The remarkable design potential of two-dimensional (2D) polymers has attracted considerable interest due to their wide range of geometric and topological possibilities. Lattice topology and layer stacking collectively influence the distinct properties and potential applications of 2D polymers. A thorough study of these factors is essential for a comprehensive understanding. The thesis focuses on the most common structural types of 2D polymers with square and hexagonal pores, which are readily available by many experimental methods. I will detail my investigation into how lattice topology and fine structural features influence the electronic properties and crystal structure of 2D polymers, which often deviate significantly from the current understanding. Lattice topology crucially influences the stability, electronic, and topological properties of 2D polymers. Various lattice topologies represent intriguing electronic features, e.g. Dirac cones appearing in kagome (kgm), hcb, fes and Lieb lattices, and flat bands in kgm and Lieb. Among these, the Lieb lattice stands out as one of the most intriguing topologies, characterized by both Dirac cones and flat bands which intersect at the Fermi level. However, materials with Lieb lattice remain experimentally unreached. In Chapter 3, I explore 2D polymers derived from zinc-phthalocyanine (ZnPc) building blocks with a square lattice (sql) as potential electronic Lieb lattice materials. By systematically varying the linker lengths (ZnPc-xP), I found that some ZnPc-xP exhibit a characteristic Lieb lattice band structure. Interestingly though, fes bands are also observed in ZnPc-xP, including locally flat bands and Dirac cones. The coexistence of fes and Lieb in sql 2D polymers challenges the conventional perception of the structure-electronic structure relationship. In addition, I show that manipulation of the Fermi level effectively preserves the unique characteristics of Lieb bands. Chern number calculations confirm the non-trivial nature of the Lieb Dirac bands. The inherent disorder in the stacking of layered covalent organic frameworks (COFs), invalidating standard theoretical three-dimensional (3D) models, makes determining their exact structure challenging. In Chapter 4, I represent the structures of COF-1, COF-5, and ZnPc-pz by stacking layers following the Maxwell–Boltzmann energy distribution of their stacking modes. The simulated PXRD patterns of the statistical COF models are close to the experimental ones, featuring an unprecedented agreement in peak intensity, width, and asymmetry, far exceeding current state-of-the-art. The rarely considered ABC stacking mode proves important in layered COFs, as well as including solvent molecules. Our model also reveals several general features in PXRD originating from the stacking disorder. In Chapters 5 and 6, I apply methods developed in Chapter 4 to determine the structure and electronic properties of newly synthetized materials in collaboration with experimental colleagues. The investigation of the statistical model used in structures of Ni3(HATI_CX)2, TpEtBr, TpDPP, TpTab, and TpTta offers further examples. The statistical models provide improved agreement with experimental PXRD patterns. Chapter 7 then demonstrates the application of the statistical to investigate defects in 2D polymer structure. In particular, interstitial defects in form of unreacted molecules between layers impact high-resolution transmission electron microscopy (HRTEM) images, inducing unexpected bright points, which are accurately reproduced by the statistical model.

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