Algebraic Method for Solving Multiple Degenerate Eigenvalues in [r]Triangulenes.

Area of Science:

• Organic Chemistry
• Theoretical Chemistry
• Quantum Chemistry

Background:

• Molecular graphs, particularly triangulenes, present challenges in eigenvalue determination due to degeneracy.
• Understanding the electronic structure of polyradicals is crucial in chemical research.

Purpose of the Study:

• To develop an algebraic procedure to resolve multiple degeneracy in eigenvalue determination for 3-fold symmetrical molecular graphs.
• To tabulate Hückel molecular orbital binding energies and eigenvalues for [2]triangulene to [9]triangulene.

Main Methods:

• An algebraic procedure was developed to address the multiple degeneracy problem.
• Characteristic polynomial eigenvalues were determined for a series of triangulenes.

Main Results:

• The study successfully tabulated Hückel molecular orbital binding energies (Eπ) and eigenvalues for [2]triangulene to [9]triangulene.
• This marks the first time these specific electronic properties have been systematically documented.

Conclusions:

• The developed algebraic method is effective for solving degeneracy issues in eigenvalue calculations for symmetrical molecular graphs.
• The findings provide fundamental electronic data for triangulenes, the smallest condensed benzenoid polyradicals.