Formal Derivatives

The structures of many methylene sugar derivatives have not been determined, but those of many of the alditol derivatives are known. The greater ease of acetolysis of methylene groups attached to primary hydroxyls over those attached to secondary hydroxyls, has been of considerable value in the elucidation of the structures of these compounds by Hudson and co-workers (96), Thus the linkages at carbons 1 and 6 of 1,3 2,4 5,6-tri-O-methylene-D-glucitol are cleaved with sulfuric acid in acetic anhydride and acetic acid as shown in the formulas. The structure of the mono-0-methylene-D-glucitol is demonstrated by its oxidation with periodic acid 

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Resins formed from the reaction of poly(vinyl alcohol) with aldehydes. The formal derivative (from methanal) is used in wire coatings and adhesives and the bulyral (from butanal) is used in metal paints, wood-sealers, adhesives and in safety glass interlayers. 

A formal derivation of the location of the zeros of Cg t) for a general adiabatic Hamiltonian can be given, following proofs of the adiabatic principle (e.g., [250-252]). The last source, [252] derives an evolution operator U, which is written there, with some slight notational change, in the form... 

A readily accessible carborane is nido-1 -(]5 i])- l- 1( 12 [I d-5], a 2witterionic species formally derived from [CB2qH23] by replacement of a by NH3. It has been shown (124) that this monocarbaborane can be obtained in excellent yield by treatment of B2QH24 with CN followed by passage through an acidic ion-exchange column (eq. 61). 

Dioxopiperazines are amongst the most ubiquitous of natural products (75FOR(32)57) and they are formally derived by the cyclodimerization of a-amino acids (69CCC4000) or their esters. A number of methods are available for their oxidation to the corresponding pyrazines. Treatment of 2,5-dioxopiperazines with triethyl- or trimethyl-oxonium fluorobor-ate followed by oxidation with DDQ, chloranil or iodine results in pyrazine formation, usually in high yields (Scheme 63) (72JCS(P1)2494). 

The 1,2-dithiolylium and 1,3-dithiolylium ions (115) and (116) are iso-rr-electronic with the tropylium ion, from which they may be formally derived by replacing double bonds by sulfur atoms. Various calculations and structural data demonstrate that the rings are stabilized by tt-electron delocalization. 

These compounds are usually written in the unionized form as in (8 Z = NH, NR, O, S). Canonical forms of types (9) or (10) are important, i.e. these compounds can also be considered as betaines formally derived from azolium ions. Many compounds of this type are tautomeric and such tautomerism is discussed in Section 4.01.5.2. 

In the main, the physical and chemical properties of saturated and partially unsaturated alicyclic compounds closely resemble those of the analogous acyclic compounds formally derived by cleavage of the carbon ring at a point remote from any functionality. Relatively small, but often significant, differences in properties arise from conformational effects, and from strain effects in small rings, and these differences can be striking in properties which are particularly sensitive to molecular shape. 

Alternatively, A- ylium names may be formed by a special application of the A convention, according to which the affected atom is considered to be formally derived from a hypothetical parent that has a hydridic hydrogen attached in lieu of the positive charge. Such an operation... 

A formal derivation of diffusion in a restricted, high diffusivity path which uses no atomic model of the grain boundary is that due to Fisher, who made a flux balance in unit width of a grain boundary having a drickness of <5. There is flux accumulation in the element according to Pick s second law given by... 

The simplified failure envelopes are not derived from physical theories of failure in which the actual physical processes that cause failure on a microscopic level are integrated to obtain a failure theory. We, instead, deal with phenomenological theories in which we ignore the actual failure mechanisms and concentrate on the gross macroscopic events of failure. Phenomenological theories are based on curve-fitting, so they are failure criteria and not theories of any kind (the term theory implies a formal derivation process). 

Mass spectrometry played an important role in the recent characterization of small cyclic sulfur imides that are formally derived from the unstable cyclic sulfur allotropes Se and S7 by the replacement of one sulfur atom by an NR group. The compounds SsNOct and SeNOct (Section 6.2.2), which are yellow oils, exhibit molecular ions of medium intensity in their mass spectra. ... 

The sulfur nitrides S15N2 and S sN2 are (formally) derived from cyclo-Sg (or S7NH) and can be prepared by reacting S7NH with SCI2 and S2CI2 respectively ... 

The formal derivation of the analogs, described in the foregoing, represents, from the point of view of systematic organic chemistry, a shift to the derivatives of other heterocyclic systems. In the case of pyrimidine aza analogs we arc dealing with derivatives of symmetrical or asymmetrical triazine in the case of purine aza analogs, the derivatives produced are those of imidazo[4,5]-i -triazine and z -triazolo [4,5-d] pyrimidine. 

The names of 2-aza analogs are derived by formal substitution of the methine group in the 2-position of the purine skeleton by a nitrogen atom (140). Since this position is substituted in some purine bases, only the aza analogs of adenine or hypoxanthine are amenable to such formal derivation. 

