This review presents the covalent chemistry of carbon within the spin-radical concept of electron interaction. Using the language of valence bond trimodality, the regions of classical spinless covalence and its spin counterpart are defined. Carbon is the only element exhibiting spin covalent chemistry. Classical covalent chemistry of carbon concerns molecular substances whose valence bond structure includes segregate or chained single sp3C-C bonds. Substances with double sp2C-C and triple sp1C-C bonds are the subject of spin covalent chemistry of carbon. The mathematical apparatus of spin covalence forms the basis of algorithms governing the chemical modification of carbon substances, polymerization processes, and catalysis involving them, making it possible to supplement the empirical spin covalent chemistry of carbon with its virtual analog.

A virtual vibrational spectrometer HF Spectrodyn, based on efficient software exploring unrestricted Hartree-Fock approximation, was used to perform computational spectrometry of C-60, C-66 and C-70 carbon clusters as well as C-60 dimers. All the species are presented as digital twins, the structure and properties of which were discussed. The obtained IR absorption and Raman scattering spectra are analyzed to point out strengths, limitations and ongoing developments of the virtual spectrometry.

Abstract The article presents the first consideration of virtual vibrational spectrometry of big molecules as a branch of the overall digitalization. The concept ability is illustrated by the example of fullerene C60. Connected in a single chain, digital twins, virtual devices and IT products related to the molecule and its isomers significantly enrich standard pool of molecular spectroscopic knowledge. Currently, the approach removes the problem of the C60 ‘silent’ vibrational modes providing a convincing interpretation of the fine structure of vibrational spectra and makes it possible to resolve the issue of the isolation of the only structure from numerous C60 isomers in practice. The practical implementation of the concept is provided by a virtual vibrational spectrometer HF Spectrodin exploiting semi-empirical Hartree–Fock approximation.

Two-mode valence electron configuration of carbon atoms lays the foundation of the unique two-mode amorphous state of the monoatomic carbon solid. From the fundamentals of solid-state physics, sp$^3$ and sp$^2$ amorphous carbons are two different amorphous species characterized by conceptually different short-range orders, namely, groups of tetrahedrally bonded sp3 configured atoms and size-restricted sp$^2$ graphene domains framed with heteroatom necklaces. Molecular character of sp$^2$ amorphics is coherent with the reaction mechanism of the solid amorphicity in due course of the forced fragmentation.

A virtual vibrational spectrometer HF-Spectrodyn, based on efficient computational codes and exploring both restricted and unrestricted Hartree-Fock approximations, is proposed to perform computational vibrational spectroscopy of large sp2 carbon clusters. The computational device allows obtaining one-quantum harmonic spectra of IR absorption and Raman scattering of closed-shell and open-shell molecules. The spectrometer facilities are manifested for the sp2 hydrocarbons on the example of polyacenes (naphthalene and pentacene) and polycyclic benzenoid-fused compounds (coronene as well as (5,5) and (9,9) periacenes). The observed trends disclose a new spectrometric approach for the consideration of vibrational spectra of the molecules in terms of standard valence bonds subjected to particular structural and atomic-content affects.

In the case ofsp(2)amorphous carbons, formed by nanoscale graphene domains framed by heteroatom necklaces (basic structure units in total), inelastic neutron scattering and photoabsorption ensure studying vibrational spectra of the latter mainly. Examination of a set of samples of the highest carbonization rank representing natural substances (shungite carbon, anthraxolite, and anthracite), technical graphenes (laboratory reduced graphene oxides), and industrial products (carbon blacks) has shown, that while INS spectra revealed the hydrogen-enriched component of these necklaces only, the DRIFT spectra exhibited two components determined by both hydrogen and oxygen compositions. Taking together, INS and DRIFT spectra exhibit methine groups, typifying the hydrogen component of all natural amorphics as well as hydroxymethyls and methyls doing the same job for the studied technical graphenes, and hydroxyfurans - for carbon blacks. A comparable analysis of DRIFT and XPS spectra has allowed a reliable personification of the oxygen functional groups compositions. Based on the results obtained, a set of reliable molecular models of the amorphics' basic structural units has been proposed.

The paper presents a joint consideration of Raman spectra of sp2 amorphous carbons alongside with the nature and type of their amorphicity. The latter was attributed to the enforced fragmentation. The fragments, presented with size-restricted graphene domains with heteroatom necklaces in the circumference, are the basic structural units (BSUs) of the solids, determining them as amorphics with molecular structure. The standard G-D-2D pattern of Raman spectra of polycyclic aromatic hydrocarbons, sp2 amorphous carbons, graphene and/or graphite crystal is attributed to BSUs graphene domains. The molecular approximation allows connecting the G-D spectra image of one-phonon spectra with a considerable dispersion of the C=C bond lengths within graphene domains, governed by size, heteroatom necklace of BSUs as well as BSUs packing. The interpretation of 2D two-phonon spectra reveals a particular role of electrical anharmonicity in the spectra formation and attributes this effect to a high degree of the electron density delocalization in graphene domains.

