Quantum chemical calculations of N@Cn endofullerenes (n ≤ 60)

The geometric parameters and energy characteristics of small endofullerenes N@C_n (n = 20, 24, 30, 32, 40, 50) and N@C₆₀ in the quartet ground state were calculated by the B3LYP/6-31G* method. The N atom is located at the center of the carbon cage in all molecules except N@C₃₀, where it is bound to the cage wall. Encapsulation of nitrogen atom has little effect on the fullerene cage geometry for n = 40, 50, and 60. No significant charge transfer from the N endo-atom to the cage was revealed for all the N@C_n endofullerenes studied. The calculated spin density on the nitrogen endo-atom increases as the size (n) of the carbon cage increases. The relative stabilities of C_n fullerenes and corresponding endofullerenes N@C_n are discussed. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 1, pp. 15–20, January, 2006.     

Energy of compressed endoatoms and the energy capacity of small endohedral rare-gas fullerenes

The excess energies of the endoatoms within endofullerenes X@C_n (X = He, Ne, Ar; n = 20–50) as compared with the energies of the free atoms X were estimated using the simplest Thomas-Fermi model and density functional calculations at the B3LYP/6-311G* level. The energy capacities of the endofullerenes under study are primarily determined by the contributions of the compressed electronic systems of the endoatoms rather than the stretched fullerene cages. Dedicated to Academician A. L. Buchachenko on the occasion of his 70th birthday. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 9, pp. 1939–1942, September, 2005.     

Stable Non‐IPR C60 and C70 Fullerenes Containing a Uniform Distribution of Pyrenes and Adjacent Pentagons

The most abundant fullerenes, C₆₀ and C₇₀, and all the pure carbon fullerenes larger than C₇₀, follow the isolated‐pentagon rule (IPR). Non‐IPR fullerenes containing adjacent pentagons (APs) have been stabilized experimentally in cases where, according to Euler’s theorem, it is topologically impossible to isolate all the pentagons from each other. Surprisingly, recent experiments have shown that a few endohedral fullerenes, for which IPR structures are possible, are stabilized in non‐IPR cages. We show that, apart from strain, the physical property that governs the relative stabilities of fullerenes is the charge distribution in the cage. This charge distribution is controlled by the number and location of APs and pyrene motifs. We show that, when these motifs are uniformly distributed in the cage and well‐separated from one other, stabilization of non‐IPR endohedral and exohedral derivatives, as well as pure carbon fullerene anions and cations, is the rule, rather than the exception. This suggests that non‐IPR derivatives might be even more common than IPR ones.     

Buckycatcher polymer versus fullerene‐buckycatcher complex: Which is stronger?

The C₆₀H₂₈ buckycatcher (BC) is an excellent host for fullerenes. This receptor features two corannulene pincers which trap C₆₀/C₇₀ via π stacking interactions. Although, the formation of C₆₀@C₆₀H₂₈ complexes is readily observed, the dimerization of C₆₀H₂₈ is not a competitive process, even at high concentrations. By means of first principle calculations, we have studied the thermodynamics of the polymerization of BCs and the formation of fullerene complexes. The results obtained with the M06‐2X, B97‐D, B3LYP‐D3BJ, PBE‐D2, and PBE‐D3 functionals indicated that the interaction energy of (C₆₀H₂₈)₂ is larger than the one computed for C₆₀@C₆₀H₂₈, by 8–10 kcal/mol. Because of the greater number of atoms, and due to the presence of more hydrogens, the inclusion of free energy corrections lowers the energetic separation between (C₆₀H₂₈)₂ and C₆₀@C₆₀H₂₈, even though the dimer maintains its position as being slightly more bound than that of the C₆₀@C₆₀H₂₈. Our calculations indicated that up to the C₆₀H₂₈ trimer could be formed with a free energy change larger than that corresponding to the dimerization and fullerene complexation processes. Finally, we found that the inversion of the corannulene pincers attached to the cyclooctatetraene core is 2–3 kcal/mol lower than that corresponding to free corannulene. We expect that this work can motivate new investigations that may lead to the observation of C₆₀H₂₈ polymers. © 2015 Wiley Periodicals, Inc.     

Influence of cluster size on the structures and stability of trimetallic nitride fullerenes M3N@C80.

