Structural Principles of Polyhedral Allotropes of Phosphorus

We derive the structural principles of polyhedral allotropes of phosphorus, introducing three distinct families of black phosphorus nanostructures. The predicted tetrahedral, octahedral, and icosahedral phosphorus cages can also be considered as phosphorus fullerenes. Phosphorus cages up to P₈₈₈ are systematically investigated by quantum chemical methods, and their thermodynamic stabilities are compared with the experimentally known allotropic forms of phosphorus. The tetrahedral cages are thermodynamically favored over the octahedral and icosahedral structures, although large octahedral structures become nearly as stable as the tetrahedral ones. The stability trends of the studied polyhedral families can be rationalized on the basis of their structural characteristics. The phosphorus polyhedra can be further stabilized by fitting smaller structures inside larger ones, resulting in multilayered, bulk‐like cages. The synthesis of the predicted black phosphorus nanostructures is suggested to be viable from the thermodynamic point of view, and several approaches for their experimental preparation can be envisaged.     

Two‐, One‐, and Zero‐Dimensional Elemental Nanostructures Based on Ge9‐Clusters

We investigated the structural principles of novel germanium modifications derived by oxidative coupling of Zintl‐type [Ge₉]^4?clusters in various ways. The structures, stabilities, and electronic properties of the predicted {²_∞[Ge₉]_n} sheet, {¹_∞[Ge₉]_n} nanotubes, and fullerene‐like {Ge₉}_n cages were studied by using quantum chemical methods. The polyhedral {Ge₉}_n cages are energetically comparable with bulk‐like nanostructures of the same size, in good agreement with previous experimental findings. Three‐dimensional structures derived from the structures of lower dimensionality are expected to shed light on the structural characteristics of the existing mesoporous Ge materials that possess promising optoelectronic properties. Furthermore, 3D networks derived from the polyhedral {Ge₉}_n cages lead to structures that are closely related to the well‐known LTA zeolite framework, suggesting further possibilities for deriving novel mesoporous modifications of germanium. Raman and IR spectra and simulated X‐ray diffraction patterns of the predicted materials are given to facilitate comparisons with experimental results. The studied novel germanium modifications are semiconducting, and several structure types possess noticeably larger band gaps than bulk α‐Ge.     

Size effect of fullerene cages and encaged clusters in M<Subscript>3</Subscript>N@C<Subscript>2<Emphasis Type="Italic">n</Emphasis></Subscript>

Based on the calculated findings that the sizes of encaged clusters determine the structures and the stability of C₈₀-based trimetallic nitride fullerenes (TNFs), more extensive density functional theory calculations were performed on M₃N@C₆₈, M₃N@C₇₈ and M₃N@C₈₀ (M=Sc, Y and La). The calculated results demonstrated that the structures and stability undergo a transition with the increasing of the sizes of the cages and clusters. Sc₃N is planar inside the three considered cages, Y₃N is slightly pyramidal inside C₆₈-6140 and C₇₈-5 and planar inside I_h C₈₀-7, however, La₃N is pyramidal inside all the three cages. Those cages with pyramidal clusters inside deformed considerably, compared with their parent cages. In these cases, the bonding of metallic atoms toward the cages does not play an important role, and the encaged cluster tends to be located inside the cages with the largest M-M and M-C distances so that the strain energy can be released mostly. These calculations revealed the size effect of fullerene cages and encaged clusters, and can explain the position priority of M3N inside fullerene cages and the differences in yield of M₃N@C_2n . Supported by the Southwest University, China (Grant No. SWNUB2005002)     

First-principle Study of AunSc (n=2～13) Clusters

The geometries, stabilities, electronic, and magnetic properties of Au_nSc clusters have been systematically investigated by density functional theory. The lowest energy structures of Au_nSc favor planar structure and the doped Sc atom does not disturb the frame of Au_nclusters with n≤11. For n≥12, Sc atom is fully encapsulated by the Au cages. From theanalysis of the second-order energy difference, the fragmentation energies, vertical ionizationpotential, vertical electron affinity, and HOMO-LUMO gap, the clusters with odd Au atoms possess relatively higher stabilities than their neighbor size. The doping of Sc atom can greatly improve the stability and change the sequence of chemical activity for Au_n. For n≤11, the total magnetic moments of Au_nSc appear the alternation between 0.00 and 1.00 μB. The total magnetic moments are quenched when Sc is trapped into the Au cages with n≥12.     

