Concrete quantum logics with covering properties

LetL be a concrete (=set-representable) quantum logic. Letn be a natural number (or, more generally, a cardinal). We say thatL admits intrinsic coverings of the ordern, and writeL C _n , if for any pairA, BL we can find a collection {C _i iI}, where cardI<n andC _i L for anyiI, such thatA B= _il C _i . Thus, in a certain sense, ifLC _n , then the rate of noncompatibility of an arbitrary pairA,BL is less than a given numbern. In this paper we first consider general and combinatorial properties of logics ofC _n and exhibit typical examples. In particular, for a givenn we construct examples ofL C _n+1\C _n . Further, we discuss the relation of the classesC _n to other classes of logics important within the quantum theories (e.g., we discover the interesting relation to the class of logics which have an abundance of Jauch-Piron states). We then consider conditions on which a class of concrete logics reduce to Boolean algebras. We conclude with some open questions.     

Influence of solvents on the insertion of methacrolein into zirconacyclopropenes

The reaction of Cp₂Zr(L)(η²-Me₃SiC₂) (L = THF, py) with equimolar amounts of H₂C = CMe-CHO at room temperature depends strongly on the ligands L and the solvents that are used. With L = THF, in the THF solution the insertion product

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1 was isolated, whereas by conducting the reaction in n-hexane solution an alkyne substitution with 1,4-coordination of the methacrolein takes place and the binuclear complex [

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2 was obtained. In conttrast, with L = py (a stronger ligand) only a 1:1 ratio of 1 and 2 was observed in both THF and in n-hexane. At 50°C complex 1 was converted into 2 and the alkyne was eliminated quantitatively.

Complexes 1 and 2 were characterized by IR and NMR spectroscopical measurements and 1 by an additional X-ray structure determination.     

Novel fluorogenic calix[4]arene-bis(crown-6-ether) for selective recognition of thallium(I)

A new fluorogenic, dansyl group-containing derivative of 1,3-alternate calix[4]arene-bis(crown-6-ether) provides optical recognition of Tl+ with selectivity over many other metal cations, including Na+, K+, Ca2+, Ag+, Hg2+ and Pb2+, and embodies the first example of a calixarene-based fluorescent Tl+-chemosensor.     

Mechanism of a strongly anisotropic MoIII-CN-MnII spin-spin coupling in molecular magnets based on the [Mo(CN)(7)](4-) heptacyanometalate: a new strategy for single-molecule magnets with high blocking temperatures

Unusual spin coupling between Mo(III) and Mn(II) cyano-bridged ions in bimetallic molecular magnets based on the [Mo(III)(CN)(7)](4-) heptacyanometalate is analyzed in terms of the superexchange theory. Due to the orbital degeneracy and strong spin-orbit coupling on Mo(III), the ground state of the pentagonal-bipyramidal [Mo(III)(CN)(7)](4-) complex corresponds to an anisotropic Kramers doublet. Using a specially adapted kinetic exchange model we have shown that the Mo(III)-CN-Mn(II) superexchange interaction is extremely anisotropic: it is described by an Ising-like spin Hamiltonian JS(z)(Mo) S(z)(Mn) for the apical pairs and by the J(z)S(z)(Mo) S(z)(Mn) + J(xy)(Sx(Mo) Sx(Mn) + Sy(Mo) Sy(Mn)) spin Hamiltonian for the equatorial pairs (in the latter case J(z) and J(xy) can have opposite signs). This anisotropy resulted from an interplay of several Ising-like (Sz(Mo) Sz(Mn)) and isotropic (S(Mo)S(Mn)) ferro- and antiferromagnetic contributions originating from metal-to-metal electron transfers through the pi and sigma orbitals of the cyano bridges. The Mo(III)-CN-Mn(II) exchange anisotropy is distinct from the anisotropy of the g-tensor of [Mo(III)(CN)(7)](4-); moreover, there is no correlation between the exchange anisotropy and g-tensor anisotropy. We indicate that highly anisotropic spin-spin couplings (such as the Ising-like JS(z)(Mo) S(z)(Mn)) combined with large exchange parameters represent a very important source of the global magnetic anisotropy of polyatomic molecular magnetic clusters. Since the total spin of such clusters is no longer a good quantum number, the spin spectrum pattern can differ considerably from the conventional scheme described by the zero-field splitting of the isotropic spin of the ground state. As a result, the spin reorientation barrier of the magnetic cluster may be considerably larger. This finding opens a new way in the strategy of designing single-molecule magnets (SMM) with unusually high blocking temperatures. The use of orbitally degenerate complexes with a strong spin-orbit coupling (such as [Mo(III)(CN)(7)](4-) or its 5d analogues) as building blocks is therefore very promising for these purposes.     

