Weak-measurement elements of reality

A brief review of the attempts to define elements of reality in the framework of quantum theory is presented. It is noted that most definitions of elements of reality have in common the feature to be a definite outcome of some measurement. Elements of reality are extended to pre- and post- selected systems and to measurements which fulfill certain criteria of weakness of the coupling. Some features of the newly introduced concepts are discussed.This research was supported in part by grant 614/65 of the Basic Research Foundation (administered by the Israel Academy of Sciences and Humanities.     

Representation of elements of a sequence by sumsets

In this note the method of [5] and a result from [3] are combined to treat the following classical problem: Given a finite setA and an infinite sequenceS (both inZ), what is the minimal number of elements ofA whose sum lies inS? We obtain an upper bound depending only on the densities ofA andS (but not on their arithmetic nature).     

Phenanthroline-polyoxometalate hybrid compounds and the observation of intramolecular charge transfer

A phenanthroline ligand has been covalently modified at the 2 and 9 positions by an aminophenylhexamolybdate substituent. The 1H NMR spectrum indicated a strong electron-withdrawing effect of the hexamolybdate (Mo6O19(2-)) moiety on the phenanthroline ligand. UV-vis and cyclic voltammetry showed extended conjugation of the hybrid phenanthroline-polyoxometalate compound and the possibility of easy oxidation of the extended phenanathroline ligand. Further EPR experiments provided strong evidence for an intramolecular charge-transfer process with the formation of a phenanthroline cation radical and a reduced hexamolybdate.     

Sol-gel-derived prussian blue-silicate amperometric glucose biosensor

A new type of inorganic biosensor is introduced. The sensor comprises glucose oxidase enzymes encapsulated in a sol-gel-derived Prussian blue-silicate hybrid network. Glucose is detected by the biocatalytic reduction of oxygen followed by catalytic reduction of hydrogen peroxide by the Prusian blue catalyst. The sol-gel silicate entails a rigid encapsulating matrix, the Prussian blue provides chemical catalysis and charge mediation from the reduction site to the supporting electrode, and the enzyme is responsible for the biocatalysis. The feasibility of a dual optical/electrochemical mode of analysis is also demonstrated.     

Bis(m-phenylene)-32-crown-10-based cryptands, powerful hosts for paraquat derivatives

Four new bis(m-phenylene)-32-crown-10-based cryptands with different third bridges were prepared. Their complexes with paraquat derivatives were studied by proton NMR spectroscopy, mass spectrometry, and X-ray analysis. It was found that these cryptands bind paraquat derivatives very strongly. Specifically, a diester cryptand with a pyridyl nitrogen atom located at a site occupied by either water or a PF(6) anion in analogous complexes exhibited the highest association constant K(a) = 5.0 x 10(6) M(-1) in acetone with paraquat, 9000 times greater than the crown ether system. X-ray structures of this and analogous complexes demonstrate that improved complexation with this host is a consequence of preorganization, adequate ring size for occupation by the guest, and the proper location of the pyridyl N-atom for binding to the beta-pyridinium hydrogens of the paraquat guests. This readily accessible cryptand is one of the most powerful hosts reported for paraquats.     

Asymmetrical nonbridgehead nitrogen-17: Complete separation into antipodes and absolute configuration of chiralic n-alkoxyisoxazolidines

trans-Stereospecificity of the amidation of 1-alkoxyisoxazolidine-3,3-dicarboxylic ester (1) has been elucidated. Alkaline hydrolysis of monester 4 yielded the salt 6 which after its ion exchange in the form of S(?) and R-(+)-phenylethylammonium salts was completely separated into the enantiomeric salts (+10 and ?10). Esterification and amidation of these salts afforded antipodes 2 S-( +12) and 2 R-( ?12) containing only a nitrogen asymmetric center. Optical purities of the products were established on the basis of their NMR spectra with shift-reagent. Molecular and crystal structure as well as an absolute configuration of +10 were detected by means of X-ray analysis.     

