A family of multiderivative methods for the numerical solution of the Schrödinger equation

A family of multiderivative methods with minimal phase-lag are introduced in this paper, for the numerical solution of the Schrödinger equation. The methods are called multiderivative since uses derivatives of order two, four or six. Numerical application of the new obtained methods to the Schrödinger equation shows their efficiency compared with other similar well known methods of the literature.Active Member of the European Academy of Sciences and Arts     

The Synthesis of Unusual Organic Molecules Using Cyclic Peroxides. New synthetic methods (3)

The photodecarboxylation of malonyl peroxides into α-lactones^[1] and the thermal conversion of the 1,4-endo-peroxide 4,5-epoxy-3,6-epidioxy-1-cyclohexene into the novel benzene trioxide^[2] are two recent examples of the potential of cyclic peroxides in the synthesis of unusual organic molecules. The former transformation entails a fragmentation, the latter a rearrangement process. Most reported examples fall into one of these two gross reaction types. Of the numerous examples that have been reported in the literature during the last two decades, only those shall be focused on that lead to unusual compounds or constitute efficient syntheses of known compounds, in order to stress the convenience of cyclic peroxides in the synthesis of organic compounds.     

Intramolecular,Stoichiometric (Li,Mg, Zn) and Catalytic (Ni,Pd, Pt) Metallo-Ene Reactions in Organic Synthesis [New Synthetic Methods (75)]

Metallo-ene reactions, hardly recognized until very recently, have experienced a breathtaking development when applied in an intramolecular sense. Efficient regio- and stereoselective magnesium-ene cyclizations have served as a cornerstone for numerous syntheses of structurally diverse natural products (e.g., sesquiterpenes of marine or plant origin, alkaloids, fragrances, insect defense compounds, and a fungitoxin). A brilliant example is the synthesis of the elusive odorant (+)-khusimone which outshines 20 years of work in the field of tricyclovetivane synthesis. Palladium-, platinum-, and nickel-catalyzed versions of the metallo-ene reaction are in a comparatively early stage of exploration, but, nevertheless, reveal intriguing potential. Hence an almost 100% stereospecific C? O→C? ;Pd-→ C? C chirality transfer permits simple and selective, cis- or trans-annelation processes. The mild cyclization conditions are compatible with various functional groups, such as nitrogen moieties, which offer interesting perspectives for the preparation of heterocycles (e.g., alkaloids) difficult to obtain by other methods. Carbon monoxide insertion reactions of the cyclized σ-metal intermediates were shown to afford annelated cyclopentanones and cyclopentenones with concomitant stereocontrolled formation of four carbon–carbon bonds. These and other observations, highlighted in this article, provide a platform for further extensions and applications of this powerful method in organic synthesis.     

Integrated Dust Analysis by Physical Methods

Environmental analyses show that the air which we breathe, and which is so essential to life, is in general a mixture of gaseous, liquid, and solid components. The solid airborne particles, whose concentration, homogeneity, chemical composition, size, and shape can vary over wide ranges, and whose origin may be “natural” or “artificial” are referred to as “dust”. Dust particles can act, inter alia, as condensation nuclei, catalysts, and directly as hazardous materials. Unfortunately, we still know far too little about dust. Dust analysis is extremely difficult and challenging, even for modern analytical chemistry; it is still far from being fully automated. The simultaneous determination of as many “dust parameters” as possible, and particularly the synoptic consideration of all available data against a background of physicochemical and technological knowledge on the development, transformation, and effects of dust, are summarized as “integrated dust analysis”.     

Primary methods of measurement in chemical analysis

 Primary methods of measurement have a central function in metrology. They are an essential component in the realisation of the SI units and therefore are indispensable for establishing traceability of measurements of all kinds of physical quantities to the corresponding SI units. This is also true for chemical analysis. Gravimetry, titrimetry, coulometry, and isotope dilution mass spectrometry (IDMS) are evaluated with regard to their potential to be primary methods according to a general definition of primary methods recently given by the Comité Consultatif pour la Quantité de Matière (CCQM). Optical absorption spectrometry and methods based on colligative properties are also considered. A general scheme for establishing traceability of chemical measurements to the SI units using primary methods is discussed. Received: 17 April 1997 · Accepted: 9 August 1997     

The Formation of C?C Bonds with the Aid of α-Halogeno Ethers,Sulfides, and Amines

α-Halogeno ethers, sulfides, and amines are reactive compounds which can be used for the formation of new C? C bonds, either as nucleophilic or as electrophilic reagents, or by α-elimination. The use of these compounds in the synthesis of many classes of organic compounds is reviewed.     

Chromatography with Supercritical Fluids

Chromatography with supercritical fluids unites the features of both gas chromatography and liquid chromatography, yet retains special characteristics of its own. The diffusion coefficient and particularly the viscosity of fluid phases may approach values for low-pressure gases, while the solvent power may be similar to that of liquids. However, with supercritical fluids it is possible to control chromatographic separations very effectively by pressure programming, since the solubility increases with increasing density. Temperature programming, on the other hand, can have the opposite effect to that in gas- or liquid-chromatography since the density decreases with increasing temperature at a given pressure. Supercritical fluid chromatography is primarily of interest for the separation of higher molecular weight compounds. The efficiency of this method of separation is demonstrated on several homologous series. Thus, a styrene oligomer with nominal M_w=2200 can be resolved by a pressure and temperature program into 40 species.     

Phosphaalkynes—Syntheses,Reactions, Coordination Behavior [New Synthetic Methods (73)]

Organophosphorus compounds have been applied in two ways in chemical synthesis. They can either be used as a reagent in a step of the synthesis (for example, in the Wittig reaction) or they can be incorporated directly into the target molecule. This second application, in particular, has expanded greatly in the last few years with the preparation of low-coordination phosphorus compounds. These include the phosphaalkynes, which are of great interest to organic and inorganic chemists. Phosphaalkynes have been employed in the synthesis of heterocyclic compounds, phosphaarenes and their valence isomers, and polycyclic compounds. Further applications have been the use of phosphaalkynes as new ligand systems in complex chemistry and their cyclooligomerization with organometallic reagents. While the chemical properties of phosphaalkynes have little in common with those of nitriles, they are in many ways very similar to those of the isoelectronic acetylenes.     

Prescriptions and Ingredients for Controlled CC Bond Formation with Organometallic Reagents. New synthetic methods (5)

Merits and drawbacks of known carbon-carbon linking procedures are outlined. Two novel methods are discussed in some detail: the copper-catalyzed alkylation of Grignard reagents and reactions with allylpotassium compounds. Both methods provide a very efficient access to saturated, unsaturated, as well as functionally substituted hydrocarbons and moreover permit an astonishing degree of regio- and stereoselective control of olefin synthesis.