  Citation: Sheka, E.F. Virtual Vibrational Spectrometry of Stable Radicals—Necklaced Graphene Molecules. Nanomaterials 2022, 12, 597. https://doi.org/10.3390/nano 12040597 Academic Editor: Guang-Ping Zheng Received: 27 December 2021 Accepted: 5 February 2022 Published: 10 February 2022 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affil- iations. Copyright: © 2022 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). nanomaterials Article Virtual Vibrational Spectrometry of Stable Radicals—Necklaced Graphene Molecules Elena F. Sheka Institute of Physical Research and Technologies, Peoples’ Friendship University of Russia (RUDN University), 117198 Moscow, Russia; sheka@icp.ac.ru Abstract: The article presents results of an extended virtual experiment on graphene molecules performed using the virtual vibrational spectrometer HF Spectrodyn that exploits semiempirical Hartree–Fock approximation. The molecules are composed of flat graphene domains surrounded with heteroatom necklaces. Not existing individually, these molecules are met in practice as basic structure units of complex multilevel structure of all sp 2 amorphous carbons. This circumstance deprives the solids’ in vitro spectroscopy of revealing the individual character of basic structural elements, and in silico spectrometry fills this shortcoming. The obtained virtual vibrational spectra allow for drawing first conclusions about the specific features of the vibrational dynamics of the necklaced graphene molecules, caused by spatial structure and packing of their graphene domains as well as by chemical composition of the relevant necklaces. As shown, IR absorption spectra of the molecules are strongly necklace dependent, once becoming a distinct spectral signature of the amorphous body origin. Otherwise, Raman spectra are a spectral mark of the graphene domain’s size and packing, thus disclosing the mystery of their universal D-G-band standard related to graphene-containing materials of various origins. Keywords: virtual vibrational spectrometry; virtual spectrometer; semiempirical Hartree–Fock approximation; digital twins; necklaced graphene molecules; sp 2 amorphous carbons 1. Introduction The concept of virtual spectrometry has arisen recently, but it has turned out to be attractive and productive for placing things in order in the field of computational spectroscopy. A virtual spectrometer, as any device, is usually designed to carry out a large number of measurements. Certainly, these measurements’ accuracy is limited by the device’s technical characteristics. Whatever these characteristics are, there will always be reasons for their inconsistency, with some specific requirement of a real experiment. Underlying computational software determines the technical characteristics of a virtual spectrometer. In the case of vibrational spectrometry, the programs must allow for solving the dynamical problem of an object using the methods of quantum theory. Thus, in the first realized virtual multi-frequency spectrometer (VMS) [1], the calculations were carried out using available CCSD(T) and DFT codes, supplemented with VPT2 approximation concerning dynamical problems. In the second case of the spectrometer HF Spectrodyn [2], the calculations were performed in the Hartree–Fock (HF) approximation using its either restricted (RHF) or unrestricted (UHF) versions. The result of the five-year use of the VMS [3] allowed for the clarification of the requirements for basic programs that would provide a close agreement of the virtual and experimental vibrational and electronic spectra. This was solved for small molecules. In the second case, the main attention was directed to the calculation of the vibrational spectra of large-size molecules, including molecular radicals, carried out using semiempirical UHF approximation. In contrast with the former case, the basic computational program does not foresee correction to the force matrix elements, due to which an accurate fitting of virtual and experimental spectra could not Nanomaterials 2022, 12, 597. https://doi.org/10.3390/nano12040597 https://www.mdpi.com/journal/nanomaterials