QSym²: A Quantum Symbolic Symmetry Analysis Program for Electronic Structure

Huynh, Bang; Wibowo-Teale, Meilani; Wibowo-Teale, Andrew

Abstract

Symmetry provides a powerful machinery to classify, interpret, and understand quantum-mechanical theories and results. However, most contemporary quantum chemistry packages lack the ability to handle degeneracy and symmetry breaking effects, especially in non-Abelian groups, nor are they able to characterize symmetry in the presence of external magnetic or electric fields. In this article, a program written in Rust entitled QSym² that makes use of group and representation theories to provide symmetry analysis for a wide range of quantum-chemical calculations is introduced. With its ability to generate character tables symbolically on-the-fly, and by making use of a generic symmetry-orbit-based representation analysis method formulated in this work, QSym² is able to address all of these shortcomings. To illustrate these capabilities of QSym², four sets of case studies are examined in detail in this article: (i) high-symmetry C_{84}H_{64}, C_{60}, and B_9^– to demonstrate the analysis of degenerate molecular orbitals (MOs); (ii) octahedral Fe(CN)_6^{3–} to demonstrate the analysis of symmetry-broken determinants and MOs; (iii) linear hydrogen fluoride in a magnetic field to demonstrate the analysis of magnetic symmetry; and (iv) equilateral H_3^+ to demonstrate the analysis of density symmetries.

• Journal Article Type: Article
• Acceptance Date: Nov 29, 2023
• Online Publication Date: Dec 25, 2023
• Publication Date: Jan 9, 2024
• Deposit Date: Dec 8, 2023
• Publicly Available Date: Dec 26, 2024
• Journal: Journal of Chemical Theory and Computation
• Print ISSN: 1549-9618
• Electronic ISSN: 1549-9626
• Publisher: American Chemical Society
• Peer Reviewed: Peer Reviewed
• Volume: 20
• Issue: 1
• Pages: 114-133
• DOI: https://doi.org/10.1021/acs.jctc.3c01118
• Public URL: https://nottingham-repository.worktribe.com/output/28151556
• Publisher URL: https://pubs.acs.org/doi/10.1021/acs.jctc.3c01118