Derivatives directed

The function/( C) may have a very simple form, as is the case for the calculation of the molecular weight from the relative atomic masses. In most cases, however,/( Cj will be very complicated when it comes to describe the structure by quantum mechanical means and the property may be derived directly from the wavefunction for example, the dipole moment may be obtained by applying the dipole operator. 

The term ah initio is Latin for from the beginning. This name is given to computations that are derived directly from theoretical principles with no inclusion of experimental data. This is an approximate quantum mechanical calculation. The approximations made are usually mathematical approximations, such as using a simpler functional form for a function or finding an approximate solution to a dilferential equation. 

As in the case of the thiazoles, a variation on the Hantzsch s method has been used. This consists of using a nonhalogenated carbonyl derivative directly in the presence of iodine in the reaction with selenourea (Scheme 7) (20). However, in this case the reaction with selenourea is slower than with thiourea, and normally an excess of carbonyl compound is used. 

The only method that yields the 2-unsubstituted thiazoie derivatives directly involves the condensation of a-haloketones with thioformamide. As in the case of previously reported a-haloaldehydes, yields are better when more reactive bromoketones are used instead of a-chloroketones. Cyclization can be achieved by adding ketones dissolved in dioxane in small quantities to the thioformamide formed in situ at below 40°C. The temperature is kept below 70°C during the addition, and then the... 

Notice that the eclipsed conformation of d ribose derived directly from the Fischer pro jection does not have its C 4 hydroxyl group properly oriented for furanose ring forma tion We must redraw it m a conformation that permits the five membered cyclic hemi acetal to form This is accomplished by rotation about the C(3)—C(4) bond taking care that the configuration at C 4 is not changed... 

This equation shows that at small deformations individual chains obey Hooke s law with the force constant kj = 3kT/nlo. This result may be derived directly from random flight statistics without considering a network. 

Other synthetic routes to pyrazinones and quinoxalinones are from the halo compounds, by dealkylation of ethers (8lJCS(Pl)3111> or by diazotization of the corresponding amines, but since the halo derivatives are normally derived from the hydroxy compounds, and the amines from the halo derivatives, direct synthesis seems to represent the most practical approach. 

This is the equation for a plug flow reactor. It can be derived directly from the rate equations with the aid of Laplace transforms. The sequences of second-order reactions of Figs. 7-5n and 7-5c required numerical integrations. 

Calculations for Ceo in the LDA approximation [62, 60] yield a narrow band (- 0.4 0.6 eV bandwidth) solid, with a HOMO-LUMO-derived direct band gap of - 1.5 eV at the X point of the fee Brillouin zone. The narrow energy bands and the molecular nature of the electronic structure of fullerenes are indicative of a highly correlated electron system. Since the HOMO and LUMO levels both have the same odd parity, electric dipole transitions between these levels are symmetry forbidden in the free Ceo moleeule. In the crystalline solid, transitions between the direct bandgap states at the T and X points in the cubic Brillouin zone arc also forbidden, but are allowed at the lower symmetry points in the Brillouin zone. The allowed electric dipole... 

The oxidation of alcohols with lead tetraacetate was the first reaction used for oxygenation of an angular methyl group in steroids. It is a simple and efficient method and produces tetrahydrofuran derivatives directly from alcohols. 

Reaction of 2 or 3 aminopyndine with trifluoronitrosomethane forms the trifluoromethaneazo derivative directly 4-Aminopyridine fails to give the azo product [12] (equation 11)... 

A further group of elements, the transuranium elements, has been synthesized by artificial nuclear reactions in the period from 1940 onwards their relation to the periodic table is discussed fully in Chapter 31 and need not be repeated here. Perhaps even more striking today are the predictions, as yet unverified, for the properties of the currently non-existent superheavy elements.Elements up to lawrencium (Z = 103) are actinides (5f) and the 6d transition series starts with element 104. So far only elements 104-112 have been synthesized, ) and, because there is as yet no agreement on trivial names for some of these elements (see pp. 1280-1), they are here referred to by their atomic numbers. A systematic naming scheme was approved by lUPAC in 1977 but is not widely used by researchers in the field. It involves the use of three-letter symbols derived directly from the atomic number by using the... 

