Compared Two Models for Shifted the Gap Energy in Acenes; Quantum Perturbation Theory and Topological Indices
نویسندگان
1 Department of Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares University, Tehran, Iran
2 Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran
doi
10.22052/ijmc.2024.254055.1804چکیده
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.
