Magnetic Isotope Effect in Radical Reactions

The isotope effect is a very familiar phenomenon in chemical reactions. The isotope composition of molecules affects their transformation rates in the course of chemical reactions as well as the equilibrium ratio of molecules. Both kinetic and equilibrium isotope effects can originate from the difference between isotopic masses. Isotope substitution changes molecular vibration frequencies, the energy of the molecular ground state (zero point vibration energy), the molecular momentum of inertia, and the effective mass for movement along a reaction coordinate. Atomic masses play a significant role in quantum tunnelling reactions. These isotope mass effects are well-known and are widely used in chemistry for separating isotopes, enriching compounds with definite isotopes, investigating mechanisms of chemical reactions, elucidating structures of transition states and other details of molecular dynamics in the elementary steps of chemical transformations. There are many monographs and reviews discussing comprehensively isotope mass effects (see, e.g., [1–3]).

This chapter is aimed to discuss the theoretical background of MIE in more detail. We will present the basic concepts and main parameters exploited in the applications of MIE. When analyzing experimental data, the observables should be expressed in terms of the effect of the isotope substitution on the recombination of intermediate radical pairs (RPs) or biradicals. Therefore, the chapter starts with a discussion of the relations between observables and RP’s recombination probabilities for some types of reactions. However, the focus of the chapter is the concept of radical pair and singlet-triplet transitions in RPs induced by hyperfine interaction. The illustrations will demonstrate how singlet-triplet transitions change after an isotope substitution.

Chemical reactions usually take place in the Earth’s magnetic field which is about 5 · 10^-5 T. The contribution of the Zeeman interaction of unpaired electrons with the Earth’s field to singlet-triplet evolution of shortlived RPs can be ignored with reasonable accuracy. Typically, the hfi in free radicals is an order of magnitude larger than the Zeeman interaction with the Earth’s field. By virtue of this argument the results obtained for zero field can be applied to the theoretical description of MIE in the Earth’s magnetic field. Thus, the Zeeman interaction of the RP’s unpaired electrons will be ignored throughout this chapter.

In this chapter we will discuss one of the MIE’s most remarkable features: its dependence on constant and alternating external magnetic fields. The influence of the external magnetic fields on the isotope effect parameters suggests that MIE operates. The physical origin of the phenomenon was briefly discussed in Chap. 2. The constant field splits the triplet sublevels (see, e.g., Fig. 2.6) so that the transitions between the RP singlet S and T₊₁, T₋₁ triplet sublevels induced by the hyperfine interaction with the magnetic nuclei can be suppressed at high field intensities. The external field also affects spin conservation properties (see the discussion of this problem in Sect. 2.6). Alternating fields are able to affect spin dynamics in the RPs with a definite isotope composition as well. How an external magnetic field influences the contribution of the hfi to the RP recombination depends on the spin-spin interactions (Heisenberg exchange and dipole-dipole interaction) between unpaired electrons. For that reason this chapter also includes a brief discussion of the role played by the interradical interaction in the RP spin dynamics. This problem may be of great significance for reactions that proceed through biradical states or for reactions in restricted spaces like micelles. At high constant magnetic field intensities, the mechanisms of RP singlet-triplet transitions caused by the difference in Larmor frequencies of two radicals in a pair (the so-called Δg-mechanism) and by paramagnetic relaxation originating from anisotropy of the radicals g-tensors start operating.

This chapter deals with experimental data concerning MIE. It is not our aim to present all experimental results available. The most comprehensive studies of MIE were undertaken for the photolysis of dibenzyl ketone [15, 17, 20, 42, 51–53], as discussed in a review paper [6] and monograph [5] among others. The photolysis of DBK may serve as a model case to demonstrate the basic concepts and predictions of the MIE theory. Therefore, this chapter starts with the consideration of the photolysis of DBK. There are several main trends in the studies of MIE, as outlined throughout this chapter. MIE can be used as a way to determine the mechanism of chemical reactions. Some examples are described below. Quite intriguing is the possibility to use MIE for the separation of isotopes of heavy elements. This and several other potential applications are also presented in this chapter.

The magnetic isotope effect offers interesting aspects from many points of view.