Quantifying the Chirality of Vibrational Modes in Helical Molecular Chains

TL;DR

This study quantifies the chirality of vibrational modes in helical molecular chains using two methods, revealing how twist influences mode chirality and its potential impact on physical phenomena like thermal chirality.

Contribution

It introduces two approaches for quantifying vibrational mode chirality in helical molecules and analyzes how molecular twist affects this property.

Findings

Increasing twist raises the CCM of normal modes, linking mode chirality to molecular structure.

Twisting induces asymmetry in normal mode handedness, affecting frequency band characteristics.

Normal mode chirality correlates strongly with the molecular structure's chirality.

Abstract

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.