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.     

From C58 to C62 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.     

Structural interconnections and the role of heptagonal rings in endohedral trimetallic nitride template fullerenes

Recent experiments indicate that fullerene isomers outside the classical definition can also encapsulate metallic atoms or clusters to form endohedral metallofullerenes. Our systematic study using DFT calculations, suggests that many heptagon‐including nonclassical trimetallic nitride template fullerenes are similar in stability to their classical counterparts, and that conversion between low‐energy nonclassical and classical parent cages via Endo–Kroto insertion/extrusion of C₂ units and Stone–Wales isomerization may facilitate the formation of endohedral trimetallic nitride fullerenes. Close structural connections are found between favored isomers of trimetallic nitride template fullerenes from C₇₈ to C₈₂. It appears that the lower symmetry and local deformations associated with introduction of a heptagonal ring favor encapsulation of intrinsically less symmetrical mixed metal nitride clusters. © 2016 Wiley Periodicals, Inc.     

Benzene Adsorption on C<Subscript>24</Subscript>, Si@C<Subscript>24</Subscript>, Si-Doped C<Subscript>24</Subscript>, and C<Subscript>20</Subscript> Fullerenes

The absorption feasibility of benzene molecule in the C₂₄, Si@C₂₄, Si-doped C₂₄, and C₂₀ fullerenes has been studied based on calculated electronic properties of these fullerenes using Density functional Theory (DFT). It is found that energy of benzene adsorption on C₂₄, Si@C₂₄, and Si-doped C₂₄ fullerenes were in range of –2.93 and –51.19 kJ/mol with little changes in their electronic structure. The results demonstrated that the C₂₄, Si@C₂₄, and Si-doped C₂₄ fullerenes cannot be employed as a chemical adsorbent or sensor for benzene. Silicon doping cannot significantly modify both the electronic properties and benzene adsorption energy of C₂₄ fullerene. On the other hand, C₂₀ fullerene exhibits a high sensitivity, so that the energy gap of the fullerene is changed almost 89.19% after the adsorption process. We concluded that the C₂₀ fullerene can be employed as a reliable material for benzene detection.     

A new pillared lithium bismuth phosphate,LiBi7.37P3O19, with elliptical channels

The structure of a new lithium bismuth phosphate, LiBi_7.37P₃O₁₉, consists of infinite OBi₄ edge‐sharing tetrahedral chains in the ac plane, which form Bi₂O₂ layers parallel to the b axis. They are sandwiched between PO₄ tetrahedral and Bi polyhedral layers. The PO₄–Bi–PO₄ layers are bridged by columns formed by one Bi polyhedron flanked on each side by LiO₄ tetrahedra. This bridging Bi atom lies on a twofold axis, special position 4e of the C2/c space group. This arrangement creates pillared open elliptical channels parallel to [010].     

Template‐Dependent Photochemical Reactivity of Molecular Metal Oxides

A combined experimental and theoretical study shows that the photooxidative activity of two isostructural metal oxide clusters depends on their internal templates. To this end, two halide‐templated bismuth vanadium oxide clusters [X(Bi(dmso)₃)₂V₁₂O₃₃]^? (X=Cl^?, Br^?) are reported and fully characterized. The two clusters show similar absorption features and illustrate that bismuth incorporation results in increased visible‐light absorption. Significantly higher photooxidative activity is observed for the bromide‐templated cluster compared with the chloride‐templated one. Detailed photophysical assays and complementary DFT calculations suggest that the more efficient triplet excited state formation in the Br^?‐containing cluster is the decisive step in the photocatalysis and is due to the heavy‐atom effect of the bromide. This concept can therefore open new pathways towards the optimization of photocatalytic activity in metal oxide clusters.     

Metallacarboranes of the C2B4-cage systems

A comprehensive review of the chemistry of polyhedral cluster complexes in whichs,p,d, andf-block metals are incorporated into C₂B₄-carborane cages to form the respective metallacarboranes is presented. The main focus of the review is directed toward systematizing the chemistry of metallacarboranes in order to promote their use as possible electronic, ceramic, and/or catalytic materials in addition to providing information on which we can test and expand our knowledge about the fundamental interactions that are at work in determining the structures and properties of these cluster complexes.     

