Cage connectivity and frontier π orbitals govern the relative stability of charged fullerene isomers

On the thermodynamic stability of polycations

We present a simple approximation to estimate the largest charge that a given molecule can hold until fragmentation into smaller charged species becomes more energetically favorable. This approximation solely relies on the ionization potentials, electron affinities of the parent and fragment species, and also on the neutral parent's dissociation energy. By parameterizing these quantities, it is possible to obtain analytical phase diagrams of polycationic stability. We demonstrate the applicability of this approach by discussing the maximal charge dependence on the size of the molecular system. A numerical demonstration for linear polyenes, monocyclic annulenes, and helium clusters is provided.

Two Metastable Endohedral Metallofullerenes Sc2C2@C1(39656)-C82 and Sc2C2@C1(51383)-C84: Direct-C2-Insertion Products from Their Most Stable Precursors

Endohedral metallofullerenes (EMFs) are sub-nano carbon materials with diverse applications, yet their formation mechanism, particularly for metastable isomers, remains ambiguous. The current theoretical methods focus mainly on the most stable isomers, leading to limited predictability of metastable ones due to their low stabilities and yields. Herein, we report the successful isolation and characterization of two metastable EMFs, Sc₂C₂@C₁(39656)-C₈₂ and Sc₂C₂@C₁(51383)-C₈₄, which violate the isolated pentagon rule (IPR). These two non-IPR EMFs exhibit a rare case of planar and pennant-like Sc₂C₂ clusters, which can be considered hybrids of the common butterfly-shaped and linear configurations. More importantly, the theoretical results reveal that despite being metastable, these two non-IPR EMFs survived as the products from their most stable precursors, Sc₂C₂@C_2v(5)-C₈₀ and Sc₂C₂@C_s(6)-C₈₂, via a C₂ insertion during the post-formation annealing stages. We propose a systematic theoretical method for predicting metastable EMFs during the post-formation stages. The unambiguous molecular-level structural evidence, combined with the theoretical calculation results, provides valuable insights into the formation mechanisms of EMFs, shedding light on the potential of post-formation mechanisms as a promising approach for EMF synthesis.

Self-driven carbon atom implantation into fullerene embedding metal-carbon cluster

Hundreds of members have been synthesized and versatile applications have been promised for endofullerenes (EFs) in the past 30 y. However, the formation mechanism of EFs is still a long-standing puzzle to chemists, especially the mechanism of embedding clusters into charged carbon cages. Here, based on synthesis and structures of two representative vanadium-scandium-carbido/carbide EFs, VSc₂C@I_h (7)-C₈₀ and VSc₂C₂@I_h (7)-C₈₀, a reasonable mechanism-C₁ implantation (a carbon atom is implanted into carbon cage)-is proposed to interpret the evolution from VSc₂C carbido to VSc₂C₂ carbide cluster. Supported by theoretical calculations together with crystallographic characterization, the single electron on vanadium (V) in VSc₂C@I_h (7)-C₈₀ is proved to facilitate the C₁ implantation. While the V=C double bond is identified for VSc₂C@I_h (7)-C₈₀, after C₁ implantation the distance between V and C atoms in VSc₂C₂@I_h (7)-C₈₀ falls into the range of single bond lengths as previously shown in typical V-based organometallic complexes. This work exemplifies in situ self-driven implantation of an outer carbon atom into a charged carbon cage, which is different from previous heterogeneous implantation of nonmetal atoms (Group-V or -VIII atoms) driven by high-energy ion bombardment or high-pressure offline, and the proposed C₁ implantation mechanism represents a heretofore unknown metal-carbon cluster encapsulation mechanism and can be the fundamental basis for EF family genesis.

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.

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.

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.

When is the Bell-Evans-Polanyi principle fulfilled in Diels-Alder reactions of fullerenes?

We present a theoretical study on the thermodynamic and kinetic reactivity of Diels-Alder cycloadditions to several empty fullerenes in order to investigate the relationship between reaction energies and energy barriers. The results show that fullerenes with large HOMO-LUMO gaps present good correlation coefficients. In all other cases, two factors are responsible for the lack of correlation. First, the formation of unexpected adducts which are not the ones resulting from a [4+2] addition and second the change in the electronic structure of some adducts due to the mixing of the ground state with excited states close in energy.

The Effect of the Polyaromatic Hydrocarbon in the Formation of Fullerenes

Tremendous advances in nanoscience have been made since the discovery of fullerenes. However, the short timescale of the growth process and high-energy conditions of synthesis result in severe constraints to investigation of the mechanism of fullerene formation. In this work, we attempted to reveal the formation process by analyzing the variation in the yield of fullerenes under different conditions. Experiments and theoretical analysis show that the formation of fullerenes could be affected by the addition of polycyclic aromatic compounds. It is proposed that the formation of C₆₀ during arc-discharge synthesis is fragment assembling, while the yield of C_2m (m=35, 38, 39) is strongly enhanced by building-block splicing. In addition, several features of the building blocks are put forward to predict the extent of their influence to the formation of larger fullerenes C_2n (n≥42). This work not only provides essential insight into the formation process of fullerenes, but more importantly also paves the way to improving the yield of larger fullerenes selectively.

