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= 07 7B , is rationalized via a second-rank anapole magnetizability tensor a \u3b1\u3b2, defined as minus the second derivative of the second-order interaction energy with respect to the components C \u3b1 and B \u3b2. The average anapole magnetizability a equals 12\u3c7 , the pseudoscalar obtained by spatial averaging of the dipole-quadrupole magnetizability \u3c7\u3b1,\u3b2\u3b3. 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 A\u3b1 , having the same magnitude, but opposite sign, for two enantiomorphs

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