Local channels preserving maximal entanglement or Schmidt number

Maximal entanglement and Schmidt number play an important role in various quantum information tasks. In this paper, it is shown that a local channel preserves maximal entanglement state(MES) or preserves pure states with Schmidt number $r$($r$ is a fixed integer) if and only if it is a local unitary operation.Comment: 10 page

Synthesis and characterisation of magnesium complexes containing sterically demanding N,N' -bis(aryl)amidinate ligands

Condensation reactions of carboxylic acids and anilines in the presence of polyphosphoric acid trimethylsilyl ester (PPSE) afforded a range of sterically demanding N,N′-bis(aryl)amidines, RN{C(R′)}N(H)R [R = Mes (Mes = 2,4,6-trimethylphenyl), R′ =

Synthesis and characterization of group IV metal complexes featuring tridentate diamidoamine ligands

New synthetic routes for the preparation of five-coordinate zirconium and titanium complexes featuring tridentate diamidoamine ligands were developed. Zirconium dichloride complexes, [(Mes)N(CH2)2NR(CH 2)2N(Mes)]ZrCl2 (R=H, SiMe3), were synthesized via a one step toluene elimination reaction. Analogous titanium dichloride complexes, [(Mes)N(CH2)2NR(CH2) 2N(Mes)]TiCl2 (R=H, SiMe3), were prepared using a one-step amine elimination reaction.;The NMR data for all four of the [(Mes)N(CH2)2NR(CH 2)2N(Mes)]MCl2-type complexes demonstrated that they exhibit CS symmetry in solution, as indicated by the observation of six carbon resonances for the aryl carbons and three 1H and 13C NMR resonances for the methyl groups of the mesityl substituents. Molecular structures obtained from crystals of [(Mes)N(CH 2)2NH(CH2)2N(Mes)]ZrCl2 and [(Mes)N(CH2)2N(SiMe3)(CH2) 2N(Mes)]MCl2 (M=Zr, Ti) confirmed the identity of the five-coordinate zirconium and titanium dichloride complexes. The bond angles about the zirconium or titanium atom in the respective complexes indicate that they adopt a geometry that is consistent with the fac structure

Synthetic, Catalytic, and Mechanistic Studies of Supermesityl Phosphiranes and Phosphines

Methylation of P-stereogenic phosphiranes Mes*PCH2CH(R) (Mes* = 2,4,6-(t-Bu)3C6H2, R = Me, Ph) with MeOTf gave P-stereogenic phosphiranium cations; [Mes*P(Me)CH2CH(Ph)][OTf] underwent syn-anti isomerization via P-epimerization. Mechanistic studies suggested ring opening gave a hyperconjugation-stabilized carbocation in which pyramidal inversion at P was promoted by s-interaction with the pendant cation. Attempted phosphirane protonation with HOTf resulted in ring opening and C-H activation of an o-t-Bu group to give phospholanium cations. Treatment of [Mes*P(Me)CH2CH(Ph)][OTf] with LiPPh2 gave bis(phosphino)ethanes. Copper- catalyzed P-alkylation of the secondary phosphine PHPh(Mes*) with benzyl bromides gave P-stereogenic tertiary phosphines with a supermesityl substituent

Attempted reduction of a carbazolyl-diiodoalane

We report details of our attempts to reduce the bulky carbazolyl diiodoalane [R–AlI$_{2}$]. The reducing agents employed include KC$_{8}$, Cp$^{*}$$_{2}$Co and the Mg(I) compound [($^{Mes}$BDI)Mg]$_{2}$. The use of KC$_{8}$ allowed the spectroscopic observation of the alanediyl [R–Al]. With Cp$^{*}$$_{2}$Co as the reducing agent, the alanediyl [R–Al] was obtained as a crystalline material in low yield, but paramagnetic impurities remained. When diiodoalane [R–AlI$_{2}$] was treated with [($^{Mes}$BDI)Mg]$_{2}$, no reduction but a 2 : 1 addition was observed

Novel polyoxometalates: Is antimony the new molybdenum?

Polyoxometalates based on Mo, W or V have been known for a long time and present a diverse range of structures, with the [XMo₁₂O₄₀]ⁿ⁻ Keggin ions (X = P, Si ,…) perhaps the best known.¹ They are still subject to intense research with >4000 papers published in the past five years. Following on from our study² of aryl arsonic acids RAsO₃H₂, which are straightforward molecular species based on four-coordinate As(V), we became interested in the corresponding antimony compounds. Although aryl stibonic acids of nominal formula RSbO₃H₂ have been known for over 100 years,³ their composition has remained uncertain, as they form only amorphous solids, have complicated titration behaviour and only limited solubility. The presumption has been that they are polymeric, based on 5- or 6-coordinate Sb with Sb-O-Sb linkages, though direct evidence is sparse.⁴ Recently, it has been shown by Beckman that if very bulky R groups are used, then relatively simple dimers such as (2,6-Mes₂C₆H₃Sb₂O₂(OH)₄(Mes=mesityl) can be isolated, but these represent a special case.

