The influence of macrocyclic polyether constitution upon ammonium ion/crown ether recognition processes

Secondary dialkylammonium (R2NH2+) ions are bound readily by dibenzo[24]crown-8 (DB24C8) to form threaded complexes, namely [2]pseudo-rotaxanes. The effect of replacing one or both of the catechol rings in DB24C8 with resorcinol rings upon the crown ether's ability to bind R2NH2+ ions has now been investigated. When only one aromatic ring is changed from catechol to resorcinol, a crown ether with a [25]crown-8 constitution is created-namely benzometaphenylene[25]crown-8 (BMP25C8). A [2]pseudorotaxane is formed in the solid state when BMP25C8 is co-crystallized with dibenzylammonium hexafluorophosphate, as evidenced by its X-ray crystal structure. Furthermore, this crown ether has been shown to bind R2NH2+ ions in solution, an observation which has been exploited in the synthesis of the first BMP25C8-containing [2]rotaxane. The methodology employed to generate this [2]rotaxane--the reaction of an amine with an isocyanate to form a urea--was tested initially on a system incorporating DB24C8 and was shown to work efficiently. Both [2]rotaxanes have been fully characterized by 1H and 13C NMR spectroscopies, FAB mass spectrometry and X-ray crystallography. Interestingly, the unsymmetrical nature of the dumbbell-shaped component in each of the two [2]rotaxanes renders each face of the encircling macrocyclic polyether diastereotopic, a feature that is apparent upon inspection of their 1H NMR spectra. The resonances associated with the diastereotopic protons on each face of the macrorings are well enough resolved to enable the faces of the crown ethers to be readily identified with respect to their protons by 1H NMR spectroscopy. Unambiguous assignments can be made as a result of the fact that the protons on each face of the macrocyclic polyether experience a unique set of through-space interactions, as evidenced by T-ROESY experiments. Additionally, the two-dimensional NMR analyses are in agreement with the X-ray crystallographic studies performed on these [2]rotaxanes, indicating that the crown ethers are located intimately around the NH2+ centers as expected. Replacement of both catechol rings in the DB24C8 constitution with resorcinol rings results in a crown ether with a [26]crown-8 constitution--namely bismetaphenylene[26]crown-8 (BMP26CS). All the evidence to date points to the fact that this further change in constitution results in a crown ether that does not bind R2NH2+ ions in either the solution or solid states.     

The Aqueous Ca2+ System,in Comparison with Zn2+, Fe3 +, and Al3 +: An Ab Initio Molecular Dynamics Study

Herein, we report on the structure and dynamics of the aqueous Ca²⁺ system studied by using ab initio molecular dynamics (AIMD) simulations. Our detailed study revealed the formation of well‐formed hydration shells with characteristics that were significantly different to those of bulk water. To facilitate a robust comparison with state‐of‐the‐art X‐ray absorption fine structure (XAFS) data, we employ a 1st principles MD‐XAFS procedure and directly compare simulated and experimental XAFS spectra. A comparison of the data for the aqueous Ca²⁺ system with those of the recently reported Zn²⁺, Fe³⁺, and Al³⁺ species showed that many of their structural characteristics correlated well with charge density on the cation. Some very important exceptions were found, which indicated a strong sensitivity of the solvent structure towards the cation′s valence electronic structure. Average dipole moments for the 2nd shell of all cations were suppressed relative to bulk water.     

OPTIMAL FISH HARVESTING FOR A POPULATION MODELED BY A NONLINEAR PARABOLIC PARTIAL DIFFERENTIAL EQUATION

As the human population continues to grow, there is a need for better management of our natural resources in order for our planet to be able to produce enough to sustain us. One important resource we must consider is marine fish populations. We use the tool of optimal control to investigate harvesting strategies for maximizing yield of a fish population in a heterogeneous, finite domain. We determine whether these solutions include no‐take marine reserves as part of the optimal solution. The fishery stock is modeled using a nonlinear, parabolic partial differential equation with logistic growth, movement by diffusion and advection, and with Robin boundary conditions. The objective for the problem is to find the harvest rate that maximizes the discounted yield. Optimal harvesting strategies are found numerically.     

Pfaffian systems and Radon transforms on affine Grassmann manifolds

Mathematische Annalen -