Stone-Wales Transformation Research Articles

Nitrogen-doped amorphous monolayer carbon.

Monoatomic-layered carbon materials, such as graphene1 and amorphous monolayer carbon2,3, have stimulated intense fundamental and applied research owing to their unprecedented physical properties and a wide range of promising applications4,5. So far, such materials have mainly been produced by chemical vapour deposition, which typically requires stringent reaction conditions compared to solution-phase synthesis. Herein, we demonstrate the solution preparation of free-standing nitrogen-doped amorphous monolayer carbon with mixed five-, six- and seven-membered (5-6-7-membered) rings through the polymerization of pyrrole within the confined interlayer cavity of a removable layered-double-hydroxide template. Structural characterizations and first-principles calculations suggest that the nitrogen-doped amorphous monolayer carbon was formed by radical polymerization of pyrrole at the α, β and N sites subjected to confinement of the reaction space, which enables bond rearrangements through the Stone-Wales transformation. The spatial confinement inhibits the C-C bond rotation and chain entanglement during polymerization, resulting in an atom-thick continuous amorphous layer with an in-plane π-conjugation electronic structure. The spatially confined radical polymerization using solid templates and ion exchange strategy demonstrates potential as a universal synthesis approach for obtaining two-dimensional covalent networks, as exemplified by the successful synthesis of monolayers of polythiophene and polycarbazole.

M@C78 (M = U, Th): Inherent Topological Connectivity Existed in Thermodynamically Stable Isomers and the Possibility of an Endohedral Fullerene Containing One Heptagon Ring.

The density functional theory combined with statistical thermodynamic analyses of M@C78 (M = U and Th) demonstrated that four isomers, M@D3h(24109)-C78, M@C2v(24107)-C78, M@C1(22595)-C78, and M@C1(23349)-C78, and a nonclassical isomer, M@C1(id7)-C78, containing one heptagon ring possess outstanding thermodynamic stabilities in the two M@C78 series. Especially, the M@C1(id7)-C78 isomer is the first nonclassical C78 fullerene that can exist stably. Importantly, these five fullerene cages are found to be related in the form of Stone-Wales (SW) transformations. Geometric analyses disclosed that, unlike lanthanide metals, actinide metals are more likely to bond with sumanene-type hexagonal rings when they are encapsulated in IPR C78 cages. Frontier molecular orbital analysis showed that both U and Th atoms donate four electrons to the C78 carbon cages.

2D honeycomb transformation into dodecagonal quasicrystals driven by electrostatic forces

Dodecagonal oxide quasicrystals are well established as examples of long-range aperiodic order in two dimensions. However, despite investigations by scanning tunneling microscopy (STM), low-energy electron diffraction (LEED), low-energy electron microscopy (LEEM), photoemission spectroscopy as well as density functional theory (DFT), their structure is still controversial. Furthermore, the principles that guide the formation of quasicrystals (QCs) in oxides are elusive since the principles that are known to drive metallic QCs are expected to fail for oxides. Here we demonstrate the solution of the oxide QC structure by synchrotron-radiation based surface x-ray diffraction (SXRD) refinement of its largest-known approximant. The oxide QC formation is forced by large alkaline earth metal atoms and the reduction of their mutual electrostatic repulsion. It drives the n = 6 structure of the 2D Ti2O3 honeycomb arrangement via Stone–Wales transformations into an ordered structure with empty n = 4, singly occupied n = 7 and doubly occupied n = 10 rings, as supported by DFT.