Conformal and kinetic couplings as two Jordan frames of the same theory

Non-minimal scalar-tensor (ST) theories may admit an Einstein frame representation, where gravity is described by the Einstein-Hilbert action plus the scalar sector. Some STs become just {\em minimal} Einstein-scalar (MES) theories, notable examples are Brans-Dicke and $R\phi^2$. ST theories with {\em derivative} coupling can also be reduced to an Einstein frame by disformal transformations, but, as a rule, their scalar sector will contain higher derivative terms. Here we draw attention to a new Palatini kinetically coupled theory which can be reduced to pure MES by an invertible disformal transformation. This theory can then be converted into the Jordan frame of another ST, $R\phi^2$, which also admits an invertible transformation to MES. Two theories, each of which is dual to MES, will be {\em sequentially dual} to each other and can be considered as two different Jordan frames of the same theory. Both chosen theories violate null energy condition. Transforming the same singular MES solutions, we find the desingularization signs in both Jordan frames, but these are more pronouned in the framework of kinetic theory, leading, in the cosmological case, to Genesis-type behavior.Comment: 25 page

Functionalization of Pentaphosphorus Cations via Complexation

The chemistry of polyphosphorus cations has rapidly developed in recent years, but their coordination behavior has remained mostly unexplored. Herein, we describe the reactivity of [P5R2]+ cations with cyclopentadienyl metal complexes. The reaction of [CpArFe(μ‐Br)]2 (CpAr=C5(C6H4‐4‐Et)5) with [P5R2][GaCl4] (R=iPr and 2,4,6‐Me3C6H2 (Mes)) afforded bicyclo[1.1.0]pentaphosphanes (1‐R, R=iPr and Mes), showing an unsymmetric “butterfly” structure. The same products 1‐R were formed from K[CpAr] and [P5R2][GaCl4]. The cationic complexes [CpArCo(η4‐P5R2)][GaCl4] (2‐R[GaCl4], R=iPr and Cy) and [(CpArNi)2(η3:3‐P5R2)][GaCl4] (3‐R[GaCl4]) were obtained from [P5R2][GaCl4] and [CpArM(μ‐Br)]2 (M=Co and Ni) as well as by using low‐valent “CpArMI” sources. Anion metathesis of 2‐R[GaCl4] and 3‐R[GaCl4] was achieved with Na[BArF24]. The P5 framework of the resulting salts 2‐R[BArF24] can be further functionalized with nucleophiles. Thus reactions with [Et4N]X (X=CN and Cl) give unprecedented cyano‐ and chloro‐functionalized complexes, while organo‐functionalization was achieved with CyMgCl

Preparation, Characterization and X-ray Crystal Structures of New Axially Functionalized Phthalocyanines and Phthalocyanine Modified SBA-15 Materials

We investigated the typical metathetical reaction patterns of PcTiO with arylisocyanates aiming at the synthesis of its isoelectronic compounds (PcTiX; X = S, Se, NR, etc). Furthermore novel organoimido compounds of the general formula [PcM(NR)Cl] (M = Mo, W, Re; R = tBu, Mes) were prepared using the typical fusion reaction of phthalonitrile (PN) in the presence of metal complex [M(NR)2Cl2(dme)] (M = Mo, W; R = tBu, Mes) or [Re(NR)3Cl] (M = Re; R = tBu, Mes). The prepared compounds were characterized by MS, EA, UV-VIS, FT-IR, 1H-NMR, etc. The crystal structures of some prepared compounds have been solved. When the (PcTiO) oligomer was refluxed with 2,6-diisopropyl-phenylisocyanate in DMF, the corresponding oligomer containing the imido ligand was obtained. Similarly, the reaction of TCB with [Mo(NMes)2Cl2(dme)] produces a phthalocyanine pentamer pocessing the [Mo(NMes)Cl] functionality. The time-resolved photoluminescence measurements were carried out for PcTiO and N,N`-di-4-tolylureato(phthalocyaninato)titanium(IV). PcTi@SBA-15 and PcTi&TiOx@SBA-15 materials have been prepared by impregnation of the [TiPc] selectively in the pores of SBA-15 and TiOx@SBA-15 templates