Procedure analoging

The KS orbitals can be determined by a numerical procedure, analogous to numerical HF methods. In practice such procedures are limited to small systems, and essentially all calculations employ an expansion of the KS orbitals in an atomic basis set. 

This salt is prepared, by a procedure analogous to that employed for the methyl salt, from ethyl bromide and triphenyl phosphine (Chapter I , Section II). 

By a procedure analogous to that described in the preceding experiment, octalone-2 (12 g, 0.08 mole, Chapter 9, Section III) in ether is added to methylmagnesium iodide in the presence of cuprous bromide (0.2 g). After decomposition with ice-acetic acid, extraction with ether, and washing of the ether extract, the ethereal solution is shaken with an equal volume (50-60 ml) of saturated aqueous sodium bisulfite for 3 hours. The mixture is filtered and the filtrate is reserved. The crystals are washed with ether. The filtrate is separated and the aqueous phase is combined with the filtered solid. The combination is acidified (dilute hydrochloric acid) and heated under reflux for 30 minutes. The product thus liberated is extracted into ether, the ether is washed with bicarbonate, then with saturated aqueous sodium chloride solution, and then dried and evaporated. The residual oil is the desired product, bp 250-254°. 

Sintered metal fibers with filaments of uniform size (2-40 (tm), made of SS, Inconel, or Fecralloy , are fabricated in the form of panels. Gauzes based on thicker wires (100-250 tm) are made from SS, nickel, or copper. They have a low surface area of about 10 m g. Several procedures are used to increase the surface area, for example, leaching procedures, analogous to the production of Ra-Nickel, and electrophoretic deposition of particles or colloid suspensions. The porosity of structures formed from metal fibers range from 70 to 90%. The heat transfer coefficients are high, up to 2 times larger than for random packed beds [67]. 

A procedure analogous to the one followed can be used for non-Newtonian fluids that follow the power law or Bingham plastic models (Darby and Melson, 1982). 

David and Lubineau191 reported the synthesis of pseudocytidine [5-/3-D-ribofuranosylcytosine (270)] and its a anomer by a procedure analogous to that used in preparing pseudouridine.155-157 Thus, 2,4 3,5-di-O-benzylidene-a/de/iydo-D-ribose (223) was condensed with the dilithio derivative of 2-0,4-N-(trimethylsilyl)cytosine, and the resulting, epimeric, acyclic derivatives were subjected to acid-catalyzed cyclization. The anomeric configuration of the free C-nucleosides was ascertained by spectroscopic methods and by their transformation into a- and /3-pseudouridine in the presence of nitrous acid. The anomeric 5-(/3-D-ribofuranosyl)isocytosines have also been prepared by Fox and coworkers.1913... 

Synthesis of the other ring system ([ 1,2,4]tnazolo[3,4-r][l,2,4]tnazinc), mentioned in the title of this section, has been carried out by a procedure analogous to those shown in Scheme 52 <2004JCM174>. Thus, the diazotriazole 263 was reacted with an cr,/3-unsaturated ketone in ethanolic solution in the presence of sodium acetate at room temperature to yield the cyclized product 264 in good yield (70%). 

We now introduce a Fourier transform procedure analogous to that employed in the solution theory, s 62 For the purposes of the present section a more detailed specification of defect positions than that so far employed must be introduced. Thus, defects i and j are in unit cells l and m respectively, the origins of the unit cells being specified by vectors R and Rm relative to the origin of the space lattice. The vectors from the origin of the unit cell to the defects i and j, which occupy positions number x and y within the cell, will be denoted X 0 and X for example, the sodium chloride lattice is built from a unit cell containing one cation site (0, 0, 0) and one anion site (a/2, 0, 0), and the translation group is that of the face-centred-cubic lattice. However, if we wish to specify the interstitial sites of the lattice, e.g. for a discussion of Frenkel disorder, then we must add two interstitial sites to the basis at (a/4, a/4, a]4) and (3a/4, a/4, a/4). (Note that there are twice as many interstitial sites as anion-cation pairs but that all interstitial sites have an identical environment.) In our present notation the distance between defects i and j is... 

AWM Lee, WH Chan and HC Wong, Synth. Comntun., 1988, 18, 1531. [It is claimed that trithio-carbonates are obtained using a procedure analogous to 4.1.16, although there appears to be a discrepancy in the description of the experimental procedure.]... 

TV-Aminoethylazoles, which are frequently encountered as intermediates in the preparation of pharmacologically active compounds, are readily obtained by solid liquid phase-transfer catalysed reaction of the azole, diazole or triazole and their benzo derivatives with 2-chloroethylammonium chloride at reflux temperature using a procedure analogous to 5.3.3 [25]. 

Alkylation of p-oxophosphonates, using a procedure analogous to 6.2.19.A, produces both C- and O-alkylated products [74] in ratios varying from ca. 2 1 to 5 1 depending on the alkylating agent and the structure of the p-oxophosphonate. 