Reactions of Allyl Alcohols of the Pinane Series and of Their Epoxides in the Presence of Montmorillonite Clay

The reactivity of allyl alcohols of the pinane series and of their epoxides in the presence of montmorillonite clay in intra‐ and intermolecular reactions was studied. Mutual transformations of (+)‐trans‐pinocarveol ((+)‐ 2 ) and (?)‐myrtenol ((?)‐ 3a ) were major reactions of these compounds on askanite–bentonite clay (Schemes 1 and 2). However, the two reactions gave different isomerization products, indicating that the reactivity of the starting alcohol (+)‐ 2 or (?)‐ 3a was different from that of the same compound (+)‐ 2 or (?)‐ 3 formed in the course of the reactions. (?)‐cis‐ and (+)‐trans‐Verbenol ((?)‐ 16 and (+)‐ 12 , resp.), as well as (?)‐cis‐verbenol epoxide ((?)‐ 20 ) reacted with both aliphatic and aromatic aldehydes on askanite–bentonite clay giving various heterocyclic compounds (Schemes 4, 5 and 7); the reaction path depended on the structure of both the terpenoid and the aldehyde.     

Effects of Photobiomodulation on Daphnia magna Straus and their Sensitivity to Toxicant

This paper deals with the effect of photobiomodulation (PBM) on Daphnia magna S. and their sensitivity to cadmium sulfate, a known high toxic pollutant. In a first series of experiments, the effect of different He-Ne laser fluences irradiation (range 0.9-4300 mJ cm⁻²) on the fertility of both parent and filial generations (F1–F3) of the crustacean was studied. It was found that PBM in some cases significantly influenced the fertility of both irradiated crustaceans and their nonirradiated offspring. By selecting two fluences (9 ± 2 mJ cm⁻² reducing fertility and 4.3 ± 0.9 J cm⁻² increasing it), the effect of these on toxicity of cadmium sulfate was evaluated. These experiments have shown that prior irradiation with low-intensity light of a helium–neon laser with 632.8 nm wavelength can change the sensitivity of aquatic organisms to toxin cadmium sulfate. The degree and direction of changes depend on the toxicant concentration and the irradiation dose.     

First investigation of non-classical dihydrogen bonding between an early transition-metal hydride and alcohols: IR, NMR, and DFT approach

The interaction of [NbCp(2)H(3)] with fluorinated alcohols to give dihydrogen-bonded complexes was studied by a combination of IR, NMR and DFT methods. IR spectra were examined in the range from 200-295 K, affording a clear picture of dihydrogen-bond formation when [NbCp(2)H(3)]/HOR(f) mixtures (HOR(f) = hexafluoroisopropanol (HFIP) or perfluoro-tert-butanol (PFTB)) were quickly cooled to 200 K. Through examination of the OH region, the dihydrogen-bond energetics were determined to be 4.5+/-0.3 kcal mol(-1) for TFE (TFE = trifluoroethanol) and 5.7+/-0.3 kcal mol(-1) for HFIP. (1)H NMR studies of solutions of [NbCp(2)H(2)(B)H(A)] and HFIP in [D(8)]toluene revealed high-field shifts of the hydrides H(A) and H(B), characteristic of dihydrogen-bond formation, upon addition of alcohol. The magnitude of signal shifts and T(1) relaxation time measurements show preferential coordination of the alcohol to the central hydride H(A), but are also consistent with a bifurcated character of the dihydrogen bonding. Estimations of hydride-proton distances based on T(1) data are in good accord with the results of DFT calculations. DFT calculations for the interaction of [NbCp(2)H(3)] with a series of non-fluorinated (MeOH, CH(3)COOH) and fluorinated (CF(3)OH, TFE, HFIP, PFTB and CF(3)COOH) proton donors of different strengths showed dihydrogen-bond formation, with binding energies ranging from -5.7 to -12.3 kcal mol(-1), depending on the proton donor strength. Coordination of proton donors occurs both to the central and to the lateral hydrides of [NbCp(2)H(3)], the former interaction being of bifurcated type and energetically slightly more favourable. In the case of the strong acid H(3)O(+), the proton transfer occurs without any barrier, and no dihydrogen-bonded intermediates are found. Proton transfer to [NbCp(2)H(3)] gives bis(dihydrogen) [NbCp(2)(eta(2)-H(2))(2)](+) and dihydride(dihydrogen) complexes [NbCp(2)(H)(2)(eta(2)-H(2))](+) (with lateral hydrides and central dihydrogen), the former product being slightly more stable. When two molecules of TFA were included in the calculations, in addition to the dihydrogen-bonded adduct, an ionic pair formed by the cationic bis(dihydrogen) complex [NbCp(2)(eta(2)-H(2))(2)](+) and the homoconjugated anion pair (CF(3)COO...H...OOCCF(3))(-) was found as a minimum. It is very likely that these ionic pairs may be intermediates in the H/D exchange between the hydride ligands and the OD group observed with the more acidic alcohols in the NMR studies.     

