What Are the Structures of the Octet Rule Obeying All-Carbon Species Cx (2 ≤ x ≤ 7 and Larger x)?: A Pedagogical, Mathematical, and Pictorial Study

What Are the Structures of the Octet Rule Obeying All-Carbon Species Cx (2 ≤ x ≤ 7 and Larger x)?: A Pedagogical, Mathematical, and Pictorial Study

Kori D. McDonald (University of Maryland – Baltimore County (UMBC), USA), Evelyn O. Ojo (University of Maryland – Baltimore County (UMBC), USA) and Joel F. Liebman (University of Maryland – Baltimore County (UMBC), USA)
Copyright: © 2017 |Pages: 45
DOI: 10.4018/978-1-5225-0492-4.ch001
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Abstract

With most carbon structures still unknown and undiscovered, it becomes increasingly important to find a way to discover, characterize, and understand them. This paper discusses the possible structures for all-carbon species in which each carbon obeys the octet rule. The number and structural diversity of such compounds strongly increases with the number of carbons: C2, 1; C3, 1; C4, 3; C5, 6; C6, 15. Only some of the C7 species were drawn -- merely 23 isomers were given. To guarantee structural uniqueness, names and visual inspection appear to be insufficient. Instead, a new method, using the eigenvalues and eigenvectors of the structure's adjacency matrix and modified matrices, was introduced and then employed. With this we hoped to gain a better understanding of what was chemically reasonable and realizable for our produced structures.
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Introduction

Compounds of Carbon

With its most common valence of covalence of 4, and generally participating with both strong σ and π bonds, carbon forms compounds that exhibit an exceptionally wide range of structural possibilities. A simple perusal of any study of organic compounds documents this diversity: indeed, the adjective “organic” before the noun “compounds” tells us explicitly that there is carbon present and most generally so is hydrogen.

Organic Chemistry in the Absence of Hydrogen

Even should hydrogen be absent, classes of species known as chlorocarbons, cyanocarbons (and other types of carbon nitrides), fluorocarbons, nitrocarbons and oxocarbons (and other types of carbon oxides) are well-represented in the chemical literature. Examples for CnXm include X = Cl, CCl4 (carbon tetrachloride), C19Cl15 = (C6Cl5)3C (perchlorotriphenylmethyl radical and the corresponding anion and cation) (Butin, Mohammed, & Reutov, 1978) and C60Cl30 (a “fullerene chloride”) (Papina, Luk'yanova, Troyanov, Chelovskaya, Buyanovskaya, & Sidorov, 2007); X = CN and N, [C20N8]2- = {C4[CC(CN)2]4}2-(octacyano[4]radialene dianion, and related radical anion (Blinka & West, 1983), and C3N12 = C3N3(N3)3 (cyanuric triazide (Ott& Ohse, 1921)); X = F, C2F4 (tetrafluoroethylene and its polymer PTFE (Teflon®), C6(CF3)6 (hexakis(trifluoromethyl)prismane) and its benzene and Dewar benzene valence isomers (Lemal& Dunlap, 1972); X = NO2, C2(NO2)2 (dinitroacetylene, known as a cobalt carbonyl, i.e., Co2(CO)6 complex (Windler, Zhang, Zitterbart, Piggoria, & Vollhardt, 2012) but not yet the free nitrocarbon), C8(NO2)8 (octanitrocubane) (Zhang, Eaton, & Gilardi, 2000) and C12(NO2)10 = [C6(NO2)5]2, (decanitrobiphenyl) (Nielsen, Norris, Atkins, & Vuono, 1983); X = O, CO2 and [CO3]2- (the nearly ubiquitous carbon dioxide and carbonate), C7O2 (heptahexaenedione) (Maier, Reisenauer, & Ulrich, 1991) and C12O9 = C6[C(O)OC(O)]3 (mellitic trianhydride) (Adamson & Rees, 1996) respectively. There are even a “few” bromocarbons such as C4Br4 (tetrabromobutatriene) (Liu, Li, Webb, Zhang, & Goroff, 2004), iodocarbons such as C6I6 (hexaiodobenzene (Sagl & Martin, 1988),its radical cation (Molski,et al., 2012) and its dication (Sagl & Martin, 1988) and carbon sulfides such as C6S6, benzotri(1,2)dithiete and its radical cation and anion (Sülzle, Beye, Fanghänel, & Schwarz, 1989) with X = Br, I and S respectively.

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