Collective dynamics of Ca atoms encapsulated in C60 endohedral fullerenes

Endohedral C60 fullerenes with up to four encapsulated Ca atoms were investigated by ab initio molecular dynamics simulations (AIMD). The relatively long runs allow us to describe the correlated movement of the Ca atoms inside the fullerene cage. For the systems with one or two Ca atoms a relatively unimpeded rotation was conjectured by earlier nuclear magnetic resonance experiments and supported by previous ab initio calculations used to sample the potential energy landscape. Here, by AIMD calculations, we confirm not only the circular motion, but also the correlated movement of the two Ca atoms, which is due to electric dipole interactions on the inner surface of the C60 molecule. Furthermore, systems with three and four Ca atoms present highly symmetric configurations of the embedded atoms, which are shown to rotate consistently within the fullerene cage, while more complex charge density patterns emerge. Employing artificial neural network models we perform a force-field mapping, which enables us to reproduce the main characteristics of the actual dynamics, such as the circular motion and the correlated movement of the Ca atoms.

[K2(Bi@Pd12@Bi20)]4-: An Endohedral Inorganic Fullerene with Spherical Aromaticity

Inorganic fullerene clusters have attracted widespread attention due to their highly symmetrical geometric structures and intrinsic electronic properties. However, cage-like clusters composed of heavy metal elements with high symmetry are rarely reported, and their synthesis is also highly challenging. In this study, we present the synthesis of a [K2(Bi@Pd12@Bi20)]4- cluster that incorporates a {Bi20} cage with pseudo-Ih symmetry, making it the largest main group metal cluster compound composed of the bismuth element to date. Magnetic characterization and theoretical calculations suggest that the spin state of the overall cluster is a quartet. Quantum chemical calculations reveal that the [Bi20]3- cluster has a similar electronic configuration to C606- and the [Bi@Pd12@Bi20]6- cluster exhibits a unique open-shell aromatic character.

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.

The role of aromaticity in the cyclization and polymerization of alkyne-substituted porphyrins on Au(111)

Aromaticity is an established and widely used concept for the prediction of the reactivity of organic molecules. However, its role remains largely unexplored in on-surface chemistry, where the interaction with the substrate can alter the electronic and geometric structure of the adsorbates. Here we investigate how aromaticity affects the reactivity of alkyne-substituted porphyrin molecules in cyclization and coupling reactions on a Au(111) surface. We examine and quantify the regioselectivity in the reactions by scanning tunnelling microscopy and bond-resolved atomic force microscopy at the single-molecule level. Our experiments show a substantially lower reactivity of carbon atoms that are stabilized by the aromatic diaza[18]annulene pathway of free-base porphyrins. The results are corroborated by density functional theory calculations, which show a direct correlation between aromaticity and thermodynamic stability of the reaction products. These insights are helpful to understand, and in turn design, reactions with aromatic species in on-surface chemistry and heterogeneous catalysis.

Theoretical Insights into the Metal-Nonmetal Interaction Inside M2O@C 2v (31922)-C80 (M = Sc or Gd)

The metal-nonmetal interaction is complicated but significant in organometallic chemistry and metallic catalysis and is susceptible to the coordination surroundings. Endohedral metallofullerene is considered to be an excellent model for studying metal-nonmetal interactions with the shielding effect of fullerenes. Herein, with the detection of ScGdO@C₈₀ in a previous mass spectrum, we studied the effects of metal atoms (Sc and Gd) on the metal-nonmetal interactions of the thermodynamically stable molecules M₂O@C _2v (31922)-C₈₀ (M = Sc and Gd), where metal atoms M can be the same or different, using density functional theory calculations. The inner metal atom and the fullerene cage show mainly ionic interactions with some covalent character. The Sc atom with higher electronegativity plays a greater important role in the metal-nonmetal interactions than the Gd atom. This study would be useful for the further study of the metal-nonmetal interaction.

3D and 2D aromatic units behave like oil and water in the case of benzocarborane derivatives

A large number of 2D/2D and 3D/3D aromatic fusions that keep their aromaticity in the fused compounds have been synthesized. In addition, we have previously proven the electronic relationship between the 3D aromaticity of boron hydrides and the 2D aromaticity of PAHs. Here we report the possible existence of 3D/2D aromatic fusions that retain the whole aromaticity of the two units. Our conclusion is that such a 3D/2D aromatic combination is not possible due to the ineffective overlap between the π-MOs of the planar species and the n + 1 molecular orbitals in the aromatic cage that deter an effective electronic delocalization between the two fused units. We have also proven the necessary conditions for 3D/3D fusions to take place, and how aromaticity of each unit is decreased in 2D/2D and 3D/3D fusions.