Rh(II) and Rh(I) two-legged piano-stool complexes: structure,reactivity, and electronic properties

The ligand 1,4-bis[4-(diphenylphosphino)butyl]-2,3,5,6-tetramethylbenzene, 3, was used to synthesize a mononuclear Rh(II) complex [(eta(1):eta(6):eta(1)-1,4-bis[4-(diphenylphosphino)butyl]-2,3,5,6-tetramethylbenzene)Rh][PF(6)](2), 6+, in a two-legged piano-stool geometry. The structural and electronic properties of this novel complex including a single-crystal EPR analysis are reported. The complex can be cleanly interconverted with its Rh(I) form, allowing for a comparison of the structural properties and reactivity of both oxidation states. The Rh(I) form 6 reacts with CO, tert-butyl isocyanide, and acetonitrile to form a series of 15-membered mononuclear cyclophanes [(eta(1):eta(1)-1,4-bis[4-(diphenylphosphino)butyl]-2,3,5,6-tetramethylbenzene)Rh(CO)(3)][PF(6)] (8), [(eta(1):eta(1)-1,4-bis[4-(diphenylphosphino)butyl]-2,3,5,6-tetramethylbenzene)Rh(CNC(CH(3))(3))(2)][PF(6)] (10), and [(eta(1):eta(1)-1,4-bis[4-(diphenylphosphino)butyl]-2,3,5,6-tetramethylbenzene)Rh(CO)(CH(3)CN)][PF(6)] (11). The Rh(II) complex 6+ reacts with the same small molecules, but over shorter periods of time, to form the same Rh(I) products. In addition, a model two-legged piano-stool complex [(eta(1):eta(6):eta(1)-1,4-bis[3-(diphenylphosphino)propoxy]-2,3,5,6-tetramethylbenzene)Rh][B(C(6)F(5))(4)], 5, has been synthesized and characterized for comparison purposes. The solid-state structures of complexes 5, 6, 6+, and 11 are reported. Structure data for 5: triclinic; P(-)1; a = 10.1587(7) A; b = 11.5228(8) A; c = 17.2381(12) A; alpha = 96.4379(13) degrees; beta = 91.1870(12) degrees; gamma = 106.1470(13) degrees; Z = 2. 6: triclinic; P(-)1; a = 11.1934(5) A; b = 12.4807(6) A; c = 16.1771(7) A; alpha = 81.935(7) degrees; beta = 89.943(1) degrees; gamma = 78.292(1) degrees; Z = 2. 6+: monoclinic; P2(1)/n; a = 11.9371(18) A; b = 32.401(5) A; c = 12.782(2) A; beta = 102.890(3) degrees; Z = 4. 11: triclinic; P(-)1; a = 13.5476(7) A; b = 13.8306(7) A; c = 14.9948(8) A; alpha = 74.551(1) degrees; beta = 73.895(1) degrees; gamma = 66.046(1) degrees; Z = 2.     

Does alpha-fluorination affect the structural trans-influence and kinetic trans-effect of an alkyl ligand? Molecular structures of Pd(TMEDA)(CH(3))(R(F)) and a kinetic study of the trans to cis isomerization of Pt(TMEDA)(CH(3))(2)I(R(F)) [R(F) = CF(2)CF(3), CFHCF(3), CH(2)CF(3)

Reaction of Pd(TMEDA)(CH(3))(2) [TMEDA = tetramethylethylenediamine] with fluoroalkyl iodides R(F)I affords a series of square planar Pd(II) complexes Pd(TMEDA)(CH(3))(R(F)) [R(F) = CF(2)CF(3) (9), CFHCF(3) (10), CH(2)CF(3) (11)], presumably by oxidative addition followed by reductive elimination of CH(3)I. The solid-state structures of each compound have been determined by single crystal X-ray diffraction studies, allowing the effect of increasing alpha-fluorination on the structural trans-influence of alkyl ligands to be examined. In these compounds there is no significant difference observed in the trans-influence of the three fluorinated alkyl ligands toward the trans-N atom, although a significant cis-influence on the neighboring methyl ligand is apparent. Oxidative addition of the same series of fluoroalkyl ligands to the corresponding Pt(TMEDA)(CH(3))(2) affords octahedral Pt(IV) complexes trans-Pt(TMEDA)(CH(3))(2)(R(F))I [R(F) = CF(2)CF(3) (12), CFHCF(3) (13), CH(2)CF(3) (14)] as the kinetic products. In each case, subsequent isomerization to the corresponding all cis-isomers is observed; in the case of 13, the stereocenter at the alpha-carbon results in two diastereomeric cis-isomers, which are formed at different rates. The molecular structures of 13 and its more stable all cis-isomer 16b have been crystallographically determined. Kinetic studies of the trans-cis isomerization reactions show the mechanism to involve a polar transition state, presumably involving iodide dissociation, followed by rearrangement of the cation, and iodide recombination. High dielectric solvents increase the rate, but solvent coordinating ability has no effect. Dissolved salts (LiI, LiOTf) show normal accelerative salt effects, with no inhibition in the case of added iodide, consistent with the formation of an intimate ion pair intermediate. The kinetic parameters show that the trans-effects of fluoroalkyl ligands in these compounds follow the order expected from the relative sigma-donor properties of the ligands, with CF(2)CF(3) < CFHCF(3) < CH(2)CF(3).     

