Non-convergent perturbation theory and misleading inferences about parameter relationships: The case of superexchange

We discuss the well-known three-centre cation–anion–cation model for superexchange in insulating transition-metal compounds using limiting expansions for the Anderson–Hubbard model. We find that due to the interfering energy scales in the model, a limiting expression for the superexchange J$J$ for the idealized Mott–Hubbard (M–H) case t?U?Δ$t?U?\Delta$ cannot be formally defined. We further show that the decomposition of the superexchange into range-dependent components is formally invalid. The well-known t⁴$t^4$ superexchange expression, obtained from path-dependent series expansions, is not unique to these systems as it can also be obtained with many other different expansions, in which either the d$d$–p$p$ energy difference Δ$\Delta$ or the d$d$-electron correlation U$U$ can actually be small. Particularly for milder relationships between the parameters, i.e.  t?U?Δ$t?U?\Delta$, the reverse from the usual form of the series expansions can yield better agreement with the exact results. This implies that the fitting of experimental data to the simple expressions derived from path-dependent series expansions can lead to qualitatively incorrect relationships between the parameters, fictitiously within the M–H regime.     

Zinc-adeninate metal-organic framework for aqueous encapsulation and sensitization of near-infrared and visible emitting lanthanide cations

Luminescent metal-organic frameworks (MOFs), Ln(3+)@bio-MOF-1, were synthesized via postsynthetic cation exchange of bio-MOF-1 with Tb(3+), Sm(3+), Eu(3+), or Yb(3+), and their photophysical properties were studied. We demonstrate that bio-MOF-1 encapsulates and sensitizes visible and near-infrared emitting lanthanide cations in aqueous solution.     

Development and validation of a reversed-phase ion-pair high-performance liquid chromatographic method for the determination of risedronate in pharmaceutical preparations

A stability indicating, reversed-phase ion-pair high-performance liquid chromatographic method was developed and validated for the determination of risedronate in pharmaceutical dosage forms. The determination was performed on a BDS C₁₈ analytical column (250 mm × 4.6 mm i.d., 5 μm particle size); the mobile phase consisted of 0.005 M tetrabutylammonium hydroxide and 0.005 M pyrophosphate sodium (pH 7.0) mixed with acetonitrile in a ratio (78:22, v/v) and pumped at a flow rate 1.00 mL min⁻¹. The ultraviolet (UV) detector was operated at 262 nm. The retention times of magnesium ascorbyl phosphate, which was used as internal standard and risedronate were 4.94 and 5.95 min, respectively. The calibration graph was ranged from 2.50 to 20.00 μg mL⁻¹, while detection and quantitation limits were found to be 0.48 and 1.61 μg mL⁻¹, respectively. The intra- and inter-day percentage relative standard deviations, %R.S.D., were less than 5.9%, while the relative percentage error, %E_r, was less than 0.4%. The method was applied to the quality control of commercial tablets and content uniformity test and proved to be suitable for rapid and reliable quality control.     

A Longitudinal Study Revisiting the Notion of Early Number Sense: Algebraic Arithmetic AS a Catalyst for Number Sense Development

The aim of this study was to propose a new conceptualization of early number sense. Six-year-old students’ (n = 204) number sense was tracked from the beginning of Grade 1 through the beginning of Grade 2. Data analysis suggested that elementary arithmetic, conventional arithmetic, and algebraic arithmetic contributed to the latent construct early number sense, and the invariance of the model over time was validated empirically. Algebraic arithmetic represents the dimension of early number sense that moves beyond conventional arithmetic and encompasses an abstract understanding of the relations between numbers. A parallel process growth model showed that the three components of number sense adopt a linear growth rate. A structural model showed that the growth rate of the algebraic arithmetic component has a direct effect on the growth rate of conventional arithmetic, and subsequently the growth rate of conventional arithmetic predicts the growth rate of elementary arithmetic.     

Spatial visualizers, object visualizers and verbalizers: their mathematical creative abilities

This paper investigates the relationship between the creative process in mathematical tasks and spatial, object and verbal cognitive styles. A group of 96 prospective primary school teachers completed the Object-Spatial Imagery and Verbal Questionnaire and took a mathematical creativity test. The results of a multiple regression analysis demonstrated that whereas visual cognitive styles (spatial and object imagery) were statistically significant predictors of participants’ creative abilities in mathematics, verbal cognitive style did not predict these abilities. Further analysis of the data indicated that spatial imagery cognitive style was related to mathematical fluency, flexibility and originality. On the other hand, object imagery cognitive style was negatively related to mathematical originality and verbal cognitive style was negatively related to mathematical flexibility. The study also revealed that individuals with a tendency towards different cognitive styles employed different strategies in the creative mathematical tasks.     

Multifrequency electron paramagnetic resonance and theoretical studies of a Mn(II) (S = 5/2) complex: The role of geometrical elements on the Zero Field Splitting parameters

The Zero Field Splitting (ZFS) parameters of the mononuclear Mn(II) (S = 5/2) compound [Mn(Ac4Ph)₂], where HAc4Ph stands for 4-phenyl-2-acetylpyridine thiosemicarbazone, are determined by dual mode X-band and high field/high frequency electron paramagnetic resonance spectroscopy. Density functional theory (DFT) calculations reproduce both the sign and absolute value of the axial parameter D of the ZFS tensor, whose distribution is quantitatively correlated to distribution on geometrical elements of the complex.     

Incorporating lanthanide cations with cadmium selenide nanocrystals: a strategy to sensitize and protect Tb(III)

The electronic structure of CdSe semiconductor nanocrystals has been used to sensitize Tb3+ in solution by incorporation of Tb3+ cations into the nanocrystals during synthesis. Doping of luminescent Tb3+ metal ions in semiconductor nanocrystals utilizes the positive attributes of both species' photophysical properties, resulting in a final product with long luminescence lifetimes, sharp emission bands, high absorptivities, and strong resistance to decomposition. This strategy also helps protect the lanthanide cations from nonradiative deactivation from C-H, N-H, and O-H oscillators of solvent molecules or traditional organic lanthanide ligands, leading to long Tb3+ luminescence lifetimes. This new type of nanomaterial synergistically combines the photophysical properties of nanocrystals and Tb3+.     

Light-regulated supramolecular engineering of polymeric nanocapsules

This article describes the light-driven supramolecular engineering of water-dispersible nanocapsules (NCPs). The novelty of the method lies in the utilization of an appropriate phototrigger to stimulate spherical polymer brushes, consisting of dual-responsive 2-(dimethylamino)ethyl methacrylate (DMAEMA) and light-sensitive spiropyran (SP) moieties, for the development or disruption of the NCPs in a controlled manner. The fabrication of the nanocarriers is based on the formation of H-type π-π interactions between merocyanine (MC) isomers within the sterically crowded environment of the polymer brushes upon UV irradiation, which enables the SP-to-MC isomerization of the photosensitive species. After HF etching of the inorganic core, dual-responsive polymeric vesicles whose walls' robustness is provided by the MC-MC cross-link points are formed. Disruption of the vesicles can be achieved remotely by applying a harmless trigger such as visible-light irradiation. The hydrophilic nature of the DMAEMA comonomer facilitates the engineering of the vesicles in environmentally benign aqueous media and enables the controlled alteration of the NCPs size upon variation of the solution pH. The inherent ability of the NCPs to fluoresce in water opens new possibilities for the development of addressable nanoscale capsules for biomedical applications.