Compared‎ ‎Two Models‎ ‎for Shifted the Gap Energy in Acenes; Quantum Perturbation Theory and Topological Indices

Document Type : Research Paper

Authors

1 Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran

2 Department of Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares University, Tehran, Iran

Abstract

‎Acenes‎, ‎which can be represented by the chemical formula $C_{4n+2} H_{2n+4}$‎, ‎belong to a group of organic molecules that have attracted significant attention in the fields of electronic molecules and nanoscale research‎. ‎Investigating their electronic and optical properties‎, ‎particularly for larger acenes‎, ‎is a highly resource-intensive and time-consuming endeavor‎. ‎The objective of this study is to propose a novel approach for analyzing changes in the energy gap using quantum perturbation theory and disorder theory‎, ‎relying on topological indices‎. ‎In order to quantify the alterations in the energy gap‎, ‎the Hamiltonian matrix of spin-orbit interaction‎, ‎based on quantum perturbation theory‎, ‎has been utilized‎. ‎Consequently‎, ‎the changes in the energy gap between singlet and triplet states‎, ‎denoted as $E_g$‎, ‎have been computationally determined for the carbon-carbon bonds‎. ‎Ultimately‎, ‎a comprehensive model has been developed to illustrate the variations in the energy gap between singlet and triplet spin states of linear acenes‎, ‎incorporating the concept of topological indices.

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References

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Iranian Journal of Mathematical Chemistry
Volume 15, Issue 3
September 2024
Pages 189-201

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