Magnetic Properties of the Infinitely Repulsive Hubbard Model Near Half Filling

Many theoretical works discuss the magnetic properties of the strongly repulsive Hubbard model near half filling. Several authors suggest that the system which contains a few holes does not behave as a ferromagnet, unlike in the one-hole case described by Nagaoka's famous result. We discuss the finite temperature properties of finite lattices. Using an efficient Monte Carlo method magnetic and specific heat results are presented for a 10 by 10 lattice with two holes. Our results show that the magnetization increases with decreasing temperature for such a finite system.     

Nickel complexes of a pincer NN2 ligand: multiple carbon-chloride activation of CH2Cl2 and CHCl3 leads to selective carbon-carbon bond formation

A new pincer-type bis(amino)amine (NN2) ligand and its lithium and nickel complexes, including Ni(II) methyl, ethyl, and phenyl complexes, were synthesized. The Ni(II) alkyl complexes react cleanly with alkyl halides including chlorides to form C-C coupled products and Ni(II) halides. More interestingly, the Ni(II) alkyls undergo unprecedented reactions with CH2Cl2 and CHCl3 to cleave all the C-Cl bonds and replace them with C-C bonds. The reactions are highly selective and lead to the first efficient catalytic coupling of CH2Cl2 with alkyl Grignards. A conversion of 82% and a turnover number of 47 are achieved within minutes. Coupling of CD2Cl2 and 1,1-dichloro-3,3-dimethylbutane with nBuMgCl is also realized. Preliminary mechanistic study suggests a radical initiated process for these reactions.     

Ultratrace-level radium-226 determination in seawater samples by isotope dilution inductively coupled plasma mass spectrometry

An improved and novel sample preparation method for ²²⁶Ra determination in liquid samples by isotope dilution inductively coupled plasma sector field mass spectrometry using laboratory-prepared ²²⁸Ra tracer has been developed. The procedure involves a selective preconcentration achieved by applying laboratory-prepared MnO₂ resin followed by cation exchange chromatographic separation. In order to completely eliminate possible molecular interferences, medium mass resolution (R = 4,000) combined with chemical separation was found to be a good compromise that enhanced the reliability of the method. The detection limit of 0.084 fg g⁻¹ (3.1 mBq kg⁻¹) achieved is comparable to that of the emanation method or alpha spectrometry and is suitable for low-level environmental measurements. The chemical recovery of the sample preparation method ranged from 72 to 94%. The proposed method enables a rapid, accurate and less labor-intensive approach to routine environmental ²²⁶Ra determination than the radioanalytical techniques conventionally applied.     

Comparison of means generated by two functions and a measure

Given two continuous functions f,g:I→R such that g is positive and f/g is strictly monotone, and a probability measure μ on the Borel subsets of [0,1], the two variable mean Mf,g;μ:I²→I is defined by

     

Kirchberger-type theorems for separation by convex domains

We say that a convex set K in ? ^d strictly separates the set A from the set B if A ? int(K) and B ? cl K = ø. The well-known Theorem of Kirchberger states the following. If A and B are finite sets in ? ^d with the property that for every T ? A?B of cardinality at most d + 2, there is a half space strictly separating T ? A and T ? B, then there is a half space strictly separating A and B. In short, we say that the strict separation number of the family of half spaces in ? ^d is d + 2.In this note we investigate the problem of strict separation of two finite sets by the family of positive homothetic (resp., similar) copies of a closed, convex set. We prove Kirchberger-type theorems for the family of positive homothets of planar convex sets and for the family of homothets of certain polyhedral sets. Moreover, we provide examples that show that, for certain convex sets, the family of positive homothets (resp., the family of similar copies) has a large strict separation number, in some cases, infinity. Finally, we examine how our results translate to the setting of non-strict separation.     

Equilibrium, photophysical, photochemical, and quantum chemical examination of anionic mercury(II) mono- and bisporphyrins

