Key Structural Motifs To Predict the Cage Topology in Endohedral Metallofullerenes

Simple Hückel Molecular Orbital Theory for Möbius Carbon Nanobelts

The recently synthesized Möbius carbon nanobelts (CNBs) have gained attention owing to their unique π-conjugation topology, which results in distinctive electronic properties with both fundamental and practical implications. Although Möbius conjugation with phase inversion in atomic orbital (AO) basis is well-established for monocyclic systems, the extension of this understanding to double-stranded Möbius CNBs remains uncertain. This study thoroughly examines the simple Hückel molecular orbital (SHMO) theory for describing the π electronic structures of Möbius CNBs. We demonstrate that the adjacency matrix for Möbius CNB can preserve its eigenvalues and eigenvectors under different placements of the sign inversion, ensuring identical SHMO results regardless of AO phase inversion location. Representative examples of Möbius CNBs, including the experimentally synthesized one, show that the Hückel molecular orbitals (MOs) strikingly resemble the DFT-computed π MOs, which were obtained using a herein proposed technique based on the localization and redelocalization of DFT canonical MOs. Interestingly, the lower-lying π MOs exhibit an odd number of nodal planes and are doubly quasidegenerate as a consequence of the phase inversion in Möbius macrocycles, contrasting with macrocyclic Hückel systems. Coulson bond orders derived from SHMO theory correlate well with DFT-calculated Wiberg bond indices for all C-C bonds in tested Möbius CNBs. Additionally, a remarkable correlation is observed between HOMO-LUMO gaps obtained from the SHMO and GFN2-xTB calculations for a large number of topoisomers of Möbius CNBs. Thus, the SHMO model not only captures the essence of π electronic structure of Möbius CNBs, but also provides reliable quantitative predictions comparable to DFT results.

Endohedral metallofullerene molecular nanomagnets

Magnetic lanthanide (Ln) metal complexes exhibiting magnetic bistability can behave as molecular nanomagnets, also known as single-molecule magnets (SMMs), suitable for storing magnetic information at the molecular level, thus attracting extensive interest in the quest for high-density information storage and quantum information technologies. Upon encapsulating Ln ion(s) into fullerene cages, endohedral metallofullerenes (EMFs) have been proven as a promising and versatile platform to realize chemically robust SMMs, in which the magnetic properties are able to be readily tailored by altering the configurations of the encapsulated species and the host cages. In this review, we present critical discussions on the molecular structures and magnetic characterizations of EMF-SMMs, with the focus on their peculiar molecular and electronic structures and on the intriguing molecular magnetism arising from such structural uniqueness. In this context, different families of magnetic EMFs are summarized, including mononuclear EMF-SMMs wherein single-ion anisotropy is decisive, dinuclear clusterfullerenes whose magnetism is governed by intramolecular magnetic interaction, and radical-bridged dimetallic EMFs with high-spin ground states that arise from the strong ferromagnetic coupling. We then discuss how molecular assemblies of SMMs can be constructed, in a way that the original SMM behavior is either retained or altered in a controlled manner, thanks to the chemical robustness of EMFs. Finally, on the basis of understanding the structure-magnetic property correlation, we propose design strategies for high-performance EMF-SMMs by engineering ligand fields, electronic structures, magnetic interactions, and molecular vibrations that can couple to the spin states.

Steering Single-Electron Metal-Metal Bonds and Hyperfine Coupling between a Transition Metal-Lanthanide Heteronuclear Bimetal Confined in Carbon Cages

