and 99 wt- % of glass beads. This ratio enables the desired low temperature to be used in the analysis. Figure 1 shows the separation of Cs- to C13-n-paraffins at 54°C. Methane was added to the sample in order to mark the passage time of an inert substance. Not only is the analysis temperature low and the rate of separation high, but also it is noteworthy that the later bands remain symmetrical even at high capacity ratios (k' = 50). A considerable disadvantage of this column is the oxygensensitivity of the rubrene. If the traces of oxygen in commercial nitrogen carrier gas are not removed, the life of the column is only a few weeks. fatty acids at 300 "C within 30 sec. In the separation of methyl esters of higher fatty acids under the same conditions the bands remain symmetrical even at extraordinarily high capacity ratios (k' = 215). Figure 3 shows the flow-programmed separation of the Cs- to C14-normal paraffins on the same stationary phase. The broken line shows the decrease in pressure in the column as a function of time - it increases almost exponentially from c1 to c12. _~_ .~ Interesting separations can be carried out on graphitized carbon black [2,6,73. As well as many advantages, this stationary phase has two disadvantages: the carbon black pellets have not sufficient mechanical strength, and high analysis temperatures are necessary. To overcome these disadvantages, pelleted graphitized carbon black [**I was covered with 1 wt-% of 2', 3', 5', 6', 2"', 3"', 5"'. 6"'-octaphenyl-p-quinquephenyl [*I (m.p. -470 "C). For this operation a solution of the compound in boiling tetralin was mixed with the carbon black and the solvent was evaporated in a vacuum. The product does not become dusty, neither when the column is filled nor in the flow-programmed gas-chromatographic analysis. The favorable relative retentions of individual components on carbon black are retained with this low coverage[7J, the bands are substantially symmetrical, and the analysis temperature can he selected to be somewhat lower. The vapor pressure of this stationary phase is less than 10-4 torr at 300 "C; thus the column does not "bleed" and has a long life and an impeccable base line. Figure 2 shows the separation of the ethyl esters of four 30 20 t Received: June 24th, 1968. [ Z 81 5 IE] German version: Angew. Chem. 80,754 (1968) Publication delayed at the authors' request ~~ [ * ] D. Freitag and Prof. W. Ried Institut fur Organische Chemie der Universitat 6 FrankfurtiMain, Robert-Meyer-Str. 7-9 (Germany) F. A. Holdinghausen and Prof. I. Halasz Institut fur Physikalische Chemie der Universitat 6 Frankfurt/Main, Robert-Meyer-Str. 11 (Germany) [* "1 Degussa, FrankfurtiMatn, Type CK-3, graphitized at Siemens-Plania-WerkeAG., Meitingen bei Augsburg, Germany. [l] C. G. Scott in M . van Swaay: Gas Chromatography 1962, Hamburg. Butterworths, London 1962, p. 36 and 176; H. Kelker, 2. Elektrochem. Ber., Bunsenges. physik. Chem. 67, 698 (1963): S. Dal Nogare, Analytic. Chem. 37, 1450 (1965). [2] I. Halasz and C. Horvuth, Analytic. Chen;. 36, 1178 (1964). [3] H . Bruderreck, W . Schneider, and I . Halasz, Analytic. Chem. 36, 461 (1964). [4] I. HuIasz and G . Deininger, 2. analyt. Chem. 228, 321 (1967); G. Deininger and 1. Halasz, ibid. 229, 14 (1967). [ 5 ] Ch. Moureu, Ch. Dufraisse, and P. M . Dean, C. R . hebd. Seances Acad. Sci. 182, 1441 (1926). [ 6 ] I. Halasz and C. Horvaatk, Nature (London) 197, 71 (1963); I. Halasz, E. Heine, C. Horvaih, and H . G . Sternagel, BrennstoffChem. 44, 387 (1963); L. D . Belyakova, A . V. Kiselev, and N . V. Kovaleva, Analytic. Chem. 36, 1517 (1964); T. F. Broclasky, ibid. 36, 1604 (1964). [7] W. Schneider, H. Bruderreck, and I . Halbsz, Analytic. Chem. 36. 1533 (1964). [S] W . Ried and K. H . BBnnighausen, Chem. Ber. 93, 1769 (1960). Ligand Reorganization in the Trigonal Bipyramid 0 10 Isecl By J. D . Dunitz and V. Prelog[*l Fig. 2. Separation of fatty acid ethyl esters on graphitized carbon black coated with 1 % of octaphenylquinquephenyl. 1 : Methane. 2: Ethyl acetate. 3: Ethyl propionate. 4: Ethyl butyrate. 5: Ethyl valerate. Length of column 1 m; internal diameter 2 mm; sieve fraction 0.20-0.25 mm. Carrier gas N2.pi = 2.4 atm; p o = 1.6 atm; = 10 cmjsec. Amount of sample 5 wg c\3 c\ * /c 7/ c In a recent paper Muefrerfies[ll has discussed the interconvertibility of isomers [A (1,2,3,4,5)]with trigonal bipyramidal geometry through the process: trigonal bipyramid -+ square pyramid -+ trigonal bipyramid [2J. Irrespective of whether the square pyramid is regarded as corresponding to a transition state or to an intermediate, the process can be regarded (Fig. 1) as one in which the angle between a pair of apical ligands (1,2) decreases from 180° to 120", while the angle between a pair of equatorial ligands (3,4) increases from 120 to 180". At some stage in this process the angle between 1 and 2 must equal the angle between 3 and 4 to give the square pyramidal geometry. 