Pairs Of Pentagons Research Articles

Nonclassical C86 and C88 Chlorofullerenes via Complex Chlorination-Promoted Skeletal Transformations of IPR Isomers of C88 and C96.

Upon high-temperature (340-360 °C) chlorination with VCl4, an isolated-pentagon-rule (IPR) C2-C88(33) fullerene is just chlorinated to C88(33)Cl22 and C88(33)Cl28, but a VCl4/SbCl5 mixture promotes a five-step cage transformation to nonclassical C86(NC2)Cl30 with two heptagons and five pairs of fused pentagons. Another chlorination-promoted seven-step transformation of an IPR fullerene removes as many as four C2 fragments from C96 to give a nonclassical C88(NC1)Cl30 with cage heptagon and six fused pairs of pentagons. We discuss the driving forces behind the observed transformations and probable detailed pathways thereof.

Fusion of Cyclohepta[def]fluorene Units: Toward Synthesis of High‐Spin Non‐Benzenoid Nanographenes

AbstractNon‐benzenoid diradicaloids possessing high‐spin ground states are attractive synthetic targets given their high potential for spintronics and quantum computing. Nevertheless, the synthesis of such compounds remains highly challenging due to their inherent instability. In this work, we present the synthetic attempt towards creating a non‐benzenoid diradicaloid (1) with a triplet ground state by fusing two cyclohepta[def]fluorene units onto a benzene ring. Our synthetic approach involves both oxidation and reduction pathways. In the oxidation path, we obtained the partially dehydrogenated products 1+H and 1+2H containing an indeno[1,2‐b]fluorene core from the tetrahydro precursor (2). However, further dehydrogenation to afford the target molecule (1) did not proceed. On the other hand, with the reduction pathway, a novel tetraketone precursor (9) with two pairs of pentagons and heptagons was successfully synthesized. The subsequent nucleophilic attack however was proved to be difficult probably due to the unselective nucleophilic addition on the zigzag nanographene ketones. Furthermore, UV‐vis absorption, cyclic voltammetry, and theoretical calculations were conducted to explore the optical, electrochemical properties, and aromaticity of all the obtained molecules (1+H, 1+2H and 9). Although the desired target 1 is not achieved, our work provides insight into designing novel high‐spin non‐benzenoid NGs based on nonalternant cyclohepta[def]fluorene system.

The road to bis‐periazulene (cyclohepta[def]fluorene): Realizing one of the long‐standing dreams in nonalternant hydrocarbons

AbstractThe chemistry of nonalternant hydrocarbons has recently experienced a considerable resurgence. As the relationship between naphthalene and azulene shows, an important design concept for a nonalternant framework is to replace the two hexagons of an alternant system with a pentagon and heptagon pair. The pursuit of the nonalternant isomers of pyrene, which has seven possible nonalternant isomers, has been the most significant related project. Through enormous dedication by many pioneering works, six of the seven possible nonalternant isomers of pyrene have been isolated and characterized as stable aromatic molecules, differentiating themselves from pyrene in terms of optoelectronic properties. However, the only unsynthesized isomer, bis‐periazulene (cyclohepta[def]fluorene), had remained an uncharacterized hydrocarbon until 2022, despite many synthetic and theoretical investigations since it was first reported in 1955. In this review, we summarize the chemistry of the pyrene's nonalternant isomers, including our recent achievements in synthesizing and characterizing bis‐periazulene derivatives. The historical perspectives, synthetic approaches, fundamental properties, and comparisons to related systems are documented.

Electrical resistivity of polycrystalline graphene: effect of grain-boundary-induced strain fields

We have revealed the decisive role of grain-boundary-induced strain fields in electron scattering in polycrystalline graphene. To this end, we have formulated the model based on Boltzmann transport theory which properly takes into account the microscopic structure of grain boundaries (GB) as a repeated sequence of heptagon–pentagon pairs. We show that at naturally low GB charges the strain field scattering dominates and leads to physically reasonable and, what is important, experimentally observable values of the electrical resistivity. It ranges from 0.1 to 10 kOmegaupmu m for different types of symmetric GBs with a size of 1 upmum and has a strong dependence on misorientation angle. For low-angle highly charged GBs, two scattering mechanisms may compete. The resistivity increases markedly with decreasing GB size and reaches values of 60 kOmegaupmum and more. It is also very sensitive to the presence of irregularities modeled by embedding of partial disclination dipoles. With significant distortion, we found an increase in resistance by more than an order of magnitude, which is directly related to the destruction of diffraction on the GB. Our findings may be of interest both in the interpretation of experimental data and in the design of electronic devices based on poly- and nanocrystalline graphene.