A density functional computational investigation on electronic properties of the stable irregular boron fullerenes with 20–56 atoms

The various irregular B_n (n=20‐56) cages are optimized at the B3LYP/6‐311G level. The geometries and electronic properties are systemically discussed. New B₂₄ and B₂₈ geometries are revealed. The calculated results show that the number of polygonal vacancies is apparently increased as the size of irregular cages being increased and that the irregular cage configurations with uneven distribution of different sized holes enhances the stabilities of the fullerenelike cages. The magic numbers of stabilities are predicted to be B₄₈. HOMO and LUMO gaps are discussed. Furthermore, the delocalized π orbitals are mainly distributed around the polygonal vacancies of irregular cages and enhance the stabilities of the irregular boron cages. © 2015 Wiley Periodicals, Inc.     

Exohedral Silicon Fullerenes: Si<Subscript>60</Subscript>Pn<Subscript>60</Subscript> and Si<Subscript>80</Subscript>Pn<Subscript>60</Subscript> (Pn = P,As, Sb and Bi)

Based on density functional theory (DFT) calculations, we predict that the icosahedral structures of the silicon fullerenes Si₆₀ and Si₈₀ can be stabilized by 12 exohedral pentagons of group V-A unit Pn₅ (Pn = P, As, Sb or Bi). The 12 pentagons can fully passivate the dangling bonds associated with 12 pentagonal Si₅ rings on the silicon fullerene cages, thereby resulting in stable exohedral silicon fullerenes Si₆₀Pn₆₀ and Si₈₀Pn₆₀. Properties of the eight Si₆₀Pn₆₀ and Si₈₀Pn₆₀ clusters, including harmonic vibrational frequencies, electron affinity (EA), the HOMO–LUMO gap and NICS values, are computed. We find that all eight Si₆₀Pn₆₀ and Si₈₀Pn₆₀ fullerenes possess relatively large HOMO–LUMO gaps, high electron affinities, and that the Si₆₀Pn₆₀ fullerenes exhibit weak aromaticity. Among eight clusters examined, the exohedral fullerene I _h-Si₆₀P₆₀ possesses the largest cohesive energy per atom. Ab initio molecular dynamics (AIMD) simulation is performed to demonstrate thermal stability of the hollow cage structure of Si₆₀P₆₀ at the room temperature.     

Further test of the isolated pentagon rule: Thermodynamic and kinetic stabilities of C84 fullerene isomers

Thermodynamic and kinetic stabilities of 73 C₈₄ fullerene isomers were estimated from the MM3 heats of formation and the recently defined bond resonance energies (BREs), respectively. The BRE represents the contribution of a given π bond in a molecule to the topological resonance energy (TRE). All π bonds shared by two pentagons turned out to be highly reactive without exceptions. C₈₄ fullerene isomers with such π bonds must be incapable of survival during harsh synthetic processes. Thus, the isolated pentagon rule (IPR) proved to be applicable to such large fullerene cages. For sufficiently large fullerenes like C₈₄, some isolated-pentagon isomers are also predicted to be very unstable with highly antiaromatic π bonds. © 1996 by John Wiley & Sons, Inc.     

Some aspects of the symmetry and topology of possible carbon allotrope structures