1 4.,~ 3 2 Fig. 1 4 - 3 2 1 0 I lminl Fig. 3. Flow-programmed separation of Cg- to C,d-normal paraffins. Stationary phase as in Fig. 2. T = 320°C. Length of column 2 m; internal diameter 2.3 mm; sieve fraction 0.20-0.25 mm. Carrier gas N2. Amount of sample 50 pg. Ordinate: see Fig. 1. Angew. Clzern. internat. Edit. f Vol. 7 (1968) No. 9 The problem of keeping track of the various interconversion paths between the ten possible diastereomeric pairs of enantiomers may at first sight appear somewhat intricate; for example, it is not immediately obvious how to convert a given diastereomer into its enantiomer, an interconversion for which at least five steps are necessaryW In view of the current interest in problems of this kind, e.g. in phosphorus chemistry[l.3'41, we wish to draw attention to the usefulness of simple graph theory in dealing with them. We assume, with Muetrerfies, that the result of each interconversion step 725 depends at most o n the result of the immediately preceding interconversion and not on any earlier interconversion. This implies that, starting from any given state of the system, the possible results of any sequence of interconversions can be represented by a Markov chain [51 o r , alternatively, by the corresponding tree diagram 151. In particular. all such interconversion paths leading from one stereoisomer to another are represented by a Petersen graph, a bridgeless regular graph of degree 3 that is constructed as follows161: Each of the ten couples (1,2), (1,3), . . . (4,5) that can be formed from five elements is assigned to a vertex, and the vertices are then connected by edges if and only if the corresponding couples contain no elements in common (Fig. 2). 15 13 [*I Prof. Dr. J. D. Dunitz and Prof. Dr. V. PreIog Organisch-chemisches Laboratorium der Eidgenossischen Technischen Hochschule 8006 Ziirich, Universitstsstr. 6 (Switzerland) 111 E. L . Muefterfies,Inorg. Chem. 6, 635 (1967). [21 This process has sometimes been called "pseudo-rotation", a term that has been also used in a quite different context (see J . E. Kilpntrick, K. S. Pitzer, and R . Spitzer, J. Amer. chem. SOC. 69, 2483 (1947)). [3] M . J. Gallagher and I. D . Jenkins in E. L . Eliel and N. L . ANinger: Topics in Stereochemistry, Vol. 3, Interscience, New York 1968 (in press). [41 F . H . Westheimer, Accounts Chem. Res. I , 70 (1968). 151 See, for example, S. Lipschutz, Finite Mathematics. Schaum Publishing Co., New York 1966. [61 D. Konig: Theorie der endlichen und unendlichen Graphen, Akademische Verlagsgesellschaft Leipzig 1936, reprinted by Chelsea Publishing Company, New York, p. 194. Course of Acid Hydrolysis of 4-Alkylidene- and 4-Arylalk ylideneoxazol-5-ones By W. Steglich, V. Austel, and A . Prox[*I In principle, water can add to the C=O or to the C-N double bond o n acid hydrolysis of 4-alkylidene- and 4-arylalkylideneoxazol-5-ones (I) to 2-acylaminoacrylic acids ( 2 ) . 1.5 Fig. 2 C The ten diastereomeric pairs of enantiomers obtainable by permutation of five different ligands in a trigonal bipyramidal arrangement may be specified by the two ligands in the apical positions (1,2), (1,3), . . . (4,5) in each case. If each diastereomer is now associated with one of the vertices of a Petersen graph, the fifteen edges each represent possible interconversion steps. Any sequence of interconversions i s thus associated with a corresponding path between vertices of the graph. For any such path the chirality of the resulting diastereomer depends o n the chirality of the diastereomer associated with the origin of the path and on the parity of the path (whether the number of edges traversed is even o r odd). In particular, a cyclic path leads back to the original enantiomer if the number of interconversion steps is even, and to the opposite enantiomer if the number is odd. From Fig. 2 it follows that a cyclic path leading to inversion of the original diastereomer must contain at least five interconversion steps. The probability that a sequence of five random steps leads back to the origin is easily seen to be 3 x 2 x 2 x 1x 1/35 or 4/81. Various stereochemical restrictions (e.g. two ligands linked so that they cannot simultaneously occupy apical positions, one ligand constrained to occupy an equatorial position) can be introduced by appropriate moditications of the graph (e.g. all paths passing through a given vertex or through a given sub-set of vertices may be regarded as forbidden). In Fig. 2 we have shown in addition to the usual representations A, B, and C of the Petersen graph another representation D that may have some mnemonic value for chemists. I n this new representation the ten couples (1.2). (1,3), . . . (4,5) are associated with the ten vertices of an adamantane skeleton in which the six secondary atoms are linked by the three diagonals of the corresponding octahedron. Notice that all cyclic paths that run exclusively along the adamantane skeleton contain an even number of edges and hence lead back to the original enantiomer; cyclic paths that contain an odd number of edges must include a n odd number of diagonals. Received: June 20, 1968 [ Z 817 IEI German version: Angew. Chem. 80, 700 (1968) 726 If H2*80 is used, the carboxyl group of the 2-acylaminoacrylic acid (2a) is labeled by route (a), but the acyl group becomes labeled by route (b). The position of the label can be easily determined, namely, by recyclizing the 2-acylaminoacrylic acids ( 2 ) by trifluoroacetic anhydride to the oxazolones ( 3 ) and opening these to 2-acylaminoacrylic acids ( 4 ) by H2160/H+. (3al H kz H kz (4b) On cyclization, the acid ( 2 a ) loses 50 % of its 1 8 0 , but (26) does not lose any. Opening of (3a) by H2160 according to route (a) yields (401, which in contrast to (2a) contains only 50 "/, of the 1 8 0 in the carboxyl group. However, (2b) gives (46) by mechanism (b), without loss of 1 8 0 . In the conversion of ( 2 6 ) into (46) the label of the acyl group migrates to the carboxyl group. Angew. Chem. internat. Edit. 1 Vol. 7 (I9681 1 No. 9

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