A density-based continuous local symmetry measure.

Area of Science:

• Quantum Chemistry
• Computational Chemistry
• Chemical Physics

Background:

• Continuous symmetry theory is gaining traction in chemistry.
• Local symmetry and its relationship to chemical behavior are under-investigated.
• Existing symmetry measures have limited practical applications due to obscured structure-property relationships.

Purpose of the Study:

• To introduce a novel framework for evaluating local symmetry.
• To develop continuous symmetry representations for molecules.
• To explore local chirality (chirotopicity) and its relation to local symmetry.

Main Methods:

• Developing a new framework for local symmetry evaluation.
• Utilizing electron density localization as a basis for symmetry measures.
• Applying continuous symmetry representations to representative molecules.

Main Results:

• The novel framework quantitatively captures global symmetry.
• Distinctive local symmetry features within the chemical environment are revealed.
• The study presents continuous symmetry representations for various molecules.

Conclusions:

• The proposed local symmetry measures offer valuable insights into molecular structure.
• The framework enhances understanding of structure-property relationships.
• Local chirality and its connection to local symmetry are discussed.