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Normal modes for the out-of-phase (top panels), breathing (middle panels) and ω (bottom panels) for the clusters N=12 (left panel) and N=13 (right panel).
Source publication
The eigenmodes and the vibrational density of states of the ground state configuration of graphene clusters are calcu-lated using atomistic simulations. The modified Brenner po-tential is used to describe the carbon-carbon interaction and carbon-hydrogen interaction in case of H-passivated edges. For a given configuration of the C-atoms the eigenve...
Contexts in source publication
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... an even number of particles, there is a nearly common frequency (i.e. N=8 (545 cm −1 ), N=10 (543 cm −1 ), N=12 (546 cm −1 ), N=14 (547 cm −1 ), N=16 (549 cm −1 ), N=18 (550 cm −1 )) which is almost independent of N (see Fig. 1). This mode corresponds to out of phase oscillations of nearest-neighbor atoms (see Fig. 5(b) the k=38 mode for N=18 and Fig. 6(a) the k=24 mode for N=12). But for odd ring clusters i.e. N=13, the corresponding normal mode corresponds to nearest-neighbor atoms oscillating out of phase with different amplitudes except for the two neighbor atoms that oscillate in phase (see Fig. 6 frequency by about 20 % as compared to the corresponding even N ring clusters. A ...
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... out of phase oscillations of nearest-neighbor atoms (see Fig. 5(b) the k=38 mode for N=18 and Fig. 6(a) the k=24 mode for N=12). But for odd ring clusters i.e. N=13, the corresponding normal mode corresponds to nearest-neighbor atoms oscillating out of phase with different amplitudes except for the two neighbor atoms that oscillate in phase (see Fig. 6 frequency by about 20 % as compared to the corresponding even N ring clusters. A breathing mode exists for all the ring clusters as shown in Fig. 6 [34] predicts that this breathing mode has the frequency ω=(π × )/N which remarkably agrees with our numerical ...
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... i.e. N=13, the corresponding normal mode corresponds to nearest-neighbor atoms oscillating out of phase with different amplitudes except for the two neighbor atoms that oscillate in phase (see Fig. 6 frequency by about 20 % as compared to the corresponding even N ring clusters. A breathing mode exists for all the ring clusters as shown in Fig. 6 [34] predicts that this breathing mode has the frequency ω=(π × )/N which remarkably agrees with our numerical ...
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... eigenmodes corresponding to ω have similar vibrational modes for even number of particles. We plotted the normal modes of ω of cyclic structures for N=12 (ω 36 = 2183 −1 ) as shown in Fig. 6(e) and they correspond to dipole-type of oscillations between nearest neighbor particles while for odd number of ring structures i.e. N=13 (ω 39 = 2187 cm −1 in Fig. 6(f)), similar dipole-type of oscillations between nearest neighbor particles are found but with decreasing magnitude towards opposite sides. Now we investigate the ...
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... corresponding to ω have similar vibrational modes for even number of particles. We plotted the normal modes of ω of cyclic structures for N=12 (ω 36 = 2183 −1 ) as shown in Fig. 6(e) and they correspond to dipole-type of oscillations between nearest neighbor particles while for odd number of ring structures i.e. N=13 (ω 39 = 2187 cm −1 in Fig. 6(f)), similar dipole-type of oscillations between nearest neighbor particles are found but with decreasing magnitude towards opposite sides. Now we investigate the eigenmodes for out-of-plane vibrations for ring clusters. For N=10 and mode k=10, the normal mode corresponds to a bending mode while for mode k=16, the normal mode corresponds ...
Citations
... Greek symbols τ, δ and ν mark the molecule torsions, bendings and stretchings, respectively; 2 Out-of-plane bendings; 3 In plane bendings; 4 Benzene molecule data [118]; 5 Virtual data for nanographene [126]. ...
Presented is a concentrated synopsis of facilities of empirical and virtual analytics that, once applied, have provided a fully new vision of sp2 amorphous carbons. This study proved that the solids are multilevel structures, started with the first-level basic structural units (BSUs) and accomplished as macroscopic agglomerates of globular structures, consisting, in its turn, of stacked BSUs. BSUs present necklaced graphene molecules, size, and shape of which are governed by the relevant graphene domains while chemical composition in addition to basic carbon is controlled with heteroatoms of the necklaces. This study shows that BSUs and stacks of BSUs determine the short-range order of the solids and are the main subject of the applied analytics. The synopsis consists of two parts related to empirical and virtual analytics. The former is composed of sections related to structural determination, total and atomic chemical content evaluation and elicitation of the covalent bond composition. The second presents new analytic approaches based on the Digital Twins concept and virtual vibrational spectrometry. The synopsis is configured as an atlas composed of generalized pictures accompanied with necessary explanations to be discussed in detail in the extended references.
