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Molecular graphs and molecular conduction: the d-omni-conductors
Patrick W Fowler1, Martha Borg1, Barry T Pickup1
1Department of Chemistry, University of Sheffield, Sheffield, S3 7HF, UK. P.W.Fowler@sheffield.ac.uk B.T.Pickup@sheffield.ac.uk msmarthaborg@gmail.com.
This study classifies molecular graph conduction properties using the source-and-sink-potential (SSP) model. It introduces d-omni-conduction/insulation for classifying electron transport in molecular systems.
Area of Science:
- Quantum Chemistry
- Materials Science
- Condensed Matter Physics
Background:
- The source-and-sink-potential (SSP) model describes ballistic electron conduction in conjugated π systems.
- Molecular graphs and their subgraphs' characteristic polynomials determine electron transmission.
- Previous work defined near-omni-conduction/insulation for bipartite graphs.
Purpose of the Study:
- To provide a comprehensive classification of conduction properties for all molecular graphs within the SSP model.
- To generalize the concept of omni-conduction/insulation to all graphs.
- To establish a systematic method for predicting molecular conduction behavior.
Main Methods:
- Utilizing the SSP model to analyze electron transmission through molecular graphs.
- Defining d-omni-conduction/insulation based on Fermi-level behavior for varying graph distances (d).
- Classifying molecular graphs by nullity and a three-letter code (C, I, X) representing conduction behavior at different distances.
Main Results:
- A complete classification of conduction properties for all molecular graphs under the SSP model is presented.
- The study defines d-omni-conduction/insulation, generalizing previous concepts.
- 35 out of 81 possible nullity and code combinations are exemplified with graphs, and 42 non-existent combinations are proven.
Conclusions:
- The developed classification scheme provides a robust framework for understanding molecular conduction.
- The nullity class and compact code offer a predictive tool for electronic properties of molecular systems.
- Four classification cases remain open, suggesting avenues for future research.
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