On quantum entangled nano-portation: C39 & C43 fullerenes

Key concept in nano-topological chemistry like the Stone–Wales transformation of chemical bonds is reformulated in terms of spin-up like quantum information natural basis transformation; it naturally self-contains the four entangled couplings in its collective chemical bonding transformation toward tree fold exist corresponding with special quantum teleportation Alice-Bob phenomenology while turning inner quantum products into a global outré quantum fungible multi-verse. On nano-portation perspective, the fullerenic pentagon-hexagon systems and the Yoshida-Fowler insertion of 4vertices are then merged with quantum portation Alice-Bob entangled communication, to produce a unified quantum nano-portation phenomenology. Applied to the fullerenic systems C39 and C43 the present approach reveals various nano-universes observation realities depending on the topological tool under consideration.; it unveils the fact that the nano-topological average roundness closes to hierarchical evolution but distorts the transmitted signal over the lattice, while the nano-topological extreme roundness (eccentricity) allows a tuned signal which escapes from a multi/hidden nano-universe picture.

Size-dependent melting of onion-like fullerenic carbons: a molecular dynamics and machine learning study

The melting thermodynamic characteristics of 2- to 20-layered onion-like fullerenes (OLF n ) (C60@C240 to C60@···@C6000···@C24000) are comprehensively explored using first-principles-based ReaxFF atomistic simulations and random forest machine learning (RF ML). It is revealed that OLF n shows lower thermal stability than the counterparts of single-walled fullerenes (SWF n ). The melting point of SWF n increases monotonically with increasing size, whereas for OLF n , an unusual size-dependent melting point is observed; OLF n with intermediate size shows the highest melting point. For small OLF n , the melting occurs from the inner to the outer, whereas for large OLF n , it nucleates from the inner to the outer and to intermediate fullerenes. The melting and erosion behaviors of both SWF n and OLF n are mainly characterized by the nucleation of non-hexagons, nanovoids, carbon chains and emission of C2. RF ML model is developed to predict the melting points of both SWF n and OLF n . Moreover, the analysis of the feature importance reveals that the Stone-Wales transformation is a critical pathway in the melting of SWF n and OLF n . This study provides new insights and perspectives into the thermodynamics and pyrolysis chemistry of fullerenic carbons, and also may shed some lights onto the understanding of thermally-induced erosion of carbon-based resources and spacecraft materials.

Emerging exotic properties of two-dimensional ternary tetrahexagonal BCN: Tunable anisotropic transport properties with huge excitonic effects for nanoelectronics and optoelectronics

A two-dimensional ternary tetrahexagonal BCN monolayer (th-BCN) is designed by applying Stone-Wales transformation to its pentagonal counterpart (p-BCN). Using first-principles calculations, we examine the dynamical, mechanical, thermal, and environment stability of th-BCN. The monolayer exhibits superior anisotropic electronic and optical properties compared to its counterparts (the domains of C and BN in the tetrahexagonal network and p-BCN). Direct band gap of 3.05 eV and excellent band edge alignment with the oxidation and reduction reactions of water heralds the use of th-BCN in photocatalytic water splitting. The band gap energy and band edge positions can be further adjusted by strain. The anisotropic high carrier mobility of th-BCN improves fast carrier separation and low recombination rate. The electronic transport direction can be easily controlled by strain engineering. For instance, one can rotate the preferred transport direction of hole by 90° with a very small uniaxial strain. Many-body effects beyond DFT reveal that the monolayer has strong light-harvesting capability (105cm−1) in the visible-ultraviolet region and exhibits strong excitonic effects with large excitonic binding energy of 0.98 eV. All these appealing properties make th-BCN a promising and tunable anisotropic 2D material for nanoelectronic and optoelectronic applications.

Crippling the C70 fullerene: non-classical C68Cl26(OH)2 and C68Cl25(OH)3 with three heptagons and only fused pentagons via chlorination-promoted skeletal transformations.

High-temperature (440 °C) chlorination of C70 with SbCl5 promotes Stone-Wales transformations and loss of the C2 fragment, which results in a non-classical C68Cl28 partially hydrolyzed to C68Cl26(OH)2 and C68Cl25(OH)3. X-ray diffraction reveals an unprecedented C68 cage with three heptagons and 15 pentagons arranged in fused pairs and triples. The shortest possible transformation pathways include one C2 loss step and four Stone-Wales transformation steps.

