Molecules 2014, 19, 15468-15506; doi:10.3390/molecules191015468 OPEN ACCESS molecules ISSN 1420-3049 www.mdpi.com/journal/molecules Review Quantum-Mechanical Calculations on Molecular Substructures Involved in Nanosystems Beata Szefler 1 and Mircea V. Diudea 2,* 1 Department of Physical Chemistry, Collegium Medicum, Nicolaus Copernicus University, Kurpińskiego 5, Bydgoszcz 85-096, Poland 2 Faculty of Chemistry and Chemical Engineering, Babes-Bolyai University, Arany Janos street 11, Cluj-Napoca RO-400028, Romania * Author to whom correspondence should be addressed; E-Mail:
[email protected]; Tel.: +40-264-593-833; Fax: +40-264-590-818. External Editor: Mihai V. Putz Received: 2 July 2014; in revised form: 21 August 2014 / Accepted: 10 September 2014 / Published: 26 September 2014 Abstract: In this review article, four ideas are discussed: (a) aromaticity of fullerenes patched with flowers of 6-and 8-membered rings, optimized at the HF and DFT levels of theory, in terms of HOMA and NICS criteria; (b) polybenzene networks, from construction to energetic and vibrational spectra computations; (c) quantum-mechanical calculations on the repeat units of various P-type crystal networks and (d) construction and stability evaluation, at DFTB level of theory, of some exotic allotropes of diamond D5, involved in hyper-graphenes. The overall conclusion was that several of the yet hypothetical molecular nanostructures herein described are serious candidates to the status of real molecules. Keywords: ab initio; HOMA; NICS; nanotube junction; circulene; fullerene; polybenzene; periodic network; vibrational spectra 1. Introduction Among the carbon allotropes discovered in the nano-era, fullerenes (zero-dimensional), nanotubes (one dimensional), graphene (two dimensional), spongy carbon and hyper-diamonds (three dimensional) are the most challenging [1–3].