Nice pairs of pentagons in chamfered fullerenes

Fullerenes graphs are 3-connected, 3-regular planar graphs with faces including only pentagons and hexagons. If be a graph with a perfect matching, a subgraph H of G is a nice subgraph if G-V(H) has a perfect matching. In this paper, we show that in every fullerene graph arising from smaller fullerenes via chamfer transformation, each pair of pentagons is a nice subgraph.

Nice pairs of disjoint pentagons in fullerene graphs

A subgraph H of a graph G with a perfect matching is called nice, if $$G-V(H)$$ has a perfect matching. Very recently, Doslic (JMC 58:2204-2222, 2020) pointed out that every fullerene graph contains a nice pair of disjoint odd cycles and proposed a series of problems on whether such a pair of odd cycles can be chosen as pentagons. In this paper, we show that any fullerene graph always contains a nice pair of disjoint pentagons, which solves completely Problems 1 and 2. Further, we prove that if a fullerene graph satisfies that each pentagon is adjacent to at most two other pentagons, then any pair of disjoint pentagons is nice except for only one fullerene graph on 36 vertices. As a consequence, for the IPR fullerenes (any two pentagons are disjoint), the result also holds, which thus answers positively Problems 4 and 6.

All Pairs of Pentagons in Leapfrog Fullerenes Are Nice

A subgraph H of a graph G with perfect matching is nice if G−V(H) has perfect matching. It is well-known that all fullerene graphs have perfect matchings and that all fullerene graphs contain some small connected graphs as nice subgraphs. In this contribution, we consider fullerene graphs arising from smaller fullerenes via the leapfrog transformation, and show that in such graphs, each pair of (necessarily disjoint) pentagons is nice. That answers in affirmative a question posed in a recent paper on nice pairs of odd cycles in fullerene graphs.

(Invited) Capturing the Double-Heptagon-Containing C70 with Negative Curvature

Heptagon-containing fullerenes (heptafullerenes) exhibit negative curvature. Herein, we report the first double negatively curved C70 isomer containing two symmetric heptagons moieties. The compound was captured in situ as dihept-C70Cl6 from a chlorine-involving carbon arc. As demonstrated by X-ray crystallography, the dihept-C70Cl6 isomer with two negatively curved heptagon moieties contained 14 pentagons and 21 hexagons, in which four of the 14 pentagons are fused. The unfavorable local tensile of the adjacent pentagons was dramatically decreased by the binding of chlorine atoms. The two pairs of adjacent pentagons are exactly fused to two concave heptagons, resulting in the negative curvature with a symmetric plane. The occurrence of heptagon moieties provides an additional stabilizing effect on the heptafullerene. Theoretical studies suggest that captured dihept-C70Cl6 can be rationally regarded as a product of C66 via successive C2 insertions. This present study provides insight into the mechanism responsible for heptafullerene formation in a carbon arc. Figure 1

Diels-Alder Cycloaddition on Nonisolated-Pentagon-Rule C2v(19 138)-C76 and YNC@C2v(19 138)-C76: The Difference in Regioselectivity Caused by the Inner Metallic Cluster.