To provide insight into the influence of encaged clusters on the structures and stability of trimetallic nitride fullerenes (TNFs), extensive density functional theory calculations were performed on Sc3N@C80, Y3N@C80, and La3N@C80 as well as their encaged clusters. The calculated results demonstrated that both Sc3N and Y3N units are planar, whereas La3N units are pyramidal inside C80-I(h), and that both of the Y3N@C80 and La3N@C80 cages deform considerably in the planes of Y3 and La3. The calculated results suggest that M-cage attraction/repulsion and M-M repulsion interactions determine the geometries of these three complex molecules and the dynamics of the corresponding encaged clusters. These calculated findings distinctly reveal the influence of the size of the encaged clusters on the structures and stability of TNFs and may rationalize their significant differences in yields and chemical reactivity.     

DFT study on electronic properties of single- and double-shell icosahedral fullerenes

Multi-shell fullerenes are widely studied for their interesting properties although comparative studies on single- and multi-shell structures remain scarce. In this work, important electronic features of single- and double-shell icosahedral fullerenes as a function of their sizes were calculated in the framework of the density functional theory. Fully optimized structures were used to get the gap between the highest occupied molecular and the lowest unoccupied molecular orbital (H-L gap), electronegativity, softness and density of the electronic states. This work shows that the H-L gap of the single-shell fullerenes decreases nonlinearly as the nanoparticles size increases, whereas for the double-shell fullerenes an opposite trend is obtained. A decrease of the H-L gap is found going from single- to double-shell fullerenes with similar external sizes, up to a diameter of 3.13 nm. The electron density of states revealed that isolated peaks give way to more dense electronic states for nanoparticles with diameters above 2 nm.     

Chlorination of IPR C100 Fullerene Affords Unconventional C96Cl20 with a Nonclassical Cage Containing Three Heptagons

Chlorination of C₁₀₀ fullerene with a mixture of VCl₄ and SbCl₅ afforded C₉₆Cl₂₀ with a strongly unconventional structure. In contrast to the classical fullerenes containing only hexagonal and pentagonal rings, the C₉₆ cage contains three heptagonal rings and, therefore, should be classified as a fullerene with a nonclassical cage (NCC). There are several types of pentagon fusions in the C₉₆ cage including pentagon pairs and pentagon triples. The three‐step pathway from isolated‐pentagon‐rule (IPR) C₁₀₀ to C₉₆(NCC‐3hp) includes two C₂ losses, which create two cage heptagons, and one Stone–Wales rotation under formation of the third heptagon. Structural reconstruction established C₁₀₀ isomer no. 18 from 450 topologically possible IPR isomers as the starting C₁₀₀ fullerene. Until now, no pristine C₁₀₀ isomers have been confirmed based on the experimental results.     

Robust metal-pentagon interactions in the Th-based endohedral metallofullerenes revealed by DFT calculations

Endohedral metallofullerenes (EMFs) all feature obvious charge transfer from the metallic core to the carbon shell with the donated electrons largely accepted by the cage pentagons. In this work, a series of Th@C_2n (2n = 64-88) were thoroughly investigated by means of density functional theory calculations. Interestingly, we found that the tetravalent thorium atom mainly coordinates to three pentagonal rings with the metal–pentagon interactions independent on the distribution and distance among these pentagons. This coordination pattern is not only in sharp contrast to that of common organometallic complexes, where four pentagons are indispensable for stabilizing Th(IV), but also different from that of Ti-containing fullerenes, whose valence state highly depends on the pentagon distribution. The specificity of Th-based EMFs was rationalized by the synergetic effect of small metal ion size, low electronegativity, strong metal-cage electrostatic attractions and effective orbital overlap between the metal and cage orbitals. Our work highlights the role of cage pentagons in the Th-cage interactions, and points out the fundamental difference between EMFs and common organometallic complexes.     

libKEDF: An accelerated library of kinetic energy density functionals

Kinetic energy density functionals (KEDFs) approximate the kinetic energy of a system of electrons directly from its electron density. They are used in electronic structure methods that lack direct access to orbitals, for example, orbital‐free density functional theory (OFDFT) and certain embedding schemes. In this contribution, we introduce libKEDF, an accelerated library of modern KEDF implementations that emphasizes nonlocal KEDFs. We discuss implementation details and assess the performance of the KEDF implementations for large numbers of atoms. We show that using libKEDF, a single computing node or (GPU) accelerator can provide easy computational access to mesoscale chemical and materials science phenomena using OFDFT algorithms. © 2017 Wiley Periodicals, Inc.     