Metal complexes bearing single-electron metal-metal bonds (SEMBs) exhibit unusual electronic structures evoking strong magnetic coupling, and such bonds can be stabilized in the form of dimetallofullerenes (di-EMFs) in which two metals are confined in a carbon cage. Up to now, only a few di-EMFs containing SEMBs are reported, which are all based on a high-symmetry icosahedral (Ih) C80 cage embedding homonuclear rare-earth bimetals, and a chemical modification of the Ih-C80 cage is required to stabilize the SEMB. Herein, by introducing 3d-block transition metal titanium (Ti) along with 4f-block lanthanum (La) into the carbon cage, we synthesized the first crystallographically characterized SEMB-containing 3d-4f heteronuclear di-EMFs based on pristine fullerene cages. Four novel La-Ti heteronuclear di-EMFs were isolated, namely, LaTi@D3h(5)-C78, LaTi@Ih(7)-C80, LaTi@D5h(6)-C80, and LaTi@C2v(9)-C82, and their molecular structures were unambiguously determined by single-crystal X-ray diffraction. Upon increasing the cage size from C78 to C82, the La-Ti distance decreases from 4.31 to 3.97 Å, affording fine-tuning of the metal-metal bonding and hyperfine coupling, as evidenced by an electron spin resonance (ESR) spectroscopic study. Density functional theory (DFT) calculations confirm the existence of SEMB in all four LaTi@C2n di-EMFs, and the accumulation of electron density between La and Ti atoms shifts gradually from the proximity of the Ti atom inside C78 to the center of the LaTi bimetal inside C82 due to the decrease of the La-Ti distance. The electronic properties of LaTi@C2n heteronuclear dimetallofullerenes differ apparently from their homonuclear La2@C2n counterparts, revealing the peculiarity of heteronuclear dimetallofullerenes with the involvement of 3d-block transition metal Ti.

Cage-size effects on the encapsulation of P2 by fullerenes

The classic pnictogen dichotomy stands for the great contrast between triply bonding very stable N₂ molecules and its heavier congeners, which appear as dimers or oligomers. A banner example involves phosphorus as it occurs in nature as P₄ instead of P₂ , given its weak π-bonds or strong σ-bonds. The P₂ synthetic value has brought Lewis bases and metal coordination stabilization strategies. Herein, we discuss the unrealized encapsulation alternative using the well-known fullerenes' capability to form endohedral and stabilize otherwise unstable molecules. We chose the most stable fullerene structures from C_n (n = 50, 60, 70, 80) and experimentally relevant from C_n (n = 90 and 100) to computationally study the thermodynamics and the geometrical consequences of encapsulating P₂ inside the fullerene cages. Given the size differences between P₂ and P₄ , we show that the fullerenes C₇₀ -C₁₀₀ are suitable cages to side exclude P₄ and host only one molecule of P₂ with an intact triple bond. The thermodynamic analysis indicates that the process is favorable, overcoming the dimerization energy. Additionally, we have evaluated the host-guest interaction to explain the origins of their stability using energy decomposition analysis.

Structures and Electromagnetic Properties of Boron Nitride Nanoribbons Doped with Transition Metals

Inspired by the recent discovery of the Ti-doped BN nanocages, here we report the design of novel BN nanoribbons (BNNRs) doped with fourth-row transition metals (Sc-Cu) and the prediction of their structural and electromagnetic properties. First-principles calculations and ab initio molecular dynamics simulations show that Ti-doped BNNR possesses both thermodynamic and kinetic stability at high temperatures for synthesis of BN materials. Metal doping may make the nonmagnetic pristine BNNR ferromagnetic or antiferromagnetic, depending on the metal. The doping with all considered metals reduces substantially the band gap of pristine BNNR. For example, Sc-doped BNNR is ferromagnetic with an indirect band gap of 1.18 eV, while V-doped nanoribbon is antiferromagnetic with a direct gap of 2.50 eV. Remarkably, the carrier mobility in both materials is significantly enhanced compared to the pristine BNNR. Our findings suggest that doping with different metals may endow BNNRs with versatile electronic and magnetic properties.

Extension and Quantification of the Fries Rule and Its Connection to Aromaticity: Large-Scale Validation by Wave-Function-Based Resonance Analysis

The Fries rule is a simple, intuitive tool to predict the most dominant Kekulé structures of polycyclic aromatic hydrocarbons (PAHs), which is valuable for understanding the structure, stability, reactivity, and aromaticity of these conjugated compounds. However, it still remains an empirical hypothesis, with limited qualitative applications. Herein, we verify, generalize, and quantify the Fries rule based on the recently developed resonance analysis of the DFT wave functions of over 1500 PAH and fullerene molecules with over a billion Kekulé structures. The extended rules, counting the numbers of electrons within all rings (not just sextets), are able to rank the relative importance of all Kekulé structures for all considered systems. The statistically meaningful quantification also opens a way to evaluate ring aromaticity based on the resonance theory, which generally agrees well with conventional aromaticity descriptors. Furthermore, we propose a purely graph-based aromaticity indicator nicely applicable to PAHs and fullerenes, with no need of any quantum chemistry calculations, so that it can make valuable predictions for molecular properties that are related to local aromaticity.

