Recursion Equations in Polycyclic Hydrocarbon Series and the Number of Dewar Long-Bond Resonance Structures with...

Area of Science:

• Theoretical Chemistry
• Organic Chemistry
• Mathematical Chemistry

Background:

• Polycyclic polyenes exhibit complex electronic properties influencing their stability and reactivity.
• Resonance theory is crucial for understanding aromaticity and stabilization energy in conjugated systems.
• Previous studies often focused on Kekulé structures, potentially overlooking contributions from other resonance forms.

Purpose of the Study:

• To derive fundamental recursion equations for characteristic and matching polynomials.
• To investigate the role of Dewar resonance structures (DS) in polycyclic polyene series.
• To establish a comprehensive method for evaluating resonance energy and aromaticity.

Main Methods:

• Derivation of basic recursion equations for polynomials and Dewar resonance structures.
• Analysis of Fibonacci-like number series in analytical expressions for resonance energy.
• Comparison of topological resonance energy (TRE) and topological conjugation energy (TCE).

Main Results:

• Fibonacci-like sequences frequently appear in resonance energy calculations for polycyclic polyenes.
• Polycyclic polyenes with fixed pπ bonds exhibit aromatic stabilization due to aromatic circuits in Dewar structures.
• Including both Dewar and Kekulé structures provides a more accurate assessment of relative resonance energy and aromaticity.

Conclusions:

• The study provides a systematic approach to understanding resonance phenomena in polycyclic polyenes.
• Dewar resonance structures are essential for accurate valence-bond determinations of aromaticity.
• Topological conjugation energy remains consistent across different bonding scenarios, highlighting its robustness.