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THE NUMBERS AND STRUCTURES OF ISOMERS OF HEXACOVALENT COMPLEXES JOHN C. BAILAR, JR. University of Illinois, Urbana, Illinois
IN
1893, Werner suggested that hexacovalent complexes are octahedral and that the violet and green forms of dichlorotetrammine cobalt(II1) chloride are stereoisomers. Ever since that time, chemists have bad a continuing interest in the stereoisomerism of hexacovalent complexes containing varying numbers of different ligands, and in methods of counting these isomers. Several authors have published articles on this subject. MainSmith (1) has prepared extensive tables of the isomeric forms possible for monodentate and bidentate groups, and Trimble (a) has published tables for many non-branching polydentate ligands as well as for monodentate ligands. Tables prepared by Fernelius and Bryant (3) show the numbers of isomers theoretically possible for complexes containing ligands which have three or more coordinating groups, but do not show their structures. None of these authors gives details of t l e methods which he used in counting the isomers or determining their structures. I n general, however, they have drawn figures or built models, progressing from simpler forms to the more complex, and eliminating duplicates. The purncse of this article is to outline a simple method of counting the stereoisomers which can be theoretically formed by monodentate or polydentate ligands and of showing their structures. No account is taken here of isomerism which may arise because of isomerism in the ligand itself; this may usually be calculated easily after the number of possible arwngements in the octahedron bas been found. Any optical isomerism shown by the octahedral complex enters as a secondary consideration, as will be described later.
The groups "c", "d", "e", and "f", which occupy the equatorial plane of the octahedron, can be arranged in three different ways, with "en trans to either "d", lie", or "f". If "c" is trans to "d", the symbol cd is written directly below the symbol ab. Groups "en and "f" can then be only trans to each other; this is indicated by the symbol ef. The entire configuration which has been described is denoted by the symbol ab cd ef
Chernyaev (4) has used a somewhat similar system to denote configurations of octahedral complexes containing monodentate ligands. His system differs widely from the one described here in describing complexes containing chelate rings, and is not adapted for use in counting the numbers of isomers. The fact that the complex ab cd ef
is asymmetric and optically active is not indicated, but can easily be seen by drawing the octahedron, or, with a little practice, from the symbol itself. It would be possible, of course, t o write the symbol according to a predetermined convention, and so to designate the relative configurations of the isomeric complexes. For example, one might say that the dextro configuration is indicated when the letters are placed in alphabetical order from top to bottom and, secondarily, from left to right. The symbol written above would then represent the configuration
ISOMERS CONTAINING S I X DIFFERENT GROUPS
The method starts with a complex containing six different monodentate groups. These will he designated by the small letters "a", "b", "c", "d", "en, and "f". It will be supposed t,hat one axis of the octahedron is vertical, and that group "a" is a t the top. Of the rem a i ~ n gfive groups, one occupies a unique position trans to "a", whereas the other four are all .alike in that they occupy positions which are cis to "a". Suppose that grou? "b" is trans to "a". This is indicated by placing the two letters side by side:
which would be called dextro. The mirror image, levo, form would be indicated by interchanging the symbols of any two ligands which are trans to each other, or by interchanging any two trans pairs. Thus, it could be represented by ba cd ef,
ab do ef,
ab cd fe,
ab ef ed,
etc
Simplifications of this might be introduced by adopting other conventions, but the system has been found to be too complex to be useful. The configurations of optiJOURNAL OF CHEMICAL EDUCATION
cally active complexes are more easily expressed in other ways. The possible isomers in which "b" is trans t o "a" are shown by the symbols ab cd ef
ab ce
df
ab of de
Similarly, there are three sets of symbols for each of the configurations in which "c", "d" , "e", and "f" are trans to "a". All of the possible complexes [Mabcdefl are shown by the fifteen symbols given in Table 1. In that table, the horizontal rows are numbered and the vertical rows are lettered only for convenience in the discussion which follows. Since each of these complexes TABLE 1