Mercury(II) ion and 5,10,15,20-tetrakis(parasulfonato-phenyl)porphyrin anion can form 1:1, 2:2, and 3:2 (metal ion/porphyrin) out-of-plane (OOP) complexes, from which Hg2P2(8-) has not been identified until now. Identification of this species significantly promoted the confirmation of the composition and the precise elucidation of the equilibrium of Hg3P2(6-). Since the formation of each complex is too fast, their kinetic behavior was studied from the side of dissociation. The rate-determining step in dissociations, as well as in the formation of the 2:2 complex, that is, the dimerization of 1:1 complex, proved to be virtually first-order under these conditions, while the consecutive formations of HgP(4-) and Hg3P2(6-) are second-order reactions. The equilibria can be spectrophotometrically investigated because the Soret- as well as the Q-absorption bands of the free-base ligand are more and more red-shifted in the series of 1:1, 2:2, and 3:2 complexes, and the split of Q-bands disappears as the singlet-1 excited states become degenerate; in the case of bisporphyrins, the bands broaden, especially in the longer-wavelength region of the spectra. The quantum yield and the lifetime of S1-fluorescence from the macrocycle is decreased by the insertion of a mercury(II) ion due to distortion, and in bisporphyrins the luminescence totally ceases because their more complicated structure promotes other ways of energy dissipation. The lifetime of the triplet excited-state is also reduced by metalation. The transient absorption measured upon excitation of Hg3P2(6-) probably originates from Hg2P2(8-) formed by efficient photodissocation during the laser pulse. This photoinduced dissociation is characteristic to out-of-plane complexes, but in metallo-monoporphyrins it needs the energetically higher Soret-excitation; in bisporphyrins, it can take place during irradiation at the longer Q-wavelengths. Investigation of the intramolecular photoredox reactions has proved that for the increased efficiency of the indirect photoinduced LMCT, not the redox potential, but the position of the metal center is responsible. The two orders of magnitude higher photoredux quantum yield for the 3:2 complex, compared to that of the 2:2 species, can be explained by the repulsive effect of the inner mercury(II) ion pushing the other two farther out of the ligand cavity. In bisporphyrins the second excited states are photochemically more reactive than the first ones, while most of the photochemical processes of HgP(4-) originate from the first excited state. According to our quantum chemical calculations, the mercury(II) ion causes the expansion of the porphyrin-cavity; therefore its out-of-plane position is smaller than the value expected based on its ionic radius. In the hitherto unknown 2:2 dimer two 1:1 saucer-shaped monomers are kept together by secondary forces, mostly by pi-pi interaction, but their relative arrangement was not unequivocally determined by the two DFT functionals used. The arrangements with a symmetry axis or plane perpendicular to both rings are not favored; instead, the two monomers are shifted along the porphyrin planes, either in a Hg-P-Hg-P or a Hg-P-P-Hg order. Our time-dependent density functional theory (TD-DFT) calculations indicate that the electronic spectra are not very sensitive to the structure of the dimer, even though the environment of the porphyrin rings is quite different if one of the metal ions is between or outside of both macrocycles. The calculated spectral shifts agree only partially with the experimental data. The TD-DFT calculations suggest that the chromophores are not fully independent in the bisporphyrins and that the observed spectral shift cannot be uniquely assigned to the geometrical distortion of the porphyrin macrocyle.     

Synthesis, potentiometric, kinetic, and NMR Studies of 1,4,7,10-tetraazacyclododecane-1,7-bis(acetic acid)-4,10-bis(methylenephosphonic acid) (DO2A2P) and its complexes with Ca(II), Cu(II), Zn(II) and lanthanide(III) ions

