Trigonal system

Next to tetrahedral systems, trigonal systems are considered as reaction centres in Baldwin s rules. These predict that 3- to 1-exo-trig reactions are all favoured processes. Very accurate EM s have been reported by Bruice and Benkovic (1963) for intramolecular nucleophilic attack on carbonyl in [39] and [40]. When Ar is varied from C6H5 to p-NOzC6H4, the EM of [39]... 

Rhomobohedral is a subset of the trigonal system in which the unit cell can be chosen on either hexagonal or rhombohedral axes. 

Whether this condition can be fulfiUed depends on the electron count of the metal, and the stereochemistry of the elimination. For instance, in m-elimination from octahedral d , or square planar d , systems, metal ndipP -y ) acts as acceptor, and this should be a facile process ( e Fip. 1, 2). For /rans-elimination, on tiie other hand, the lowest empty orbital of correct symmetry is (n + l)p. Such elimination Kerns energetically less Ukely, unless a non-concerted pathway (such as successive anionic and cationic loss) is available. The same arguments apply, of course, to oxidative additions. It foUows that the many known cases of traits oxidative addition to square planar t/ systems are unlikely to take place by a concerted mechanism, and this conclusion is now generally accepted There are special complexities in reductive elimination from trigonal systems, and these are discussed furdier in Part III. 

Cr CNNi(tetren) 6](C104)9 is a red-purple solid, soluble in water-acetonitrile mixtures where the undissociated heptanuclear entity can be identified by electrospray ionization mass spectrometry. IR spectroscopy shows the presence of a unique /cn band at 2146 cm of the bridging cyano ligand and an intense band of the perchlorate anion at cr = 1090 cm The IR spectrum of the C-enriched compound prepared from K3[Cr( CN)6] displays a /cn band at 2103 cm The compound crystallizes in a trigonal system, space group R3, with parameters a = b = 15.274 A and c = 41.549 A. The magnetic properties indicate a ferro-... 

Figure A.1.1. Miller axes applied to crystal systems other than hexagonal (including rhombohedral = trigonal) system.

Figure A.1.3. Relation between hexagonal and rhombohedral (trigonal) systems.

Since a subsidiary axis is assumed in addition to the and axes in the hexagonal system (and in the hexagonal expression of the trigonal system), the index is expressed by four indices for a general face (hktl). This is called the Miller-Bravais index. For example, in Fig. A.3.1(b) a face ACB cuts the + and + axes at 1 (= OA, OB), and the - axis at 0C = 0D = OB/2. Therefore this face is indexed as (1120). From geometry, h(l) + k(l) = i(2). 

The crystals of potassium bromate were at first thought to be cubic, but C. F. Rammelsberg 30 showed that they are pseudo-cubic and belong to the trigonal system, where a c=l 1 3572, and a=85° 57. They are isodimorphous with potassium chlorate in that the two salts form trigonal mixed crystals if the bromate is in... 

Crystalline form,—Lithium nitrate crystallizes in rhombohedra (trigonal system).15 P. W. Bridgman observed no new form of lithium nitrate between 20° and 200°, and press, between 1 and 12,000 kgrms. per sp. cm. The older authorities—e.g. P. Kremers—supposed this salt to be trimorphic, but the supposed polymorphism is probably due to their mistaking hydrates for polymers of the anhydrous salt. It is doubtful if lithium nitrate is isomorphous with silver or sodium nitrate, although J. W. Retgers says that sodium and lithium nitrates are isomorphous. 

Fig. 35. Hexagonal and trigonal systems. (See also Figs. 24, 27 and 29.) a. Hexagonal- type unit cell. 6. Apatite, 3Ca3(P04)I.CaFB. Class 6/rm c. riydrocinchonine sulphate hydrate, (C19H940N9)9.H2S04. llHaO. Class 6m. d. Rhombohedral-type uriit cell, e. A habit of calcite, CaC()s. Class 3m. /. KBr03. Class 3m.

Crystalline Tellurium. — Molten tellurium solidifies to a brittle, silvery, crystalline mass, which is easily powdered. The crystalline modification can also be obtained by sublimation of the element or by its slow formation, for example in the gradual decomposition of hydrogen telluride5 or in the slow atmospheric oxidation of an aqueous solution of an alkali telluride.6 When obtained of appreciable size the crystals are generally found to be prismatic, of the trigonal system, and isomorphous with metallic selenium (a c=l 1-3298 a=86-8°).7... 

By analogy, die formation of diastereomers is observed for additions to other trigonal systems, such as olefins, which have a chiral center elsewhere in the molecule. In these cases, if optically active starting materials are used, then the diastereomers will be optically active. If racemic starting materials are employed, the diastereomeric mixture will be optically inactive. In either case it is common to find different amounts of the two diastereomers. 

The rules of Baldwin (55) for ring closure in trigonal systems (see p. 171 for an introduction) are the following 3- to 7-Exo-Trig processes (152-156) are all favored processes. 3- to 5-Endo-Trig (157-159) are disfavored but 6- and 7-Endo-Triq (160-161) are favored. The literature is replete with examples of 3- to 7-Exo-Trig for instance, lactonization of u-hydroxy-acids and esters are of this type, the formation of lactams from w-aminoacids and also the Dieckmann cyclization of diesters. 

For example, the 5-Exo-Tet, 5-Exo-Trig, and 5-Exo-Dig processes are represented by 49, 50, and 51 while the 5-Endo-Tet, 5-Endo-Trig, and 5-Endo-Dig corresponds to 52, 53, and 54 respectively. In this Chapter, we will consider the tetrahedral systems only. The trigonal systems are considered in Chapter 6. 

This uniaxial crystal belongs to the trigonal system (factor group D3) and has 9 atoms in the elementary cell. Vibrations of species E are polar and Ra-... 

The trigonal system can be considered as a subdivision of the hexagonal unit. On this basis there would be only six different crystal systems, but conventionally, the trigonal system (also called the rhombohedral system) is retained separately. Figure 2.1 shows two rhombohedral cells within a hexagonal cell. 

Q -SeBr4 crystallizes in the trigonal system and contains cubane-like [SeBr4]4 units. Monoclinic /3-SeBr4 also consists of tetrameric cubane-Uke [SeBr4]4 molecules. /3-SeBr4 is isotypic withTeCU and with jS-SeCU its chemical behavior and reactions are similar to SeCU-... 

Amorphous chromium sesquioxide is a green powder, the tint of which depends upon the method of preparation the colour becomes brownish on heating. The crystalline oxide forms very dark green hard crystals belonging to the trigonal system (ditrigonal scaleno-hedral) ... 

Molecular weight 101.11 colourless crystals of the rhombic system specific gravity 2.109(16 0) makes transition to trigonal system at 129 C ... 

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