Static and optical anapole magnetizabilities and polarizabilities

Electronic Currents and Anapolar Response Induced in Molecules by Monochromatic Light

It is shown that the electric dipole- and electric quadrupole–anapole polarizabilities, denoted respectively by fαβ′ and gα,βγ′, and the anapole magnetizability aαβ, are intrinsic properties of the electron cloud of molecules responding to optical fields. fαβ′ is a nonvanishing property of chiral and achiral compounds, whereas aαβ is suitable for enantiomer discrimination of chiral species. They can conveniently be evaluated by numerical integration, employing a formulation complementary to that provided by perturbation theory and relying on the preliminary computation of electronic current density tensors all over the molecular domain. The origin dependence of the dynamic anapolar response is rationalized via related computational techniques employing numerical integration, as well as definitions of molecular property tensors, for example, electric dipole and electric quadrupole polarizabilties and magnetizability. A preliminary application of the theory is reported for the Ra enantiomer of the hydrogen peroxide molecule, evaluating tensor components of electric dipole-anapole polarizability and anapole magnetizability as functions of the dihedral angle ϕ≡∠ H-O-O-H in the range 0∘≤ϕ≤180∘.

Physical achirality in geometrically chiral rotamers of hydrazine and boranylborane molecules

The diagonal components and the trace of tensors which account for chiroptical response of the hydrazine molecule N₂ H₄ , that is, static anapole magnetizability and frequency-dependent electric dipole-magnetic dipole polarisability, are a function of the ϕ ≡ ∠ H─N─N─H dihedral angle. They vanish for symmetry reasons at ϕ = 0° and ϕ = 180°, corresponding respectively to C_2v and C_2h point group symmetries, that is, cis and trans conformers characterized by the presence of molecular symmetry planes. Nonetheless, vanishing diagonal components have been observed also in the proximity of ∠ H─N─N─H = 90°, in which the point group symmetry is C₂ and hydrazine is unquestionably chiral. In the boranylborane molecule B₂ H₄ , assuming the B─B bond in the y direction, the a_yy component of the anapole magnetizability tensor approximately vanishes for dihedral angles ∠ H─B─B─H corresponding to chiral rotamers which belong to D₂ symmetry. Such anomalous effects have been ascribed to physical achirality of these conformers, that is, to their inability to sustain electronic current densities inducing either anapole moments, or electric and magnetic dipole moments, about the chiral axis connecting heavier atoms, as well as perpendicular directions. In other terms, the structure of certain geometrically chiral rotamers may be such that neither toroidal nor helical flow, which determine chiroptical phenomenology, can take place in the presence of perturbing fields parallel or orthogonal to the chiral axis.