Diels-Alder reactions of cyclopentadiene to C2v(19 138)-C76 and YNC@C2v(19 138)-C76 violating the isolated pentagon rule have been systematically studied by means of density functional theory calculations. As for the free fullerene, the pentalene-type [5,5]-bond in the adjacent pentagon pair is the most favorable from thermodynamic and kinetic viewpoints, which is attributed to the highly strained carbon atoms accompanied by the suitable lowest unoccupied molecular orbital shape with a large distribution to interact with cyclopentadiene. Upon encapsulating the YNC cluster, a corannulene-type [5,6]-bond and a pyracylene-type [6,6]-bond become the two most reactive addition sites under thermodynamic and kinetic conditions, which possess similar reaction energies and energy barriers. Especially, the [5,6]-bond exhibits a larger reaction energy and a lower energy barrier than that on the free fullerene, which should be ascribed to its shorter bond length and larger π-orbital axis vector value after trapping the metallic cluster. The suitable unoccupied molecular orbital lobes with large distributions on the [5,6]- and [6,6]-bonds are also an advantage of cycloadditions. This work presents the first example that the most favorable addition site is remote from the adjacent pentagon pair in the fullerene cage after encapsulating a metallic cluster.

Desorption of Fullerene Dimers upon Heating Non-IPR Fullerene Films on HOPG

Low energy ion beam deposition of mass-selected fullerene ions was used to generate thin films of non-IPR fullerenes, C2n (2n = 48–58 and 52–68) on graphite under UHV. These were probed by mass-resolved thermal desorption spectroscopy. We observe the emission of dimers in addition to dominant monomer desorption for 2n = 58–68, while for 2n = 48–56 no dimer desorption was detected. Dimer signals were typically at <1% level compared to the monomers. The desorption temperature ranges of these dimer species were higher and much narrower than for the corresponding monomers. Building also on theoretical considerations, we came to the conclusion that coalescence reactions between the fullerenes must take place below 1000 K and that fullerenes with more than three pairs of adjacent pentagons cross-link too strongly to allow the desorption of dimers.

Exploring Adjacent Pentagons in Non-IPR and SW Defective Si60 and Si70 Silicon Fullerenes: a Computational Study

We have applied DFT calculations to investigate the effect of the adjacent pentagons (APs) on the geometries, stabilities, and electronic structures of the non-IPR isomers of Si60 and Si70 fullerenes containing three adjacent pentagon pairs, Si60(D3) and Si70(C2v), and the SW defective Si60 and Si70 fullerenes with four AP pairs. These non-IPR isomers of Si60 and Si70 cages are more stable than their IPR ones. Natural bond orbital analyses and electrostatic potential surfaces indicate the charge densities are more localized at the pentagon-pentagon edges of the non-IPR fullerenes, which increase by going to the charged ones. Based on our results, the SW rearrangement process in the Si60 and Si70 silicon fullerenes is exothermic. A silylene-like transition state along a stepwise reaction path is characterized at the B3LYP/6-311 + G* level of theory. The barrier for the SW rearrangement of Si60 fullerene is obtained to be 5.36 eV which is smaller than that reported for SW rearrangement of C60 fullerene.

Rebuilding C60: Chlorination-Promoted Transformations of the Buckminsterfullerene into Pentagon-Fused C60 Derivatives.

In recent years, many higher fullerenes that obey the isolated pentagon rule (IPR) were found capable of rearranging into molecules with adjacent pentagons and even with heptagons via chlorination-promoted skeletal transformations. However, the key fullerene, buckminsterfullerene I h-C60, long seemed insusceptible to such rearrangements. Now we demonstrate that buckminsterfullerene yet can be transformed by chlorination with SbCl5 at 420-440 °C and report X-ray structures for the thus-obtained library of non-IPR derivatives. The most remarkable of them are non-IPR C60Cl24 and C60Cl20 with fundamentally rearranged carbon skeletons featuring, respectively, four and five fused pentagon pairs (FPPs). Further high-temperature trifluoromethylation of the chlorinated mixture afforded additional non-IPR derivatives C60(CF3)10 and C60(CF3)14, both with two FPPs, and a nonclassical C60(CF3)15F with a heptagon, two FPPs, and a fully fused pentagon triple. We discuss the general features of the addition patterns in the new non-IPR compounds and probable pathways of their formation via successive Stone-Wales rearrangements.

Theoretical Insights into Monometallofullerene Th@C76: Strong Covalent Interaction between Thorium and the Carbon Cage.

