Adjacent Pentagon Pairs Research Articles

(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

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.

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.

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.

Maximum Aromaticity As a Guiding Principle for the Most Suitable Hosting Cages in Endohedral Metallofullerenes

Encapsulation of metal clusters in endohedral metallofullerenes takes place in cages that in most cases are far from being the most stable isomer in the corresponding hollow fullerenes. In large metal clusters and small fullerene cages, the election is mainly driven by the need to reduce strain. For the not so large metal clusters, it is usually said that the cage is chosen to minimize the electrostatic repulsion between charged five-membered rings.1 We have proved that maximizing the aromaticity is the main driving force that determines the most suitable hosting carbon cage for a given metallic cluster.2 This simple rule, the so-called Maximum ARomaticity Criterion (MARC), allow us to directly compare IPR (isolated pentagon rule) and non-IPR anionic isomers regardless the number of adjacent pentagon pairs (APP) they have. We have tested the MARC for the majority of endohedral metallofullerenes from C66 to C104 reported to date and the results show that MARC successfully predicts the most suitable C2n cage for hosting a given metal cluster among the manifold existing C2n isomers. In addition, using the Maximum ARomaticity Criterion, one can justify why the IPR rule is not always fulfilled when EMFs are considered.[Figure 1 here]Figure 1. Classification in terms of the ALA index of the anionic IPR and non-IPR fullerene isomers with 1-3 Adjacent Pentagon Pairs (APPs) for the most common C2 n (2n = 66–104) EMFs reported to date. Isomers experimentally observed are marked using black dots, and their corresponding isomer numbers are indicated. The ALA prediction ordering for the experimentally observed isomers are given in parentheses. A. Rodríguez-Fortea, N. Alegret, A.L. Balch, J.M. Poblet, Nat. Chem. 2010, 2, 955.M. Garcia-Borràs, S. Osuna, M. Swart, J.M. Luis, and M. Solà, Angew. Chem. Int. Ed. 2013, 52, 9275.

La2@Cs(17 490)‐C76: A New Non‐IPR Dimetallic Metallofullerene Featuring Unexpectedly Weak Metal–Pentalene Interactions

Although all the pure-carbon fullerene isomers above C60 reported to date comply with the isolated pentagon rule (IPR), non-IPR structures, which are expected to have different properties from those of IPR species, are obtainable either by exohedral modification or by endohedral atom doping. This report describes the isolation and characterization of a new endohedral metallofullerene (EMF), La2@C76, which has a non-IPR fullerene cage. The X-ray crystallographic result for the La2@C76/[Ni(II)(OEP)] (OEP=octaethylporphyrin) cocrystal unambiguously elucidated the C(s)(17,490)-C76 cage structure, which contains two adjacent pentagon pairs. Surprisingly, multiple metal sites were distinguished from the X-ray data, which implies dynamic behavior for the two La(3+) cations inside the cage. This dynamic behavior was also corroborated by variable-temperature (139)La NMR spectroscopy. This phenomenon conflicts with the widely accepted idea that the metal cations in non-IPR EMFs invariably coordinate strongly with the negatively charged fused-pentagon carbons, thereby providing new insights into modern coordination chemistry. Furthermore, our electrochemical and computational studies reveal that La2@C(s)(17,490)-C76 has a larger HOMO-LUMO gap than other dilanthanum-EMFs with IPR cage structures, such as La2@D(3h)(5)-C78 and La2@I(h)(7)-C80, which implies that IPR is no longer a strict rule for EMFs.

Aromaticity as the driving force for the stability of non-IPR endohedral metallofullerene Bingel–Hirsch adducts

We have studied the relative stabilities of Bingel-Hirsch non-IPR endohedral metallofullerene monoadducts having one, two, or three adjacent pentagon pairs. The most stable addition always leads to an open adduct and never occurs on [5,5] bonds. Our results show that the thermodynamics of the addition is governed by the additive local aromaticity of the rings of the final adducts.

