Theoretical investigation into structures and magnetic properties of smaller fullerenes and their heteroanalogues

The smaller fullerenes, C₂₀, C₂₄, C₂₈, C₃₂, C_36, C₄₀ and C₅₀, their hydrogenation products and selected B-, N- and P-doped analogues have been investigated systematically at the B3LYP/6-31G* density functional level of theory. The degree of spherical electron delocalization is evaluated by using the computed nucleus-independent chemical shifts ( NICS) at the cage center and the individual ring centers of interest. The calculated NMR chemical shifts and the NICS values at the cage center, which can be accessed by endohedral ³He chemical shifts, should provide a basis for further experimental characterization of these compounds. Received: 26 March 2001 / Accepted: 10 May 2001 / Published online: 11 October 2001     

Accurate calculation,prediction, and assignment of 3He NMR chemical shifts of helium-3-encapsulated fullerenes and fullerene derivatives

Helium-3 NMR chemical shifts of various (3)He-encapsulated fullerenes ((3)He@C(n)()) and their derivatives have been calculated at the GIAO-B3LYP/3-21G and GIAO-HF/3-21G levels with AM1 and PM3 optimized structures. A good linear relationship between the computed (3)He NMR chemical shifts and the experimental data has been determined. Comparisons of the calculation methods of (3)He NMR chemical shifts show that GIAO-B3LYP/3-21G with AM1-optimized structures yields the best results. The corrected (3)He NMR chemical shifts were calculated from the correction equation that is obtained through linear regression fitting of the experimental and calculated (3)He NMR chemical shifts over a wide range of (3)He-encapsulated fullerene compounds. The corrected (3)He NMR chemical shifts match the experimental data very well. The current computational method can serve as a prediction tool and can be applied to the assignments and reassignments of the (3)He NMR chemical shifts of (3)He@C(n)() and their derivatives.     

Endohedral chemical shifts in higher fullerenes with 72–86 carbon atoms

For all isolated pentagon isomers of the fullerenes C₆₀–C₈₆ with nonzero HOMO–LUMO gap and for one nonclassical C₇₂ isomer (C_{2 v} ), endohedral chemical shifts have been computed at the GIAO-SCF/3-21G level using B3LYP/6-31G* optimized structures. The experimental ³He NMR signals are reproduced reasonably well in cases where assignments are unambiguous (e.g. C₆₀, C₇₀ and C₇₆). On the basis of the calculated thermodynamic stability order and the comparison between the computed and experimental ³He chemical shifts, the assignments of the observed ³He NMR spectra are discussed for all higher fullerenes, and new assignments are proposed for one C₈₂ and one C₈₆ isomer (C₈₂:3 and C₈₆:17). The calculated helium chemical shifts also suggest the reassignment of the δ(³He) resonances of two C₇₈ isomers. Received: 26 March 2001 / Accepted: 10 May 2001 / Published online: 11 October 2001     

Helium entry and escape through a chemically opened window in a fullerene

(3)He has been inserted into the cavity of an open-cage fullerene derivative close to room temperature, reaching an incorporation fraction of 0.1%. The rate of escape of (3)He from this fullerene was monitored by (3)He NMR to yield the activation barrier and to compare the size of the orifice to those of other open-cage fullerenes. The equilibrium constant was also measured.     

NMR Properties of Polylithiated C60

Endohedral, ¹³C, ⁷Li, and nucleus‐independent (NICS) chemical shifts are reported for selected Li_nC₆₀ isomers (n = 6, 12, 18) at the GIAO (gauge‐including atomic orbitals)‐SCF/DZP//BP86/3–21G level. Li₆C₆₀ closely resembles C₆₀^6– in terms of NMR criteria for aromaticity, as evidenced by an exceptionally high endohedral shielding. In contrast, nonaromaticity is indicated for Li₁₂C₆₀, based on a positive endohedral chemical shift. NICS and δ(endo) values very similar to those of Li₁₂C₆₀ are obtained for Li₁₈C₆₀. According to population analysis, indeed the same number of electrons are transferred to the fullerene cage in both cases. Endohedral chemical shifts, accessible via ³He NMR of the corresponding endohedral helium compounds, could thus be a valuable indicator for the extent of reduction of the C₆₀ molecule. Energetic estimates suggest that in the bulk, Li₁₂C₆₀ should be unstable with respect to decomposition into Li₆C₆₀ and lithium metal.     