Transforming lanthanide and actinide chemistry with nanoparticles

Lanthanides and actinides are used in a wide variety of applications, from energy production to life sciences. To address toxicity issues due to the chemical, and often radiological, properties of these elements, methods to quantify and recover them from industrial waste are necessary. When used in biomedicine, lanthanides and actinides are incorporated in compounds that show promising therapeutic and/or bioimaging properties, but lack robust strategies to target cancer and other pathologies. Furthermore, current decorporation protocols to respond to accidental actinide exposure rely on intravenous injections of soluble chelating agents, which are inefficient for treatment of inhaled radionuclides trapped in lungs. In recent years, nanoparticles have emerged as powerful tools in both industry and clinical settings. Because some inorganic nanoparticles are sensitive to external stimuli, such as light and magnetic fields, they can be used as building blocks for sensitive bioassays and separation techniques. In addition, nanoparticles can be functionalized with multiple ligands and act as carriers for selective delivery of therapeutic and contrast agents. This review summarizes and discusses recent progress on the use of nanoparticles in lanthanide and actinide chemistry. We examine different types of nanoparticles based on composition, functionalization, and properties, and we critically analyze their performance in a comparative mode. Our focus is two-pronged, including the nanoparticles free of lanthanides and actinides that are used for the detection, separation, or decorporation of f-block elements, as well as the nanoparticles that enhance the inherent properties of lanthanides and actinides for therapeutics, imaging and catalysis.

On the formation of spherical aromatic endohedral buckminsterfullerene. Evaluation of M@C60 (M = Cr, Mo, W) from relativistic DFT calculations

Endohedral metallofullerenes are key species for expanding the range of viable fullerenes, their versatility, and applications. Here we report our computational evaluation on the formation of spherical aromatic counterparts of the C60 fullerene from relativistic DFT calculations, based on the inclusion of Cr, Mo and W endohedral atoms. The resulting M@C60 endohedral fullerenes are 66-π electron neutral species exhibiting bonding properties and electronic structure mimicking the aromaticity and diamagnetic insulator behavior of alkali-C606- phases. The resulting structures are interesting candidates for further experimental realization as novel neutral building blocks for more flexible nanostructured organic materials, highlighting truly spherical aromatic neutral species retaining the truncated icosahedral structure of the seminal Buckminster fullerene.

Th@C86, Th@C82, Th@C80, and Th@C76: role of thorium encapsulation in determining spherical aromatic and bonding properties on medium-sized endohedral metallofullerenes

Thorium encapsulated metallofullerenes (Th-EMFs) with external C76, C80, C82, and C86 cages have been synthesized, with the 13C-NMR spectrum recorded for Th@C82. Here, we explore computationally the chemical bonding, NMR and spherical aromaticity of Th@C82 and related thorium-encapsulated metallofullerenes. Our results show that these Th-EMFs are new examples of spherical aromatic structures, representing interesting low-symmetry exceptions to the Hirsch 2(N + 1)2 rule of spherical aromaticity. Their electronic structures are based on π-electron counts of 80, 84, 86, and 90, respectively, with a shell structure ranging from S2P6D10F14G18H22I8 to S2P6D10F14G18H22I18, where the partially filled I-shell remains as a frontier orbital. Their behavior is comparable to that of the spherical aromatic alkali-C606- phases, which in addition to the favorable endohedral Th-fullerene bonding account for their particular abundance exhibiting the ability to sustain a long-range shielding cone as a result of the favorable metal-cage bonding. This rationalization of such species as neutral spherical aromatic EMFs suggests the possibility of an extensive series of aromatic fullerenes with nuclearity larger than C60 buckminsterfullerene as stable building blocks towards nanostructured metal-organic materials.

