Theoretical estimates of the anapole magnetizabilities of C4H4X2 cyclic molecules for X=O, S, Se, and Te

Abstract

Calculations have been carried out for C4H4X2 cyclic molecules, with X=O, S, Se, and Te, characterized by the presence of magnetic-field induced toroidal electron currents and associated orbital anapole moments. The orbital anapole induced by a static nonuniform magnetic field B, with uniform curl C =∇× B, is rationalized via a second-rank anapole magnetizability tensor aαβ , defined as minus the second derivative of the second-order interaction energy with respect to the components Cα and Bβ. The average anapole magnetizability a equals −χ, the pseudoscalar obtained by spatial averaging of the dipole-quadrupole magnetizability χα,βγ . It has different sign for D and L enantiomeric systems and can therefore be used for chiral discrimination. Therefore, in an isotropic chiral medium, a homogeneous magnetic field induces an electronic anapole Aα, having the same magnitude, but opposite sign, for two enantiomorphs.