Probing the role of encapsulated alkaline earth metal atoms in endohedral metallofullerenes M@C76 (M = Ca, Sr, and Ba) by first-principles calculations

By means of density functional theory and statistical mechanics, we investigate the geometric and electronic structures, thermodynamic stability and infrared (IR) vibrational frequencies of alkaline earth metal endohedral fullerenes, M@C(76) (M = Ca, Sr, and Ba). The results reveal that M@C(1)(17,459)-C(76) possesses the lowest energy followed by M@C(2v)(19,138)-C(76) with a very small energy difference. Both the structures have a pair of adjacent pentagons and are related by a single Stone-Wales transformation. Equilibrium statistical thermodynamic analyses based on Gibbs energy treatments suggest that M@C(1)(17,459)-C(76) has a prominent thermodynamic stability at higher temperatures, in contrast with M@C(2v)(19,138)-C(76) whose thermodynamic stability is affected by the encapsulated metal atom. The encapsulated metallic atoms as well as cage structures significantly influence the electronic properties of endohedral fullerenes such as electron affinities and ionization potentials. On the other hand, the singlet-triplet splitting energy ΔE(S-T) depends on the cage structures. In addition, IR spectra and chemical shifts of these compounds have been computed to assist further experimental characterization.

Synthesis, Isolation, Characterization, and Theoretical Studies of Sc3NC@C78-C2

Following the first isolation of Sc3NC@C80, a second member of this family of endohedral metallofullerenes, Sc3NC@C78, was prepared by an arc-discharging method. Experimental and theoretical studies demonstrated that the Sc3NC@C78 has a C78-C2 cage with two pairs of adjacent pentagons, which is different from the IPR-satisfying Sc3N@C78-D3h. It was revealed that the size of C78-D3h is appropriate for the Sc3N cluster, but not large enough for encaging the large planar species Sc3NC. Theoretical calculations were preformed on Sc3NC@C78-C2 and Sc3NC@C78-D3h. The results show that Sc3NC would bear a strong depression inside the C78-D3h fullerene cage due to the limited internal space of C78-D3h; on the contrary, C78-C2 has two pairs of adjacent pentagons that induce a large curvature in these sites to form an oblate ellipsoid structure. Thus, it is more favorable to encapsulate the planar species Sc3NC. Ab initio calculations were also performed to further disclose the electronic and electrochemical properti...

The maximum pentagon separation rule provides a guideline for the structures of endohedral metallofullerenes

Fullerenes tend to follow the isolated pentagon rule, which requires that each of the 12 pentagons is surrounded only by hexagons. Over the past decade many violations to this rule were reported for endohedral fullerenes. Based on the ionic model M(3)N(6+)@C(2n)(6-) and the orbital energies of the isolated cages, in 2005 we formulated a molecular orbital rule to identify the most suitable hosting cages in endohedral metallofullerenes. Now, we give physical support to the orbital rule, and we propose the maximum pentagon separation rule, which can be applied to either isolated pentagon rule cages or to non-isolated pentagon rule cages with the same number of adjacent pentagon pairs. The maximum pentagon separation rule can be formulated as 'The electron transfer from the internal cluster to the fullerene host preferentially adds electrons to the pentagons; therefore, the most suitable carbon cages are those with the largest separations among the 12 pentagons'.

