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Ligand Reorganization in the Trigonal Bipyramid.

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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
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
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.
3 2
Fig. 1
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
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).
[*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 ) .
Fig. 2
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)
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+.
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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