... 6 Benzene molecule data [56]. 7 Virtual data for nanographene [57]. 8 The author approximated suggestions for GO. 9 Virtual sp 3 C-C stretchings of graphane [58]. ...
Digital Twins concept presents a new trend in virtual material science, common to all computational techniques. Digital twins, virtual devices and intellectual products, presenting the main constituents of the concept, are considered in detail on the example of a complex problem, which concerns an amazing identity of the D-G-doublet Raman spectra of parental and reduced graphene oxides. Digital twins, presenting different aspects of the GO and rGO structure and properties, were virtually synthesized using a spin-density algorithm emerging from the Hartree-Fock approximation. Virtual device presents AM1 version of the semi-empirical unrestricted HF approximation. The equilibrium structure of the twins as well as virtual one-phonon harmonic spectra of IR absorption and Raman scattering constitute a set of intellectual products. It was established that in both cases the D-G doublets owe their origin to the sp3 and sp2 C-C stretchings, respectively. This outwardly similar community reveals different grounds. Thus, multilayer packing of individual rGO molecules in stacks provides the existence of the sp3 D band in addition to sp2 G one. The latter is related to stretchings of the main pool of sp2 C-C bonds, while the sp3 constituent presents out-of-plane stretchings of dynamically stimulated interlayer bonds. In the GO case, the sp3 D component, corresponding to stretchings of the main pool of sp3 C-C bonds, is accompanied by an sp2 G component, which is related to stretchings of the remaining sp2 C-C bonds provided with the spin-influenced prohibition of the 100% oxidative reaction in graphene domain basal plane.
... Greek symbols and mark the molecule bendings and stretchings, respectively 2 The assignment of frequencies in the experimental spectra is based on the papers [54][55][56][57]. 3 Obtained in the current study 4 Out-of-plane bendings 5 In plane bendings 6 Benzene molecule data [58] 7 Virtual data for nanographene [59] 8 The author approximated suggestions for GO 9 sp 3 C-C stretchings cover regions of 1 ...
A still amazing identity of the D-G doublet Raman spectra of parental and reduced graphene oxides is considered from the digital twins viewpoint. About thirty DTs, presenting different aspects of the GO structure and properties, were virtually synthesized using atomic spin-density algorithm, which allowed reliably displaying reasons for this extraordinary spectral feature. In both cases, it was established that the D-G doublets owe their origin to the sp3-sp2 C-C stretchings, respectively. This outwardly similar community of the doublets origin of GO and rGO is thoroughly analyzed to reveal different grounds of the feature in the two cases. Multilayer packing of individual rGO molecules in stacks, in the first case, and spin-influenced prohibition of the 100% oxidative reaction, the termination of which is accompanied with a particular set of highly ordered by length sp3- and sp2 C-C bonds, protecting the carbon carcass from destruction caused by the stress induced sp2-to-sp3 transformation, in the second, are the main reasons. The DT concept has been realized on the basis of virtual vibrational spectrometer HF Spectrodyn.
... puckering, ring breathing, H II C66H22 538 729,807, 832, 896, 1011 1244, 1393 1451, 1530, 1579 3200 1 Greek symbols and mark the molecule bending and stretching, respectively; 2 Equilibrated structures, AM1 UHF calculations; 3 Reference is taken from [20]; frequency regions are given in the experimental spectra scale; 4 Out-of-plane deformations; 5 In plane deformations; 6 Collective vibrations of the graphene domain atoms [21]. ble 2. UHF general frequencies kits of necklaced graphene oxides, based on IR spectra 1 , cm −1 . 1 Greek symbols δ and ν mark the molecule bending and stretching, respectively; 2 Equilibrated structures, AM1 UHF calculations; 3 Reference is taken from [20]; frequency regions are given in the experimental spectra scale; 4 Out-of-plane deformations; 5 In plane deformations; 6 Collective vibrations of the graphene domain atoms [21]. ...
