l1 solution of linear inequalities

The numerical solution of a possible inconsistent system oflinear inequalities in the l₁ sense is considered. The non-differentiablel₁ norm minimization problem is approximated by a piecewisequadratic Huber smooth function. A continuation algorithm isdesigned to find an l₁ solution of the inequality system. Inthe case where the linear inequality system is consistent, asolution is obtained by solving any smoothed problem. Otherwise,the algorithm is shown to terminate in a finite number of iterations.We also consider an alternative smoothing scheme which sharessimilar properties with the first one, but results in an improvedcomputational performance of the continuation algorithm on inconsistentsystems. Numerical experiments are conducted to test the efficiencyof the algorithm.     

Dead Ends and Detours En Route to Total Syntheses of the 1990s A list of abbreviations can be found at the end of the article

From the very beginning organic chemistry and total synthesis have been intimately joined. In fact, one of the first things that freshmen in organic chemistry learn is how to join two molecules together to obtain a more complex one. Of course they still have a long way to go to become fully mature synthetic chemists, but they must have the primary instinct to build molecules, as synthesis is the essence of organic chemistry. With the different points of view that actually coexist in the chemical community about the maturity of the science (art, or both) of organic synthesis, it is clear that nowadays we know how to make almost all of the most complex molecules ever isolated. The primary question is how easy is it to accomplish? For the readers of papers describing the total synthesis of either simple or complex molecules, it appears that the routes followed are, most of the time, smooth and free of troubles. The synthetic scheme written on paper is, apparently, done in the laboratory with few, if any, modifications and these, essentially, seem to be based on finding the optimal experimental conditions to effect the desired reaction. Failures in the planned synthetic scheme to achieve the goal, detours imposed by unexpected reactivity, or the absence of reactivity are almost never discussed, since they may diminish the value of the work reported. This review attempts to look at total synthesis from a different side; it will focus on troubles found during the synthetic work that cause detours from the original synthetic plan, or on the dead ends that eventually may force redesign. From there, the evolution from the original route to the final successful one that achieves the synthetic target will be presented. The syntheses discussed in this paper have been selected because they contain explicit information about the failures of the original synthetic plan, together with the evolution of the final route to the target molecule. Therefore, they contain a lot of useful negative information that may otherwise be lost.     

Influence of H-bond strength on chelate cooperativity

Intermolecular complexes formed between metalloporphyrins and pyridine ligands equipped with multiple H-bond donors and acceptors have been used to measure the free energy contributions due to intramolecular ether-phenol H-bonding in the 24 different supramolecular architectures using chemical double mutant cycles in toluene. The ether-phenol interactions are relatively weak, and there are significant populations of partially bound states where between zero and four intramolecular H-bonds are made in addition to the porphyrin-ligand coordination interaction. The complexes were analyzed as ensembles of partially bound states to determine the effective molarities for the intramolecular interactions by comparison with the corresponding intermolecular ether-phenol H-bonds. The properties of the ether-phenol interactions were compared with phosphonate diester-phenol interactions in a closely related ligand system, which has more powerful H-bond acceptor oxygens positioned at the same location on the ligand framework. This provides a comparison of the properties of weak and strong H-bonds embedded in the same 24 supramolecular architectures. When the product of the intermolecular association constant and the effective molarity KEM > 1, there is a linear increase in the free energy contribution due to H-bonding with log EM, because the intramolecular interactions contribute fully to the stability of the complex. When KEM < 1, the H-bonded state is not significantly populated, and there is no impact on the overall stability of the complex. Intermolecular phosphonate diester-phenol H-bonds are 2 orders of magnitude stronger than ether-phenol H-bonds in toluene, so for the phosphonate diester ligand system, 23 of the 24 supramolecular architectures make intramolecular H-bonds. However, only 8 of these architectures lead to detectable H-bonding in the ether ligand system. The other 15 complexes have a suitable geometry for formation of H-bonds, but the ether-phenol interaction is not strong enough to overcome the reorganization costs associated with making intramolecular contacts, i.e., KEM < 1 for the ether ligands, and KEM > 1 for the phosphonate diester ligands. The values of EM measured for two different types of H-bond acceptor are linearly correlated, which suggests that EM is a property of the supramolecular acrchitecture. However, the absolute value of EM for an intramolecular phosphonate diester H-bond is about 4 times lower than the corresponding value for an intramolecular ether-phenol interaction embedded in the same supramolecular framework, which suggests that there may be some interplay of K and EM.     

Steric desolation enhances the effective molarities of intramolecular H-bonding interactions

Free energy contributions due to intramolecular phosphonate diester-phenol H-bonds have been measured for 20 different supramolecular architectures in cyclohexanone solution. High throughput UV/Vis titrations were used in combination with chemical double mutant cycles to dissect out the contributions of different functional group interactions to the stabilities of over 100 different zinc porphyrin-pyridine ligand complexes. These complexes have previously been characterised in toluene and in 1,1,2,2-tetrachloroethane (TCE) solution. Intramolecular ester-phenol H-bonds that were measured in these less polar solvents are too weak to be detected in cyclohexanone, which is a more competitive solvent. The stability of the intermolecular phosphonate diester-phenol H-bond in cyclohexanone is an order of magnitude lower than in TCE and two orders of magnitude lower than in toluene. As a consequence, only seven of the twenty intramolecular phosphonate diester-phenol interactions that were previously measured in toluene and TCE could be detected in cyclohexanone. The effective molarities (EM) for these intramolecular interactions are different in all three solvents. Determination of the EM accounts for solvent effects on the strengths of the individual H-bonding interactions and the zinc porphyrin-pyridine coordination bond, so the variation in EM with solvent implies that differences in the solvation shells make significant contributions to the overall stabilities of the complexes. The results suggest that steric effects lead to desolvation of bulky polar ligands. This increases the EM values measured in TCE, because ligands that fail to replace the strong interactions made with this solvent are unusually weakly bound compared with ligands that make intramolecular H-bonds.