Synthesis of Enantiomerically Pure Thiocrown Ethers Derived from 1,1'-Binaphthalene-2,2'-diol

Synthetic methodology is given for the preparation of two different types of thiocrown ethers from optically pure 1,1'-binaphthalene-2,2'-diol (10). The conceptually simplest approach starts from optically pure 10 itself, which is alkylated (4 equiv of K(2)CO(3) in DMF at 110 degrees C) with 2-chloroethanol followed by mesylation to provide 2,2'-bis(2-(mesyloxy)ethoxy)-1,1'-binaphthyl (14). When allowed to react with ethane-1,2-dithiol, propane-1,3-dithiol, 1,4,7-trithiaheptane, 1,4,8,11-tetrathiaundecane, 2,2-dimethylpropane-1,3-dithiol, 2-(mercaptomethyl)-1-propene-3-thiol, and 1,2-benzenedithiol in the presence of Cs(2)CO(3) in DMF at 60 degrees C the corresponding thiocrown ethers 22-25, 28, 30, and 32 are formed in 30-54% yields. Test reactions were carried out to establish that no racemization occurs during alkylation under these conditions. Reaction of optically pure 10 with tetrahydropyranyl (THP)-protected 3-chloropropanol under similar conditions for the preparation of 14 proceeded more sluggishly but cleanly. Removal of the THP protecting groups afforded 2,2'-bis(3-bromopropoxy)-1,1'-binaphthyl (20), which on reaction with propane-1,3-dithiol, 1,5,9-trithianonane, 2,2-dimethylpropane-1,3-dithiol, 2-(mercaptomethyl)-1-propene-3-thiol, and 1,2-bis(mercaptomethyl)benzene provided the respective thiocrown ethers 26, 27, 29, 31, and 33 in 24-68% yields. Another class of thiocrown ethers was prepared from optically active 10, which was converted via ortho-lithiation to 3,3'-bis(bromomethyl)-2,2'-dimethoxy-1,1'-binaphthyl (39) by means of methylation (K(2)CO(3)/CH(3)I), ortho-lithiation followed by formylation (n-C(4)H(9)Li/N,N,N',N'-tetramethylethylenediamine (TMEDA)/ether followed by DMF and H(2)O workup) followed by reduction (NaBH(4)) followed by bromination (PBr(3) in C(5)H(5)N). Reaction (Cs(2)CO(3) in DMF at 60 degrees C) with 1,4,7-trithiaheptane, 1,4,8-trithiaoctane, 1,4,7,10-tetrathiadecane, 1,4,8,11-tetrathiaundecane, and 1,5,10,14-tetrathiatetradecane afforded the corresponding thiocrown ethers 40-44 in 40-75% yields. Despite repeated attempts using a wide range of reagents, demethylation of the methoxy ether functionalities failed. Attempts to prepare the free phenol derivatives of the latter type of crown ethers by oxidative coupling of two naphthol units failed.     

Very empirical treatment of solvation and entropy: a force field derived from Log Po/w

A non-covalent interaction force field model derived from the partition coefficient of 1-octanol/water solubility is described. This model, HINT for Hydropathic INTeractions, is shown to include, in very empirical and approximate terms, all components of biomolecular associations, including hydrogen bonding, Coulombic interactions, hydrophobic interactions, entropy and solvation/desolvation. Particular emphasis is placed on: (1) demonstrating the relationship between the total empirical HINT score and free energy of association, G _interaction; (2) showing that the HINT hydrophobic-polar interaction sub-score represents the energy cost of desolvation upon binding for interacting biomolecules; and (3) a new methodology for treating constrained water molecules as discrete independent small ligands. An example calculation is reported for dihydrofolate reductase (DHFR) bound with methotrexate (MTX). In that case the observed very tight binding, G _interaction–13.6 kcal mol^–1, is largely due to ten hydrogen bonds between the ligand and enzyme with estimated strength ranging between –0.4 and –2.3 kcal mol^–1. Four water molecules bridging between DHFR and MTX contribute an additional –1.7 kcal mol^–1 stability to the complex. The HINT estimate of the cost of desolvation is +13.9 kcal mol^–1.     

Layers and corner singularities in singularly perturbed elliptic problems

Some recent work and open problems are reviewed concerning the numerical solution of singularly perturbed elliptic boundary value problems whose solutions have boundary layers and corner singularities. AMS subject classification (2000)  65N15, 65N50, 35J25     

Diffusion and convection in a family of tubes

Global existence theorems are given for the solutions of the renal flow equations for a system of parallel tubes. In the system, a solute moves in a fluid through the tubes by diffusion and convection and the tubes exchange fluid and solute with each other through the tube walls. The proofs use a fixed point argument. It is shown that the hypotheses of the theorems include the passive and convective flux formulas used in renal models.     

Pulsed laser atom-probe study of the dissociation of CO on molybdenum

The thermal decomposition of molecular CO on molybdenum surfaces has been studied using the pulsed laser atom-probe (PLAP). Field emitter tips, cleaned by vacuum field evaporation, were dosed with CO at low temperatures (<60 K) and heated to 180–350 K under fieldfree conditions. The fraction of undissociated CO⁺ ions compared to all carbon- and oxygen-containing species appearing in subsequently recorded PLAP mass spectra was taken as a measure of the extent of surface CO dissociation. Molecular (virgin) CO was found to convert to dissociated (β) CO at temperatures between 200—300 K. The analyzed surface area included both flat single crystal planes and stepped regions. Assuming first-order kinetics, the dissociation occurred with an activation energy of 0.7 ± 0.1 eV. The dissociation on the flat (110) plane, measured using the same technique but with the rest of the surface masked, occurred with a 0.12 eV higher activation energy.     

A regularity result for the Stokes problem in a convex polygon

In this paper we show that the solution of the Stokes problem has square integrable second derivatives provided that the domain is a convex polygon in the plane and the nonhomogeneous term is square integrable.     

On the rate of convergence of some difference schemes for second order elliptic equations

The purpose of this paper is to estimate the rate of convergence for some natural difference analogues of Dirichlet's problem for uniformly elliptic differential equations, $$\begin{gathered} \sum\limits_{j,k = 1}^N {\frac{\partial }{{\partial x_j }}} \left( {a_{jk} \frac{{\partial u}}{{\partial x_k }}} \right) = F in R, \hfill \\ u = f on B, \hfill \\ \end{gathered}$$ in aN-dimensional domainR with boundaryB. These schemes will in general not be of positive type, and the analysis will therefore be carried out in discreteL ²-norms rather than in the maximum norm. Since our approximation of the boundary condition is rather crude, we will only arrive at a rate of convergence of first order for smoothF andf. Special emphasis will be put on appraising the dependence of the rate of convergence on the regularity ofF andf.