Topology-Based Approach to Predict Relative Stabilities of Charged and Functionalized Fullerenes

Stereo- and Regioselectivity of Hydrogenation of a Recently Synthesized Carboncone and Its Predictive Models

Since its atomically precise synthesis in recent experiments, the carboncone molecule presents a novel example of discrete nanocarbons with promising applications, but little is known yet about its chemical properties. In this work, we present a comprehensive computational study on the hydrogenation of carboncone with a varying number of added H atoms (from 1 to 12). Unlike planar benzenoid hydrocarbons, carboncone prefers that all H atoms be added to its external, convex surface. The previous topology-based model for hydrogenated fullerenes and benzenoid hydrocarbons is shown to be no longer valid for carboncone. We here propose an extended model capable of predicting the hydrogenation regioselectivity for carboncone, which is largely governed by π delocalization. Yet the H···H repulsion at rim sites also plays an important role in adduct stability. Interestingly, some preferred addition patterns can be understood by counting the size of intact π rings upon H addition. These findings may provide insightful guidance to the functionalization of carboncones and related nanocarbons.

On the Origins of Stereo- and Regio-Selectivities in the Formation of Fullerene-Fluorene Dyads

Recently, a novel [2+2] cycloaddition between the classical I_h-C₆₀ and a fluorenylideneallene complex has been achieved experimentally. In the fullerene-fluorene dyad product, stereo- and regio-selectivities were found in the experiment, but the reasons are still unknown. Our theoretical studies suggest that, based on a diradical pathway, the structural selectivity of the product strongly depends on the structural/electronic features of the fluorenylideneallene and C₆₀ complexes. When the R¹ group in fluorenylideneallene denotes the H atom, the E-type product is more stable than the Z-type one, whereas other bulkier R¹ groups lead to the reverse due to their steric hindrance. The π orbital conjugation between the fluorenyl group and the C^β═C^γ bond in fluorenylideneallene is the main reason for the high selectivity of β,γ-cycloaddition. Analyses of both frontier orbitals and spin density for the intermediate structure suggest a diradical pathway of the reaction between fluorenylideneallene and C₆₀ and uncover a decisive role of the LUMO of C₆₀ toward regio-selectivity, which conduces to a high selectivity of the (6,6)-addition product.

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.

Hydrogenated polycyclic aromatic hydrocarbons: isomerism and aromaticity

A simple model based on adjacency matrices is introduced to study the stability of hydrogenated polycyclic aromatic hydrocarbons. Aromaticity governs their relative stability having the most stable isomers the higher number of non-hydrogenated rings.

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.

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.

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.