Algorithms for computer detection of symmetry elements in molecular systems.

Area of Science:

• Computational Chemistry
• Molecular Symmetry
• Quantum Chemistry

Background:

• Accurate determination of molecular symmetry is crucial for understanding chemical properties and reactivity.
• Traditional methods for identifying symmetry elements can be computationally intensive, especially for large molecules.

Purpose of the Study:

• To develop simple and computationally efficient procedures for locating proper and improper rotation and reflection planes in molecules.
• To introduce a method that leverages subsets of symmetrically equivalent atoms (SEA) for symmetry analysis.

Main Methods:

• The proposed method analyzes subsets of symmetrically equivalent atoms (SEA) as individual molecular units.
• It utilizes interatomic distances and the inertia tensor of SEA to identify symmetry elements.
• The algorithms are designed to be invariant to molecular orientation, reducing computational cost.

Main Results:

• The approach effectively identifies proper and improper rotations and reflection planes.
• For symmetric rotors, SEA properties directly reveal rotational symmetry.
• A Fortran implementation successfully identified all 120 symmetry operations for fullerene C720 (Ih point group) in seconds.
• The method demonstrated the ability to symmetrize the geometry of slightly unsymmetrical molecules using interatomic distance matrices.

Conclusions:

• This SEA-based approach offers a computationally efficient and straightforward way to determine molecular symmetry.
• The method is applicable to a wide range of molecules, including large and highly symmetrical ones.
• It provides a practical tool for computational chemistry, aiding in structural analysis and property prediction.