Th@C76 has been studied by density functional theory combined with statistical mechanics calculations. The results reveal that Th@ T d(19151)-C76 satisfying the isolated pentagon rule possesses the lowest energy. Nevertheless, considering the enthalpy-entropy interplay, Th@ C1(17418)-C76 with one pair of adjacent pentagons is thermodynamically favorable at elevated temperatures, which is reported for the first time. The bonding critical points in both isomers were analyzed to disclose covalent interactions between the inner Th and cages. In addition, the Wiberg bond orders of M-C bonding in different endohedral metallofullerenes (EMFs) were investigated to prove stronger covalent interactions of Th-C in Th-based EMFs.

Electronic and Spectroscopic Properties of La2@C112 Isomers

Among the 3352 isolated pentagon rule(IPR) isomers and 129073 non-IPR isomers satisfying adjacent pentagon pairs(APPs)≤2 of fullerene C112, the lowest-energy IPR and non-IPR isomers of C112 and C1126- have been fully screened by the density functional tight-binding(DFTB) and density functional theory(DFT) methods for studying the electronic and spectroscopic properties of La2@C112. The structural features and infrared and absorption spectra of those isomers were analyzed in detail, and the characteristic fingerprint absorption peaks were assigned. To clarify the relative stabilities of La2@C112 isomers at high temperature, entropy contributions were determined at the B3LYP level. IPR isomer La2@C112(C2:860136) is not the lowest-energy isomer but is one of the most important isomers. This is the first work that considers non-IPR C112 isomers when exploring the structure and properties of La2@C112.

Electronic structures and stabilities of the defective nanotube-like fullerenes C58+10n and their derivatives C58+10nCl8

The stability and electronic properties of the defective nanotube-like fullerenes C58+10n obtained by removing a 5–6 bond closest to the poles of C60+10n and their derivatives C58+10nCl8 (n=1, …, 10) have been investigated by using the density functional theory method. For each system, two isomer structures (the nonclassical fullerene with a heptagon and non-IPR fullerene with two pentagon pairs) and two electronic states (singlet and triplet) were examined. The results show that the non-IPR fullerenes C58+10n with two pentagon pairs are more stable than their nonclassical isomer with a heptagon. Both the relative energies and the gap energies between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) reveal that the ground state for non-IPR Cs-C68, Cs-C98, Cs-C128, and Cs-C158 is the triplet state, whereas the singlet state is the ground state for non-IPR Cs-C78, Cs-C88, Cs-C108, Cs-C118 Cs-C138, and Cs-C148. Further chlorination on non-IPR fullerenes enhances the stability of chlorofullerenes. Especially, Cs-C68Cl8, Cs-C98Cl8, Cs-C128Cl8, and Cs-C158Cl8 have the most enhance stability both thermodynamically and kinetically exhibiting high negative reaction energies and large HOMO-LUMO gap energies. In addition, the nucleus-independent chemical shift (NICS) analysis shows that the triplet spin state is more aromatic than the corresponding singlet spin state for non-IPR Cs-C68, Cs-C98, Cs-C128, and Cs-C158. All derivatives C58+10nCl8 are also aromatic.

Deciphering the Role of Long-Range Interaction in Endohedral Metallofullerenes: A Revisit to Sc2C70

Structure elucidation is a vital step to study endohedral metallofullerene (EMF), and theoretical investigation is a useful complementary way to elucidate structures of EMFs. However, our recent work exposed that density functional theory (DFT) methods without long-range corrections are prone to overestimate energies of Sc2C2@C72 isomers. In this work, the role of long-range interaction in energy estimation of EMFs was rigorously investigated by comparing energies and interaction energies of Sc2C70 and La2C96 series with wB97XD, M06-2X, B3LYP, and PBE0 methods, and it was disclosed that long-range interaction is ubiquitously imperative for metal cluster fullerenes and conventional metallofullerenes whose cages are absent of adjacent pentagon pair(s). Meanwhile, thermodynamic stabilities of the controversial Sc2C70 series were thoroughly investigated, and Sc2C2@C2v(6073)-C68 with the highest abundance on the temperature range of EMF formation instead of Sc2@C2v(7854)-C70 was confirmed to be the experimenta...