Isolation and Crystallographic Characterization of Two, Nonisolated Pentagon Endohedral Fullerenes: Ho3 N@C2 (22010)-C78 and Tb3 N@C2 (22010)-C78

Purified samples of Ho₃ N@C₂ (22010)-C₇₈ and Tb₃ N@C₂ (22010)-C₇₈ have been isolated by two distinct processes from the rich array of fullerenes and endohedral fullerenes present in carbon soot from graphite rods doped with Ho₂ O₃ or Tb₄ O₇ . Crystallographic analysis of the endohedral fullerenes as cocrystals with Ni(OEP) (in which OEP is the dianion of octaethylporphyrin) shows that both molecules contain the chiral C₂ (22010)-C₇₈ cage. This cage does not obey the isolated pentagon rule (IPR) but has two sites where two pentagons share a common C-C bond. These pentalene units bind two of the metal ions, whereas the third metal resides near a hexagon of the cage. Inside the cages, the Ho₃ N or Tb₃ N unit is planar. Ho₃ N@C₂ (22010)-C₇₈ and Tb₃ N@C₂ (22010)-C₇₈ use the same cage previously found for Gd₃ N@C₂ (22010)-C₇₈ rather than the IPR-obeying cage found in Sc₃ N@D_3h -C₇₈ .

Aromaticity, Coulomb repulsion, π delocalization or strain: who is who in endohedral metallofullerene stability?

Three different models for endohedral metallofullerene structure prediction are compared, revealing the physical origin of the stability of these compounds.

Fullerene size controls the selective complexation of [11]CPP with pristine and endohedral fullerenes

The ability of the carbon nanoring [11]cycloparaphenylene ([11]CPP) for coordinating fullerenes has been tested using a series of hosts, including the pristine fullerenes C60, C70, C76 and C78, the clusterfullerene Sc3N@C80, monometallic endofullerenes Y@C82 and Tm@C82, and dimetallic endofullerenes Y2@C82 and Lu2@C82. A systematic theoretical study employing dispersion corrected density functional methods has been carried out in order to explore the characteristics of the complexes and the strength of the interaction. Depending on the dimer, complexation energies span from around -36 kcal mol-1 with C60 to -53 kcal mol-1 with the C82 derivatives. Dispersion is the main stabilizing contribution in these dimers, so the molecules arrange to maximize the number of close interatomic contacts. Since most fullerenes can properly fill the cavity of the nanoring the stability of the complexes is pretty similar, with the exception of the smallest fullerenes. The complexes with endohedral fullerenes show similar stabilities in all cases studied, with no noticeable dependence on the nature of the endohedral species. The results obtained suggest that fullerenes larger than C76 could be selectively encapsulated by [11]CPP compared to smaller fullerenes.

Formation of Spherical Aromatic Endohedral Metallic Fullerenes. Evaluation of Magnetic Properties of M@C28 (M = Ti, Zr, and Hf) from DFT calculations

The small C₂₈ cage has been shown experimentally to encapsulate titanium, zirconium, and hafnium (M), among other elements. Here, we explore computationally its magnetic response properties accounting for both global and local shielding tensors. Our results exhibit a continuous shielding region for M@C₂₈ for an orientation-averaged applied field thereby differing from that observed for the hollow C₂₈ structure. Moreover, under a specific orientation of the applied field a long-ranged shielding cone is obtained supporting the spherical aromatic behavior expected by the 2(N + 1)² Hirsch rule for M@C₂₈, standing for its particular abundance. The comparison between the hollow and endohedral C₂₈ fullerenes exhibits a characteristic long-range behavior at the outside region of the structure. The particular shape of the local chemical shift anisotropy tensor at a representative carbon atom exhibits inherent patterns as a consequence of the spherical aromatic behavior. This shows the capabilities from NMR experiments to account for the nonaromatic → aromatic variation. We envisage that the current approach will be beneficial in comparative studies of aromatic and electronic structure properties, to gain a deeper understanding of the geometrical and electronic structure situation in other endohedral species beyond that available from the information provided by routine NMR measurements.

