a radical pair, the intensity of the cross peaks may be reduced due to dephasing processes occurring in the paramagnetic intermediate. This reduction is different for transverse and longitudinal nuclear spin magnetization. First, an expression for the amount of transferred magnetization and thus for the 2D cross peak intensity is derived in terms of the strength of the electron-nuclear hyperfine interaction and the lifetime of the radical pair; the influence of electron and nuclear spin relaxation is discussed as well. Then, the nuclear spin magnetization that is transferred to product is expressed as function of the reencounter probability and of the expectation value of finding the radical pair in a singlet electronic state. Two models that describe the reencounter probability are considered: an exponential model and a diffusion model. The resulting theoretical expressions are compared with experimental results of the SCOTCH experiment performed on the photochemical reaction of methyl tert-butyl ketone with tetrachloromethane.