Elemental carbon has recently been shown to form molecular polyhedral allotropes known as fullerenes in addition to the familiar graphite and diamond known since antiquity. Such fullerenes contain polyhedral carbon cages in which all vertices have degree 3 and all faces are either pentagons or hexagons. All known fullerenes are found to satisfy the isolated pentagon rule (IPR) in which all pentagonal faces are completely surrounded by hexagons so that no two pentagonal faces share an edge. The smallest fullerene structures satisfying the IPR are the known truncated icosahedral C₆₀ of I _h symmetry and ellipsoidal C₇₀ of D _5h symmetry. The multiple IPR isomers of families of larger fullerenes such as C₇₆, C₇₈, C₈₂ and C₈₄ can be classified into families related by the so-called pyracylene transformation based on the motion of two carbon atoms in a pyracylene unit containing two linked pentagons separated by two hexagons. Larger fullerenes with 3ν vertices can be generated from smaller fullerenes with ν vertices through a so‐called leapfrog transformation consisting of omnicapping followed by dualization. The energy levels of the bonding molecular orbitals of fullerenes having icosahedral symmetry and 60n ² carbon atoms can be approximated by spherical harmonics. If fullerenes are regarded as constructed from carbon networks of positive curvature, the corresponding carbon allotropes constructed from carbon networks of negative curvature are the polymeric schwarzites. The negative curvature in schwarzites is introduced through heptagons or octagons of carbon atoms and the schwarzites are constructed by placing such carbon networks on minimal surfaces with negative Gaussian curvature, particularly the so-called P and D surfaces with local cubic symmetry. The smallest unit cell of a viable schwarzite structure having only hexagons and heptagons contains 168 carbon atoms and is constructed by applying a leapfrog transformation to a genus 3 figure containing 24 heptagons and 56 vertices described by the German mathematician Klein in the 19th century analogous to the construction of the C₆₀ fullerene truncated icosahedron by applying a leapfrog transformation to the regular dodecahedron. Although this C₁₆₈ schwarzite unit cell has local O _h point group symmetry based on the cubic lattice of the D or P surface, its larger permutational symmetry group is the PSL(2,7) group of order 168 analogous to the icosahedral pure rotation group, I, of order 60 of the C₆₀ fullerene considered as the isomorphous PSL(2,5) group. The schwarzites, which are still unknown experimentally, are predicted to be unusually low density forms of elemental carbon because of the pores generated by the infinite periodicity in three dimensions of the underlying minimal surfaces. This revised version was published online in July 2006 with corrections to the Cover Date.     

A spectroscopic and ab initio study on Bi(III) complex formation with 3-mercaptopropanesulfonic acid

This article deals with complex formation of Bi(III) with 3-mercaptopropanesulfonic acid (H₂MPS) in aqueous perchloric acid solutions, with synthesis and characterization of a solid 3-mercaptopropanesulfonate complex of bismuth(III). The stoichiometry and structures of Bi-MPS species in aqueous solution and of a solid complex have been studied by UV–Vis, ¹H-NMR, ICP-AES, Raman, and EXAFS spectroscopic methods; the structures have also been simulated with DFT/PBE0 calculations. The Bi(III) L_III-edge EXAFS oscillation for a solid compound with the empirical formula [Bi(HMPS)₂(ClO₄)]⁰ was simulated with two Bi–S interatomic distances at 2.50 ± 0.01 Å, two Bi–O distances at 2.56 ± 0.02 Å and two Bi–O distances at 2.75 ± 0.02 Å. Implementation of the same approach for aqueous solutions on the assumption of S₃BiO₃ coordination at the H₂MPS?:?Bi(III) mole ratio ≥ 3.0 revealed three Bi–S bonds at 2.53 ± 0.02 Å and three Bi–O bonds at 2.68 ± 0.02 Å, respectively. Optimized geometries, electronic structures of Bi(HMPS)₃ and [Bi(HMPS)₂ClO₄]⁰, vibrational properties of [Bi(HMPS)₂ClO₄]⁰, and electronic absorption spectrum of Bi(HMPS)₃ species obtained by DFT and TD–DFT modeling are consistent with empirical parameters. In the UV–Vis spectrum of Bi(HMPS)₃ the LMCT and MLCT S^2? ? Bi³⁺ band appears at 268 nm.     

A Redox‐Confused Bismuth(I/III) Triamide with a T‐Shaped Planar Ground State

Reaction of a tethered triamine ligand with Bi(NMe₂)₃ gives a Bi triamide, for which a Bi^I electronic structure is shown to be most appropriate. The T‐shaped geometry at bismuth provides the first structural model for edge inversion in bismuthines and the only example of a planar geometry for pnictogen triamides. Analogous phosphorus compounds exhibit a distorted pyramidal geometry because of different Bi?N and P?N bond polarities. Although considerable Bi^I character is indicated for the title Bi triamide, it exhibits reactivity similar to Bi^III electrophiles, and expresses either a vacant or a filled p orbital at Bi, as evidenced by coordination of either pyridine N‐oxide or W(CO)₅. The product of the former shows evidence of coordination‐induced oxidation state change at bismuth.     