An orifice-size index for open-cage fullerenes

In the field of open-cage fullerenes, there was a lack of a universal standard that could correlate and quantify the orifice size of open-cage fullerenes. One cannot compare the relative orifice size by simple comparison of the number of atoms that composes the orifice. We present a general term for easy estimation of relative orifice size by defining an index for open-cage fullerenes. We estimated the corresponding effective areas A(area) for orifices of open-cage fullerenes by matching calculated activation energies Ea(calcd) for hydrogen release from open-cage fullerenes (B3LYP/6-31G**//B3LYP/3-21G) to the computed energies required for a hydrogen molecule passing through a cyclo[n]carbon ring. Then we define an index K(orifice) based on experimental hydrogen release rate, where K(orifice) = ln k/k degrees (k is rate constant of hydrogen-release rate of any open-cage fullerenes taken for comparison at 160 degrees C; k degrees is the hydrogen release rate from H2@4a taken as the standard compound). We synthesized several open-cage fullerenes and studied kinetics of a set of H2-encapsulated open-cage fullerenes to evaluate their K values. A correlation of the index K(orifice) with the effective areas A(area) showed a good linear fit (r2 = 0.972) that demonstrated a good interplay between experiment and theory. This allows one to estimate K(orifice) index and/or relative rate k of hydrogen release through computing activation energy Ea(calcd) for a designed open-cage fullerene.     

Metallic nitride endohedral fullerenes: synthesis and electrochemical properties

Metallic nitride endohedral fullerenes (MNEFs) are one of the most interesting types of metallofullerenes due to their high yields and interesting electronic properties. The synthesis of these compounds allows the encapsulation of different metals inside fullerenes making it possible to combine the properties of the metal with those of the fullerene. Their interesting electrochemical and optical features make them potential candidates for several applications such as molecular electronics, biomedical imaging, non-linear optical devices, and MRI agents. We report herein the synthesis, isolation, and electrochemical properties of the larger MNEFs including Gd₃N@C₈₂ and Gd₃N@C₈₆, reported here for the first time.     

Isolation and Spectroscopic Characterization of New Endohedral Fullerenes in the Size Gap of C74 to C76

New alkaline earth metal endohedral fullerenes Sr@C₇₄, Sr@C₇₆‐I, II and Ca@C₇₄, prepared by means of the RF‐method, have been isolated using multistep HPLC. The purity was ascertained by anionic LDI TOF mass spectroscopy, considering the isotopic patterns of the compounds. The influence of the incorporated metal on the electronic structure has been studied by VIS‐NIR and Raman spectroscopy. Photoexcited triplet‐state EPR spectroscopy was used to investigate the structure of these otherwise EPR‐silent fullerenes. Displaying the frequency of the cage vs. encapsulated metal vibrational modes as a function of the square root of the reciprocal masses of the metals clearly separates the M³⁺@C_n^3— and the M²⁺@C_n^2— families. This seems to be a generally applicable tool for monitoring the metal to fullerene charge transfer.     

BN-Substituted fullerenes C60−2x (BN) x : a computational 11B and 15N NMR study

Density functional theory has been used to investigate the ¹⁵N and ¹¹B NMR parameters of heterofullerenes C_60?2x (BN) _x (x = 1, 2, 3, 6, 9, 12, 15, 18, 21, and 24). Geometry structures of all the BN-substituted fullerenes have been optimized at the B3LYP/6-31+G* level of theory. Afterward, ¹¹B and ¹⁵N chemical shielding isotropy and anisotropy (CSI, CSA) parameters have been calculated at the same level. The obtained results illustrate the electrostatic environment divisions of the nuclei into few layers, which have been then confirmed by calculating natural charges at B and N sites. A good correlation has been seen between the layers of CSI and CSA values and three local structures around boron and nitrogen atoms. The effects of curvature of fullerene structure on chemical shielding (CS) parameters of heterofullerenes have also been investigated by computing CS tensors for curved and relaxed structures of a set of small fragments separated from the heterofullerenes, suggesting high sensitivity of CS parameters to the curvature of fullerene structure.     