Fivefold Symmetry and 2D Crystallization: Self-Assembly of the Buckybowl Pentaindenocorannulene on a Cu(100) Surface

The modification of metal electrode surfaces with functional organic molecules is an important part of organic electronics. The interaction of the buckminsterfullerene fragment molecule pentaindenocorannulene with a Cu(100) surface is studied by scanning tunneling microscopy, dispersion-enabled density functional theory, and force field calculations. Experimental and theoretical methods suggest that two adjacent indeno groups become oriented parallel to the surface upon adsorption under mild distortion of the molecular frame. The binding mechanism between molecule and surface is dominated by strong electrostatic interaction owing to Pauli repulsion. Two-dimensional aggregation at room temperature leads to a single lattice structure in which all molecules are oriented unidirectionally. Their relative arrangement in the lattice suggests noncovalent intermolecular interaction through C−H⋅⋅⋅π bonding.     

Solvent effects on the geometry,electronic structure,and bonding style of Zn(N5)2: A theoretical study

Nitrogen-rich compounds involving the cyclo-pentazole anion (cyclo-N₅⁻) have attracted extensive attention due to higher energy release and environmental friendliness than traditional high energy density materials (HEDMs). However, the synthesis of stable HEDMs with cyclo-N₅⁻ is still a challenge. In this study, the effect of nine solvents on the geometrical and electronic structures and solvation energies of Zn(N₅)₂, one of the recently synthesized nitrogen-rich compounds, was studied using the density functional theory and the polarized continuum model. The results indicated an increase in the stability of Zn(N₅)₂ in the solution phase compared to the vacuum phase, and the stability of Zn(N₅)₂ increases with increasing dielectric constants. The energy gap of frontier molecular orbitals and the absolute value of total energy in water are the largest, revealing that Zn(N₅)₂ is more stable in water than in other solvents. To understand the stabilization mechanism of Zn(N₅)₂ by water, further studies were performed with the natural bond orbital (NBO) analysis and the quantum theory of atoms in molecules (QTAIM) analysis using the explicit solvent model. The charge transfer and the hydrogen bonds are observed between Zn(N₅)₂ and water, which are beneficial to improvement of the stability of Zn(N₅)₂. This may indicate the solvents that have strong interactions with the cyclo-N₅⁻ candidate may improve the possibility of success of synthesis.     

Temperature effects,energy shifts,and band entropies of Si semiconductors

Understanding the electronic properties of silicon semiconductors is important for the preparation of high-performance semiconductor materials. We calculated the band entropies, electronic structures, and bonding properties of a silicon semiconductor using density functional theory and the binding-energy and bond-charge model. The relationship between Si energy and temperature was studied using the tight binding (TB) approximation and bond-order-length-strength (BOLS) theory (BOLS-TB), with the Si (111) surface as an example. The specific binding energies and bonding properties of Si atoms in different surface atomic layers are discussed by analyzing the X-ray photoelectron spectra of the Si (111) surface at 953 and 1493 K. This study improves our understanding of how surface properties reflect local bonding states and deepens our understanding of how atomic-relaxation-derived Hamiltonian perturbations and temperature influence the binding energy of the surface region. It also contributes to the development of Si-based semiconductor materials by providing new ideas and methods.     

In search of fullerene-based superacids: synthesis, X-ray structure, and DFT study of C60(C2F5)(5)H

Simply super! The perfluoroalkylfullerene C(60)(C(2)F(5))(5) H is the first structurally characterized perfluoroalkylated fullerene-based acid and is also predicted to be the first gas-phase fullerene-based superacid.     

Chlorination of Two Isomers of C86 Fullerene: Molecular Structures of C86(16)Cl16, C86(17)Cl18, C86(17)Cl20, and C86(17)Cl22

Chlorination of a mixture of C₈₆ isomers no. 16 (C_s) and no. 17 (C₂) with VCl₄ or a (TiCl₄+Br₂) mixture afforded crystalline chlorides with 16 to 22 Cl atoms per fullerene cage. Single crystal X‐ray diffraction with the use of synchrotron radiation enabled us to determine the chlorination patterns of C₈₆(16)Cl₁₆, C₈₆(17)Cl₁₈, C₈₆(17)Cl₂₀, and C₈₆(17)Cl₂₂. At these degrees of chlorination, addition patterns of C₈₆(16) and C₈₆(17) chlorides have some features in common, owing to the close similarity in the cage structures of both isomers. The average energy of C?Cl bonds decreases with increasing number of attached Cl atoms.     

