Little co-group

Therefore, k+bm and k label the same representation and are said to be equivalent (=). By definition, no two interior points can be equivalent but every point on the surface of the BZ has at least one equivalent point. The k = 0 point at the center of the zone is denoted by T. All other internal high-symmetry points are denoted by capital Greek letters. Surface symmetry points are denoted by capital Roman letters. The elements of the point group which transform a particular k point into itself or into an equivalent point constitute the point group of the wave vector (or little co-group of k) P(k) C P, for that k point. 

Each block in the matrix on the right corresponds to a different irreducible representation (IR) of the so-called little co-group, and the number... 

Relatively little work has been done on the flash photolysis of gas phase metal carbonyls, partly because of the low volatility of many of the compounds. Early work by Callear (41,42) provided some evidence for Ni(CO)3 generated from Ni(CO)4 in the gas phase (41) and Fe atoms produced from Fe(CO)5 (42). This latter process has even been used as the basis of an Fe atom laser (43). More recently Breckenridge and Sinai (44) studied the flash photolysis of Cr(CO)6. Their results, interpreted largely on the basis of data from matrix isolation experiments, were in broad agreement with Kelly and Bonneau s solution work (JJ). In particular, they found no evidence for loss of more than one CO group [Eqs. (4) and (5)]. 

The methods of estimating the heats of reaction, AE, as given in the last column merit a little amplification. They show how estimates can be made with little effort. Reaction (1) involves the breaking of two C —C bonds 70,000 calories each, the formation of one C —C bond 70,000 (exothermic) and the formation of CO which is 64,000 calories more stable than the CO group which is present in the ketone. In the language of quantum chem-... 

Very little is known about the formation of the less volatile products. Taking into consideration only the gaseous products, it can be seen that the hypothetical ratio, methyl groups/CO molecules, is over 2. This indicates that some of the less volatile products containing CO groups escaped detection. Biacetyl could be detected, in rather small quantities, using a fluorinated cyclic ether medium . In aqueous solution, a considerable amount of acetic acid is formed, probably the result of the hydrolysis of the ketene . ... 

This reaction is worth looking at in a little more detail. It depends upon formation of an intermediate species, the iodonium ion 105. There is nothing to stop the diastereomeric iodonium ion 106 from forming but cyclisation with the carboxylate ion cannot occur and, since the reaction is reversible, the reaction will run back to the unsaturated acid 103 and try again. The two alternative iodonium ion conformations with equatorial CO, groups cannot cyclise until the chain flexes to put the C02 axial. 

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