Since geometry derivatives are important for optimizing geometries, it may be useful to look in more detail at the quantities involved in calculating first and second derivatives of an HF wave function. Such formulas are most easily derived directly from the HF energy expressed in terms of the atomic quantities (eq. (3.53). ... 

A classical description of M can for example be a standard force field with (partial) atomic charges, while a quantum description involves calculation of the electronic wave function. The latter may be either a semi-empirical model, such as AMI or PM3, or any of the ab initio methods, i.e. HF, MCSCF, CISD, MP2 etc. Although the electrostatic potential can be derived directly from the electronic wave function, it is usually fitted to a set of atomic charges or multipoles, as discussed in Section 9.2, which then are used in the actual solvent model. 

Alkylation at the ind-N of l,2,3,4-tetrahydro-j8-carbolines has been carried out with alkyl halide after treatment with sodamide in the usual manner. Cyanoethylation of a p /r-V-substituted tetrahydro-jS-carboline in the presence of Triton B yields the corresponding 9-cyanoethyl derivative. Similarly, treatment of p / -V-methyl-l,2,3,4,4a,9b-hexahydro-y-carboline with sodamide, followed by benzyl chloride, leads to the ind-A -benzyl-substituted derivatives. l-Oxo-l,2,3,4-tetrahydro-j8-carboline yields the ind-A -methyl derivative directly with dimethyl sulfate.Prolonged treatment with sodium hydride, followed by methyl iodide, yields the 2,9-dimethyl derivative. Heating with sodium hydride in acetone followed by the addition of dimethyl sulfate gives rise to the ind-V-methyl derivative. ... 

In spite of these successful results, we continue to search for a proper reagent that can transform indole derivatives directly to the corresponding 1-hydroxyindoles. 

The Institut Fran ais du Petrole has developed and commercialized a process, named Dimersol X, based on a homogeneous catalyst, which selectively produces dimers from butenes. The low-branching octenes produced are good starting materials for isononanol production. This process is catalyzed by a system based on a nickel(II) salt, soluble in a paraffinic hydrocarbon, activated with an alkylalumini-um chloride derivative directly inside the dimerization reactor. The reaction is sec-... 

Petrochemicals in general are compounds and polymers derived directly or indirectly from petroleum and used in the chemical market. Among the major petrochemical products are plastics, synthetic fibers, synthetic ruhher, detergents, and nitrogen fertilizers. Many other important chemical industries such as paints, adhesives, aerosols, insecticides, and pharmaceuticals may involve one or more petrochemical products within their manufacturing steps. 

Chapter 5 discusses chemicals derived directly or indirectly from methane. Because synthesis gas is the main intermediate from methane. 

The entries of this index were derived directly by computer program from the lists of references. The accuracy of the references was the sole responsibility of the authors. No editorial check, except for format and journal-title abbreviation, was applied. Consequently, errors occurring in authors names in the references will recur in this index. 

Acetyl-CoA, formed from pyruvate by the action of pyruvate dehydrogenase, is the major building block for long-chain fatty acid synthesis in nonruminants. (In ruminants, acetyl-CoA is derived directly from acetate.)... 

Voltammetry Ratio derivative Direct measurement using hanging mercury Soft drinks o D 0) o (/)... 

Certainly, Equations (1.127 and 1.128) can be derived directly from Equation (1.6), but it requires a rather cumbersome integration. This example also allows us to illustrate the fact that the gravitational field has a finite value inside any mass. With this purpose in mind, imagine that the observation point p is located at the center of a small and homogeneous sphere. Fig. 1.12a. Then, the total field can be represented as a sum ... 

The form and shape of a molecule (i.e. its steric and geometric features) derive directly from the molecular genotype , but they cannot be observed without a probe. Furthermore, they vary with the conformational, ionization and tautomeric state of the compound. Thus, the computed molecular volume can vary by around 10% as a function of conformation. The same is true of the molecular surface area, whereas the key (i.e. pharmacophoric) intramolecular distances can vary much more. 

Alternatively, the difference-equation model form can be derived directly by dividing the length of the heat exchanger into N finite-difference elements or segments, each of length AZ, as shown in Fig. 4.27. 

The true energy scale of the y-spectrum in units of keV usually cannot be derived directly from the pulse height spectrum because the overall amplification of the detection system is not known. Therefore, the y-lines eventually have to be identified by trial and error when a new system is set up by checking for the occurrence of the Mossbauer effect. 

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