Interelectron magnetic coupling in electrides with one-dimensional cavity-channel geometry

Abstract

Dye and coworkers [J. L. Dye, Acc. Chem. Res., 2009, 42, 1564] established experimentally that the strength of interelectron coupling in electrides with open intercavity channels critically depends on the channel diameter but is less sensitive to the channel length. We explain these observations by theoretical analysis of model electrides with a simple geometry. Our model consists of two electrons confined in a dogbone-shaped cavity—two spherical cages connected by a cylindrical channel. The coupling constant J is obtained from the calculated singlet–triplet gap of this system. By approximating the confining potential of the dogbone-shaped cavity with a one-dimensional double-well potential we show that ln(−J/k_B), where k_B is the Boltzmann constant, is a near-linear function of , where s and S are the cross-sectional areas of the channel and the cages, respectively. This prediction is in excellent agreement with the experiment for real electrides that have essentially one-dimensional cavity-channel networks.