The inner-induced effects of YCN in C76 on the structures and nonlinear optical properties

Very recently, an unprecedented novel monometallic cluster of fullerenes entrapping a yttrium cyanide (YCN) cluster inside a popular C82 cage YCN@Cs(6)-C82 was synthesized and characterized. Inspired by this investigation, four non-IPR YCN@C1(17459)-C76, YCN@C2v(19138)-C76, YCN@C2(17646)-C76, and YCN@C1(17894)-C76 (1, 2, 3, and 4) containing a pair of adjacent pentagons are designed to explore the encapsulated molecular effect on their interaction energies and nonlinear optical properties. The interaction energy (E int) values of 1, 2, 3, and 4 are -481.35 (1), -477.91 (2), -482.04 (3), -482.69 (4) kcal mol(-1), respectively, which shows that the E int value of 4 is the largest. Furthermore, the electron-transfer is mainly from the YCN to C76 cage. When YCN is encapsulated into C76 cage, we can find that the α0 values of the four molecules are very close, ranging from 6.50 × 10(2) to 6.65 × 10(2) au. Significantly, the first hyperpolarizabilities are in relation to the encapsulated molecular: 1.63 × 10(3) (1) > 8.03 × 10(2) (2) > 7.76 × 10(2) (4) > 4.86 × 10(2) au (3), the results show that the βtot value of 1 is the largest. Besides this, the encapsulation of the YCN to C76 cage brings some distinctive changes in its UV-vis spectra along with its other electronic properties that might be used by the experimentalists to develop the potential nonlinear optical nanomaterials based on endohedral metallofullerenes.

First-principles theory of Si(110)-(16 × 2) surface reconstruction for unveiling origin of pentagonal scanning tunneling microscopy images

The origin of the scanning tunneling microscopy (STM) zigzag chain structures composed of pairs of pentagons on the Si(110)-(16 × 2) surface is unveiled through the first-principles calculation method. Stable Si(110) surface structures, on both flat and stepped surfaces, have been discovered. The energy gain of the stable step structure is larger than those of previously proposed models by 5.0 eV/(16 × 2) cell or more. The structure consists of buckled tetramers, heptagonal rings, tetragonal rings, and threefold-coordinated Si atoms, but no pentagonal rings. It reproduces the experimental STM images only when frequent flip-floppings of the buckled tetramers at room temperature are considered.

General rules for predicting the local aromaticity of carbon polyhedra

The aromaticity of classical and nonclassical C24 fullerene isomers and their anions were studied using the topological resonance energy (TRE) method. Local aromaticity was studied using the bond resonance energy (BRE) method. On the basis of BRE values, the contributions of different types of chemical bonds to the molecular global aromaticity were analyzed and general rules for predicting the local aromaticity of fullerenes are proposed. It was found that pentagons, heptagons, and squares preferred hexagons as neighbors rather than squares as neighbors. In the hexaanionic state, pentagon pair sites exhibit larger local aromaticity than other places in the same molecule.

Dimetallic sulfide endohedral metallofullerene Sc2S@C76: density functional theory characterization.

In terms of density functional theory combined with statistic mechanics computations, we investigated a dimetallic sulfide endohedral fullerene Sc2S@C76 which has been synthesized without any characterization in experiments. Our theoretical study reveals that Sc2S@Td(19151)-C76 which satisfies the isolated-pentagon rule (IPR) possesses the lowest energy, followed by three non-IPR structures (Sc2S@C2v(19138)-C76, Sc2S@Cs(17490)-C76, and Sc2S@C1(17459)-C76). To clarify the relative stabilities of those isomers at high temperatures, enthalpy-entropy interplay has been taken into consideration. Calculation results indicate that three species Sc2S@Td(19151)-C76, Sc2S@C2v(19138)-C76, and Sc2S@C1(17459)-C76 have noticeable molar fractions at the fullerene-formation temperature region (500-3000K), and the Sc2S@C1(17459)-C76 with one pentagon pair becomes the most predominant isomer above 1800 K, suggesting that the unexpected non-IPR structure is thermodynamically favorable at elevated temperatures. In addition, the structural characteristics, electron features, UV-vis-NIR adsorptions, and (13)C NMR spectra of those three stable structures are introduced to assist experimental identification and characterization in future.