The "anthracene problem": closed-form conjugated-circuit models of ring currents in linear polyacenes

Area of Science:

• Theoretical Chemistry
• Computational Chemistry
• Quantum Chemistry

Background:

• Induced π ring currents are crucial for understanding aromaticity and electronic properties of molecules.
• Existing conjugated-circuit models vary in their inclusion of circuits and weighting schemes.
• The choice of circuits in these models can be represented using graph theory.

Purpose of the Study:

• To analyze and compare different conjugated-circuit models for induced π ring currents.
• To derive and apply closed-form solutions for linear polyacenes.
• To assess the predictive accuracy of these models against ab initio calculations.

Main Methods:

• Development of a graph-matching approach for selecting circuits in π systems.
• Derivation of closed-form solutions for conjugated-circuit models applied to linear polyacenes.
• Comparison of model predictions with ipsocentric ab initio, pseudo-π, and Hückel-London methods.

Main Results:

• All analyzed models predict the most intense perimeter current in the central rings of linear polyacenes.
• The models provide simple closed-form solutions for these systems.
• A tendency for models to overestimate the rate of increase in central ring current with system size (N) was observed.

Conclusions:

• Conjugated-circuit models offer valuable insights into induced π ring currents, particularly regarding current distribution.
• Despite variations in assumptions, models consistently identify central rings as having the strongest perimeter currents.
• Further refinement is needed to match the accuracy of advanced molecular orbital treatments for quantitative predictions.