2D/2D fusion of aromatic halves leading to a global aromatic is found in many polycyclic aromatic hydrocarbons, whereas 2D/3D aromaticity is difficult to achieve. Here the authors report a computational chemistry investigation showing that 3D/2D aromatic combination is not possible.

Three-Dimensional Fully π-Conjugated Macrocycles: When 3D-Aromatic and When 2D-Aromatic-in-3D?

Several fully π-conjugated macrocycles with puckered or cage-type structures were recently found to exhibit aromatic character according to both experiments and computations. We examine their electronic structures and put them in relation to 3D-aromatic molecules (e.g., closo-boranes) and to 2D-aromatic polycyclic aromatic hydrocarbons. Using qualitative theory combined with quantum chemical calculations, we find that the macrocycles explored hitherto should be described as 2D-aromatic with three-dimensional molecular structures (abbr. 2D-aromatic-in-3D) and not as truly 3D-aromatic. 3D-aromatic molecules have highly symmetric structures (or nearly so), leading to (at least) triply degenerate molecular orbitals, and for tetrahedral or octahedral molecules, an aromatic closed-shell electronic structure with 6n + 2 electrons. Conversely, 2D-aromatic-in-3D structures exhibit aromaticity that results from the fulfillment of Hückel’s 4n + 2 rule for each macrocyclic path, yet their π-electron counts are coincidentally 6n + 2 numbers for macrocycles with three tethers of equal lengths. It is notable that 2D-aromatic-in-3D macrocyclic cages can be aromatic with tethers of different lengths, i.e., with π-electron counts different from 6n + 2, and they are related to naphthalene. Finally, we identify tetrahedral and cubic π-conjugated molecules that fulfill the 6n + 2 rule and exhibit significant electron delocalization. Yet, their properties resemble those of analogous compounds with electron counts that differ from 6n + 2. Thus, despite the fact that these molecules show substantial π-electron delocalization, they cannot be classified as true 3D-aromatics.

Successive Diels-Alder Cycloadditions of Cyclopentadiene to [10]CPP⊃C60: A Computational Study

Fullerenes have potential applications in many fields. To reach their full potential, fullerenes have to be functionalized. One of the most common reactions used to functionalize fullerenes is the Diels–Alder cycloaddition. In this case, it is important to control the regioselectivity of the cycloaddition during the formation of higher adducts. In C₆₀, successive Diels–Alder cycloadditions lead to the T_h-symmetric hexakisadduct. In this work, we explore computationally using density functional theory (DFT) how the presence of a [10]cycloparaphenylene ring encapsulating C₆₀ ([10]CPP⊃C₆₀) affects the regioselectivity of multiple additions to C₆₀. Our results show that the presence of the [10]CPP ring changes the preferred sites of cycloaddition compared to free C₆₀ and leads to the formation of the tetrakisadduct. Somewhat surprisingly, our calculations predict formation of this particular tetrakisadduct to be more favored in [10]CPP⊃C₆₀ than in free C₆₀.

Effects of orbital angles on the modeling of conjugated systems with curvature

Models with angle corrections give well predictions of both neutral and charged fullerenes. The integrals of nonparallel orbitals explain why angle features of designed and deep-learning models are necessary to describe conjugated systems.

Ground and excited electronic structures of metal encapsulated nanocages: the cases of endohedral M@C20H20 (M = K, Rb, Ca, Sr) and M@C36H36 (M = Na, K, Rb)

High-level electronic structure calculations were performed to analyze ground and excited states of neutral and cationic endohedral M@C₂₀H₂₀ (M = K, Rb, Ca, Sr) and M@C₃₆H₃₆ (M = Na, K, Rb). In their ground states, one or two electrons occupy a diffuse atomic s-type orbital, thus 1s¹ and 1s² superatomic electronic configurations are assigned for M = Na, K, Rb and M = Ca, Sr cases, respectively. These species populate 1p-, 1d-, 1f-superatomic orbitals in electronically excited states. The specific superatomic Aufbau model introduced for M@C₂₀H₂₀ (M = K, Rb) is 1s, 1p, 1d, 2s, 1f, 2p, 2d, 1g, 2f. On the other hand, excited electronic spectra of M@C₂₀H₂₀ (M = Ca, Sr) are rich in multireference characters. Excited states of bigger M@C₃₆H₃₆ molecules were investigated up to the 1d level and the transitions were found to require slightly higher energies compared to M@C₂₀H₂₀. These superatoms possess lower ionization potentials, hence can also be categorized as superalkalis.

