QSym: A Quantum Symbolic Symmetry Analysis Program for Electronic Structure.

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, and they are not able to characterize symmetry in the presence of external magnetic or electric fields. In this article, a program written in Rust entitled QSym 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, QSym is able to address all of these shortcomings. To illustrate these capabilities of QSym, four sets of case studies are examined in detail in this article: (i) high-symmetry CH, C, and B to demonstrate the analysis of degenerate molecular orbitals (MOs); (ii) octahedral Fe(CN) 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 to demonstrate the analysis of density symmetries.