Properties of non-IPR fullerene films versus size of the building blocks

This perspective focuses on the cage size dependent properties of novel solid fullerene nanofilms grown by soft-landing of mass-selected C(n)(+) (48, 50, 52, 54, 56, 58, 62, 64, 66 and 68) onto room temperature graphite surfaces under ultra-high vacuum conditions. Such non-isolated-pentagon-ring (non-IPR) fullerene materials are not accessible to standard fullerene preparation methods. The component molecular building blocks of non-IPR films were generated by electron impact induced ionization/fragmentation of sublimed IPR-C(70)(D(5h)) (-->C(n) (n = 68, 66, 64, 62)) or IPR-C(60)(I(h)) (-->C(n) (n = 58, 56, 54, 52, 50)). Non-IPR fullerene films on graphite grow via formation of dendritic C(n) aggregates, whereas deposition of IPR fullerenes under analogous conditions (via deposition of unfragmented C(60)(+) and C(70)(+)) leads to compact islands. The latter are governed by weak van der Waals cage-cage interactions. In contrast, the former are stabilized by covalent intercage bonds as mediated by the non-IPR sites (primarily adjacent pentagon pairs, AP). A significant fraction of the deposited non-IPR C(n) cages can be intactly (re)sublimed by heating. The corresponding mean desorption activation energies, E(des), increase from 2.1 eV for C(68) up to 2.6 eV for C(50). The densities of states in the valence band regions (DOS), surface ionization potentials (sIP) and HOMO-LUMO gaps (Delta) of semiconducting non-IPR films were measured and found to vary strongly with cage size. Overall, the n-dependencies of these properties can be interpreted in terms of covalently interconnected oligomeric structures comprising the most stable (neutral) C(n) isomers-as determined from density functional theory (DFT) calculations. Non-IPR fullerene films are the first known examples of elemental cluster materials in which the cluster building blocks are covalently but reversibly interconnected.

Non-IPR C60 solids

Films comprising predominantly novel isomers of C(60) [=C(60)(nIPR)] have been generated by low energy ion beam deposition of vibronically excited C(60)(+) onto graphite followed by selective sublimation of C(60)(I(h)) from the deposited isomer mixture. The incident ions were generated by electron impact ionization/fragmentation of sublimed C(70). Images of the C(60)(nIPR) films obtained by applying atomic force microscopy show aggregates, which we attribute to covalently interlinked C(60)(nIPR) units. The covalent bonds are inferred from the significantly higher thermal stability of the C(60)(nIPR) films compared to the C(60)(I(h)) van der Waals solid-as measured by thermal desorption with mass spectrometric detection of the C(60) mass channel (the only desorbable species). In contrast to the characteristic doublet structure of the occupied valence band in the ultraviolet photoelectron spectrum of pure C(60)(I(h)), the valence band of C(60)(nIPR) films exhibits a triplet feature with the additional peak occurring at a binding energy of approximately 2.6 eV. This is an indicator of the electronic modifications induced by intermolecular bonding. C(60)(nIPR) films exhibit a narrower band gap than found for C(60)(I(h)). They also have significantly different chemical reactivity toward incorporation of thermal energy deuterium atoms. In order to model the experimental photoelectron spectra, various covalently linked oligomers of (#1809)C(60)(C(2v)), the second most stable conventional 60-atom fullerene cage, were calculated by means of the density functional theory. These spectral predictions together with analogous previous observations on related fullerene solids such as C(58) lead us to infer that C(60)(nIPR) films consist of fullerene cage isomers containing one or more adjacent pentagon pairs, which mediate covalent cage-cage interconnection.

First- and second-electron affinities ofC60andC70isomers

We present density functional theory calculations of C{sub 60}{sup q-} and C{sub 70}{sup q-} (q=0-2) isomers that contain zero to three pairs of adjacent pentagons. The first- and second-electron affinities for the archetype structures of C{sub 60} and C{sub 70} are close to the experimental results, while isomers with pentagon adjacencies have significantly higher values. The results are rationalized in view of the numbers and locations of pentagon adjacencies in the fullerene cages and the spherical aromaticity for the magic number C{sub 70}{sup 2-} with a closed (l=5) electronic shell in the spherical gas model.