The 8-aza analogs are formally derived by substitution of the methine group in position 8 of the purine ring. The names thus derived preserve the numbering of the purine ring (146), and are frequently used in papers of biochemical character, but in chemical papers only along with systematic names. 

Condensation of an appropriately substituted phenylacetic acid with phthalic anhydride in the presence of sodium acetate leads to aldol-like reaction of the methylene group on the acid with the carbonyl on the anhydride. Dehydration followed by decarboxylation of the intermediate affords the methylenephthal-ides (12). Treatment of the phthalides with base affords directly the indandiones, probably via an intermediate formally derived from the keto-acid anion (13). The first agent of this class to be introduced was phenindandione (14) this was followed by anisindandione (1S) and chlorindandione (16). ... 

Replacement of the carbamate function by an amide seems to be compatible with meprobamate-like activity in a compound formally derived from a 1,2-glycol. Oxidation of the commercially available aldehyde, 22, under controlled conditions affords the corresponding acid (23). This is then converted to its amide (24) via the acid chloride. Epoxidation by means of perphthalic acid affords oxanamide (25). ... 

Terpenoid (Chapter 6 Focus On. Section 27.5) A lipid that is formally derived by head-to-tail polymerization of iso-prene units. 

Porphyrins are formally derived from the porphin (1) nucleus by substitution of some or all peripheral positions with various side chains. In the classical system of nomenclature T, introduced by H. Fischer,Sc the peripheral /5-pyrrolic positions are numbered front 1 to 8 and the methine positions (also named meso positions) between the pyrrole rings are designated a, //, y, and 5. The rings are lettered clockwise A, B, C, and D. The classical nomenclature was in the past more and more displaced by a nomenclature which numbers all the carbon... 

Chlorophyll a, the green photosynthesis pigment, is the prototype of the chlorin (2,3-dihydro-porphyrin) class of products. It was first isolated by Willstatter1 at the turn of the century. The common structural unit in this class is the chlorin framework named after chlorophyll. The chromophore with a partially saturated pyrrole ring, which is formally derived from the completely unsaturated porphyrin, is less symmetric than the latter and systematically named according to IUPAC nomenclature as 2,3-dihydroporphyrin. 

The bacterioehlorin structural-type is formally derived from porphyrin by saturation of two peripheral C —C double bonds in oppposite pyrrole rings and therefore systematically named according to IUPAC nomenclature as 7,8,17,18-tetrahydroporphyrin. 

The synthesis of [261hexaphyrin(l. 1.1.1.1.1) which is formally derived from porphyrin by extension of two pyrrole subunits and the corresponding methine bridges follows a classical analogous McDonald [3 + 3] approach by condensation of two tripyrrane building blocks.2 2a d... 

The account of the formal derivation of kinetic expressions for the reactions of solids given in Sect. 3 first discusses those types of behaviour which usually generate three-dimensional nuclei. Such product particles may often be directly observed. Quantitative measurements of rates of nucleation and growth may even be possible, thus providing valuable supplementary evidence for the analysis of kinetic data. Thereafter, attention is directed to expressions based on the existence of diffuse nuclei or involving diffusion control such nuclei are not susceptible to quantitative... 

Monocarboxylic acids formally derived from aldoses by replacement of the aldehydic group by a carboxy group are termed aldonic acids (see 2-Carb-20). 

Oxo carboxylic acids formally derived from aldonic acids by replacement of a secondary CHOH group by a carbonyl group are called ketoaldonic acids (see 2-Carb-21). 

In a different type of reaction, alkenes are photooxygenated (with singlet O2, see 14-8) in the presence of a Ti, V, or Mo complex to give epoxy alcohols formally derived from allylic hydroxylation followed by epoxidation, for example, ... 

The most known and investigated substrate of this class is poly[bis(trifluo-roethoxy)phosphazene], PTFEP, a polymer formally derived by the general formula above by putting x=y=l and Z=R The general structure of this compound is shown below. 

Nolan and colleagues published in 1999 the first coupling between aryl chlorides, bromides or iodides and aryl Grignards, in which an in situ generated NHC-Pd complex served as catalyst. The reaction proceeded in most cases in excellent yields, however, very sterically hindered products formally derived from aryl halides and aryl Grignards both possessing orf/io-substituents could not be obtained [75] (Scheme 6.16). 

We have not covered the case of a zero term in the numerator. Here, we are just guessing that its result is the reciprocal of the first order function result in Eq. (8-9). The formal derivation comes later in Example 8.4. Note that x has units of time, is radian/time, and x is in radian. 

This is the largest group of tropanes, consisting of 39 representatives. All members of the group (1-39) are formally derived from 3ot-hydroxytropane (1) or from the not yet naturally found 3a-hydroxynortropane. 

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