A cyclen-based ligand containing trans-acetate and trans-methylenephosphonate pendant groups, H 6DO2A2P, was synthesized and its protonation constants (12.6, 11.43, 5.95, 6.15, 2.88, and 2.77) were determined by pH-potentiometry and (1)H NMR spectroscopy. The first two protonations were shown to occur at the two macrocyclic ring N-CH 2-PO 3 (2-) nitrogens while the third and fourth protonations occur at the two phosphonate groups. In parallel with protonation of the two -PO 3 (2-) groups, the protons from the NH (+)-CH 2-PO 3 (2-) are transferred to the N-CH 2-COO (-) nitrogens. The stability constants of the Ca (2+), Cu (2+), and Zn (2+) (ML, MHL, MH 2L, and M 2L) complexes were determined by direct pH-potentiometry. Lanthanide(III) ions (Ln (3+)) form similar species, but the formation of complexes is slow; so, "out-of-cell" pH-potentiometry (La (3+), Eu (3+), Gd (3+), Y (3+)) and competitive spectrophotometry with Cu(II) ion (Lu (3+)) were used to determine the stability constants. By comparing the log K ML values with those of the corresponding DOTA (H 4DOTA = 1,4,7,10-tetraazacyclododecane-1,4,7,10-tetraacetic acid) and DOTP (H 8DOTP = 1,4,7,10-tetraazacyclododecane-1,4,7,10-tetramethylenephosphonic acid) complexes, the order DOTA < DO2A2P < DOTP was found for all the metal ion complexes examined here with the exception of the Ca (2+) complexes, for which the order is reversed. The relaxivity of Gd(DO2A2P) decreases between pH 2 and 7 but remains constant in the pH range of 7 < pH < 12 ( r 1 = 3.6 mM (-1) s (-1)). The linewiths of the (17)O NMR signals of water in the absence and presence of Gd(DO2A2P) (at pH = 3.45 and 8.5) between 274 and 350 K are practically the same, characteristic of a q = 0 complex. Detailed kinetic studies of the Ce (3+) and Gd (3+) complexes with DO2A2P showed that complex formation is slow and involves a high stability diprotonated intermediate Ln(H 2DO2A2P)*. Rearrangement of the diprotonated intermediate into the final complex is an OH (-) assisted process but, unlike formation of Ln(DOTA) complexes, rearrangement of Ln(H 2DO2A2P)* also takes place spontaneously likely as a result of transfer of one of the protons from a ring nitrogen to a phosphonate group. The order of the OH (-) assisted formation rates of complexes is DOTA > DO2A2P > DOTP while the order of the proton assisted dissociation rates of the Gd (3+) complexes is reversed, DOTP > DO2A2P > DOTA. (1)H and (13)C NMR spectra of Eu(DO2A2P) and Lu(DO2A2P) were assigned using two-dimensional correlation spectroscopy (2D COSY), heteronuclear multiple quantum coherence (HMQC), heteronuclear chemical shift correlation (HETCOR), and exchange spectroscopy (EXSY) NMR methods. Two sets of (1)H NMR signals were observed for Eu(DO2A2P) characteristic of the presence of two coordination isomers in solution, a twisted square antiprism (TSAP) and a square antiprism (SAP), in the ratio of ~93% and ~7%, respectively. Line shape analysis of the (1)H NMR spectra of Lu(DO2A2P) gave lower activation parameters compared to La(DOTP) for interconversion between coordination isomers. This indicates that the Ln(DO2A2P) complexes are less rigid probably due to the different size and spatial requirements of the carboxylate and phosphonate groups.     

Synthesis, magnetism and electronic structure of YbNi2−xFexAl8 (x=0.91) isolated from Al flux

The combination of ytterbium, nickel, iron in liquid aluminum resulted in the formation of the new intermetallic compound YbNi_2−xFe_xAl₈ (x=0.91) which adopts the CaCo₂Al₈ structure type with a=14.458(3) Å, b=12.455(3) Å, c=3.9818(8) Å and space group Pbam. Its resistivity drops with decreasing temperature, saturating to a constant value at lower temperatures. Above 50 K, the inverse magnetic susceptibility data follows Curie-Weiss Law, with a calculated μ_eff=2.19 μ_B. Although the observed reduced moment in magnetic susceptibility measurement suggests that the Yb ions in this compound are of mixed-valent nature, ab initio electronic structure calculations within density functional theory using LDA+U approximation give an f¹³ configuration in the ground state.     

A Genealogy of Convex Solids Via Local and Global Bifurcations of Gradient Vector Fields

Three-dimensional convex bodies can be classified in terms of the number and stability types of critical points on which they can balance at rest on a horizontal plane. For typical bodies, these are non-degenerate maxima, minima, and saddle points, the numbers of which provide a primary classification. Secondary and tertiary classifications use graphs to describe orbits connecting these critical points in the gradient vector field associated with each body. In previous work, it was shown that these classifications are complete in that no class is empty. Here, we construct 1- and 2-parameter families of convex bodies connecting members of adjacent primary and secondary classes and show that transitions between them can be realized by codimension 1 saddle-node and saddle–saddle (heteroclinic) bifurcations in the gradient vector fields. Our results indicate that all combinatorially possible transitions can be realized in physical shape evolution processes, e.g., by abrasion of sedimentary particles.     

Heat extraction of corn fiber hemicellulose

Water-soluble hemicellulose was extracted from corn fiber with microwave-assisted heat treatment. The effects of treatment temperature and initial pH of the aqueous extraction media were investigated regarding hemicellulose recovery and molecular mass of the isolated polysaccharides. In treatments carried out at neutral pH (simple water extraction), it has been demonstrated that hemicellulose recovery could be increased by applying higher treatment temperatures. However, the molecular weight of isolated hemicellulose gets significantly lower. For example, 10% of the raw materials' xylan was extracted at 160 degrees C and about 30% recovery was reached at 210 degrees C. However, the molecular mass of the isolated polysaccharide at 210 degrees C (5.82 x 10(4)) was about half of that measured at 160 degrees C (1.37 x 10(5)). Reducing the pH with sulfuric acid resulted in shorter polymer chains (1.7 x 10(4)) and lower hemicellulose yields (2.2%). Application of sodium hydroxide in the treatment showed that, compared with acid, considerably higher yields (11%) with longer polysaccharide chains (1.3 x 10(5)) could be obtained.