NMR study of solid C60(γ-cyclodextrin)2

A solid complex of C₆₀ with γ-cyclodextrin (γ-CyD) was examined with NMR spectroscopic methods in order to understand the dynamics of C₆₀, and the interaction between C₆₀ and γ-CyD. A ¹³C solid-state cross-polarization magic angle spinning (CP/MAS) NMR spectra shows C₆₀ resonance at 142.6 ppm. This provides the evidence of interaction between ¹³C spins in C₆₀ and ¹H spins in the γ-CyD host. Ambient temperature experiments on the ¹³C CP/MAS NMR, with varying contact time, shows that the water associated with γ-CyDs plays an important role in the nuclear relaxation processes. The dynamics of C₆₀ in γ-CyD was investigated using temperature and field-dependent ¹³C spin-lattice relaxation time measurements. The influence of water on the dynamics of C₆₀ was less significant below 250 K.     

A screening strategy for the development of enantiomeric separation methods in capillary electrophoresis

Method development of enantiomeric separations in capillary electrophoresis (CE) is a time-consuming task, since finding the appropriate chiral selector is usually a "trial and error" process. It is impossible to predict the selectivity of a selector towards a certain enantiomer. Therefore, the affinity of all selectors has to be examined one at a time. In order to speed up this process, a strategy is proposed based on simple experimental design methodology. The approach includes first a screening in function of the pH to determine the optimal migration conditions followed by a selection of the right chiral selector by means of Taguchi designs. In the approach several variables, such as the type and concentration of cyclodextrin, the concentration of buffer electrolyte, and the percentage of organic modifier, are varied simultaneously to find initial separation conditions rapidly. The resulting initial separation conditions can be optimized in further steps to be more reproducible. We discuss the results of the approach when applied on a number of selected compounds that are recently in development at Johnson & Johnson--Pharmaceutical Research and Development. Parameters, such as quality of the separation and analysis time, are evaluated to determine initial separation conditions for each compound.     

Polymer complexes stabilized through hydrogen bonds: A semiquantitative theoretical model

Many studies have been devoted to the formation and behavior of polymer complexes. Unfortunately, the complexity of such systems do not allow a rigorous theoretical approach presently. In this paper we develop a semiquantitative theoretical model for cooperative association between macromolecules. The model is especially adapted for reversible polymer complexes stabilized through weak interactions, e.g., through hydrogen bonds. Theoretical predictions are compared with potentiometric and viscometric experimental results of poly(acrylic acid)/polybase system and a good agreement is established. The influence of parameters such as degree of neutralization of the polyacid, concentration, and molecular weight of polymers is also conveniently predicted.     

Applying change of variable to calculus problems

This article describes the technique of introducing a new variable in some calculus problems to help students master the skills of integration and evaluation of limits. This technique is algorithmic and easy to apply.     

Percentage problems in bridging courses

Research on teaching high school mathematics shows that the topic of percentages often causes learning difficulties. This article describes a method of teaching percentages that the authors used in university bridging courses. In this method, the information from a word problem about percentages is presented in a two-way table. Such a table gives a logical structure to the problem and provides an algorithm for finding a simple equation for the unknown value of interest. The use of this procedure is illustrated by several examples of different levels of difficulty. The method can be applied to many types of percentage problems, so it is quite universal.     

Jahn-Teller and related effects in the silver trimer. I. The ab initio calculation of spectroscopically observable parameters for the X 2E' and A 2E" electronic states

Extensive ab initio calculations were performed for the X2E' and A2E" states of Ag3, using a newly constructed basis set for Ag. An important goal of these calculations is to guide the analysis of the experimentally observed A 2E"-X2E' electronic spectrum. Vibrational frequencies of Ag(3) for both the X and A states are reported. Spectroscopically obtainable parameters describing the Jahn-Teller effect are calculated for the X and A states. The magnitude of the spin-orbit effects for this relativistic system was also calculated for the X2E' and A 2E" states. Using all this information, the X-A electronic spectrum is predicted for Ag(3). Additionally, the geometries and symmetries of the global minima and saddle points as well as the barrier to pseudorotation around the moat of the potential energy surface are determined for both states.     

An infinite-order two-component relativistic Hamiltonian by a simple one-step transformation

The authors report the implementation of a simple one-step method for obtaining an infinite-order two-component (IOTC) relativistic Hamiltonian using matrix algebra. They apply the IOTC Hamiltonian to calculations of excitation and ionization energies as well as electric and magnetic properties of the radon atom. The results are compared to corresponding calculations using identical basis sets and based on the four-component Dirac-Coulomb Hamiltonian as well as Douglas-Kroll-Hess and zeroth-order regular approximation Hamiltonians, all implemented in the DIRAC program package, thus allowing a comprehensive comparison of relativistic Hamiltonians within the finite basis approximation.