Iranian Journal of Mathematical Chemistry
Volume:10 Issue: 1, Winter 2019

Rhombellanes are mathematical structures existing in various environments, in crystal or quasicrystal networks, or even in their homeomorphs, further possible becoming real molecules. Rhombellanes originate in the K2.3 complete bipartite graph, a tile found in the linear polymeric staffanes. In close analogy, a rod-like polymer derived from hexahydroxy-cyclohexane was imagined. Further, the idea of linear polymer synthesized from dehydro-adamantane was extended in the design of a three-dimensional crystal network, named dia(s), of which tile is a hyper-adamantane (an adamantane of which vertices are just adamantanes). It was suggested that this network could be synthesized starting from the real molecule tetrabromo-adamantane, by dehydrogenation and polymerization. The crystal structures herein proposed were characterized by connectivity and ring surrounding sequences and also by the Omega polynomial.

A C4C8 net is a trivalent decoration made by alternating squares C4 and octagons C8. It can cover either a cylinder or a torus. In this paper, we study the adjacency spectrum of rhomboidal C4C8 tori. We also give lower and upper bounds for a chemical quantity, namely Estrada index, for a C4C8 net.

In this study, the insecticidal activity against Cowpea aphids (Aphis craccivora) of a series of 23 phenylazo, pyrrole-, dihydropyrrole-fused and chain-opening nitromethyleneneonicotinoids was evaluatedby using the multiple linear regression (MLR) and pharmacophore modelling. Conformer insecticide ensembles were modeled using the MMFF94s force field. Minimum energy conformers were employed to calculate structural parameters, which were related to the experimental pLC50 values. Several statistical criteria of goodness of fit and predictivity were checked to validate the models. Robust and predictable MLR models were obtained. Further, the Phase module from Schrodinger suite was engaged in the generation of the ligand-based pharmacophore models. The atom-based 3D-QSAR module from the aforementioned software was used for the validation of a best four-point pharmacophore model. The obtained significant statistical parameters attested thepharmacophore model validity. The MLR and pharmacophore models are useful for the prediction of new insecticides with activity against Cowpea aphids.

A spongy hypercube is a Cartesian product of a d-connected polyhedral graph and a k-dimensional hypercube‎. ‎The aim of this paper is to compute the energies of signed spongy hypercubes T□□(Q_k ) and O□□(Q_k )‎, ‎where T and O are tetrahedron and octahedron‎, ‎respectively‎.

Fullerenes have wide application in various fields including electronic and optic, medical science, biotechnology and have received a lot of recent chemists and mathematicians’ attention. Due to many applications of fullerenes, the study of their stability is important. In this paper, we study the effective parameters that affect the fullerene's stability and then according to these parameters, we introduce a new function to examine the stability of every fullerene. By using this function, we determine the stable isometric of each fullerene in a unique way.

Aromaticity is used to describe the durability and reactivity of structures containing delocalized  electrons.In this review article, the aromaticity of fullerenes patched with flowers of 6-and 8-membered ringsis discussed, optimized at the HF and DFT levels of theory, in terms of HOMA and NICS criteria. The aromatic character of these nanostructures allows for functionalization and finally for increasing their solubility in polar solvents. The overall conclusion is that several of the yet hypothetical molecular nanostructures herein described are serious candidates for new medicinal products, as a proposal for personalized medicine.