Experimental and computational studies of trialkylaluminum and alkylaluminum chloride reactions with silica

Reactions of trimethylaluminum, triethylaluminum, and diethylaluminum chloride and ethylaluminum dichloride with silica gel have been studied experimentally by infrared spectroscopy and elemental analysis. The silica gel was subjected to different pretreatments to alter surface functionalities prior to reaction. In all cases the extent of surface modification reaction follows the trend unmodified > 600 degrees C pretreated > hexamethyldisilazane (HMDZ) pretreated > 600 degrees C/HMDZ pretreated. All of the aluminum compounds studied completely react non-hydrogen-bonded silanols, while also reacting with hydrogen-bonded silanols and siloxanes. Primarily monomeric surface species result from the surface modification reaction. Ethylaluminum chlorides preferentially react with silanols through cleavage of the Al-C bond rather than the Al-Cl bond. Singly bonded Si(s)-O-AlCl(2) surface species are readily synthesized by reaction of ethylaluminum dichloride with HMDZ-pretreated silica gel. Bridged bonded (Si(s)-O)(2)-AlCl surface species are readily synthesized by reaction of diethylaluminum chloride with HMDZ-pretreated silica gel. Computational ab initio studies of the cluster Si(4)O(6)(OH)(4) as a model to study the reaction of monomeric and dimeric methylaluminum dichloride with a silica silanol are also described. Comparison of the potential energy surface (PES) of monomer and dimer indicates that the energetics favor monomer reaction, consistent with experimental results. The energy cost in the dimer reaction is primarily from cleavage of a bridged Al-Cl bond upon adsorption. This does not occur when the monomer adsorbs. A comparison of the PES for the two reaction pathways resulting from cleavage of either an Al-Cl or Al-C bond indicates that while the former reaction is slightly kinetically favored (E(a) = 23.1 kJ/mol for Al-Cl bond cleavage versus E(a) = 31.1 kJ/mol for Al-C bond cleavage), the latter is strongly thermodynamically favored with an overall free energy difference between the two reaction pathways of 135 kJ/mol favorable to Al-C bond cleavage. These reactions are thermodynamically controlled.     

Synthesis and physico-chemical characterization of coordination compounds of 3d metals with potassium bicyclo[2.2.1]-hept-5-en-endo-2-oyl-hydroxylamine-3-carboxylate

Summary The ligand, potassium bicyclo[2.2.1]-hept-5-en-endo-2-oyl-hydroxylamine-3-carboxylate-monohydrate, KHL·H₂O₂ and its M(HL)₂ complexes, [{Fe(HL)₂}₂SO₄], K[FeL₂] and K₂[ML₂] (M=Mn^II, Fe^II, Co^II, Ni^II, Cu^II and Zn^II) were prepared and characterized. For all, except the sulphate complex of iron(III), a monomeric octahedral configuration was postulated and this is realized through the coordination of oxygen atoms of the carboxylic, carbonyl and oxime group of two mono-or di-anion ligands. The dianionic form of the ligand is the result of deprotonation of the carboxylic group and mide-alcohol form of the hydroxamic group. For the sulphate-containing iron(III) complex a dimeric coordination is proposed with two monoanions of the organic ligand (the carbonyl oxygens are not coordinated) and the bridging SO₄ group. The relative degree of covalency of the metal-carboxylic oxygen bond is 10.6–45.2% and increases in the order: Mn^IIIIIIIIIIIII. The complexes have been characterized by elemental and t.g. analysis and i.r. spectra.     

Critical Points in a Crystal and Procrystal

The critical points in the model electron density distributions of LiF, NaF, NaCl, and MgO crystals, constructed from accurate X-ray diffraction data, are determined. For LiF and MgO they are compared with those obtained from a Hartree–Fock electron density calculation. Both experiment and theory show the same type of critical points on the bond lines. The topological features in areas between structural units, where the electron density is low and near-uniform, turn out to be model dependent and cannot be established well with the data available. Topological analysis of procrystals (hypothetical systems consisting of spherical atoms or ions placed on the same sites as atoms in real crystal) show that (3, –1) critical points, usually connected with bonding interaction, are observed on interatomic lines in these nonbonded systems as well.