Six dodecahedrane assemblies as multiple of five and respectively six structures were constructed and investigated from the topological point of view. The investigation was conducted using characteristic polynomials, graph invariant encoding important properties of the graph of the chemical structure. The assemblies of 5, 6, 15 and 25 dodecahedranes proved to have the center in the same plane while the assemblies of 12 and 24 dodecahedranes degenerated from the planar central form to a chair conformation. Generally, the number of real roots of characteristic polynomials is equal to the number of atoms in the assembly. The obtained roots of the characteristic polynomial were split into intervals and the frequency apparition spectra were simulated. The obtained spectra were used to investigate the behavior of investigated assembly.
TopIntroduction
A special attention has been done to carbon-based nanostructure as nanotechnology perspective (Poma & Di Giorgio, 2008; Soldano, 2015). Nanotechnology is a scientific filed used in diverse scientific domains such as neuro- (Ajetunmobi et al., 2014; Pineda, Han, & Ostrikov, 2014) and medical sciences (Park & Im, 2015), pharmacology (Mattheolabakis, Rigas, & Constantinides, 2012; Mostafalou, Mohammadi, Ramazani, & Abdollahi, 2013; Osmani et al., 2014), materials science (Zhang & Su, 2014; Zhong, Zhang, Sun, & Lee, 2014), physics (Cole et al., 2010; Gokhale & Lee, 2014), chemistry (Acharya, Samanta, & Rao, 2012; Afreen, Muthoosamy, Manickam, & Hashim, 2015), engineering (Bai & Liu, 2012; Palmer, Robinson, & Guo, 2013), etc. being in fact a multidisciplinary field with wide application in all scientific domains.
Carbon nanoscience, a discipline that study the properties of carbon entities at nanoscale level, become a research field of itself. The experiments are also conducted in virtual laboratories to characterize nanoscale materials from structural, mechanical and optical point of view (Ramezani-Dakhel, Ruan, Huang, & Heinz, 2015; Schatz, 2007).
In the present work, several congeners of dodecahedrane complexes are introduced. The stable structures of dodecahedrane nano-congeners had been identified and characterized using characteristic polynomials.