Transition state and formation process of Stone–Wales defects in graphene

Stone–Wales (SW) defects are possibly formed in graphene and other two-dimensional materials, and have multiple influence on their physical and chemical properties. In this study, the transition state of SW defects in graphene is determined with the fully discrete Peierls theory. Furthermore, the atomic formation process is investigated by means of ab-initio simulations. The atomic structure change and energetics of the SW transformation are revealed. It is found that the transition state is at the SW bond rotation of 34.5° and the activation energy barrier is about 12 eV. This work provides a new method to investigate SW transformations in graphene-like materials and to explore unknown SW-type defects in other 2D materials.

High Temperature Accelerated Stone-Wales Transformation and the Threshold Temperature of IPR-C60 Formation.

The Stone-Wales bond rotation isomerization of nonicosahedral C60 (C2v-C60) into isolated-pentagon rule following icosahedral C60 (Ih-C60 or IPR-C60) is a limiting step in the synthesis of Ih-C60. However, extensive previous studies indicate that the potential energy barrier of the Stone-Wales bond rotation is between 6 and 8 eV, extremely high to allow for bond rotation at the temperatures used to produce fullerenes conventionally. This is also despite data indicating a possible fullerene road mechanism that necessitates low-temperature annealing. However, these previous investigations often have limiting factors, such as using the harmonic approximation to determine free energies at high temperatures or considering only the reverse Ih-C60 to C2v-C60 transition as a basis. Indeed, when the difference in energy between Ih-C60 and C2v-C60 is accounted for, this barrier is generally reduced by ∼1.5 eV. Thus, utilizing the recently developed density functional tight binding metadynamics (DFTB-MTD) interface, the effects of temperature on the bond rotation in the conversion of C2v-C60 to Ih-C60 have been investigated. We found that Stone-Wales bond rotations are complex processes with both in-plane and out-of-plane transition states, and which transition path dominates depends on temperature. Our results clearly show that at temperatures of 2000 K, the free energy for a C2v-C60 to Ih-C60 transition is only ∼4.21 eV and further reduces to ∼3.77 eV at 3000 K. This translates to transition times of ∼971 μs at 2000 K and ∼34 ns at 3000 K, indicating that defect healing is a fast process at temperatures typical of arc jet or laser ablation experiments. Conversely, below ∼2000 K, bond rotation becomes prohibitively slow, putting a lower threshold limit on the temperature of fullerene formation and subsequent annealing.

Capturing the Missing Carbon Cage Isomer of C84 via Mutual Stabilization of a Triangular Monometallic Cyanide Cluster.

Monometallic cyanide clusterfullerenes (CYCFs) represent a unique branch of endohedral clusterfullerenes with merely one metal atom encapsulated, offering a model system for elucidating structure-property correlation, while up to now only C82 and C76 cages have been isolated for the pristine CYCFs. C84 is one of the most abundant fullerenes and has 24 isomers obeying the isolated pentagon rule (IPR), among which 14 isomers have been already isolated, whereas the C2v(17)-C84 isomer has lower relative energy than several isolated isomers but never been found for empty and endohedral fullerenes. Herein, four novel C84-based pristine CYCFs with variable encapsulated metals and isomeric cages, including MCN@C2(13)-C84 (M = Y, Dy, Tb) and DyCN@C2v(17)-C84, have been synthesized and isolated, fulfilling the first identification of the missing C2v(17)-C84 isomer, which can be interconverted from the C2(13)-C84 isomer through two steps of Stone-Wales transformation. The molecular structures of these four C84-based CYCFs are determined unambiguously by single-crystal X-ray diffraction. Surprisingly, although the ionic radii of Y3+, Dy3+, and Tb3+ differ slightly by only 0.01 Å, such a subtle difference leads to an obvious change in the metal-cage interactions, as inferred from the distance between the metal atom and the nearest hexagon center of the C2(13)-C84 cage. On the other hand, upon altering the isomeric cage from DyCN@C2(13)-C84 to DyCN@C2v(17)-C84, the Dy-cage distance changes as well, indicating the interplay between the encapsulated DyCN cluster and the outer cage. Therefore, we demonstrate that the metal-cage interactions within CYCFs can be steered via both internal and external routes.

