Quantification of chirality based on electric toroidal monopole

• Published in: The Journal of chemical physics Vol. 160; no. 18
• Main Authors: Inda, A., Oiwa, R., Hayami, S., Yamamoto, H. M., Kusunose, H.
• Format: Journal Article
• Language: English
• Published: United States American Institute of Physics 14.05.2024
• Subjects: Chirality; Hydrogen atoms; Methane; Spin-orbit interactions; Wave functions
• ISSN: 0021-9606; 1089-7690; 1089-7690
• DOI: 10.1063/5.0204254

Chirality ubiquitously appears in nature; however, its quantification remains obscure owing to the lack of microscopic description at the quantum-mechanical level. We propose a way of evaluating chirality in terms of the electric toroidal monopole, a practical entity of time-reversal even pseudoscalar (parity-odd) objects reflecting relevant electronic wave functions. For this purpose, we analyze a twisted methane molecule at the quantum-mechanical level, showing that the electric toroidal monopoles become a quantitative indicator for chirality. In the twisted methane, we clarify that the handedness of chirality corresponds to the sign of the expectation value of the electric toroidal monopole and that the most important ingredient is the modulation of the spin-dependent imaginary hopping between the hydrogen atoms, while the relativistic spin–orbit coupling within the carbon atom is irrelevant for chirality.