Exchange and correlation energy in density functional theory

Several different versions of density functional theory (DFT) that satisfy Hohenberg–Kohn theorems are characterized by different definitions of a reference or model state determined by an N‐electron ground state. A common formalism is developed in which exact Kohn–Sham equations are derived for standard Kohn–Sham theory, for reference‐state density functional theory, and for unrestricted Hartree–Fock (UHF) theory considered as an exactly soluble model Hohenberg–Kohn theory. A natural definition of exchange and correlation energy functionals is shown to be valid for all such theories. An easily computed necessary condition for the locality of exchange and correlation potentials is derived. While it is shown that in the UHF model of DFT the optimized effective potential (OEP) exchange satisfies this condition by construction, the derivation shows that this condition is not, in general, sufficient to define an exact local exchange potential. It serves as a test to eliminate proposed local potentials that are not exact for ground states. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 77: 521–525, 2000     

Electronic structure and spectroscopic properties of 6‐aminophenanthridine and its derivatives: Insights from density functional theory

6‐Aminophenanthridine (6AP) and its derivatives show important biological activities as antiprion compounds and inhibitors of the protein folding activity of the ribosome. Both of these activities depend on the RNA binding property of these compounds, which has been recently characterized by fluorescence spectroscopy. Hence, fundamental insights into the photophysical properties of 6AP compounds are highly important to understand their biological activities. In this work, we have calculated electronic structures and optical properties of 6AP and its three derivatives 6AP8CF₃, 6AP8Cl, and 6APi by density functional theory (DFT) and time‐dependent density functional theory (TDDFT). Our calculated spectra show a good agreement with the experimental absorption and fluorescence spectra, and thus, provide deep insights into the optical properties of the compounds. Furthermore, comparing the results obtained with four different hybrid functionals, we demonstrate that the accuracy of the functionals varies in the order B3LYP > PBE0 > M062X > M06HF. © 2015 Wiley Periodicals, Inc.     

Conjugation‐Promoted Reaction of Open‐Cage Fullerene: A Density Functional Theory Study

Density functional theory calculations are performed to study the addition mechanism of e‐rich moieties such as triethyl phosphite to a carbonyl group on the rim of a fullerene orifice. Three possible reaction channels have been investigated. The obtained results show that the reaction of a carbonyl group on a fullerene orifice with triethyl phosphite most likely proceeds along the classical Abramov reaction; however, the classical product is not stable and is converted into the experimental product. An attack on a fullerene carbonyl carbon will trigger a rearrangement of the phosphate group to the carbonyl oxygen as the conversion transition state is stabilized by fullerene conjugation. This work provides a new insight on the reactivity of open‐cage fullerenes, which may prove helpful in designing new switchable fullerene systems.     

Possible effects on the polyethene chain structure of trimethylaluminum coordination to zirconocene catalysts

Ethene was polymerized with the catalytic systems L₂ZrCl₂/MAO/TMA (where L = Cp, Me₅Cp, or Me₄Cp; Cp = η⁵‐cyclopentadienyl; MAO = methylaluminoxane; and TMA = trimethylaluminum) at 60 °C, 2 bar, and Al_TMA/Zr ratios of 0–2700. The polymerization activity was reduced with the addition of TMA for L = Cp but was almost unaffected for the methyl‐substituted catalysts. Increasing the TMA concentration resulted in a lower molecular weight of the polymer, with the largest effect for L = Me₅Cp. A gel permeation chromatography analysis of the polymers revealed a high molecular weight shoulder and a nearly bimodal distribution for L = Me₅Cp at high TMA concentrations. A possible explanation of such a shoulder in terms of long‐chain branching was ruled out by dynamic viscosity measurements. The origin of this effect more likely stemmed from competition between chain transfer to aluminum and β‐hydrogen transfer reactions at two different sites, one TMA‐sensitive and one TMA‐insensitive. Polymerizations at various pressures and temperatures substantiated this assumption. A clue to the underlying mechanism came from investigations of chain transfer to TMA studied with density functional calculations. Complexation of Me₃Al to Zr was much stronger for L = Cp than for L = Me₅Cp. However, the overall chain‐transfer barrier was much higher for L = Cp. These results agreed both with the reduced activity for L = Cp and with the strongly reduced molecular weight for L = Me₅Cp observed with the addition of TMA. © 2001 John Wiley & Sons, Inc. J Polym Sci Part A: Polym Chem 39: 3566–3577, 2001     

Nitrogen-doped carbon nanotubes: growth, mechanism and structure

Nitrogen-doped bamboo-structured carbon nanotubes have been successfully grown using a series of cobalt/molybdenum catalysts. The morphology and structure of the nanotubes were analysed by transmission electron microscopy and Raman spectroscopy. The level of nitrogen doping, as determined by X-ray photoelectron spectroscopy, was found to range between 0.5 to 2.5 at.%. The growth of bamboo-structured nanotubes in the presence of nitrogen, in preference to single-walled and multi-walled nanotubes, was due to the greater binding energy of nitrogen for cobalt in the catalyst compared to the binding strength of carbon to cobalt, as determined by density functional theory.