Discovery of Non-Isolated-Pentagon-Rule Fullerenes from Computational Characterization of U2O@C72.

The reported actinide-based endohedral clusterfullerenes (ECFs) are rather scarce thus far. Though several members have been detected in mass spectra, their exact structures and properties mostly remain unclear. Herein, density functional theory calculations revealed that the U2O@C72 observed in recent experiments should be U2O@D2(10611)-C72, U2O@C1(10610)-C72, or U2O@Cs(10616)-C72. Featuring two pairs of fused pentagons, their outer cages all break the well-known isolated pentagon rule. U2O@D2(10611)-C72 is the first clusterfullerene based on the D2(10611)-C72 cage, which only encapsulated dimetals (Sc2, La2, Ce2, Pr2) before. It is also the first time to reveal that C1(10610)-C72 and Cs(10616)-C72 can serve as the parent cage of an endohedral fullerene. Interestingly, the three isomers could interconvert with each other via Stone-Wales transformation with one internal U atom dynamically changing its orientation according to the position of pentagon adjacencies. A common electronic structure of (U4+)2(O)2-@C726- can be formally assigned to the three ECFs but with obvious covalent character for both U-O and U-C bonds. Their spatially extended U-5f orbitals substantially enhance the metal-cage interactions. Their various spectra were also simulated to assist future experiments. Moreover, our work shows that the careful choice of exchange-correlation functionals is rather critical for the structural characterization of ECFs.

Two-dimensional carbon allotropes with tunable direct band gaps and high carrier mobility

Using first-principles calculations, two sp2 + sp3-hybridized two-dimensional (2D) carbon allotropes with stable orthorhombic structures are predicted in this work. Both structures are composed of tetra-, penta-, and hexa-rings of carbon atoms, known as TPH-I carbon and TPH-II carbon. We demonstrate that they can be obtained from penta-graphene by the Stone-Wales (SW) transformation. TPH-I carbon has an inherent direct band gap of 2.704 eV, while TPH-II carbon has a quasi-direct band gap of 2.361 eV. After applying uniaxial strain, TPH-I and TPH-II carbon will have tunable direct band gaps in the range of 2.441–2.812 eV and 2.468–2.7562 eV, respectively. Their electrons and holes mobilities are found to be anisotropic. TPH-I carbon shows extraordinary room temperature in-plane electron mobility of ~7.9 × 104 cm2 V−1 s−1 and TPH-II carbon shows high hole mobility of ~1.5 × 104 cm2 V−1 s−1. Both novel carbon sheets exhibit strong absorption of visible light. And their intrinsic anisotropic optical properties allow optical determination of the crystalline orientation. In addition, TPH-I carbon is a potential photocatalyst for the water splitting reaction.

Electron-beam irradiation of photopolymerized C60 film studied using in situ scanning tunneling microscope, in situ Fourier-transform infrared spectroscopy, and first-principles calculations

