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This review article highlights recent developments in symmetry, combinatorics, topology, entropy, chirality, spectroscopy and thermochemistry pertinent to 2D and 1D nanomaterials such as circumscribed-cyclopolyarenes and their heterocyclic analogs, carbon and heteronanotubes and heteronano wires, as well as tessellations of cyclopolyarenes, for example, kekulenes, septulenes and octulenes. We establish that the generalization of Sheehan’s modification of Pólya’s theorem to all irreducible representations of point groups yields robust generating functions for the enumeration of chiral, achiral, position isomers, NMR, multiple quantum NMR and ESR hyperfine patterns. We also show distance, degree and graph entropy based topological measures combined with techniques for distance degree vector sequences, edge and vertex partitions of nanomaterials yield robust and powerful techniques for thermochemistry, bond energies and spectroscopic computations of these species. We have demonstrated the existence of isentropic tessellations of kekulenes which were further studied using combinatorial, topological and spectral techniques. The combinatorial generating functions obtained not only enumerate the chiral and achiral isomers but also aid in the machine construction of various spectroscopic and ESR hyperfine patterns of the nanomaterials that were considered in this review. Combinatorial and topological tools can become an integral part of robust machine learning techniques for rapid computation of the combinatorial library of isomers and their properties of nanomaterials. Future applications to metal organic frameworks and fullerene polymers are pointed out. Full article

The iron doped tungsten-oxide (Fe and WO₃) thin film with different morphology and crystalline structures were obtained for different substrate temperatures at the oxygen pressure of 14.66 Pa. The Fe-doped WO₃ films were deposited by pulsed laser deposition (PLD). The influence of the substrate temperature on the surface and on the crystalline phases of the films was studied. The XRD (X-ray diffraction) analysis indicates the changing in the crystalline phases from γ-monoclinic to a mixture of γ-monoclinic and hexagonal phases dependent on the temperature of annealing and as-grown films. Related to the as-grown and annealing films conditions, the SEM (scanning electron microscopy) shows a change in the image surface from nanoneedles, to nanoporous, and further to long nanowires and broad nanobands. Energy-dispersive X-ray spectroscopy (EDX) shows the elemental composition of the Fe-doped WO₃ film as-grown and after annealing treatment. Raman spectroscopy presented the main vibration mode of the Fe-doped WO₃ thin film. The optical energy bandgap of the films is decreasing as the substrate temperature increases. Full article