The topological way—A new methodology to construct symmetric sets of valence-bond structures

Classical valence bond (VB) theory has advanced significantly in recent years, evolving into a quantitative tool comparable to molecular orbital-based methods. A key advantage of VB is its high interpretability through Lewis-like resonance structures. However, traditional VB theory faces challenges with symmetric systems, as it often fails to generate symmetric sets of structures, leading to a loss of wavefunction interpretability. In this work, we extend the chemical insight approach and present a method for constructing symmetric VB sets. Rather than relying on conventional symmetry techniques, our method is predominantly based on topological information. It utilizes molecular geometry and connectivity and integrates scoring criteria for atoms, bonds, and structures. This approach enables the classification of VB structures into symmetry-adapted subsets guided by chemical intuition and topological features. We have successfully applied this method to a variety of molecular systems, demonstrating its ability to generate symmetric VB sets even in cases where traditional Rumer rules fail. These advancements contribute meaningfully to the interpretability of VB wavefunctions, marking a significant step forward in the development of VB theory.