Antiaromaticity-aromaticity transition of cyclo[16]carbon upon metal encapsulation

In contrast to aromatic compounds with particular stability, antiaromatic compounds are usually less stable due to their high reactivity and unfavorable formation energies. Cyclo[16]carbon (C₁₆) is a carbon ring molecule with a dual antiaromatic character. In this study, we demonstrate that C₁₆ can be transformed into highly aromatic molecules upon metal encapsulation. The geometrical characteristics, electronic properties and thermodynamic stability of MC₁₆ compounds (M = Ca, Sc, Ti, V, Ce, U) are fully investigated from a theoretical perspective. Based on natural population analysis, atom-in-molecules theory and localized molecular orbital analysis, the nature of the metal-carbon interaction in the MC₁₆ compounds is investigated. It has been proved that the bonding between Ca and C₁₆ corresponds to a typical ionic interaction, while other metal atoms form polar covalent bonds with C₁₆. By analyzing the frontier molecular orbitals and magnetic response of MC₁₆, we have found that all the encapsulated metal atoms donate two electrons to the in-plane π orbitals via either electron transfer or orbital hybridization, which makes the in-plane π orbitals completely satisfy the 4n + 2 (n = 4) Hückel aromaticity rule. The U atom formally transfers four electrons to the carbon ring in total, two to the in-plane π orbitals and two to the out-of-plane π orbitals, which results in the remarkable dual aromaticity feature of UC₁₆. The transformation of aromaticity can be utilized to develop new strategies for the synthesis of novel carbon ring molecules.

Isolation and Reactivity of an Antiaromatic s-Block Metal Compound

The concepts of aromaticity and antiaromaticity have a long history, and countless demonstrations of these phenomena have been made with molecules based on elements from the p, d, and f blocks of the periodic table. In contrast, the limited oxidation-state flexibility of the s-block metals has long stood in the way of their participation in sophisticated π-bonding arrangements, and truly antiaromatic systems containing s-block metals are altogether absent or remain poorly defined. Using spectroscopic, structural, and computational techniques, we present herein the synthesis and authentication of a heterocyclic compound containing the alkaline earth metal beryllium that exhibits significant antiaromaticity, and detail its chemical reduction and Lewis-base-coordination chemistry.

Aromaticity Survival in Hydrofullerenes: The Case of C66 H4 with Its π-Aromatic Circuits

The isolated-pentagon rule (IPR) is a determining structural feature that accounts for hollow fullerene stabilization and properties related to C_n (n≥60) cages. The recent characterization of an unprecedented non-IPR hydrofullerene, C_2v C₆₆ H₄ , bearing two heptagons with adjacent fused-pentagon motifs, largely dismisses this feature. Herein, employing DFT calculations, the ¹³ C NMR spectroscopy and aromatic behavior of C_2v C₆₆ H₄ are explored. The results show the presence of three π-aromatic circuits at the bottom boat section of C₆₆ H₄ , indicating the unique features of this hydrofullerene in comparison to those of pristine C₆₀ . In addition, under specific orientations of the external field, certain π-aromatic circuits are enabled, resulting in a more aromatic fullerene than that of C₆₀ , but lower than that of the spherical aromatic C₆₀ ^6- fulleride. Notably, under a field aligned with the saturated carbon atoms, nonaromatic characteristics are exposed. This reveals that spherical-like cages can involve a complex magnetic response that heavily depends on the orientation of the applied field.

Metallaaromatic Chemistry: History and Development

Since the prediction of the existence of metallabenzenes in 1979, metallaaromatic chemistry has developed rapidly, due to its importance in both experimental and theoretical fields. Now six major types of metallaromatic compounds, metallabenzenes, metallabenzynes, heterometallaaromatics, dianion metalloles, metallapentalenes and metallapentalynes (also termed carbolongs), and spiro metalloles, have been reported and extensively studied. Their parent organic analogues may be aromatic, non-aromatic, or even anti-aromatic. These unique systems not only enrich the large family of aromatics, but they also broaden our understanding and extend the concept of aromaticity. This review provides a comprehensive overview of metallaaromatic chemistry. We have focused on not only the six major classes of metallaaromatics, including the main-group-metal-based metallaaromatics, but also other types, such as metallacyclobutadienes and metallacyclopropenes. The structures, synthetic methods, and reactivities are described, their applications are covered, and the challenges and future prospects of the area are discussed. The criteria commonly used to judge the aromaticity of metallaaromatics are presented.