Molecular Structure and Conformational Composition of 1-[(Methylthio)methyl]-2-nitrobenzene (MTMNB): A Theoretical and Experimental Study

The conformational composition of gaseous MTMNB and the molecular structures of the rotational forms have been studied by electron diffraction at 130^∘C aided by results from ab initio and density functional theory calculations. The conformational potential energy surface has been investigated by using the B3LYP/6-31G(d,p) method. As a result, six minimum-energy conformers have been identified. Geometries of all conformers were optimized using MP2/6-31G(d,p), B3LYP/6-31G(d,p), and B3LYP/cc-pVTZ methods. These calculations resulted in accurate geometries, relative energies, and harmonic vibrational frequencies for all conformers. The B3LYP/cc-pVTZ energies were then used to calculate the Boltzmann distribution of conformers. The best fit of the electron diffraction data to calculated values was obtained for the six conformer model, in agreement with the theoretical predictions. Average parameter values (r_a in angstroms, angle α in degrees, and estimated total errors given in parentheses) weighted for the mixture of six conformers are r(C–C) = 1.507(5), r(C–C)_{ring, av} = 1.397(3), r(C–S)_av = 1.814(4), r(C–N) = 1.495(4), r(N–O)_av = 1.223(3), ∠(C–C–C)_ring = 116.0–122.5, ∠ C6–C4–C7 = 118.2(4), ∠ C–C–S = 113.6(6), ∠ C–S–C = 98.5(12), ∠ N–C–C4 = 121.9(3), ∠(O–N–C)_av = 116.8(3), ∠ O–N–O = 127.0(4). Torsional angles could not be refined. Theoretical B3LYP/cc-pVTZ torsional angles for the rotation about C–N bond, φ_C−N, were found to be 30.5–36.5^∘ for different conformers. As to internal rotation about C–C and C–S bonds, values of φ_C−C = 68–118^∘ and φ_C−S = 66–71^∘ were obtained for the three most stable conformers with gauche orientation with respect to these bonds. Some conclusions of this work were presented in a short communication in Russ. J. Phys. Chem. 2005, 79, 1701.     

Substrate oxidation by copper-dioxygen adducts: mechanistic considerations

A series of copper-dioxygen adducts [{Cu(II)(MePY2)(R)}(2)(O(2))](B(C(6)F(5))(4))(2) (1(R)()), systematically varying in their electronic properties via ligand pyridyl donor substituents (R = H, MeO, and Me(2)N), oxidize a variety of substrates with varying C-H or O-H bond dissociation enthalpies. Detailed mechanistic studies have been carried out, including investigation of 1(R)() thermodynamic redox properties, 1(R)() tetrahydrofuran (THF) and N,N'-dimethylaniline (DMA) oxidation kinetics (including analyses of substrate dicopper binding equilibria), and application of mechanistic probes (N-cyclopropyl-N-methylaniline (CMA) and (p-methoxyphenyl)-2,2-dimethylpropanol (MDP)), which can distinguish if proton-coupled electron-transfer (PCET) processes proceed through concerted electron-transfer proton-transfer (ETPT) or consecutive electron-transfer proton-transfer (ET/PT) pathways. The results are consistent with those of previous complementary studies; at low thermodynamic driving force for substrate oxidation, an ET/PT is operable, but once ET (i.e., substrate one-electron oxidation) becomes prohibitively uphill, the ETPT pathway occurs. Possible differences in coordination structures about 1(Me)()()2(N)()/1(MeO)() compared to those of 1(H)() are also used to rationalize some of the observations.