but if it can be shown that some odd number of interchanges yields the same symbol, symmetry is established. The symbol given here may he converted in three steps: B'A
B 'A
(1) BA', el
( 2 ) A'B,
ef
A 'B (3) B'A ef
to a symbol differing only in the assignment of primes, which is quite arbitrary. On the other hand, a symbol like To the Editor: Bailar (J. CHEM.EDUC., 34, 334 (1957)) mentions a possible convention for associating his symbols for hexacovalent complexes with specific confignrations, but has found it too complicated to be useful. It may be of interest, however, t o point out some simple properties that the symbols have when his convention is followed. The convention amounts t o reading down the columns of the symbols, and placing the letters counterclockwise around the hexagonal diagram; so the symbol
AA' BB' ef
may seem symmetrical, but it can he converted to an equivalent form only by an even number of interchanges-for example, one must switch both ends of the ligands-so that its optical activity is not ruled out. But the symbol of a chelate with symmetrical tridentate ligands, AA.'
--
RR'
AA'
is associated with the structure
An "interchange" operation on a symbol, by which is meant either the exchange of any two trans pairs, or the reversal of any one trans pair, forms the symbol of the mirror image of the structure. If the structure is o p tically active, any odd number of interchanges will yield a symbol representing its enantiomorph, and any even number will yield a symbol equivalent t o the original. If the structure is not optically active, then it is its own mirror image and any number of interchanges will yield an equivalent symbol. Any symbol in which an obvious interchange does not change the structure, as for example &a
ac
ed or ac ef de
clearly represents an optically inactive form. The symmetry may he less obvious with chelate structures, such as AB' BA' ef
VOLUME 34, NO. 12, DECEMBER, 1957
looking very much like the preceding one, is converted to its equivalent either by one interchange of the AA' pairs, or alternatively by three reversals, showing that its structure is optically inactive. Bailar mentions an example of an unsymmetrical tridentate ligand, a-pyridyl-azo-o-phenol, and says in passing that for the complex formed when two molecules of this coordinate t o a chromiurn(II1) ion, six optically active pairs of structures are theoret,ically possible. Interchanges on the symbols for these "six pairs" reveal, however, that the structure represented bv AA'
--
RR'
CC'
must have only one configuration, since three reversals will yield the original. It has other equivalent forms such as AA' B'B CC'
This turns out t o he an interesting example of a structure which may be rotated into its mirror image, and hence is not optically active, even though it has no plane of symmetry.
(Letters continued on page 6%')