is optically active, there are thirty possible isomers. The presence of two or more identical groups in the complex or the introduction of a chelate ring represents a limit,ation of the pattern and reduces the number of possible isomers. I n no case i s it possible to have more than thirty different configurations. ISOMERS CONTAINING IDENTICAL GROUPS
Suppose we wish to find the number of possible stereoisomers of
$w f
NHaQ;;
NO2
, NO2
NO2
2N 0$Hf
\/
NO*
CI
NO2
and &,2N, SN, 6 L and 6 M , and 4N and 6N. When the duplicates are crossed out, six symbols remain. These are shown in expanded form in Figure 1. Of the isomers shown in Figure 1,1L, 1M, 2L, and 4N are optically inactive, for each has a plane of symmetry. This is shown in I L , 1M, and 4N by the fact that like groups are trans to each other. It is easily seen in 2L if the octahedron is turned so that the chlorine atom and the pyridine molecule are on the vertical axis:
Isomers 2M and 2N are asymmetric, so there may be four optically active forms. Three isomers of the ion [Pt (NH& py2 Clz]++have been isolated by Chernyaev and Rubinshtein (6). This does not exhaust the possibilities, however, as can be seen if we set NH3 = a = b, py = c = d, and C1 = e = f. Substitution of "a" for "b", "c" for for G L f I ) in . Table 1 leads to Table 3. "p,and TABLE 3
one of which has been prepared by Rubinshtein (6). Since "a" and "b" are the same and "c" and "d" are the same, we may rewrite Table 1, substituting "a" for "b" and "c" for "d". This gives Table 2. TABLE 2
Inspection shows that symbols 1M and I N represent a single configuration, as do 2L and SL, 2M, SM, 4L VOLUME 34, NO. 7, JULY, 1951
Of the possibilities shown in Table 3, I N , 2N, SL, S M , SN, 4L, 4M, 6L, 6 M , and 6N may be eliminated, since they are duplicates of others. Of the five remaining configurations (Figure 2) only 2M is optically active, for each of the others has a t least one pair of identical groups trans to each other, and so has a plane of symmetry. By substitution in Table 1 and inspection of the resulting symbols, it can be shown that the ion [Pt(NHa)-
TABLE 4
(C2H5NH2)py(N02)C12]+can exist in three optically inactive, and twelve optically active, forms. Chernyaev (7) prepared the inactive isomers by the addition of chlorine to the three isomers of the planar ion [Pt(NHa)(CzH5NH2)py(N02)]+. This oxidizes the platinum from the +2 state to the +4 state, and, simultaneously changes the coordination number from four to six. The chlorine atoms occupy the two new positions:
TABLE 5
ISOMERS CONTAINING CHELATING LIGANDS
The introduction of a chelating ligand limits the number of possible isomers because the chelate group can span only cis positions. The case of [M(AB)cdefIL is represented by the pattern of Table 1,except that l L , 1 M , and IN must he eliminated, for AB cannot occupy trans positions. Twenty-four isomers are theoretically possible, all of them being optically active. These can be shown in octahedral form by putting the letters A, B, c, d, e, and f on the appropriate corners of the octahedron and then ronnecting the capital letters. For the compound
4 gives Tahle 5. Structures ZN, 311.1 and Y N are the same as 2M, so can be crossed out. Of the remaining three structures, 2M is asymmetric. Bailar and Peppard (9) prepared all three forms of the ion, and resolved the one corresponding to formula 2 M . The presence of two or more similar chelate rings (AB) introduces a new factor. Although -4cannot he trans to the B in its own chelate ring, it can be trans to the B in another chelate ring. It is therefore necessary to distinguish between the chelate groups. Consider the rase [M(AB)*ef],which, for convenience, will he written
[M ( A A ) cdef] ab edef
still further limitation is imposed, as is shown in Table 1 (A = a = h). I L , IM, and I N are eliminated because the group (AA) cannot span lrans positions, and SL, 4L, 4M, JL, 5M and .5N, herause they are duplicates of ZL, 2M, SM, ZN, SN, and 4N, respectively. The remaining six configurations are all asymmetric, so there are twelve possible isomers. The case of
first studied by Chaussy (a), and late< by Bailar and Peppard (Q), represents a still further limitation, since the groups "c" and "d" are identical, 8s are "e" and "f". Substituting "c" for "d" and "e" for "f" in Table In accordance with custom, chelate groups will be shorn by capital letters, each ~ u e hgroup being enclosed in parentheses. ( A n ) represents an unsymmetrical chelating ligsnd, such as NHsCH~COO-, and (AA) or ( B B ) , a symmetrical one, such as NH:CH3C&NH,.
