Ground-state energy of a quantum chain with competing interactions

We show rigorously that the ground state of a quantum chain with competing ferromagnetic nearest and antiferromagnetic next nearest interactions undergoes a transition from ferromagnetic to helical type, in the isotropic case, for a certain value of the relevant ratio of coupling constants. Boundaries of the phase diagram are also determined in the anisotropic case. The stability of a special quantum state (corresponding to a classical modulated phase of =/3) is analyzed by an extension of Holstein-Primakoff arguments, along a line of constant ratio of couplings, showing in particular a sequence of (instability) gaps. Finally, a natural adaptation of a variational wave function due to Huse and Elser is used to study several portions of the phase diagram, with very good agreement with previous theoretical results.     

Coulomb pair density matrix I

The Coulomb pair density matrixG (r, r) for attractive and repulsive potentials is not only interesting for determining the two-particle effective potentials, but it is also essential in numerical studies of quantum systems. A high-temperature approximation is obtained for logG (r, r), in the form of simple integrals or series expansions; large-distance expansions are also given.     

The O(N) vector model in the large-N limit revisited: multicritical points and double scaling limit

The multicritical points of the O(N)-invariant N vector model in the large-N limit are re-examined. Of particular interest are the subtleties involved in the stability of the phase structure at critical dimensions. In the limit N → ∞ while the coupling g → g_c in a correlated manner (the double scaling limit) a massless bound state O(N) singlet is formed and powers of 1/N are compensated by IR singularities. The persistence of the N → ∞ results beyond the leading order is then studied with particular interest in the possible existence of a phase with propagating small mass vector fields and a massless singlet bound state. We point out that under certain conditions the double scaled theory of the singlet field is non-interacting in critical dimensions.     

三氧化铬超微粒的制备与表征

我们曾首次报道了Fe_2O_3超微粒溶胶具有大的三阶光学非线性响应,其X~((3))值与商品用的掺杂CdS_(1-x)Se玻璃相近,并对其产生机制进行了初步研究.本文用微乳液法制备了经十二烷基苯磺酸钠(DBS)和硬脂酸(ST)表面修饰的Cr_2O_3超微粒,并用TEM、IR、XPS及紫外可见吸收光谱进行了表征.     

Hydrogen–hydrogen bonding in biphenyl revisited

The evidence for the stabilizing nature of the H–H bonding in planar biphenyl is succinctly reviewed. The stabilizing nature of the H–H bonding is revealed through a comparison of the atomic energy of every atom in planar biphenyl with the same atom in the twisted equilibrium structure. It is shown that the barrier to rotation via the planar transition state is the net resultant of a stabilisation of the four ortho-hydrogen atoms (by 8 kcal/mol each), a stabilisation of the two para-carbon atoms (by 3 kcal/mol each) and by the dominant destabilisation of the two carbon atoms joining the two rings—the two junction carbon atoms—(by 22 kcal/mol each). The energetic stabilisation of the four ortho-hydrogen atoms is further shown to be in large proportion due to the formation of the hydrogen–hydrogen interatomic surface. Furthermore, neither the “bond order” between the two junction carbon atoms nor the total electron delocalisation between the two rings exhibit a significant change in going from the planar to the twisted equilibrium geometry. These findings are in contrast with the classical view of a balance between “steric non-bonded repulsion” and better electron delocalisation as a function of the twist dihedral angle. Similar conclusions have been recently reached by Pacios and Gómez through a study of the electrostatic potential at the position of the hydrogen nuclei. We dedicate this article to Professor TM Krygowski on the occasion of his 70th birthday wishing him a long and productive life.     

Role of the tautomerism of 2-azaadenine and 2-azahypoxanthine in substrate recognition by xanthine oxidase

The tautomerism of 2-azaadenine and 2-hypoxanthine has been examined in the gas phase and in aqueous solution. The tautomerism in the gas phase has been studied by means of semiempirical and ab initio quantum-mechanical computations, as well as density-functional calculations. The influence of the aqueous solvent on the relative stability between tautomers has been estimated from self-consistent reaction field calculations performed with different high-level continuum models. The results provide a detailed picture of the tautomeric preference for these purine bases. The importance of tautomerism in the substrate recognition by xanthine oxidase is discussed. Finally, the rate of oxidation of 2-azaadenine and 2- hypoxanthine by xanthine oxidase is discussed in terms of the recognition model at the enzyme active site.     

Chemical deposition of semiconducting cadmium selenide quantum dots in thin film form and investigation of their optical and electrical properties

Cadmium selenide quantum dots with cubic crystal structure are chemically deposited in thin film form using selenosulfate as a precursor for selenide ions and ammonia buffer with double role: as a ligand and as a pH value controller. The optical band gap energies of as-deposited and thermally treated cadmium selenide thin films, calculated within the framework of parabolic approximation for the dispersion relation, on the basis of equations which arise from the Fermi's golden rule for electronic transitions from valence to conduction band, are 2.08 and 1.77 eV, correspondingly. The blue shift of band gap energy of 0.34 eV for as-deposited thin films with respect to the bulk value is due to the quantum size effects (i.e., nanocrystals behave as quantum dots) and this finding is in agreement with the theoretical predictions. During the thermal treatment the nanocrystals are sintered, the increase of crystal size being in correlation with the decrease of band gap energy. The annealed thin films are practically non-quantized. From the resistance-temperature measurements, on the basis of the dependence of ln(R/Ω) vs 1/T in the region of intrinsic conduction, the thermal band gap energy (at 0 K) of 1.85 eV was calculated.     