Structural interconnections and the role of heptagonal rings in endohedral trimetallic nitride template fullerenes

Recent experiments indicate that fullerene isomers outside the classical definition can also encapsulate metallic atoms or clusters to form endohedral metallofullerenes. Our systematic study using DFT calculations, suggests that many heptagon‐including nonclassical trimetallic nitride template fullerenes are similar in stability to their classical counterparts, and that conversion between low‐energy nonclassical and classical parent cages via Endo–Kroto insertion/extrusion of C₂ units and Stone–Wales isomerization may facilitate the formation of endohedral trimetallic nitride fullerenes. Close structural connections are found between favored isomers of trimetallic nitride template fullerenes from C₇₈ to C₈₂. It appears that the lower symmetry and local deformations associated with introduction of a heptagonal ring favor encapsulation of intrinsically less symmetrical mixed metal nitride clusters. © 2016 Wiley Periodicals, Inc.     

Photoionization/fragmentation of endohedral fullerenes

Photoionizationlfragmentation of endohedral fullerenes was investigated by use of laser-de sorption time-offlight (LD-TOF) mass spectroscopy. The velocity distribution of the parent ion (LaC ₈₂ ⁺ ) was found to be bimodal, as has previously been shown for laser desorbed C ₆₀ ⁺ . The 0 fragment ions have velocity distributions corresponding predominantly to the fast parent ion distribution. The LD-TOF mass spectra taken with a relatively low laser fluence were independent of the delay time of the extraction pulse, showing only a monotonically decreasing pattern of LaC _2n ⁺ (as n decreased). However, with higher laser fluence, it was shown that the mass distributions drastically changed from the monotonically decreasing pattern to that of C _2n ⁺ and LaC _2n ⁺ with magic numbers. Based on these findings, a plausible photoionization/fragmentation mechanism is presented and discussed.     

Theoretical studies of structures and stabilities of endohedral fullerenes X0/n+ @C32 (X = H,Li, Na,K, Be,Mg, Ca,B, Al,C, Si,N, P,n = 1–3)

Based on the D₃ C₃₂ fullerene, the equilibrium geometries, electronic structures, and binding energies of the endohedral fullerenes X^0/n+@C₃₂ (X = H, Li, Na, K, Be, Mg, Ca, B, Al, C, Si, N, P, n = 1–3) have been calculated using the DFT/B3LYP/6‐31G(d) method. The results show that the C₃₂ cages are slightly enlarged due to encapsulation, and the sizes of non‐neutral molecules are smaller than the corresponding neutral ones. Cages containing Li, Na, and Ca and most of the cations, except Na⁺ and K⁺, are energetically favorable. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

A Computational NICS and 13C NMR Characterization of C60−n Si n Heterofullerenes (n = 1, 2, 6, 12, 20, 24, 30)

Density functional theory (DFT) calculations are performed for a representative set of low-energy structures of C_60-n Si _n heterofullerenes (n = 1, 2, 6, 12, 20, 24, 30) to investigate the effect of silicon doping on the electron structure of fullerene. The results show that chemical shielding (CS) parameters are so sensitive to the structural distortion made by outwardly relaxing silicon doped atoms from the fullerene surface which results in puckered Si-doped rings. As a result, the chemical shifts of the nearest carbon sites of silicon atoms considerably shift to downfield. Our survey shows that those first neighbors of silicon atoms which have minor ¹³C chemical shift belong to normal (un-puckered) rings. Meanwhile, the chemical shielding anisotropy (Δσ) parameter detects the effects of dopant so that Δσ values of the carbon atoms which are contributed to the Si–C bond are mainly larger than the others. Compensation between diatropic and paratropic ring currents lead to less negative NICS values at cage centers of Si-doped fullerenes than that of C₆₀ except C₅₈Si₂-b and C₅₄Si₆-b in which more negative NICS values may be attributed to more spherical geometries of their carbon cages.     

Structural connectivity and formation mechanism of monometallic cluster fullerenes YCN@Cn (n = 68–84)

Excited by the recently experimental reports of monometallic cluster fullerenes, we examined the electronic and geometrical properties of monometallic cluster fullerenes YCN@C_n with size from C₆₈ to C₈₄ by density functional theory and statistical thermodynamic calculations. The calculations demonstrate that the thermodynamically favored isomers of YCN@C_n are in good agreement with available experimental results. Morphology analysis shows that the lowest‐energy YCN@C_n species are structurally connected by C₂ insertion/extrusion and Stone–Wales rotation, which can be promoted under high temperature; enthalpy–entropy interplay can change the relative abundances of low‐energy isomers significantly at high temperature. All the results suggest that there is a structural evolution among these metallic cluster fullerenes in discharge condition, and thus, can rationalize their structural diversity in the soot and partly disclose their formation mechanism. The geometrical structures, electronic properties of these endohedral fullerene were discussed in detail.     

