compared‎ ‎two models‎ ‎for shifted the gap energy in acenes; quantum perturbation theory and topological indices

‎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.