Phenylacetonitriles can be induced to undergo Michael reactions with unactivated alkenes. For example, propenylarenes, formed in situ from allylarenes, react with phenylacetonitriles to form 3-aryl-l-cyano-2-methyl-l-phenylpropanes (70-98%) [3] by a procedure analogous to 6.4.1.B, Similarly, the nitriles react with alkynes giving allyl cyanides (80-95%) [38]. 

The styrene oxide (26 mmol) is added with stirring to acetylcobalt tetracarbonyl, obtained at room temperature by the addition of an excess of Mel (9.0 g, 64 mmol) to CTMA-Br (0.2 g, 0.55 mmol) and Co2(CO)8 (0.19 g, 0.55 mmol) under CO (1 atmos.). The mixture is stirred at room temperature for 12 h and the products are isolated using a work-up procedure analogous to that described in 8.2.6. 

By a procedure analogous to that used for the production of benzoic acids, it is possible to produce benzolactones and benzolactams (Scheme 8.10) in good yield (60-95%) from suitable 2-(hydroxyalkyl)- and 2-(aminoalkyl)bromobenzenes. The... 

Using a procedure analogous to 8.4.1.A, the benzyl halide is replaced by a simple bromo-or chloroalkane (1.5 mmol) and the two-phase system is stirred at room temperature for 12 h. The reactive iodoalkane (4.5 mmol) is then added and the reaction mixture is stirred for a further 5 h. The unsymmetrical ketone is isolated as described in 8.4.I.A. 

The mechanism [26] of the oxidation of non-terminal aikynes by quaternary ammonium permanganates to give vicinal diketones [e. g. 18, 27] has been studied. Normally, terminal aikynes are totally oxidized in acetic acid to carboxylic acids [13, 27, 28] using a procedure analogous to 10.2.4. 

The a,p-unsaturated ketone (10 mmol) in CH2Cl2 (10 ml) is stirred at 27 °C with aqueous NaB03 (sat. soln. 90 ml) containing NaOH (10 mmol) and THA-HS04 (23 mg, 0.5 mmol). The oxirane is isolated using a procedure analogous to that described in 10.4.4. 

Asymmetric alkylation of a-substituted benzyl cyanides has been achieved using A-benzylquininium and cinchonium salts using procedures analogous to those described in 6.2.2 [19, 20], Analogous reactions catalysed by l-alkyl-3-hydroxy-quinuclidinium salts are less effective than those catalysed by quininium salts [20], whereas 1 -methyl-1 -diphenylmethyleneimino-2(5)-hydroxymethylpyrroli-dinium iodide is a more effective catalyst (>70% ee) [18]. 

Enthalpy of dilution data can be used to calculate excess enthalpies by a procedure analogous to that we used to calculate relative molar enthalpy from enthalpy of dilution. We can describe the dilution of an aqueous solution of rii moles of water and 2 nioles of solute S with (riif — riu) moles of water by the equation... 

By procedures analogous to those described in the preceding two examples, we can obtain entropies for many aqueous ions. A list of such values is assembled in Table 20.1. 

Cyclooctylamine was purchased from Aldrich Chemical Co. It was converted to N,N-dimethylcyclooctylamine in 74% yield using a procedure analogous to that for j8-phenylethyldi-methylamine. ... 

The first synthesis of a semibuckminsterfullerene was accomplished by a procedure analogous to the preparation of corannulene except that 1,2,5,6-tetrake-topyracene served as the starting material (Scheme 5). Flash vacuum pyrolysis of the tetrachloro compound led to a remarkable quadruple ring closure to produce the semi-buckminsterfullerene 27. The NMR shows three methine carbons and five quaternary carbons at 125.5, 126.8, 127.3, 128.6, 136.7, 137.3, 142.0, and 145.4 ppm. The latter signals compare favorably to the single resonance observed at 143 ppm for buckminsterfullerene. 

Three or More Reactions. Analysis of three or more reactions can be made by procedures analogous to those presented. Of course, the mathematics becomes more involved however, much of the extra labor can be avoided by selecting experimental conditions in which only two reactions need be considered at any time. Figure 8.15 shows product distribution curves for one such reaction set, the progressive chlorination of benzene. 

The WLF equation holds over the temperature range from Tg to about + 100 K. The constants in Eq. (5.76) are related to the free volume. This is a procedure analogous to the one we used to generate time-temperature-transformation (TTT) diagrams for metallic phase transformations in Section 3.1.2.2. 

J5 Consider the wall-injection problem in an axisymmetric setting, where a uniform injection velocity flows through the wall of a cylindrical tube. There is a mean velocity U that enters through one end of the tube. Following a procedure analogous to the flow-between-plates problem (Section 5.6), develop a solution for the velocity profiles and the wall shear stress as characterized by the product of a Reynolds number and a friction factor. 

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