Fragment Molecular Orbital Configuration Interaction Methodology for the Description of Correlated States in Extended Molecular Aggregates

This thesis explores the theoretical and computational study of singlet fission in perylene diimide (PDI), perylene, and B-N-substituted perylene aggregates, with a focus on understanding and optimizing electronic interactions and pathways. Beginning with an introduction to singlet fission and its theoretical foundations, the work employs advanced quantum mechanical methods, including active space decomposition, semi-empirical approaches, CASPT2, and TDDFT, to investigate diabatic couplings, singlet fission rates in dimers, and singlet and triplet exciton energies. Subsequent work includes the development of a configuration interaction methodology for analyzing diabatic Hamiltonian elements in polymer aggregates. This approach incorporates symbolic algebra to automate the generation of analytical expressions for matrix elements in ab initio configuration interaction calculations. Using second quantization and the Jordan-Wigner transformation, fermionic operators are represented as Kronecker products of Pauli matrices, implemented with SymPy. This facilitates the symbolic generation of spin-adapted Slater determinants and Hamiltonian matrix elements, enabling detailed fragment analysis and the simulation of electron transport in complex molecular systems. The resulting programs efficiently compute molecular properties. Further studies extend the application of this model to the analysis of PDI trimers, providing a deeper understanding of electronic structures and improved singlet fission efficiency. The research introduces novel mechanisms for singlet fission and addresses the limitations of dimer models by generalizing them to incorporate separated Charge Transfer (C...T) states, \( ^{1}(T...T) \) states, and mixed triplet-charge transfer states. Analytical expressions for diabatic matrix elements are derived, enhancing the understanding of constructively and destructively interfering singlet fission pathways and electronic couplings.