Snbst,itntion in Tahle 1 gives Table 6
2
AA' BB' ef
AA' Be B'f
AB' BA' ef
AB'
S
4
I
[$,I
Be A'f
Ae A,f BB'
AB' Bf .ire
[k A'B']
8
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Configurations I L , I M , IN, 4N and 6N are eliminated because a chelating group cannot span trans positions. Now, however, i t must he remembered that A and A' are identical, as are B and B', and were distinguished only for the purpose of the isomer count. Configuration 2N is therefore identical with 2M, 5 L with SM, 4L with 3N, and 6M with 4 M , so one member of each of these pairs can be eliminated. Of the six configurations that remain, all but 3L are asymmetric, so eleven different stereoisomers are theoretically possible. The symmetly of structure SL may not he immediately apparent if it is written as
but is easily seen if it be written in the equivalent form
If the chelate ring is symmetrical; that is, if A and B are identical, and A' and B' are identical, the configurations in Table 6 simplify to those shown in Table 7. Since A and A' were distinguished only for the isomer count and are actually alike, the configurations
"c", and in which "e" is trans to "d" or "f". This leaves only dM, SM, 3N, 4 M , 4 N , 5M, and 6N, which are shown in Table 8. When duplicates are eliminated, TABLE 8 AA BB' A'A' AA ' BB' AA'
E,] [El only three configurations remain (Figure 3). Inspection shows that isomer SN is asymmetric. The sym-
metry of isomer 3M is easily seen if the structure is written in the equivalent form BB' AA' A'A
TABLE 1 AA' AA'
8
ef
AA ' Ae A'f
of Table 7 simplify to only two, which are represented by 2L and 2M. The latter is optically active. Many examples of this type of compound have been prepared; the best known perhaps, is [Co enr (NH8)C1]++, the cis isomer of which was the first complex ion to he resolved into optically active forms (10). The system can, of course, be extended to complexes cpntaining fused chelate rings if the same limitations are kept in mind. Thus, it can easily he shown that the bisdiethylenetriamine cohalt(II1) ion, [Co dien2]+3, can exist in four forms, of which two are mirror images of each other. The formula for a complex of this type may be written [M (ABA) (A'B'A')] abo
d e f
I t is not necessary to distinguish between the two A groups in a single chelating molecule, for they are alike and occupy exactly similar positions. Even before substituting in Figure 1, we can eliminate the configurations in which "h" is trans to "a" or VOLUME 34, NO. 7,
nnY,1957
AA' BA' AB'
The fact that isomer 3M is symmetrical can be seen best if the projection of the octahedron is redrawn so that one of the horizontal axes points toward the reader:
If the ligand molecule is unsymmetrical, as in the chromium (111) derivatives of the pyridyl azo dyes prepared by Liu ( I I ) ,six optically active pairs are theoretically
r
1+
possible. However, because of the presence of the double bond in the azo group, the 3M forms AC BB' A'C'
are doubtless more stable than any of the others, and may he the only ones that can exist. In the ion ( A ) prepared by Dwyer, Gill, Gyarfas, and Lions ( I t ) , the two ends of the coordinating agent are different, so this complcx illustrates the structure [M (ABCDEF)]. Elimination of the symbols in Figure 1
\
Qo
CH=NCH, CH,S CH,CH,OCHZCH N-CH
/
c\o-/
in which "a" is trans to W', "b" is trans to "c" and so on, leaves only structures BM, SM, SN, 4M and 5M. None of these are duplicates and all of them are optically active. They are shown in Figure 4.