Scandium Tetrahedron Supported by H Anion and CN Pentaanion inside Fullerene C80

Endohedral metallofullerenes have greatly expanded the range of the fullerene family due to their nesting structure and unusual encapsulated clusters protected by a fullerene cage. Herein, we report a metallofullerene Sc₄CNH@I_h-C₈₀, which has a scandium tetrahedron supported by H and CN anions inside fullerene C₈₀. Sc₄CNH@I_h-C₈₀ has a rare multilayer nesting structure, and the internal Sc₄CNH is the most complex endohedral cluster disclosed to date. Sc₄CNH@I_h-C₈₀ has so many bonding types (metal-carbide, metal-nitride, and metal-hydride), which weave a polyhedron of Sc₄CNH clusters. This work shows that the endohedral metallofullerenes have the potential to build inorganic nesting polyhedra that have distinctive architectures and unique electronic properties. Sc₄CNH@I_h-C₈₀ was synthesized by means of the arc-discharge method using scandium and graphite under the mixed atmosphere of hydrogen, nitrogen, and helium. It is the first time to disclose an unprecedented metal-hydride bond in a fullerene cage. This result shows that the endohedral fullerenes bearing hydrogen species can be synthesized by the arc-discharge technique under an atmosphere of hydrogen. This work demonstrates that a fullerene cage can be an ample carrier to encapsulate unusual cluster moieties.

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.

All-metal σ-antiaromaticity in dimeric cluster anion {[CuGe9Mes]2}4

In this work, we report a dimeric cluster anion, {[CuGe9Mes]2}4-, which was isolated as the [K(2,2,2-crypt)]+ salt and characterized by using single-crystal X-ray diffraction and ESI mass spectroscopy. The title cluster represents the first locally σ-antiaromatic compound in the solid state, as well as the first heteroatomic antiaromatic compound.

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.

An antiaromatic-walled nanospace

Over the past few decades, several molecular cages, hosts and nanoporous materials enclosing nanometre-sized cavities have been reported^1-5, including coordination-driven nanocages⁶. Such nanocages have found widespread use in molecular recognition, separation, stabilization and the promotion of unusual chemical reactions, among other applications^3-10. Most of the reported nanospaces within molecular hosts are confined by aromatic walls, the properties of which help to determine the host-guest behaviour. However, cages with nanospaces surrounded by antiaromatic walls have not yet been developed, owing to the instability of antiaromatic compounds; as such, the effect of antiaromatic walls on the properties of nanospaces remains unknown. Here we demonstrate the construction of an antiaromatic-walled nanospace within a self-assembled cage composed of four metal ions with six identical antiaromatic walls. Calculations indicate that the magnetic effects of the antiaromatic moieties surrounding this nanospace reinforce each other. This prediction is confirmed by ¹H nuclear magnetic resonance (NMR) signals of bound guest molecules, which are observed at chemical shift values of up to 24 parts per million (ppm), owing to the combined antiaromatic deshielding effect of the surrounding rings. This value, shifted 15 ppm from that of the free guest, is the largest ¹H NMR chemical shift displacement resulting from an antiaromatic environment observed so far. This cage may thus be considered as a type of NMR shift reagent, moving guest signals well beyond the usual NMR frequency range and opening the way to further probing the effects of an antiaromatic environment on a nanospace.