We have examined the formation of a two-dimensional (2D) new carbon network by inducing the general Stone–Wales transformation between adjacent C60 molecules in a 2D dumbbell-type C60 polymer film. Structural changes in pristine C60 films after ultraviolet-visible (UV-vis) light and electron-beam (EB) irradiations were studied using in situ scanning tunneling microscope (STM) and in situ Fourier-transformed infrared (IR) spectroscopy, in combination with first-principles calculations based on density functional theory. Analyses of STM images and depth profiles found that three types of photopolymerized dumbbell-shaped dimers and trimers are formed on the surface layers of pristine C60 films: (i) [2+2] C60 dimers formed in a lateral direction, (ii) [2+2] dimerization of C60 between the first and second layers, and (iii) a triangular [2+2] C60 trimer along a lateral direction. As UV-vis light irradiation time increases, a comparison between experimental and theoretical IR spectra indicated that 2D dumbbell-shaped C60 polymers are formed within a few surface layers of the C60 film (in a similar manner, a 1D dumbbell-shaped polymer is also formed in a shallow space of the C60 film), whereas a [2+2] dumbbell-shaped dimer is formed in any bulk space of the film. Thereafter, when the EB was irradiated to the photopolymerized C60 film, the evolution of IR spectra with respect to EB irradiation time suggested that the 2D dumbbell-type C60 polymer is not decomposed but structurally changed to form a new network polymer.

Theoretical Investigations of Lu2C84: Unexpected Impact of Metal Electronic Configuration toward the Metal-Metal σ-Bond in Fullerene.

Recent experimental works recovered multiformity of lutetium-involved dimetallofullerenes. On the basis of density functional theory (DFT) combined with statistical thermodynamic analyses, the relative stabilities of Lu2C84 dimetallofullerene were clarified. Besides the experimentally acknowledged Lu2@D2d(51591)-C84 and Lu2@C2v(51575)-C84, another four isomers metallofullerenes, Lu2@C1(51580)-C84, Lu2C2@Cs(39715)-C82, Lu2C2@C3v(39717)-C82, and Lu2C2@C2v(39718)-C82, are first proposed as thermodynamically stable structures. Interestingly, the geometric relationships among the pristine cages of stable Lu2C84 isomers through Stone-Wales transformation or C2 lose/insertion reveal important clues of the fullerene formation mechanism. The ionic interaction in the stable Lu2C84 isomers is revealed, and their valence states are Lu24+@C844- or (Lu2C2)4+@C824-. In the Lu2@C84 isomers, the results of frontier molecular orbital and natural bond orbital analyses suggest that a Lu-Lu single bond is formed, which is mainly composed of the 6s and 6p orbitals of the Lu atoms. Further analyses of the M2@C84 (M = Sc, Y, La, and Yb) structures disclose the importance of the electron configuration of metal element toward the formation of a single metal-metal bond in C84. Moreover, the covalent interaction between the Lu2 moiety and the C84 cages is disclosed, which is a supplement to the ionic model.

Skeletal Rearrangements of the C240 Fullerene: Efficient Topological Descriptors for Monitoring Stone–Wales Transformations

Stone–Wales rearrangements of the fullerene surface are an uncharted field in theoretical chemistry. Here, we study them on the example of the giant icosahedral fullerene C240 to demonstrate the complex chemical mechanisms emerging on its carbon skeleton. The Stone–Wales transformations of C240 can produce the defected isomers containing heptagons, extra pentagons and other unordinary rings. Their formations have been described in terms of (i) quantum-chemically calculated energetic, molecular, and geometric parameters; and (ii) topological indices. We have found the correlations between the quantities from the two sets that point out the role of long-range topological defects in governing the formation and the chemical reactivity of fullerene molecules.

Encapsulation of Monometal Uranium into Fullerenes C2n (2n = 70-74): Important Ionic U4+C2n4- Characters and Covalent U-Cage Bonding Interactions.

