Characterizations of B and N heteroatoms as substitutional doping on structure,stability, and aromaticity of novel heterofullerenes evolved from the smallest fullerene cage C20: a density functional theory perspective

The structural stabilities and electronic properties of C₂₀ fullerene and some its incorporated boron and nitrogen derivatives are probed at B3LYP/AUG‐cc‐pVTZ level of theory. According to density functional theory results, the topology of inserted B or N heteroatoms in [20]‐fullerene perturbs strongly the stability, energy, geometry, charge, polarity, nucleus‐independent chemical shifts, aromaticity, and highest‐occupied molecular orbital and lowest‐unoccupied molecular orbital (HOMO–LUMO) gap of the resulting heterofullerenes. Vibrational frequency (υ_min) calculations show that except N₁₀C₁₀, all other B_bN_nC_{20‐(b + n)} heterofullerenes with b, and n = 0, 4, 5, 8, and 10 are true minima. The calculated band gaps (?E_HOMO–LUMO) of B₈C₁₂, and N₈C₁₂ (2.86 eV), show them the most stable heterofullerenes against electronic excitations. While 10 B substituting in equatorial position increase the conductivity of B₁₀C₁₀ through decreasing its band gaps, 10 N doping in equatorial position enhance stability of N₁₀C₁₀ against electronic excitations via increasing its band gaps. High natural bond orbital and Mulliken charge transfer on the surfaces of B atoms, especially B₅N₅C₁₀with five B–N bonds in the equatorial position, provokes further investigation on its possible application for hydrogen storage. Nucleus‐independent chemical shift values show that B₅N₅C₁₀ is the most aromatic species. The calculated heat of atomization per carbon (ΔH_at/C) of B₈C₁₂ shows it the most thermodynamic stable heterofullerenes of each. Copyright © 2016 John Wiley & Sons, Ltd.     

Recognition of characteristically simple group <Emphasis Type="Italic">A</Emphasis><Subscript>5</Subscript> × <Emphasis Type="Italic">A</Emphasis><Subscript>5</Subscript> by character degree graph and order

The character degree graph of a finite group G is the graph whose vertices are the prime divisors of the irreducible character degrees of G and two vertices p and q are joined by an edge if pq divides some irreducible character degree of G. It is proved that some simple groups are uniquely determined by their orders and their character degree graphs. But since the character degree graphs of the characteristically simple groups are complete, there are very narrow class of characteristically simple groups which are characterizable by this method.We prove that the characteristically simple group A₅ × A₅ is uniquely determined by its order and its character degree graph. We note that this is the first example of a non simple group which is determined by order and character degree graph. As a consequence of our result we conclude that A₅ × A₅ is uniquely determined by its complex group algebra.     

On the composition factors of a group with the same prime graph as B n (5)

Let G be a finite group. The prime graph of G is a graph whose vertex set is the set of prime divisors of |G| and two distinct primes p and q are joined by an edge, whenever G contains an element of order pq. The prime graph of G is denoted by Γ(G). It is proved that some finite groups are uniquely determined by their prime graph. In this paper, we show that if G is a finite group such that Γ(G) = Γ(B _n (5)), where n ? 6, then G has a unique nonabelian composition factor isomorphic to B _n (5) or C _n (5).     

The Baer-invariant of a semidirect product

In 1972 K.I. Tahara [7,2, Theorem 2.2.5], using cohomological methods, showed that if a finite group is the semidirect product of a normal subgroup N and a subgroup T, then M(T) is a direct factor of M(G), where M(G) is the Schur-multiplicator of G and in the finite case, is the second cohomology group of G. In 1977 W. Haebich [1, Theorem 1.7] gave another proof using a different method for an arbitrary group G.In this paper we generalize the above theorem. We will show that scN_cM(T) is a direct factor of _cM(G), where _c[3, p. 102] is the variety of nilpotent groups of class at most c ≥ 1 and _cM(G) is the Baer-invariant of the group G with respect to the variety _c [3, p. 107].     

Electron-transfer processes in the alkylation of α,β-unsaturated sulfones by organometallic reagents

The alkyldesulfonylation of acetylenic and vinylic sulfones by organolithium and organomagnesium reagents is shown to take place via alkyl radicals arising from electron-transfer processes.     

Combined Use of Post-Ion Mobility/Collision-Induced Dissociation and Chemometrics for b Fragment Ion Analysis

Although structural isomers may yield indistinguishable ion mobility (IM) arrival times and similar fragment ions in tandem mass spectrometry (MS), it is demonstrated that post-IM/collision-induced dissociation MS (post-IM/CID MS) combined with chemometrics can enable independent study of the IM-overlapped isomers. The new approach allowed us to investigate the propensity of selected b type fragment ions from AlaAlaAlaHisAlaAlaAla-NH₂ (AAA(His)AAA) heptapeptide to form different isomers. Principle component analysis (PCA) of the unresolved post-IM/CID profiles indicated the presence of two different isomer types for b₄ ⁺, b₅ ⁺, and b₆ ⁺ and a single isomer type for b₇ ⁺ fragments of AAA(His)AAA. We employed a simple-to-use interactive self-modeling mixture analysis (SIMPLISMA) to calculate the total IM profiles and CID mass spectra of b fragment isomers. The deconvoluted CID mass spectra showed discernible fragmentation patterns for the two isomers of b₄ ⁺, b₅ ⁺, and b₆ ⁺ fragments. Under our experimental conditions, calculated percentages of the “cyclic” isomers (at the 95 % confidence level for n = 3) for b₄ ⁺, b₅ ⁺, and b₆ ⁺ were 61 (± 5) %, 36 (± 5) %, and 48 (± 2) %, respectively. Results from the SIMPLISMA deconvolution of b₅ ⁺ species resembled the CID MS patterns of fully resolved IM profiles for the two b₅ ⁺ isomers. The “cyclic” isomers for each of the two-component b fragment ions were less susceptible to ion fragmentation than their “linear” counterparts.

A new characterization of <Emphasis Type="Italic">PSU</Emphasis>(<Emphasis Type="Italic">p,q</Emphasis>)

Summary Let G be a finite group. Order components of G were introduced in Chen [5]. Let OC(G) be the set of order components of G. Some finite groups are characterizable by their order components. This assertion was proved for the simple groups PSU(p,q), where p=3, 5, 7 and 11. In this paper, we prove that the simple groups PSU(p,q) can be uniquely determined by their order components, where p&ge;13 is a prime number. Main consequences of our results are the validity of a conjecture of J. G. Thompson and another conjecture of W. Shi and J. Bi for the groups under consideration.