Identification of Molecular Point Groups Wai-Kee Li The Chinese University of Hong Kong, Shatin, N.T., Hong Kong
Symmetry and identification of molecular point groups are now standard topics in advanced undergraduate physical chemistry or inorganic chemistry courses. In the texts that treat these topics, many molecules are usually given so that students can practice identifying point groups. While these exercises are useful in their own right, it is sometimes more interesting and challenging if the pmblems are set the other way around: Ask the students to write a molecular structure for each of the point groups that are given. A few such problems are given below as examples. This type of problem also helps students understand the relationship between a group (with high symmetry) and its subgroups. Questions 1. Consider the series of octahedral complexes
Figure 1. The structure of adamantane.
[MA,B,(XX)pOrY)ql
where A and B are monodentate ligands; (XX)is a didentate ligand with two identical donating groups; and 0 is a didentate ligand with two different donating groups. An example of (3x1 is HzNCHzCHzNHz
An example of (XY) is (Me)zNCH2CHzNHz In the general formula given above, the following sum is always 6. m+n+Zp+Zq = 6
Write structural formulas for complexes that have the symmetry requested below and that meet the other specified requirements. a. Cl b. Cl c. C2
d. C2
with at least one monodentate ligand with no monodentate ligand with at least one monodentate ligand with no monodentate ligand
e. C3 f.
c,
CIOC/HI,-.
(where n = 1,2,..., 16)
Draw a member of this series that belongs to each of the following point groups. a. CI b. C, c. c, d. Cz. e. C.7" f.
D2d
3. Cycloodatetraene (cot), Cs&, has the "tub" structure shown in Figure 2 (let%).This molecule belongs to the D2d group, whose symmetry operations are visualized easily as in Figure 2 (right). Plus signs indicate atoms that are above the plane of the paper; and minus signs indicate atoms below. Consider the halogen-substituted cot species below.
Choose a molecule from this series that belongs to each of the following point groups. a. C1 2. The novel compound adamantane (Cl0HI6)has the structure shown in Figure 1.This molecule has Td symmetry and two types of carbon atoms. Consider the chlorinated adamantanes.
b. C2 c.
c,
d . S, e. c z u
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Figure 2. Cyclwctatetraene:(left ) the structure, (right) the symmetry operations.
Figure 3. Answers to Question 1.
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Journal of Chemical Education
Figure 5. Acceptable answers to Question 3.
Acceptable Answers Notice t h a t only one acceptable answer is givien below for each of the questions.
Question I. The suggested answers for Qxstion 1are given in Figure 3.
Question 2. The answers to question 2 are given in Figure 4. As a variation, instead of substituting hydrogens with halagens, replace some or all of the methine groups with nitrogen-r replace the methylene groups with oxygens. The most well-known of such "derivatives" of adamantane is probably hexarnethylenetetramine (HMT), where all four methine groups are replaced by nitrogens. Both HMT and adamantane have Tdsymmetry.
Figure 4. Acceptable answers to Question 2.
Question 3. The answers to question 3 are given in F i e 5.
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