isomers are therefore possible. As Dwyer and Lions have pointed out (IS), the presence of the double bonds in positions B and B' makes isomer 2M much less strained than any of the others. The same principles can be applied to branched-chain ligands, if care is taken to eliminate duplicating and impossible structures. In complexes of the sexidentate ligand
(enta), for example, the nitrogen atoms cannot be coordinated in positions trans to each other, nor can either of them be trans t o a carboxyl group to which it is directly attached. This means that in terms of the pattern [M a(b) cd(e) f], "c" cannot be trans to "a", "b", or "d" and "d" cannot be trans to "c", "e" or "f". When the configurations involving any of the combinations ac, bc, cd, de, or df are eliminated fromTable 1, only stmctur.es SM, 3N, 4M and 5M remain. If these are transliterated to apply to the structure [M A(A)BBf (A1)A'], they all lead to the same symbol, AA' AB' BA'
The ions (B) prepared by Dwyer and Lious (13) and (C) reported by Das Sarma and Bailar (Id), are similar
The ion [Co ental- can exist, therefore, in only one pair of mirror-image isomers (15):
LITERATURE CITED
CO
to the one just discussed, hut because the ligands in them are symmetrical, they belong to the type [M (ABCC'B'A') ],and formsSN and4M become identical. This may not beimmediately apparent, hut becomes so from a study of the symbols. Since the ligand is symmetrical, A=F, B=E, and C=D. If we interchange A and F, Band E , and C and D, the symbol for SN, which is AD ' FC BF becomes EA CE DB
which is the symbol for 4M. Four pairs of mirror image
' NOTEADDEDIN PROOF:The formula of the Ligand should show an additional H attached to each middle N, thus, ...=NCH2CH,NHCH,CH,NHCH1CH1N=. . .
( 1 ) MAIN-SMITE, J. D., "Chemistry and .ktomie Structure," Ernest Benn, Ltd., London, 1924, p. 97. R. F., JR., J. CHEM.EDUC.,31, 176 (1954). ( 2 ) TRIMBLE, W . C. AND B. E. BRYANT, J . -4nt Chen~.Sac., ( 3 ) FERNELIUB,
.-,
?< 1776 l,A""",. lO67>
( 4 ) CHERNYAEV, I. I . , Ann. inat, platine, 6 , 55 (1928): C. A,, 23, 1582' (1929). ( 5 ) R U B I N S H . ~ I N . A. M.. Ann. aecteur. olatine. Inst. chim. o m . (u.s.s.R.) NO. 13,'21 (1936); C. k.,3 l , ' l 3 1 8 ~((1937; I . I . , AND A. M. RUBINSHTEIN, Con~pt.rend. ( 6 ) CHERNYAEV, acad. sn'., U.R.S.S. (N.S.) 1, 187-0 (189-92 in English) (1934) C. A , , 28, 30215 (1934). (7) CHERNYILEV, I. I., Ann. insl. platine, 1927, No. 5 , 102-118; C . A,, 23,1581' (1929). ( 8 ) Cnaussy, F., Dissertation, Zurich, 1910. JOHNC., JR., AND DONALD F. PEPPARD, J. Am. ( 9 ) BAILAR, Chem. Soc.. 62. 105 (1940). ( 1 0 ) WERNER, ALPRED AND\. L.'KING,Ber., U, 1887 (1911). ( 1 1 ) LIU, JENNIECHINO-I,Thesis, University of Illinois (1951). ( 1 2 ) DWYER,FRANCIS P., NNDAS. GILL, ELEANORA C. GYARFAS,AND FRANCIS LIONS,J. Am. Chem. Sac.. 7 5 , 1526 (1953). P., AND FRANCIS LIONS,J . Am. Chem. ( 1 3 ) DWYER,FRANCIS Soc., 69,2917 (1947); 72,1545 (1950). BASUDEB, AND JOHNC. BIILLR,JR., J . Am. ( 1 4 ) DAS SARMA, C h a . Soe., 7 7 , 5476 (1955). ( 1 5 ) B u s c ~DARYLE , H., AND JOHNC. BAILAR, JR.,J . .4m. Chem. Sm., 75,4574 (1953).
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