Quantifying the Chirality of Vibrational Modes in Helical Molecular Chains

Chiral phonons have been proposed to be involved in various physical phenomena, yet the chirality of molecular normal modes has not been well defined mathematically. Here we examine two approaches for assigning and quantifying the chirality of molecular normal modes in double-helical molecular wires with various levels of twist. First, associating with each normal mode a structure obtained by imposing the corresponding motion on a common origin, we apply the continuous chirality measure (CCM) to quantitatively assess the relationship between the chirality-weighted normal mode spectrum and the chirality of the underlying molecular structure. We find that increasing the amount of twist in the double helix shifts the mean normal mode CCM to drastically higher values, implying that the chirality of molecular normal modes is strongly correlated with that of the underlying molecular structure. Second, we assign to each normal mode a pseudoscalar defined as the product of atomic linear and angular momentum summed over all atoms, and we analyze the handedness of the normal mode spectrum with respect to this quantity. We find that twisting the double-chain structure introduces asymmetry between right- and left-handed normal modes so that in twisted structures different frequency bands are characterized by distinct handedness. This may give rise to global phenomena such as thermal chirality.