We carried out a joint analysis of the INS, DRIFT, and XPS spectra of a set of sp2 amorphous carbons of the highest carbonization rank representing natural substances (shungite carbon, anthraxolite, and anthracite), technical graphenes (laboratory reduced graphene oxides), and industrial products (carbon blacks). It was determined, that the DRIFT spectra of the studied substances consist of two components determined by hydrogen and oxygen compositions in the circumference of graphene molecules, which represent the basic structural units of amorphic compounds. Methine groups typify the hydrogen component of natural amorphics while hydroxymethyls and methyls do the same job for the studied technical graphenes and hydroxyfurans for carbon blacks. A particular specificity of the methine-based hydrogen compositions to enhance electrooptic characteristics of the DRIFT spectrum of carbon atoms has been established. A comparable analysis of DRIFT and XPS spectra has allowed a reliable personification of the oxygen functional groups compositions of the studied amorphics resulting in a set of dependable molecular models of their basic structural units.

A set of sp2 amorphous carbons involving natural mineral shungite carbon and antraxolite as well as two synthetic carbon blacks were investigated by using neutron powder diffraction and inelastic neutron scattering at low temperature. NDP revealed nanographite-like structure of all the samples, stacks of which are formed by basic structure units representing framed graphene molecules of ~2.5 nm in lateral dimension. INS study showed the presence of hydrogen atoms in the BSU framing area as well as of adsorbed water in the samples pores. Simulated INS spectra of adsorbed water showed its mono-layer disposition within the pores of the studied amorphics. Due to BSUs radical character, their INS spectra were simulated in the framework of both spin-nondependent (DFT) and spin-dependent (UHF) molecular dynamics. The obtained results allowed suggesting a specific INS classification of sp2 amorphous carbons with respect to their hydrogeneousness based on H-standard INS spectra, on the one side, and riding-stimulated spectrum of heavy atoms, on the other.

The approach based on selected set of samples and selected set of analytical tools occurred quite efficient when applying to amorphous carbons thus leading to a transformation of the current representation of the issue based on particulars into that one based on a limited set of fixed commonalities. The approach first part implies a set of different origin solid samples. The second part concerns different analytical tools. The combining part means the application of each tool to the whole set of samples. In the current study two natural amorphous carbons shungite carbon and antraxolite, as well as two engineered products carbon blacks CB632 and CB624, all of the four belonging to the elitist highest-carbon-content species, were subjected to analytical study by using modern structural and compositional analytical techniques. The approach has allowed disclosing steady points that are common to the whole class of this carbon allotrope and that may lay the foundation of a consolidate representation of what are amorphous carbons.

Graphene is considered a specific object whose electronic structural features are presented in the light of the general concept of emergent phenomena that arise as a result of a quantum phase transition caused by the breaking of continuous symmetry. This review starts by examining the spin symmetry breaking of the graphene electron subsystem caused by the correlation of its odd p(z)-electrons that depends on the distance between these electrons and becomes noticeable when the shortest distance, determined by the C=C bond length, exceeds the critical magnitude R-cr = 1.395 angstrom. The symmetry breaking is reliably predicted by the unrestricted Hartree-Fock (UHF) formalism, which provides a sufficient level of quantitative self-consistent description for the problem. Empirical support has been given to and reliable certification obtained for UHF emergents such as (i) open-shell electron spin-orbitals; (ii) splitting and/or spin polarization of electron spectra; (iii) a spin-mixed ground state and, as a consequence, violation of the exact spin multiplicity of electronic states, and (iv) the existence of local spins at zero total spin density. Using this approach greatly expands our understanding of the ground state of graphene and other sp(2) nanocarbons and not only gives a clear insight into the spin features of graphene chemistry, accentuating its emergent character, but also expectedly predicts the occurrence of new graphene physics-related emergents. In the latter case, symmetry breaking is relevant for both the spin system and time reversal and imposes on graphene special physical properties such as ferromagnetism, superconductivity, and topological nontriviality. This review shows, for the first time, that not only the ferromagnetism but also the mechanical properties of graphene are essentially emergent, extending this feature to the entire physics of graphene.

The wide structure and chemical-composition spectrum of the main technological material of molecular graphenics-reduced graphene oxide (RGO)-is explained from a quantum-chemical standpoint. The proposed concept is used to consider the results of experimental investigations of a natural analog of RGO, namely, shungite carbon, by high-resolution electron microscopy and nanopoint energy dispersive spectral analysis. The results obtained are used to propose an atomic-microscopic model for the structure of shungite carbon.

