Jeremy I. Musher Belfer Graduate schoolof Science Yeshiva Univers~ty New York, New York 10033
Rearrangements in Five- and Six-Coordinate Systems
Every chemistry student knows that a tetrahedral carbon atom with four different substituents exists as two different isomers called D and L. A trigonal bipyramidal molecule such as a phosphorane with five different ligands can exist as 20 different geometrical isomers providing that energetics permit. An octahedral molecule, such as occurs throughout transition metal chemistry, with six different ligands exists as 30 different geometrical isomers provided that energetics permit, except for tris-chelates for which trans-ring linkages are forbidden so that the number is reduced to 16. There is thus a drastic jump in complexity going from a four-coordinate tetrahedral molecule to a five- or a six-coordinate molecule which serves to make the chemistry of these compounds a t the same time both interesting and intricate. And to show how the subject received so little attention over the years, it is only in the past year or so with the work of Gielen (I), Klemnerer (2), Balaban (3), and the nresent author (4). that the number and geometry of the stereoisomers in five- and six-coordinate compounds has become generally known. The present article is concerned with an analysis of the possible rearrangement or rearrangements consistent with the experiment. For example, with the molecule MezNPFl
(I) rearranges (5) intramolecularly by a process which takes two axial fluorines into two equatorial fluoriues. This can he interpreted as evidence for the stereochemistry of the Berry pseudorotation (6) mechanism which takes (I) into (11). I t can also, however, be interpreted as evidence for the process which takes (I) into (111) the mirror image of (11). Experiment cannot as yet distinguish between these two processes so that the exact stereochemistry .of the rearrangement is unknown. As this type of stereochemical uncertainty is quite general in five- and six-coordinate svstems it is not considered worthwhile to discuss the mechanisms involved a t the present time. Virtually all the information we have is obtained from nmr used with no greater sophistication than available ten years ago. It is, however, only recently that interest has developed in these compounds and their stereochemistry, and within the past few years a flurry of articles studying these rearrangements in one way or another has been generated. The next section considers the number of isomers in TBP's and octahedra and this is followed by a detailed analysis of rearrangements in TBP's and in octahedra. Number of Slereoisomers We now derive the number of isomers of labeled TBP's and octahedral molecules. There are clearly numerous ways to do this and we consider only two of each of the possibilities. For the TBP, label the ligand a t the top a and the bottom one b. There are ten different pairs, a , b, for each of which there are two ways of counting clockwise the remaining ligands, cde and ced. Hence 10 X 2 = 20. Another way to do this is to label the top axial ligand a 94
/ Journal of Chemical Education
running from 1 to 5. If again a clockwise sense is chosen for putting the numbers into the equatorial positions there are four ways of doing so for each a whence 4 X 5 = 20. Consider now octahedral complexes where we let substituents 5 and 6 be either trans- or cis-, respectively. In the trans case we can also fix substituent 4 and count its two neighbors, 1 and 2, 1 and 3, and 2 and 3, not referring to the intermediate substituent. As each of these occurs twice, from left to right and from right to left, the number of isomers is six. If we now let 5 and 6 he cis- we can choose the remaining numbers in coplanar pairs 1 and 2, 1 and 3, 1 and 4, etc., of which there are six which is multiplied by two when cis- and trans- orientation to 5 is considered. When the choice of up and down is made for the last two atoms the number reaches 24 whence 24 6 = 30. Another way of doing this is to fix 1 at the top and take all five trans pairs 12, 13, 14, 15, and 16. The remaining four numbers in each can be divided six ways among the four planar sites, whence 5 X 6 = 30. The number of tetrahedra, TBP's, and octahedra is also given by 4!/(4 X 3) = 2, 5!/(3 X 2) = 20and6!/(4 X 3 X 2) = 30.
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Trigonal Bipyramidal Molecules Fortunatelv the 20 and 30 transformations in the two cases can he grouped together according to the geometrical chanees involved in the rearranrements. We consider first the TBP whose set of 20 distinEt isomers can be generated from a single isomer by five different tunes of stereochemical rearrangements,- called "modes rearrangement" and the identity. These modes are easily obtained by considering the unique set of rearrangements carried out holding three, two, and one TBP substituents fixed plus the identity. First, keep the three equatorial ligands fixed and exchange the two axial ligands. There is only one such rearrangement and we say that this rearrangement which we denote as an aa process belongs to mode Ma. The remaining exchanges between pairs of like ligands, the equatorial-equatorial or ee exchanges of which there are three, give exactly the same isomer as the aa exchange and hence need not he considered further. The next rearrangement keeps two equatorial and one axial ligand fixed and exchanges one equatorial and one axial ligand. There are six such rearrangements utilizing each of the six axial-equatorial pairs arising from the three equatorial ligands and the two axial ligands. We say that these rearrangements which we denote as ae (or equivalently en) rearrangements belong to mode Mz. If instead of keeping the three ligands, two equatorial and one axial, fixed we rotate them, say in a clockwise direction, keeping the remaining two ligands fixed, theu we also get six new isomers. We say that these rearrangements which we denote as eea rearrangements belong to the mode Mp. This eea rearrangement is the only three-ligand rearrangement necessary to he considered as it is easily seen that an aae rearrangement gives a product identical to that in Mp while an eee rearrangement gives the identity. The last two modes to he considered involve the exchange of four ligands keeping only one equatorial ligand fixed. The first of these which we denote as aeae, carries the four ligands in a cyclic way so that one axial ligand goes to an equatorial site, that equatorial ligand to an axial site, the second axial ligand to a second equatorial site, and this equatori-
al ligand goes to the site of the first axial ligand. This sounds complicated but it is really quite simple as it merely involves four ligands rotating about a fifth ligand as an axis. There are three such rearrangements keeping each of the three equatorial ligands respectively fixed, rotating the other four in, say, a clockwise manner. The mode is referred to as MI. This was the first mode considered in all of phosphorane chemistry since it is the mode which corresponds to the original mechanism, called Berry pseudorotation, BPR, proposed by Berry (5) in 1960 to explain the indistinguishability in the nmr of the five fluorine atoms in PFs. The remaining rearrangement which also involves four ligands is a double pair-wise exchange of axial and equatorial ligands or an aexae process and the mode is referred to as ME. Curiously enough these rearrangements which are usually indistinguishable from their BPR analogs were only first considered in the past year (4). Again there are three distinct such rearrangements, holding each of the three equatorial ligands fixed in turn. This rearrangement can be called a disrotatory pseudorotation, DPR, as it treats the four ligands in terms of two pairs which can he looked a t as rotating in opposite directions. The five modes plus the identity, Mo, clearly account for all the 20 rearrangements possible in a TBP system. These can be drawn schematically as
IV M,111
