Chung-Sun Chung National Tsing Hua university Hsinchu, Taiwan Republic of China
Computation of the Number of k0mers of Coordination Compounds Containing Different Monodentate Ligands
The students in the coordination chemistry class in Tsing Hua University have a great interest in the methods of counting isomers of complexes. The number of isomers can be approached by using models ( I ) , drawings ( 2 ) ,permutation n o u n. formalism (3). . . . Polva's . theorem (.4.)..Bailar's scheme (5). . .. and computer programs (6). For the purpose of teaching in t h e undergraduate chemistry course Bailar's scheme ( 5 )is the most suitable of these and has been written in the inorganic textbooks (7-9). For some complexes, the numher of isomers is too large to use the Bailar's scheme. A simple method of counting isomers is essential in this case. T h e purpose of this article is to outline a simple method to calculate the stereoisomers which can be theoretically formed. Instead of employing the unfamiliar permutation group formalism, the problem of determining the numher of isomers of complexes can be approached by symmetry considerations alone.
.,
The Isomer Numbers for the Complexes which have n Different Monodentate Ligands .---~ Coordi-
The svmmetrv number. 0. is the number of nonequivalent ways in whicl; the atoms of the molecule can be interchanged by rigid rotation of the molecule in space and remain completely indistinguishable from some other such orientational rearrangement (10).If a complex Mahc, . . ., where a, b, c, . . . are dzferent monodentateligands, has the coordination number, n, then there are n! arrangements of the ligands in the complex. The isomer number, r, is the total number of the geometrical and optical isomers of the complex. Each isomer of Mabc, . . . can he rotated to give then! possible arrangements. The number of rotational operatioh needed equals the symmetry number for Ma,, provided the coordination number and geometry of Ma, and those of Mahc, . . . are the same. Thus, r ~ ~ b c. U. M . ~ ,= n .I
(1)
where r ~ ~. .,bU M~~ ,and ., n are the isomer numher of Mabc . . ., symmetry number of Ma,, and coordination number of these complexes, respectively. Therefore, the isomer numher of the complex containing n different monodentate ligands can be obtained by
Isomer Number
naI on h~moer
Sn~cturc
S~mmetryNumoer 01 the Comp er
01 the Comp ex Ootameo oy t q n 21
Examples are summarized in the table
Linear Bend Angular Trigonal Planar Trigonal Pyramidal Tetrahedral Square Planar Trigonal Bipyramidal
Literature Cited
Tetragonal Pyramidal Octahedral Trigonal Prismaticat Pentagonal Bipyramidal Cubic
161 Bennett. W. E.,lnrrrpChem..8. 1825 119691. (71 Pureell. Keith F.. and KULZ,John C., "lnl,rca-anicChemistry." R. Savnders Ca.. Philadelphis. 1977. p.630. 18) Jcmos. Mark M., "Elementary Cordinatiun Chemistry? Prentte~Hall.Inc. Endewmd Cliffs. N.J.. 1964.p 179. 19) Duu&s. Rodie E., and McDaniel. Dad H., "Cmeepts and Models of Inorganic Chemistry," Blaisdell. New Yurk. 1965. p. :MS. 110) Davir.JoffC.Jr.. "Advanced PhysicalChemistry~RunaldPrers.NewY~rk.1965.~. 296.
Square Antiprismalical Tetraaonal Prismaticat
398 / Journal of Chemical Education
Chem. Srnr.. 75.171511953)
W.