... puckering, ring breathing, H II C66H22 538 729,807, 832, 896, 1011 1244, 1393 1451, 1530, 1579 3200 1 Greek symbols and mark the molecule bending and stretching, respectively; 2 Equilibrated structures, AM1 UHF calculations; 3 Reference is taken from [20]; frequency regions are given in the experimental spectra scale; 4 Out-of-plane deformations; 5 In plane deformations; 6 Collective vibrations of the graphene domain atoms [21]. ble 2. UHF general frequencies kits of necklaced graphene oxides, based on IR spectra 1 , cm −1 . 1 Greek symbols δ and ν mark the molecule bending and stretching, respectively; 2 Equilibrated structures, AM1 UHF calculations; 3 Reference is taken from [20]; frequency regions are given in the experimental spectra scale; 4 Out-of-plane deformations; 5 In plane deformations; 6 Collective vibrations of the graphene domain atoms [21]. Greek symbols and mark the molecule bending and stretching, respectively; 2 Equilibrated structures, AM1 UHF calculations; 3 Reference is taken from [20]; frequency regions are given in the experimental spectra scale; 4 Out-of-plane deformations; 5 In plane deformations; 6 Collective vibrations of the graphene domain atoms [21]. ...
... ble 2. UHF general frequencies kits of necklaced graphene oxides, based on IR spectra 1 , cm −1 . 1 Greek symbols δ and ν mark the molecule bending and stretching, respectively; 2 Equilibrated structures, AM1 UHF calculations; 3 Reference is taken from [20]; frequency regions are given in the experimental spectra scale; 4 Out-of-plane deformations; 5 In plane deformations; 6 Collective vibrations of the graphene domain atoms [21]. Greek symbols and mark the molecule bending and stretching, respectively; 2 Equilibrated structures, AM1 UHF calculations; 3 Reference is taken from [20]; frequency regions are given in the experimental spectra scale; 4 Out-of-plane deformations; 5 In plane deformations; 6 Collective vibrations of the graphene domain atoms [21]. Table 2. UHF general frequencies kits of necklaced graphene oxides, based on IR spectra 1 , cm −1 . ...
The digital twin concept lays the foundation of the virtual vibrational analytics suggested in the current paper. The latter presents extended virtual experiments aimed at determining the specific features of the optical spectra of the studied molecules that provide reliable express analysis of the body spatial structure and chemical content. Reduced graphene oxide was selected as the virtual experiment goal. A set of nanosize necklaced graphene molecules, based on the same graphene domain but differing by the necklace contents, were selected as the relevant DTs. As shown, the Raman spectra signatures contained information concerning the spatial structure of the graphene domains, while the molecule necklaces were responsible for the IR spectra. Suggested sets of general frequency kits facilitate the detailed chemical analysis. Express analysis of a shungite carbon, composed of rGO basic structural units, revealed the high ability of the approach.
... puckering, ring breathing, H II C66H22 538 729,807, 832, 896, 1011 1244, 1393 1451, 1530, 1579 3200 1 Greek symbols and mark the molecule bending and stretching, respectively; 2 Equilibrated structures, AM1 UHF calculations; 3 Reference is taken from [20]; frequency regions are given in the experimental spectra scale; 4 Out-of-plane deformations; 5 In plane deformations; 6 Collective vibrations of the graphene domain atoms [21]. ble 2. UHF general frequencies kits of necklaced graphene oxides, based on IR spectra 1 , cm −1 . 1 Greek symbols δ and ν mark the molecule bending and stretching, respectively; 2 Equilibrated structures, AM1 UHF calculations; 3 Reference is taken from [20]; frequency regions are given in the experimental spectra scale; 4 Out-of-plane deformations; 5 In plane deformations; 6 Collective vibrations of the graphene domain atoms [21]. ...
... puckering, ring breathing, H II C66H22 538 729,807, 832, 896, 1011 1244, 1393 1451, 1530, 1579 3200 1 Greek symbols and mark the molecule bending and stretching, respectively; 2 Equilibrated structures, AM1 UHF calculations; 3 Reference is taken from [20]; frequency regions are given in the experimental spectra scale; 4 Out-of-plane deformations; 5 In plane deformations; 6 Collective vibrations of the graphene domain atoms [21]. ble 2. UHF general frequencies kits of necklaced graphene oxides, based on IR spectra 1 , cm −1 . 1 Greek symbols δ and ν mark the molecule bending and stretching, respectively; 2 Equilibrated structures, AM1 UHF calculations; 3 Reference is taken from [20]; frequency regions are given in the experimental spectra scale; 4 Out-of-plane deformations; 5 In plane deformations; 6 Collective vibrations of the graphene domain atoms [21]. Greek symbols and mark the molecule bending and stretching, respectively; 2 Equilibrated structures, AM1 UHF calculations; 3 Reference is taken from [20]; frequency regions are given in the experimental spectra scale; 4 Out-of-plane deformations; 5 In plane deformations; 6 Collective vibrations of the graphene domain atoms [21]. ...