Fused-Pentagon-Configuration-Dependent Electron Transfer of Monotitanium-Encapsulated Fullerenes

We introduce monotitanium-based endohedral metallofullerenes (EMFs) using density functional theory calculations. Isomeric C₆₄ fullerenes are initially employed as hosts, and Ti@C₆₄ species show novel features on the electronic structures. Energetically, the preference of titanium residing on triple-fused-pentagon subunits is proposed in theory. More importantly, different from current knowledge on mono-EMFs, electron transfer between titanium and carbon cages is not unified but is essentially dependent on the pentagon distribution of the binding sites, giving rise to variations of the cationic titanium of Ti@C₆₄. Such selective electron-transfer character is extended to the study of the encapsulation of other neighboring metal atoms (i.e., calcium and scandium). Because of their different capabilities to accept d electrons, fullerene cages with distinct fused-pentagon motifs show selective metal encapsulation characters. In addition, some other fullerenes (C₄₄-C₄₈ and C₈₂) are selected as hosts to study the electron-transfer behavior of titanium in smaller fullerenes and larger systems without pentagon adjacency.

Rationalizing the relative abundances of trimetallic nitride template-based endohedral metallofullerenes from aromaticity measures

The synthesis of endohedral metallofullerenes (EMFs) from a carbon soot sample of an arc discharge leads to a variety of EMFs that are obtained in different relative abundances. In the present work, we show that these abundances can be predicted from aromaticity calculations. In particular, we use the normalized Additive Local Aromaticity (ALAN) index. Our results show that the most abundant Sc3N-based and Y3N-based EMFs in fullerene soot are the most aromatic. This study reinforces the idea that aromaticity plays a key role in determining the stability of EMFs.

From C(58) to C(62) and back: Stability, structural similarity, and ring current

An increasing number of observations show that non-classical isomers may play an important role in the formation of fullerenes and their exo- and endo-derivatives. A quantum-mechanical study of all classical isomers of C₅₈ , C₆₀ , and C₆₂ , and all non-classical isomers with at most one square or heptagonal face, was carried out. Calculations at the B3LYP/6-31G* level show that the favored isomers of C₅₈ , C₆₀ , and C₆₂ have closely related structures and suggest plausible inter-conversion and growth pathways among low-energy isomers. Similarity of the favored structures is reinforced by comparison of calculated ring currents induced on faces of these polyhedral cages by radial external magnetic fields, implying patterns of magnetic response similar to those of the stable, isolated-pentagon C₆₀ molecule. © 2016 Wiley Periodicals, Inc.

Relative Stability of Empty Exohedral Fullerenes: π Delocalization versus Strain and Steric Hindrance

Predicting and understanding the relative stability of exohedral fullerenes is an important aspect of fullerene chemistry, since the experimentally formed structures do not generally follow the rules that govern addition reactions or the making of pristine fullerenes. First-principles theoretical calculations are of limited applicability due to the large number of possible isomeric forms, for example, more than 50 billion for C₆₀X₈. Here we propose a simple model, exclusively based on topological arguments, that allows one to predict the relative stability of exohedral fullerenes without the need for electronic structure calculations or geometry optimizations. The model incorporates the effects of π delocalization, cage strain, and steric hindrance. We show that the subtle interplay between these three factors is responsible for (i) the formation of non-IPR (isolated pentagon rule) exohedral fullerenes in contrast with their pristine fullerene counterparts, (ii) the appearance of more pentagon-pentagon adjacencies than predicted by the PAPR (pentagon-adjacency penalty rule), (iii) the changes in regioisomer stability due to the chemical nature of the addends, and (iv) the variations in fullerene cage stability with the progressive addition of chemical species.

An atlas of endohedral Sc2S cluster fullerenes

Low-energy Sc₂S@C_n isomers are connected by an intricate web of Stone–Wales isomerization and Endo–Kroto C₂ insertions, giving clues to their formation.

Generalized structural motif model for studying the thermodynamic stability of fullerenes: from C60to graphene passing through giant fullerenes

A generalized motif model to describe the stability of neutral fullerenes, covering the full range of cage sizes, starting from C₆₀, going through giant fullerenes, and ultimately leading to graphene.

A theoretical study of complexes between fullerenes and concave receptors with interest in photovoltaics

The proper combination of host and guest allows controlling the stability and charge transfer capability of fullerene–concave receptor complexes.

U@C36. Is there enough room for a second uranium?

The possible encapsulation of a second uranium in U@C₃₆ is evaluated theoretically.