Chromium(III) Hydroxide Solubility in the Aqueous K+-H+-OH?-CO2-HCO 3? -CO 32? -H2O System: A?Thermodynamic Model

Chromium(III)-carbonate reactions are expected to be important in managing high-level radioactive wastes. Extensive studies on the solubility of amorphous Cr(III) hydroxide solid in a wide range of pH (3–13) at two different fixed partial pressures of CO₂(g) (0.003 or 0.03 atm.), and as functions of K₂CO₃ concentrations (0.01 to 5.8 mol⋅kg⁻¹) in the presence of 0.01 mol⋅dm⁻³ KOH and KHCO₃ concentrations (0.001 to 0.826 mol⋅kg⁻¹) at room temperature (22±2 °C) were carried out to obtain reliable thermodynamic data for important Cr(III)-carbonate reactions. A combination of techniques (XRD, XANES, EXAFS, UV-Vis-NIR spectroscopy, thermodynamic analyses of solubility data, and quantum mechanical calculations) was used to characterize the solid and aqueous species. The Pitzer ion-interaction approach was used to interpret the solubility data. Only two aqueous species [Cr(OH)(CO₃)₂²⁻ and Cr(OH)₄CO₃³⁻] are required to explain Cr(III)-carbonate reactions in a wide range of pH, CO₂(g) partial pressures, and bicarbonate and carbonate concentrations. Calculations based on density functional theory support the existence of these species. The log ₁₀ K° values of reactions involving these species [{Cr(OH)₃(am) + 2CO₂(g)⇌Cr(OH)(CO₃)₂²⁻+2H⁺} and {Cr(OH)₃(am) + OH⁻+CO₃²⁻ ⇌Cr(OH)₄CO₃³⁻}] were found to be −(19.07±0.41) and −(4.19±0.19), respectively. No other data on any Cr(III)-carbonato complexes are available for comparisons.     

Proton dynamics in an extended array of hydrogen bonds: normal coordinates, proton transfer and macroscopic quantum entanglement in the ground state

After a brief introduction to neutron scattering techniques, illustrated with the scattering function for harmonic oscillators, some new aspects of proton dynamics in the KHCO₃ crystal are presented. The full scattering function for the proton modes measured on single crystals provides a graphic view of proton dynamics. Vibrational states are fully characterized with three quantum numbers. The effective oscillator mass of 1 amu confirms the decoupling of protons from the lattice. Combining infrared, Raman and inelastic neutron scattering techniques, the double minimum potential for the transfer of a single proton along hydrogen bonds is totally determined. Elastic neutron scattering techniques probe dynamics in the fully degenerate ground state. Quantum entanglement arising from normal coordinates gives rise to quantum interference. With diffraction techniques, the dynamical structure arising from large-scale quantum coherence is observed as ridges of intensity, well separated from Bragg's peaks. The vibrational wave function in the ground state must be regarded as a superposition of non-factorable macroscopic wave function.     

Patterning porous matrices and planar substrates with quantum dots

Silica hydrogels and planar substrates were patterned with CdS nanoparticles using a photolithographic method based on the photo dissociation of thiols and cadmium-thiolate complexes. Silica hydrogels were prepared via a standard base-catalyzed route. The solvent was exchanged with an aqueous solution of CdSO₄ and 2-mercaptoethanol, and the samples were then exposed to a focused ultraviolet beam. Planar substrates were patterned by illuminating a precursor solution spin coated on the substrates. CdS nanoparticles formed in the illuminated spots, and had a diameter below about 2 nm. The diameter of the spots illuminated by the UV beam could be varied from a few hundred to a few μm, on both hydrogels and planar substrates. Samples were characterized with transmission electron microscopy, X-ray photoelectron spectroscopy, X-ray diffraction, and optical absorption, photoluminescence and Raman spectroscopies. All these techniques confirmed the chemical identity of the CdS nanoparticles. To investigate the mechanism of nanoparticle formation, we took absorption spectra of the precursor solution as a function of irradiation time. In unirradiated solutions, we noticed a maximum at 250 nm, characteristic of Cd-thiolate complexes. The absorption at 250 nm decreased with increasing irradiation time. A new band appeared at 265 nm for exposures around 5 min, and that band shifted to 290 nm in samples exposed for 10 min. A yellow precipitate formed after about 30 min. XRD showed that the precipitate was cubic CdS, with a mean particle size of 1.4 nm. We attribute formation of CdS to the photodissociation of the thiols and of the Cd-thiolates. UV irradiation of these precursors yields a series of species that can react with Cd²⁺, such as RS^·, S²⁻ and H₂S. Small CdS nanoparticles form in the initial stages of illumination, and present absorption bands in the 265–290 nm region. These CdS aggregates grow, coalesce and precipitate for longer irradiation times.