... ble 2. UHF general frequencies kits of necklaced graphene oxides, based on IR spectra 1 , cm −1 . 1 Greek symbols δ and ν mark the molecule bending and stretching, respectively; 2 Equilibrated structures, AM1 UHF calculations; 3 Reference is taken from [20]; frequency regions are given in the experimental spectra scale; 4 Out-of-plane deformations; 5 In plane deformations; 6 Collective vibrations of the graphene domain atoms [21]. Greek symbols and mark the molecule bending and stretching, respectively; 2 Equilibrated structures, AM1 UHF calculations; 3 Reference is taken from [20]; frequency regions are given in the experimental spectra scale; 4 Out-of-plane deformations; 5 In plane deformations; 6 Collective vibrations of the graphene domain atoms [21]. Table 2. UHF general frequencies kits of necklaced graphene oxides, based on IR spectra 1 , cm −1 . ...
... The strongest infrared bands computed for dPAH molecules lie between 5 and 12 µm and between 17 and 28 µm. dPAH molecules are essentially nano-graphene particles, and in a theoretical vibrational study they were found to possess complicated vibrational phonon modes in the mid-infrared region, as calculated by atomistic methods using a modified Brenner potential [23]. For example, nano-graphene molecules with 53 carbon atoms have high phonon densities between 200 and 2000 cm -1 (50-5 µm). ...
... The strongest infrared bands computed for dPAH molecules lie between 5 and 12 µm and between 17 and 28 µm. dPAH molecules are essentially nano-graphene particles, and in a theoretical vibrational study they were found to possess complicated vibrational phonon modes in the mid-infrared region, as calculated by atomistic methods using a modified Brenner potential [23]. For example, nanographene . ...
... A number of exciting articles are forthcoming shortly in 2013. Among them we will mention articles [30] and [6]. In [30], by using atomistic calculations, the authors determine the eigenmodes and the vibrational properties of the ground state configuration of graphene clusters. ...
... Among them we will mention articles [30] and [6]. In [30], by using atomistic calculations, the authors determine the eigenmodes and the vibrational properties of the ground state configuration of graphene clusters. Based on their developed technique with the modified Brenner potential, they have also described the carbon-carbon interaction and carbon-hydrogen interaction in the case of H-passivated edges and calculated the specific heat of the clusters within the harmonic approximation. ...
This editorial provides an overview of both fundamental and
applied research areas covered by the journal of Nanoscale
Systems: Mathematical Modeling, Theory and Applications
(NanoMMTA), as well as of articles published in the journal inaugural
volume. The unique feature of NanoMMTA is its focus
on the interface between the study, development, and application
of systems at the nanoscale with theoretical methods and
experimental techniques on the one hand and mathematical,
statistical, and computational tools on the other. NanoMMTA
is the first international, interdisciplinary, peer-reviewed journal
focusing specifically on this interface. This emerging multidisciplinary
field at the interface of mathematical modeling,
nanoscience and nanotechnology includes applications and
advancements of these tools in all of the disciplines facing
the challenges associated with the nanoscale systems.
With the help of the recently developed SIESTA-pole (Spanish Initiative for Electronic Simulations with Thousands of Atoms) - PEXSI (pole expansion and selected inversion) method [L. Lin, A. García, G. Huhs, and C. Yang, J. Phys.: Condens. Matter26, 305503 (2014)], we perform Kohn-Sham density functional theory calculations to study the stability and electronic structure of hydrogen passivated hexagonal graphene nanoflakes (GNFs) with up to 11 700 atoms. We find the electronic properties of GNFs, including their cohesive energy, edge formation energy, highest occupied molecular orbital-lowest unoccupied molecular orbital energy gap, edge states, and aromaticity, depend sensitively on the type of edges (armchair graphene nanoflakes (ACGNFs) and zigzag graphene nanoflakes (ZZGNFs)), size and the number of electrons. We observe that, due to the edge-induced strain effect in ACGNFs, large-scale ACGNFs’ edge formation energy decreases as their size increases. This trend does not hold for ZZGNFs due to the presence of many edge states in ZZGNFs. We find that the energy gaps
E
g
of GNFs all decay with respect to 1/L, where L is the size of the GNF, in a linear fashion. But as their size increases, ZZGNFs exhibit more localized edge states. We believe the presence of these states makes their gap decrease more rapidly. In particular, when L is larger than 6.40 nm, we find that ZZGNFs exhibit metallic characteristics. Furthermore, we find that the aromatic structures of GNFs appear to depend only on whether the system has 4N or 4N + 2 electrons, where N is an integer.