Investigations in the field of higher fullerenes

Halogenation of higher fullerene mixtures or their perfluoroalkylation with R^FI followed by HPLC separation of R^F derivatives and subsequent synchrotron X-ray crystallographic study made it possible to confirm cage connectivities of higher fullerenes and, in addition, to receive information concerning their reactivity in radical addition reactions. The data obtained are compared with theoretical predictions for higher fullerenes. Addition patterns of higher fullerene derivatives are discussed. Skeletal rearrangement of the D ₂-C₇₆ cage during chlorination has been observed for the first time.     

BN-doped fullerenes: an NICS characterization

Heterofullerenes C(58)(BN), C(54)(BN)(3), C(48)(BN)(6), and C(12)(BN)(24) and their hexaanions as well as the C(58)(BN) dimer have been investigated by ab initio calculations. On the basis of the computed nucleus independent chemical shifts (NICS) at the cage center and also at the center of individual rings, BN-doped fullerenes C(58)(BN), C(54)(BN)(3), and C(48)(BN)(6) are slightly more aromatic than C(60), whereas the corresponding hexaanions are significantly less aromatic than C(60)(6)(-). The predicted NICS values may be useful for the identification of the heterofullerenes through their endohedral (3)He NMR chemical shifts. Compared to C(60), the dimerization of C(58)(BN) is calculated to be more exothermic by 16 kcal/mol.     

Open-cage fullerene derivatives suitable for the encapsulation of a hydrogen molecule

The encapsulation of molecular hydrogen into an open-cage fullerene having a 16-membered ring orifice has been investigated. It is achieved by the pressurization of H2 at 0.6-13.5 MPa to afford endohedral hydrogen complexes of open-cage fullerenes in up to 83% yield. The efficiency of encapsulation is dominantly dependent on both H2 pressure and temperature. Hydrogen molecules inside the C60 cage are observed in the range of -7.3 to -7.5 ppm in 1H NMR spectra, and the formations of hydrogen complexes are further confirmed by mass spectrometry. The trapped hydrogen is released by heating. The activation energy barriers for this process are determined to be 22-24 kcal/mol. The DSC measurement of the endohedral H2 complex reveals that the escape of H2 from the C60 cage corresponds to an exothermic process, indicating that encapsulated H2 destabilizes the fullerene.     

Construction and utilisation of planar graphs of two series of IPR fullerenes through the use of threefold rotational symmetry

Threefold rotational symmetry has been used to develop an algorithm for the construction of planar graphs of IPR fullerenes and to factorize their characteristic polynomials. Two series of fullerenes of the formula C_60+12n and C_60+18n have thus been obtained. The algorithm has been shown to be useful for predicting the nature of variation of the point groups of the fullerenes with increased n, for counting the number of ¹³C nuclear magnetic resonance (NMR) signals (along with their relative intensities), and also for obtaining a large part of their eigenspectra. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Flattened fullerenes

Quantum-chemical calculations of giant flattened fullerenes C _n (lentil-shaped) have been carried out. The topology, molecular and electronic structure of these fullerenes have been studied. Such molecules consist of two identical coronenoid fragments of a graphite layer, which are arranged one above the other, and a system of polycondensed five- and six-membered cycles, which form a side surface of the cluster. Polyhedral structures with isolated pentagons of three symmetry types (D _6h ,D _6d , andD _3h ) have been considered. The topology of these structures is described in terms of planar molecular graphs. Electronic structures of eleven flattened lentil-shaped C _n clusters (n = 72–216) have been studied in the π approximation. Most of the considered systems have closed or quasi-closed electron shells (according to Hückel) and rather large energy gaps separating the highest occupied and lowest unoccupied MO, which is indicative of their kinetic stability. Fragments of the potential energy surfaces of the C₇₂ and C₉₆ fullerenes have been studied by the MNDO, AM1, and MNDO/PM3 methods. For the C₉₆ cluster, two local energy minima, which correspond to the lentil-shaped isomers withD _6h andD _6d symmetry, have been determined. As a result of optimization of geometric parameters, it was found that all three methods give close values of heights (H = 6.7 Å) and diameters (D = 9.8 Å) for both isomers. The clusters change to quasi-two-dimensional systems (H«D) with increasing sizes of coronenoid fragments.