Synthesis and Characterization of Three Homoleptic Bismuth Silanolates: [Bi(OSiR3)3] (R = Me,Et, iPr)

The bismuth tris(triorganosilanolates) [Bi(OSiR₃)₃] ( 1 , R = Me; 2 , R = Et; 3 , R = iPr) were prepared by reaction of R₃SiOH with [Bi(OtBu)₃]. Compound 1 crystallizes in the triclinic space group with Z = 2 and the lattice constants a = 10.323(1) Å, b = 13.805(1) Å, c = 21.096(1) Å and α = 91.871(4)°, β = 94.639(3)°, γ = 110.802(3)°. In the solid state compound 1 is a trimer as result of weak intermolecular bismuth‐oxygen interactions with Bi–O distances in the range 2.686(6)–3.227(3) Å. The coordination at the bismuth atoms Bi(1) and Bi(3) is best described as 3 + 2 coordination whereas Bi(2) shows a 3 + 3 coordination. The intramolecular Bi–O distances fall in the range 2.041(3)–2.119(3) Å. Compound 3 crystallizes in the orthorhombic space group Pbcm with Z = 4 and the lattice constants a = 7.201(1) Å, b = 23.367(5) Å and c = 20.893(1) Å, whereas the triethylsilyl‐derivative 2 is liquid. In contrast to [Bi(OSiMe₃)₃] ( 1 ) compound 3 is monomeric in the solid state, but shows similar intramolecular Bi–O distances in the range 1.998(2)–2.065(5) Å. The bismuth silanolates are highly soluble in common organic solvents and strongly moisture sensitive. Compound 1 shows the lowest thermal stability.     

Selective Encapsulation and Chiral Induction of C60 and C70 Fullerenes by Axially Chiral Porous Aromatic Cages

Chiral induction has been an important topic in chemistry, not only for its relevance in understanding the mysterious phenomenon of spontaneous symmetry breaking in nature but also due to its critical implications in medicine and the chiral industry. The induced chirality of fullerenes by host–guest interactions has been rarely reported, mainly attributed to their chiral resistance from high symmetry and challenges in their accessibility. Herein, we report two new pairs of chiral porous aromatic cages (PAC), R- PAC-2 , S- PAC-2 (with Br substituents) and R- PAC-3 , S- PAC-3 (with CH₃ substituents) enantiomers. PAC-2 , rather than PAC-3 , achieves fullerene encapsulation and selective binding of C₇₀ over C₆₀ in fullerene carbon soot. More significantly, the occurrence of chiral induction between R- PAC-2 , S- PAC-2 and fullerenes is confirmed by single-crystal X-ray diffraction and the intense CD signal within the absorption region of fullerenes. DFT calculations reveal the contribution of electrostatic effects originating from face-to-face arene-fullerene interactions dominate C₇₀ selectivity and elucidate the substituent effect on fullerene encapsulation. The disturbance from the differential interactions between fullerene and surrounding chiral cages on the intrinsic highly symmetric electronic structure of fullerene could be the primary reason accounting for the induced chirality of fullerene.     

Structural, Electronic, and Magnetic Properties of MB n (M?=?Y, Zr, Nb, Mo, Tc, Ru, n?≤?8) Clusters

The geometries, stabilities, electronic, and magnetic properties of MB _n (M?=?Y, Zr, Nb, Mo, Tc, Ru, n????8) clusters have been systematically investigated by density functional theory. It is shown that the lowest energy structures of MB _n (n????3) clusters can be obtained by substituting one B atom in the lowest energy structures of B _n+1 clusters in most cases. After n????8, the 3D configurations prevail and become the lowest-energy structures. The second-order energy difference and the dissociation energy show YB₇, ZrB₇, NbB₆, MoB₆, TcB₆, RuB₆ clusters possess relatively higher stabilities. The doped-M atoms improve the chemical activity of the host clusters in most cases; but different M atom has different effect on B atom??s electronic structure. The binding strengths are strong between M and B _n , which plays an important role in the M?CB growth mechanisms. It is interesting that the relative orientation between the magnetic moments of the M (M?=?Zr, Nb, Mo, Tc, Ru) atoms and those of its neighboring B atoms exhibits ferromagnetic or antiferromagnetic alignment in contrast to the ferromagnetic alignment of YB _n .