By using density functional theory calculations combined with statistical thermodynamic analyses, the stabilization performance of a series of fullerene cages C2n (2n = 70-74) via encapsulating monometal uranium was systematically and thoroughly investigated. Results indicate that fullerene cages D5h(8149)-C70 and D3h(14246)-C74 obeying the isolated pentagon rule and C2(10612)-C72 featured with one pentalene moiety were the most promising candidates to encage uranium. Subsequent Mulliken spin density distribution and frontier molecular orbital analyses suggest that four formal electron transfer occurs from monometal U to above the carbon cages. There also exists a high degree of covalent character between the atom U and fullerenes C2n based on Mayer bond order and quantum theory of atoms in molecule (QTAIM) analyses, indicative of the cooperative stabilization by both ionic and covalent bonding interactions. In addition, investigations on the above-mentioned U@C2n isomers and other favorable candidates (U@Cs(8094)-C70, U@C1(10610)-C72, U@C1(13393)-C74, and U@C1(14049)-C74) reveal that these isomers could be closely linked via simple C2 addition and Stone-Wales transformation. These results will provide a systematic understanding on U-based endohedral metallofullerenes (EMFs) and also might be helpful for further exploration of EMF growth mechanisms.

Control of electric, optical, thermal properties of C60 films by electron-beam irradiation

We have examined the electric, optical, and thermal properties of C60 films before and after electron-beam (EB: an incident energy of 3 keV) irradiation by inducing a variety of cross-linked structures between adjacent C60 molecules via the general Stone-Wales transformation, and demonstrated that those properties can be controlled by EB-irradiation time: the resistivity ρ is continuously changed by 10−6 times and optical absorbance of C60 film increases in a range of 350–850 nm when compared to that of pristine C60 film, and the heat-resistance becomes higher that is comparable to that of polyimide film commercially available as the highest heat-resistance organic material.

Crystallographic identification of Eu@C2n (2n = 88, 86 and 84): completing a transformation map for existing metallofullerenes.

Revealing the transformation routes among existing fullerene isomers is key to understanding the formation mechanism of fullerenes which is still unclear now because of the absence of typical key links. Herein, we have crystallographically identified four new fullerene cages, namely, C 2(27)-C88, C 1(7)-C86, C 2(13)-C84 and C 2(11)-C84, in the form of Eu@C2n , which are important links to complete a transformation map that contains as many as 98% (176 compounds in total) of the reported metallofullerenes with clear cage structures (C2n , 2n = 86-74). Importantly, the mutual transformations between the metallofullerene isomers included in the map require only one or two well-established steps (Stone-Wales transformation and/or C2 insertion/extrusion). Moreover, structural analysis demonstrates that the unique C 2(27)-C88 cage may serve as a key point in the map and is directly transformable from a graphene fragment. Thus, our work provides important insights into the formation mechanism of fullerenes.

Key heptagon-containing metallofullerene intermediates in the LaSc2N@D5h(6)-C80 formation pathway: A theoretical study

Endohedral metallofullerene formation mechanisms have been proposed to involve insertion/extrusion of C2 fragment and Stone-Wales transformation (SWT). The isolation and crystallographic characterization of two isomeric LaSc2N@Ih(7)-C80 and LaSc2N@Cs(hept)-C80, which are closely related via a single step SWT, are reported to provide a clue for the trimetallic nitride template (TNT) formation pathway. Herein, we investigate three heptagon-containing isomers of LaSc2N@C80 by quantum chemistry calculations based on structural interconnections, revealing these heptagon-containing TNT links for the formation of LaSc2N@C80:D5h(6)-C80. Meanwhile, electrochemical redox properties, IR and NMR spectra of LaSc2N@C80:D5h(6)-C80 and heptagon-containing TNT isomers are simulated to help experimental identification and characterization.

Effect of Hydrogen Adsorption on the Stone–Wales Transformation in Small-Diameter Carbon Nanotubes

The effect of hydrogenation of (4, 0) and (3, 0) carbon nanotubes on the Stone–Wales transformation is studied in the framework of the nonorthogonal tight-binding model. It is shown that the atomic hydrogen adsorption can lead to both a decrease and an increase in the barriers for the direct and inverse transformations depending on the orientation of a rotating C–C bond with respect to the nanotube axis. The characteristic times of formation and annealing the Stone–Wales defects have been estimated. The Young’s moduli have been calculated.