Electron Coupled Interactions between Nuclear Spins in Molecules

In addition to the direct magnetic interaction between two nuclear spins in a molecule, the nuclei can have an effective mutual interaction as a result of the magnetic interactions between each of the nuclei and the electrons of the molecule. Although these indirect interactions are in general small, they are important in many cases, particularly as a result of the fact that the frequent collisions which characterize most nuclear paramagnetic resonance experiments cause the direct interaction to average to zero while this is not so for the indirect. In the present paper, the indirect interactions are evaluated. Contributions arise from a simple diamagnetic term, a closely related second-order orbital paramagnetism term, and terms due to the magnetic interaction of the nuclei with the electron spins. Expressions for each of these terms are given both for the general case and for the spherically symmetric case which arises when there are many collisions. Specific numerical calculations of the various effects are given for hydrogen deuteride. It is shown for HD that the diamagnetic terms are of the order of a few tenths of a cycle per second. On the other hand, if the suitable mean energy of the molecular excited states is given the reasonable value of 1.4 Rydbergs, the electron spin terms are 43 cps in agreement with experiment.