Structure, Stability, and Cluster-Cage Interactions in Nitride Clusterfullerenes M3N@C2n (M = Sc, Y; 2n = 68−98): a Density Functional Theory Study

Extensive semiempirical calculations of the hexaanions of IPR (isolated pentagon rule) and non-IPR isomers of C(68)-C(88) and IPR isomers of C(90)-C(98) followed by DFT calculations of the lowest energy structures were performed to find the carbon cages that can provide the most stable isomers of M(3)N@C(2n) clusterfullerenes (M = Sc, Y) with Y as a model for rare earth ions. DFT calculations of isomers of M(3)N@C(2n) (M = Sc, Y; 2n = 68-98) based on the most stable C(2n)(6-) cages were also performed. The lowest energy isomers found by this methodology for Sc(3)N@C(68), Sc(3)N@C(78), Sc(3)N@C(80), Y(3)N@C(78), Y(3)N@C(80), Y(3)N@C(84), Y(3)N@C(86), and Y(3)N@C(88) are those that have been shown to exist by single-crystal X-ray studies as Sc(3)N@C(2n) (2n = 68, 78, 80), Dy(3)N@C(80), and Tb(3)N@C(2n) (2n = 80, 84, 86, 88) clusterfullerenes. Reassignment of the carbon cage of Sc(2)@C(76) to the non-IPR Cs: 17490 isomer is also proposed. The stability of nitride clusterfullerenes was found to correlate well with the stability of the empty 6-fold charged cages. However, the dimensions of the cage in terms of its ability to encapsulate M(3)N clusters were also found to be an important factor, especially for the medium size cages and the large Y(3)N cluster. In some cases the most stable structures are based on the different cage isomers for Sc(3)N and Y(3)N clusters. Up to the cage size of C(84), non-IPR isomers of C(2n)(6-) and M(3)N@C(2n) were found to compete with or to be even more stable than IPR isomers. However, the number of adjacent pentagon pairs in the most stable non-IPR isomers decreases as cage size increases: the most stable M(3)N@C(2n) isomers have three such pairs for 2n = 68-72, two pairs for n = 74-80, and only one pair for n = 82, 84. For C(86) and C(88) the lowest energy IPR isomers are much more stable than any non-IPR isomer. The trends in the stability of the fullerene isomers and the cluster-cage binding energies are discussed, and general rules for stability of clusterfullerenes are established. Finally, the high yield of M(3)N@C(80) (Ih) clusterfullerenes for any metal is explained by the exceptional stability of the C(80)(6-) (Ih: 31924) cage, rationalized by the optimum distribution of the pentagons leading to the minimization of the steric strain, and structural similarities of C(80) (Ih: 31924) with the lowest energy non-IPR isomers of C(760(6-), C(78)(6-), C(82)(6-), and C(84)(6-) pointed out.

Structures, Stabilities, and Electronic and Optical Properties of C62 Fullerene Isomers

The 2385 classical isomers and four nonclassical isomers of fullerene C62 have been studied by PM3, HCTH/3-21G//SVWN/STO-3G, B3LYP/6-31G(d)//HCTH/3-21G, and B3LYP/6-31G(d)//B3LYP/6-31G(d). The Cs:7mbr isomer, with a chain of four adjacent pentagons surrounding a heptagon, is predicted to be the most stable isomer, followed by C2v:4mbr which is 3.15 kcal/mol higher in energy. C2:0032 with three pairs of adjacent pentagons is the most stable isomer in the classical framework. To clarify the relative stabilities of C62 isomers at high temperatures, the entropy contributions are taken into account on the basis of the Gibbs energy at the B3LYP/6-31G(d) level. Analyses reveal that Cs:7mbr prevails in a wide temperature range. The vibrational frequencies of the five most stable C62 fullerene isomers are also predicted at the B3LYP/6-31G(d) level, and the simulated IR spectra show important differences in positions and intensities of the vibrational modes for different isomers. The nucleus-independent chemical shift and the density of states of the three most stable isomers show that the square in C2v:4mbr and the adjacent pentagons in Cs:7mbr and C2:0032 possess high chemical reactivity. In addition, the electronic spectra and second-order hyperpolarizabilities are determined by means of ZINDO and the sum-over-states mode. The intensity-dependent refractive index gamma(-omega; omega, omega, -omega) at omega = 2.3305 eV of Cs:7mbr is very large because of resonance with the external field. The second-order hyperpolarizabilities of the five most stable isomers of C62 are predicted to be larger than those of C60.