Decomposition of the electronic activity in competing [5,6] and [6,6] cycloaddition reactions between C60 and cyclopentadiene

Fullerenes, in particular C60, are important molecular entities in many areas, ranging from material science to medicinal chemistry. However, chemical transformations have to be done in order to transform C60 in added-value compounds with increased applicability. The most common procedure corresponds to the classical Diels-Alder cycloaddition reaction. In this research, a comprehensive study of the electronic activity that takes place in the cycloaddition between C60 and cyclopentadiene toward the [5,6] and [6,6] reaction pathways is presented. These are competitive reaction mechanisms dominated by σ and π fluctuating activity. To better understand the electronic activity at each stage of the mechanism, the reaction force (RF) and the symmetry-adapted reaction electronic flux (SA-REF, JΓi(ξ)) have been used to elucidate whether π or σ bonding changes drive the reaction. Since the studied cycloaddition reaction proceeds through a Cs symmetry reaction path, two SA-REF emerge: JA'(ξ) and JA''(ξ). In particular, JA'(ξ) mainly accounts for bond transformations associated with π bonds, while JA''(ξ) is sensitive toward σ bonding changes. It was found that the [6,6] path is highly favored over the [5,6] with respect to activation energies. This difference is primarily due to the less intensive electronic reordering of the σ electrons in the [6,6] path, as a result of the pyramidalization of carbon atoms in C60 (sp2 → sp3 transition). Interestingly, no substantial differences in the π electronic activity from the reactant complex to the transition state structure were found when comparing the [5,6] and [6,6] paths. Partition of the kinetic energy into its symmetry contributions indicates that when a bond is being weakened/broken (formed/strengthened) non-spontaneous (spontaneous) changes in the electronic activity occur, thus prompting an increase (decrease) of the kinetic energy. Therefore, contraction (expansion) of the electronic density in the vicinity of the bonding change is expected to take place.

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.

Global and local aromaticity of acenes from the information-theoretic approach in density functional reactivity theory

In this work, we report a systematic study on the global and local aromaticity of acenes using a series of model structures from 2-acene to 11-acene. A recently developed ansatz, an information-theoretic approach coached into density functional reactivity theory has been employed, which essentially provides different density functionals characterizing the molecular electron density distribution. Based on the correlation analysis of six conventional aromaticity indices with eight information-theoretic quantities, we examined the aromaticity of acenes from both global and local perspectives. From the global aromaticity viewpoint, our results suggest that different descriptors based on various physicochemical properties are intrinsically dependent. A novel laminated feature ruling local aromaticity of acenes has been unveiled, from which we found that the distance from the terminal rings plays the critical role. Based on the shape of the correlation plots between the conventional aromaticity indices and information-theoretic quantities, the latter could be separated into three subgroups. The seemingly contradictory results from global and local aromaticity perspectives not only present us the uniqueness of the acene systems but all demonstrate the effectiveness of the information-theoretic approach from density functional reactivity theory. Besides strengthening the validity of a series of new aromaticity descriptors, our results should lead to more clear insights into the chemical significance of the information-theoretic quantities.

Cycloaddition reactions of pristine and endohedral fullerene molecules: possible anticancer activity

Epoxide of oestradiol is one of the main risk factors for the genesis and evolution of breast cancer; hence, in recent years there has been considerable interest in the investigation of new inhibitors capable of reducing its carcinogenic activity. The aim of this article is to study the [2 + 2] cycloaddition reaction of epoxide of oestradiol in different pristine (C₇₆ and D_5h-C₈₀) and endohedral metallofullerene (C₇₂@Sc₂C₂, C₇₆@Sc₂ and C₈₀@Sc₂) by means of molecular electrostatic potential (MEP) topological analysis. Different from other molecular scalar fields, MEP topology enables to find minima related to lone pairs and π electrons, therefore, this molecular scalar field is appropriate to identify the most reactive sites. In consonance with our results, it was found that C₈₀ was the best candidate to carry out the epoxide of oestradiol cycloaddition since more stable adducts were obtained. Furthermore, it is expected that more than one oestradiol epoxide molecule will be added to C₈₀, forasmuch as C₈₀ reactivity is enhanced once the adduct is formed. The study was carried through DFT framework included in the Gaussian 09 package (MPWB95/6-31G(d,p)).

Regioselectivity of the Pauson-Khand reaction in single-walled carbon nanotubes

Chemical functionalization of nanotubes, in which their properties can be combined with those of other classes of materials, is fundamental to improve the physicochemical properties of nanotubes for potential technological applications. In this work, we theoretically and experimentally examine the Pauson-Khand reaction (PKR) on zig-zag, armchair, and chiral single-walled carbon nanotubes (SWCNTs). Our benchmarked density functional theory (DFT) calculations show that an alternative pathway to the widely accepted Magnus reaction pathway has significantly lower energy barriers, thus suggesting the use of this alternative pathway to predict whether a PKR on SWCNTs is favored or hampered. Accessible energy barriers of up to 16 kcal mol-1 are estimated and our results suggest that semiconducting SWCNTs react faster than metallic ones, although both types can be functionalized. Guided by our theoretical predictions, cyclopentenones are successfully attached to SWCNTs by heating and are, subsequently, characterized in the laboratory.