The paper presents a comparative consideration of sp(2) nanocarbons and their silicon and higher tetrels analogues from the viewpoint of the spin molecular theory taking into account the electron correlation in open-shell molecules. High radicalization of silicene and quantum instability of flat honeycomb 2D structures of germanene and stanene make all the species phantom materials leaving graphene the only one-atom thick 2D solid free of the crucial restrictions.

Synthetic graphene oxide, in the form of graphene oxide paper (GOpp), and its reduction product-thermally exfoliated reduced graphene oxide (TErGO)-were studied by elastic and inelastic neutron scattering at low and room temperature conditions. The neutron diffraction patterns were analyzed to confirm stacking structures of both species consisting of 4-6 and similar to 8 layers of microsize lateral dimension and the interlayer distances of 7.21 angstrom and 3.36 angstrom, respectively. The one-phonon hydrogen amplitude-weighted density of vibrational states G (!) represents the inelastic incoherent neutron scattering spectra of the products. The study has revealed the retained water in the freshly made GOpp, corresponding to the lowest humidity. The analysis of the TErGO G (omega) spectrum has disclosed the chemical composition of its circumference attributing the latter to sets of CH units with a minor presence of atomic oxygen.

This paper presents a direct confirmation of graphene-like configuration and first suggests the chemical composition of basic structural elements of shungite attributing the latter to reduced graphene oxide nanosheets with an average 11:1:3 (C:O:H) atomic content ratio.

In view of the formal topology, two common terms, namely, the connectivity and adjacency, determine the ‘quality’ of the C–C bonds of sp 2 nanocarbons. The feature is the most sensitive point of the inherent topology of the species so that such external action as the mechanical deformation should obviously change it and result in particular topological effects. The current chapter describes the effects caused by uniaxial tension of a graphene molecule in due course of the mechanochemical reaction. Basing on the molecular theory of graphene, the effects are attributed to both mechanical loading and chemical modification of the edge atoms of the molecule. The mechanical behavior is shown to be not only highly anisotropic with respect to the direction of the load application, but greatly dependent on the chemical modification of the molecule edge atoms thus revealing the topological character of the graphene deformation.

PACS 73.63.Kv, 73.23.Hk, 73.43.Lp, 78.67.Wj A low-temperature study has been performed for aqueous shungite, carbon tetrachloride, and toluene dispersions. Spectral characteristics for graphene quantum dots (GQDs) of shungite, attributed to individual fragments of reduced graphene oxide (rGO), reveal a dual character of the dispersions emitting centers: individual GQDs are responsible for the spectra position while fractal structure of GQD colloids provides large broadening of the spectra due to structural inhomogeneity of the colloidal dispersions and a peculiar dependence of photoluminescence of dispersions on excitation wavelength. For the first time, photoluminescence spectra of individual GQDs were observed in frozen toluene dispersions, which pave the way for a theoretical treatment of GQDs photonics.

Viewing shungite as loosely packed fractal nets of graphene-based (reduced graphene oxide, rGO) quantum dots (GQDs), we consider photoluminescence of the latter as a convincing proof of the structural concept as well as of the GQD attribution to individual rGO fragments. We study emission from shungite GQDs for colloidal dispersions in water, carbon tetrachloride, and toluene at both room and low temperatures. As expected, the photoluminescence of the GQD aqueous dispersions is quite similar to that of synthetic GQDs of the rGO origin. The morphological study of shungite dispersions shows a steady trend of GQDs to form fractals and to drastically change the colloid fractal structure caused by the solvent exchange. Spectral study reveals a dual character of the emitting centers: individual GQDs are responsible for the spectra position while the fractal structure of GQD colloids ensures high broadening of the spectra due to structural inhomogeneity, thus causing a peculiar dependence of the photoluminescence spectra on the excitation wavelength. For the first time, photoluminescence spectra of individual GQDs were observed in frozen toluene dispersions, which paves the way for a theoretical treatment of the GQD photonics.

Graphene material science only slightly depends on the uniqueness of a regular one-atom- thick planar sheet while is mainly governed by peculiarities of electronic structure of `sp2-bonded carbon atoms that are densely packed in a honeycomb crystal'.

Odd electrons of benzenoid units and the correlation of these electrons having different spins are the main concepts of the molecular theory of graphene. In contrast to the theory of aromaticity, the molecular theory is based on the fact that odd electrons with different spins occupy different places in the space so that the configuration interaction becomes the central point of the theory. Consequently, a multi-determinant presentation of the wave function of the system of weakly interacting odd electrons is utterly mandatory on the way of the theory realization at the computational level. However, the efficacy of the available CI computational techniques is quite restricted in regard to large polyatomic systems, which does not allow performing extensive computational experiments. Facing the problem, computationists have addressed standard single-determinant ones albeit not often being aware of the correctness of the obtained results. The current chapter presents the molecular theory of graphene in terms of single-determinant computational schemes and discloses how reliable information about the electron-correlated system can be obtained by using either UHF or UDFT computational schemes.