Atomic Charge Chirality from Electric Multipoles
Abstract
We establish an electric-multipole (Qlm) criterion for chirality of local atomic charge distributions. For the 11 crystallographic chiral point groups, we identify representative lowest-rank multipole contents required to distinguish the opposite handednesses. For the axial groups Cn and Dn with n=2,3,4,6, chirality arises from the relative orientation of two azimuthal anisotropies with m=n, belonging to consecutive ranks l=n and n+1. Their coexistence produces a latitude-dependent twist of the n-fold charge distribution. The polar component, although allowed in Cn, is distinct from this chiral mechanism and is not required for handedness. The cubic groups T and O exhibit distinct realizations, with octahedral chirality first appearing at rank nine. We further show that, within a spinless s-p-d-f atomic basis, the scalar charge density contains multipoles only up to rank six and therefore cannot encode the handedness of C6, D6, or O. These results connect electric-multipole content and atomic orbital degrees of freedom to the microscopic encoding of crystallographic handedness.
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BibTeX
@misc{hayami2026atomic,
title = {{Atomic Charge Chirality from Electric Multipoles}},
author = {Satoru Hayami and Rikuto Oiwa},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.39150},
eprint = {2610.39150},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.39150},
}
RIS
TY - UNPB
TI - Atomic Charge Chirality from Electric Multipoles
AU - Satoru Hayami
AU - Rikuto Oiwa
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2610.39150
UR - https://arxiv.org/abs/2610.39150
AB - We establish an electric-multipole (Q_lm) criterion for chirality of local atomic charge distributions. For the 11 crystallographic chiral point groups, we identify representative lowest-rank multipole contents required to distinguish the opposite handednesses. For the axial groups C_n and D_n with n=2,3,4,6, chirality arises from the relative orientation of two azimuthal anisotropies with m=n, belonging to consecutive ranks l=n and n+1. Their coexistence produces a latitude-dependent twist of the n-fold charge distribution. The polar component, although allowed in C_n, is distinct from this chiral mechanism and is not required for handedness. The cubic groups T and O exhibit distinct realizations, with octahedral chirality first appearing at rank nine. We further show that, within a spinless s-p-d-f atomic basis, the scalar charge density contains multipoles only up to rank six and therefore cannot encode the handedness of C_6, D_6, or O. These results connect electric-multipole content and atomic orbital degrees of freedom to the microscopic encoding of crystallographic handedness.
ER -