A more general method

Other methods for indicating or implying the presence of an atom in a nonstandard valence state have been used, especially the use of the prefix hydro e.g. 108). Such methods are sometimes convenient for simple molecules, but they are difficult to apply generally. A more general method that has seen extensive use utilizes the italicized symbol for the element with a superscript Roman numeral to indicate the valence (e.g. 109). This method has been objected to, however, because of ambiguity the superscript Roman number is also used to indicate oxidation number in inorganic compounds, and italicized atomic symbols are customarily used as locants for substituents. The A convention is a modification of the principle of this method, and avoids the objection. It was made a Provisional Recommendation of lUPAC in 1981. 

The cis-trans naming system used in the previous section works only with disub-stituted alkenes—compounds that have two substituents other than hydrogen on the double bond. With trisubstituted and tetrasubstituted double bonds, a more general method is needed for describing double-bond geometry. (Tiisub-stitnted means three substituents other than hydrogen on the double bond tetrasubstituted means four substituents other than hydrogen.)... 

A more general method for preparation ofa-amino acids is the amidotnalmatesynthesis, a straightforward extension of the malonic ester synthesis (Section 22.7). The reaction begins with conversion of diethyl acetamidomalonate into an eno-late ion by treatment with base, followed by S 2 alkylation with a primary alkyl halide. Hydrolysis of both the amide protecting group and the esters occurs when the alkylated product is warmed with aqueous acid, and decarboxylation then takes place to vield an a-amino acid. For example aspartic acid can be prepared from, ethyl bromoacetate, BrCh CCHEt ... 

To compute each of the n(ct ), one can generalize the methods used to compute ihG- Hence, the most elegant method would be to use basis functions that satisfy the boundary conditions of Eq. (43), if this were practical to implement. A more general method would be to extend the Mead-Truhlar vector-potential approach [6]. This approach would involve carrying out h calculations, each including a... 

Among the compounds capable of forming enolates, the alkylation of ketones has been most widely studied and applied synthetically. Similar reactions of esters, amides, and nitriles have also been developed. Alkylation of aldehyde enolates is not very common. One reason is that aldehydes are rapidly converted to aldol addition products by base. (See Chapter 2 for a discussion of this reaction.) Only when the enolate can be rapidly and quantitatively formed is aldol formation avoided. Success has been reported using potassium amide in liquid ammonia67 and potassium hydride in tetrahydrofuran.68 Alkylation via enamines or enamine anions provides a more general method for alkylation of aldehydes. These reactions are discussed in Section 1.3. 

The matrices such as X and B in Eq. (33), which are composed of a single column, are usually referred to as vectors. In fact, the vectors introduced in Chapter 4 can be written as column matrices in which the elements are the corresponding components. Of course the vector X — [Xj ] in Eq. (33) is of dimension n, while those in Chapter 4 were in three-dimensional space. It is apparent that the matrix notation introduced here is a more general method of representing vector algebra in multidimensional spaces. This idea is developed further in Section 7.7. 

A more general method for preparing carbenes often involves the a elimination of halides from carbanions.1-57 PAC can be used to examine the rates and energetics of the reverse reactions, the complexation of halides with carbenes (Fig. 5).58 Plots of A//com versus the proton affinities (PA) of the halides are linear for the two carbenes studied. Although the slopes of the plots are similar, complexation of the halides with phenylchlorocarbene is more exothermic than phenylfluorocarbene. This indicates that fluoro substitution stabilizes the carbene relative to the carbanion more than chloro substitution. The rate of complexation of carbenes with salts has also been examined by nanosecond absorption spectroscopy.59... 

A more general method of predicting detonation velocities has been mentioned in Part I [Eq. (9) J and will be discussed in detail in a subsequent paper of this series. 

Having discussed the form of analytical potentials for three special categories of surfaces 1 will now describe a more general method for obtaining analytical potential energy functions for polyatomic molecules from spectroscopic data (755). The method is probably simpler to follow if a specific example is taken. 

A more general method proposed by Forster is a thermodynamic calculation based on a cycle called after his name (Figure 4.12). If AH and AH are enthalpies of proton dissociation in the ground and the excited states, respectively, then... 

The interchain effects in polymer networks are reflected in the thermomechanical inversion at low strains, which arises from a competition of intra- and interchain changes. Calorimetric studies of unidirectional deformation demonstrates this fact very obviously (Fig. 4). The point of elastic inversion of heat (Table 3) is dependent on the energy contribution and the thermal expansion coefficient in an excellent agreement with the prediction of Eq. (45). The value of (AU/W)VjT for the only one point of deformation, i.e. the inversion point, coincides with data obtained by a more general method (Fig. 3). 

A more general method for carbohydrates that can be used equally well on handsections and on sections of plastic embedded materials uses the Periodic acid SchifFs (PAS) reaction or one of its variants [29] for vicinal hydroxyl groups [22,23]. Sections are treated with 1%W/V Periodic acid at room temperature for 10 minutes and rinsed. The aldehydes created by this treatment are detected with SchifFs reagent (decolorized para-rosaniline) by immersion for 30 minutes. A red color (or fluorescence with excitation at 540 nm) indicates vicinal hydroxyl groups in starch and many other carbohydrates. If the specimen has been fixed with aldehydes then an aldehyde-blocking step must precede this reaction [22]. The best treatment is immersion for 24 hr in a saturated solution of dimedone. 

These methods are not always applicable or convenient. A more general method used by Richard and Jencks utilizes HPLC analysis of carbocation formation in alcohol-water mixtures.22 As shown in Scheme 2 for an a-aryl ethyl cation, formation of the ether product from reaction of the carbocation with the alcohol depends on the rate constant for carbocation formation kll and the partition ratio between product formation and the back reaction to form the alcohol kROiiAii2o- This ratio may be determined from the ratio of products formed from reaction of the carbocation generated from a suitable solvolytic precursor such as an alkyl halide. 

A more general method of preparation of various 10,10-dichlorophen-oxatellurines comprises intramolecular electrophilic cyclization of 2-phenoxyphenyl tellurium trichlorides, which are readily accessible from the corresponding arylmercury chlorides or aryltrimethylsilanes (83MI2). 

Given the disappointing result obtained with the C-4 o-anisyl derivative 134, it was evident that this method for setting up the C-3/C-4 cis stereochemistry would be very much dependent on the nature of the C-4 substituent in a manner that would not be readily predictable. A more general method for reduction of the enamides 89, 92, 94, and 96 was therefore still required. 

A more general method of synthesizing macromonomers by means of free-radical transfer processes has been disclosed in a Dutch patent of ICI11 > dated 1965. A number of examples were given but precise data on the species formed are missing. 

The right-hand side of this equation is the first term of the density expansion of the radial distribution function which is valid only in the limit of low concentrations (p 0). For arbitrary concentrations, the radial distribution function defines the potential of the mean force w(r) by a similar equation to Eq. (47), where u(r) is substituted by w(r). In general, the potential of the mean force does not coincide with u(r) except in the limit of low concentrations. Therefore, a more general method to determine the effective pair potential should be developed. 

A more general method for the synthesis of a,P-acetylenic ketones has been recently reported, and is indicated in Eq. 34 80). 

The employment of chiral precursors is a useful method for introducing stereochemistry provided the synthesis of the substrates is straightforward from easily accessible chiral starting materials. A more general method is required though. 

Ureato and Carbamato Complexes. These can be made in a variety of ways such as the interaction of metal carbonyls with RNCO or RN3. A more general method involves the sequence218 ... 

---