QSym²: A Quantum Symbolic Symmetry Analysis Program for Electronic Structure.

Area of Science:

• Quantum Chemistry
• Computational Chemistry
• Group Theory Applications

Background:

• Contemporary quantum chemistry packages struggle with degeneracy and symmetry breaking, particularly in non-Abelian groups.
• Characterizing symmetry in the presence of external magnetic or electric fields is a significant challenge.
• Existing tools lack comprehensive symmetry analysis capabilities for complex quantum systems.

Purpose of the Study:

• Introduce QSym², a novel Rust program for detailed symmetry analysis in quantum chemistry.
• Address the limitations of current software in handling degeneracy, symmetry breaking, and external field effects.
• Provide a versatile tool for interpreting quantum-mechanical theories and results through symmetry.

Main Methods:

• Utilizes group and representation theories for symmetry analysis.
• Employs a generic symmetry-orbit-based representation analysis method.
• Generates character tables symbolically on-the-fly for flexible application.

Main Results:

• QSym² successfully analyzes degenerate molecular orbitals (MOs) in high-symmetry molecules (C84H64, C60, B9⁻).
• Demonstrates analysis of symmetry-broken determinants and MOs for octahedral Fe(CN)6³⁻.
• Illustrates magnetic symmetry analysis for linear hydrogen fluoride in a magnetic field.
• Shows density symmetry analysis for equilateral H3⁺.

Conclusions:

• QSym² effectively overcomes limitations in current quantum chemistry software regarding symmetry analysis.
• The program provides robust tools for understanding complex symmetry behaviors in various quantum chemical scenarios.
• QSym² enhances the interpretation of quantum mechanical results through advanced symmetry characterization.