Physical achirality in geometrically chiral rotamers of hydrazine and boranylborane molecules

Abstract

The diagonal components and the trace of tensors which account for chiroptical response of the hydrazine molecule N2H4, 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 C2v and C2h 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 B2H4, assuming the B─B bond in the y direction, the ayy 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.

On the axial chirality of leucoindigo

“…In other words, the structure of certain geometrically chiral rotamers may be such that neither toroidal nor helical flow, which gives rise to chiroptical phenomenology according to models proposed by Kauzmann, 65 can take place in the presence of perturbing fields parallel or orthogonal to the rotation axis. Thus, the behavior of leucoindigo is analogous to that occurring in simpler molecules like hydrogen peroxide, hydrazine and boranylborane 36,37 …”

“…The SI units are used throughout. Electronic operators are denoted as in previous papers, 36,37 for example, for total canonical momentum , and for electric and magnetic dipoles, …”

“…The second‐rank tensor operator corresponding to the magnetic quadrupole is defined by and its antisymmetric part constitutes the paramagnetic contribution to the parity‐odd, time‐odd, anapole vector operator, 36,37 …”

“…On the other hand, different mechanisms seem to be responsible for the lack of optical rotatory power in simple molecules, for example, hydrogen peroxide and hydrazine, where vanishing values of components and trace of chiral tensors have been predicted in theoretical calculations for configurations corresponding to dihedral angles at which geometrical chirality is not disputable: achirality is to attributed to physical reasons 36,37 …”

Electronic Currents and Anapolar Response Induced in Molecules by Monochromatic Light

“…A time-independent magnetic field induces toroidal electron flow in chiral molecules [1][2][3][4][5][6][7][8], giving rise to a static toroidal moment, which can be represented by a vector odd under charge conjugation C, parity P and time reversal T. The optical fields associated with a beam of monochromatic light, oscillating with frequency ω, also induce the anapolar response, which can be rationalized in terms of dynamic anapole polarizabilities and magnetizabilities [9].…”