Structure and formation energy of carbon nanotube caps

We present a detailed study of the geometry, structure and energetics of carbon nanotube caps. We show that the structure of a cap uniquely determines the chirality of the nanotube that can be attached to it. The structure of the cap is specified in a geometrical way by defining the position of six pentagons on a hexagonal lattice. Moving one (or more) pentagons systematically creates caps for other nanotube chiralities. For the example of the (10,0) tube we study the formation energy of different nanotube caps using ab-initio calculations. The caps with isolated pentagons have an average formation energy 0.29+/-0.01eV/atom. A pair of adjacent pentagons requires a much larger formation energy of 1.5eV. We show that the formation energy of adjacent pentagon pairs explains the diameter distribution in small-diameter nanotube samples grown by chemical vapor deposition.

Mg@C 72 MNDO/d evaluation of the isomeric composition

Temperature development of the relative stabilities of isomers of Mg@C 72 (which has not yet been isolated) is computed using the recently introduced MNDO/d method. Four isomers originally considered for the Ca@C 72 case are treated: one isolated-pentagon-rule (IPR) structure, two structures with a pair of adjacent pentagons, and one cage with a heptagon. The IPR structure comes as the lowest in MNDO/d potential energy, being rather closely followed by the two structures with a pentagon–pentagon pair. On the other hand, the structure with a heptagon is located too high in potential energy to be of any experimental significance. The entropy contributions are evaluated by the MNDO/d-based partition functions so that the relative concentrations can be treated accordingly. The computations suggest that if Mg@C 72 is isolated, it should be a mixture of either two or three isomers. The prediction depends on temperature prehistory. If preparation takes place at temperatures of approximately 1000 K, two isomers should be produced. If temperatures are increased to approximately 2000 K, there will already be three isomers with significant relative concentrations. The study supplies a further interesting example of the profound role of enthalpy–entropy interplay in stabilities of isomeric fullerenic structures. © 2001 by Elsevier Science Inc.

Theoretical Investigations of Carbon Nanotube Growth

The growth of carbon nanotubes was investigated using a variety of complementary simulation techniques. Currently, a number of experimental methods are used to synthesize carbon nanotubes suggesting that different mechanisms play a role in their formation. However, it has been shown that growth of nanotubes takes place primarily at the open-ended tips of nanotubes. Ab initio simulations show that the high electric fields present at the nanotube tips in carbon arc discharges cannot be responsible for keeping the tubes open. Rather, the opening and closing of tubes is controlled by the formation of curvature-inducing defects such as adjacent pentagon pairs. On narrow tubes, the formation of such defects is favored leading to the rapid closure of the tubes. By contrast, the formation of hexagons, which lead to straight open-ended growth is favored on large-diameter tubes, with an estimated crossover radius of about 3 nm. Large-scale molecular dynamics and kinetic Monte Carle simulations have been used to verify these ideas. We have also explored the role of the so-called lip–lip interactions during growth. Such an interaction is important in producing multiwalled nanotubes, where the interaction between two open nanotube tips leads to the formation of a network of bonds. Simulations show that such an interaction is indeed significant, but does not provide the additional stabilization required for straight, open-ended, multiwalled nanotube growth. Finally, we consider the formation of nanotubes in the presence of large and small catalytic particles. In the former case, growth is believed to take place via a root-growth mechanism, while the direct adsorption and extrusion of carbon from the vapor dominates the latter. Both mechanisms lead to the formation of small-diameter, single-wall nanotubes.