Modification of boron nitride nanocages by titanium doping results unexpectedly in exohedral complexes

Despite their early experimental production and observation, the unambiguous molecular structures of metal-containing boron nitride (BN) nanocages still remain mysterious. It has been commonly assumed that this family of compounds has the metal atom confined inside the cage, just like their isoelectronic cousins, carbon metallofullerenes do. Here, we demonstrate that Ti(BN)_n (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n$$\end{document}n = 12–24) complexes have, unexpectedly, an exohedral structure instead of an endohedral one, which could be verified by collision-induced dissociation experiments. The predicted global minimum structures exhibit some common bonding features accounting for their high stability, and could be readily synthesized under typical conditions for generating BN nanoclusters. The Ti doping dramatically changes not only the cage topology, but the arrangement of B and N atoms, endowing the resultant compounds with potential for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathrm{CO}}_{2}$$\end{document}CO2 capture and nitrogen fixation. These findings may expand or alter the understanding of BN nanostructures functionalized with other transition metals.

Although isolated experimentally, the molecular structures of metal-containing boron nitride cages are still unknown. Here the authors show via DFT calculations that externally bound complexes of boron nitride fullerenes doped with a single titanium atom are strikingly more stable than the endohedral ones.

Comparing Empty and Filled Fullerene Cages with High-Resolution Trapped Ion Mobility Spectrometry

We have used trapped ion mobility spectrometry (TIMS) to obtain highly accurate experimental collision cross sections (CCS) for the fullerene C₈₀^- and the endohedral metallofullerenes La₂@C₈₀^-, Sc₃N@C₈₀^-, and Er₃N@C₈₀^- in molecular nitrogen. The CCS values of the endohedral fullerenes are 0.2% larger than that of the empty cage. Using a combination of density functional theory and trajectory calculations, we were able to reproduce these experimental findings theoretically. Two effects are discussed that contribute to the CCS differences: (i) a small increase in fullerene cage size upon endohedral doping and (ii) charge transfer from the encapsulated moieties to the cage thus increasing the attractive charge-induced dipole interaction between the (endohedral) fullerene ion and the nitrogen bath gas molecules.

Photo-ionization and fragmentation of Sc3N@C80 following excitation above the Sc K-edge

We have investigated the ionization and fragmentation of a metallo-endohedral fullerene, Sc₃N@C₈₀, using ultrashort (10 fs) x-ray pulses. Following selective ionization of a Sc (1s) electron (hν = 4.55 keV), an Auger cascade leads predominantly to either a vibrationally cold multiply charged parent molecule or multifragmentation of the carbon cage following a phase transition. In contrast to previous studies, no intermediate regime of C₂ evaporation from the carbon cage is observed. A time-delayed, hard x-ray pulse (hν = 5.0 keV) was used to attempt to probe the electron transfer dynamics between the encapsulated Sc species and the carbon cage. A small but significant change in the intensity of Sc-containing fragment ions and coincidence counts for a delay of 100 fs compared to 0 fs, as well as an increase in the yield of small carbon fragment ions, may be indicative of incomplete charge transfer from the carbon cage on the sub-100 fs time scale.

A Simple Model for Relative Energies of All Fullerenes Reveals the Interplay between Intrinsic Resonance and Structural Deformation Effects in Medium-Sized Fullerenes

Fullerenes are sheets of sp² carbon atoms wrapped around to form spheres. With this simple consideration, we have in the present study devised and (with over 3600 DFT data points) successfully validated a simple model, termed R+D, for estimating the relative energies of fullerenes. This model contains a resonance component to account for the intrinsic differences between the π-energies of different fullerenes, and a deformation component for treating the distortions from planarity. Notably, we find that both terms (and they alone) are required to obtain good relative energies, which lends support to the formulation of the R+D model. An interesting finding is that for some medium-sized IPR fullerenes, their isomers show similar variations in the two components. We deduce that these fullerenes may represent a good opportunity for tuning molecular properties for practical applications. We hope that the promising results of the present study will encourage further investigations into fullerenes from a fundamental perspective.

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.

Probing the structure of giant fullerenes by high resolution trapped ion mobility spectrometry

We present high-resolution trapped ion mobility spectrometry (TIMS) measurements for fullerene ions in molecular nitrogen.

Dipolar molecules inside C70: an electric field-driven room-temperature single-molecule switch

We propose a two-state electric field-driven room-temperature single-molecule switch based on a dipolar molecule enclosed inside ellipsoidal fullerene C₇₀. We show that the two low-energy minima of the molecular dipole inside the C₇₀ cage provide distinguishable molecular states of the system that can be switched by application of an external electric field.

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.

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.

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.

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.