On the regioselectivity of the Diels-Alder cycloaddition to C60 in high spin states

Controlling the regioselectivity in the exohedral functionalization of fullerenes and endohedral metallofullerenes is essential to produce specific desired fullerene derivatives. In this work, using density functional theory (DFT) calculations, we show that the regioselectivity of the Diels-Alder (DA) cycloaddition of cyclopentadiene to 2S+1C60 changes from the usual [6,6] addition in the singlet ground state to the [5,6] attack in high spin states of C60. Changes in the aromaticity of the five- and six-membered rings when going from singlet to high spin C60 provide a rationale to understand this regioselectivity change. Experimentally, however, we find that the DA cycloaddition of isoindene to triplet C60 yields the usual [6,6] adduct. Further DFT calculations and computational analysis give an explanation to this unanticipated experimental result by showing the presence of an intersystem crossing close to the formed triplet biradical intermediate.

Triplet state homoaromaticity: concept, computational validation and experimental relevance

Conjugation through space can give rise to aromaticity in the lowest excited triplet state, with impact for photochemistry.

Cyclic conjugation that occurs through-space and leads to aromatic properties is called homoaromaticity. Here we formulate the homoaromaticity concept for the triplet excited state (T₁) based on Baird's 4n rule and validate it through extensive quantum-chemical calculations on a range of different species (neutral, cationic and anionic). By comparison to well-known ground state homoaromatic molecules we reveal that five of the investigated compounds show strong T₁ homoaromaticity, four show weak homoaromaticity and two are non-aromatic. Two of the compounds have previously been identified as excited state intermediates in photochemical reactions and our calculations indicate that they are also homoaromatic in the first singlet excited state. Homoaromaticity should therefore have broad implications in photochemistry. We further demonstrate this by computational design of a photomechanical “lever” that is powered by relief of homoantiaromatic destabilization in the first singlet excited state.

Reliable charge assessment on encapsulated fragment for endohedral systems

A simple scheme to determine charge distribution in endohedral complexes is suggested. It is based on comparison of inner-shell atomic orbital energies of the encapsulated species to the corresponding energies in reference systems with unambiguously defined charges on X. This robust approach is applied to endohedral borospherenes X@B₃₉, for which the conventional schemes provide in some cases quite different results. Efficiency of proposed scheme also has been proven for typical fullerene based Sc₃N@C₈₀ endohedral complex.

Simple bond patterns predict the stability of Diels–Alder adducts of empty fullerenes

A systematic study of Diels–Alder cycloadditions to empty fullerenes reveals that π effects control site preference. Simple Hückel calculation allows to obtain quantitative descriptors and to understand why addition occurs preferentially at certain types of bonds. A couple of simple rules are proposed as a visual guide for a rapid prediction of Diels–Alder reactivity.

C50Cl10, a planar aromatic fullerene. Computational study of 13C-NMR chemical shift anisotropy patterns and aromatic properties

The structural characterization of D_5h-C₅₀Cl₁₀ as an IPR-violating fullerene provides an interesting case of an oblate structure displaying a planar-aromatic character provided by the face-to-face disposition of two IPR structural motifs, as unraveled by DFT calculations.

Lewis Acid-Base Adducts of Sc2C2@C3v(8)-C82/N-Heterocyclic Carbene: Toward Isomerically Pure Metallofullerene Derivatives

The addition of a bulky N-heterocyclic carbene (NHC) to Sc₂C₂@C_3v(8)-C₈₂ affords two monoadducts (2a and 2b) quantitatively and regioselectively, representing the first examples of Lewis acid-base pairs of metal carbide cluster fullerenes. 2b is likely a kinetically favorable labile product that cannot be isolated from the solution. The crystallographic results of 2a unambiguously demonstrate that one polarized C-C single bond is formed between the normal carbene site C2N of the NHC and a specific [5,6,6]-carbon atom out of 17 types of nonequivalent cage carbon atoms of Sc₂C₂@C_3v(8)-C₈₂. Theoretical calculations demonstrate that the high regioselectivity, the unexpected addition pattern, and the quantitative formation of monoadducts are synergistic results from the cage geometry and electron distribution on the cage.

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.