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Unique Atoms and the Identification of the Symmetry Elements of Molecules John P. Graham* Department of Chemistry, United Arab Emirates University, Al Ain, United Arab Emirates ABSTRACT: Explicitly stating that every symmetry element of a molecule must contain all unique atoms enables students to more easily eliminate from consideration absent symmetry elements and identify those elements present more readily. Additionally, in-class assessment of the consequences of this rule leads to interesting student discussions and conclusions. KEYWORDS: Second-Year Undergraduate, Upper-Division Undergraduate, Inorganic Chemistry, Inquiry-Based/Discovery Learning, Problem Solving/Decision Making, Molecular Properties/Structure elements are not present in a molecule, but also they tend to find the symmetry elements that are present more rapidly. Although the applicability of the rule is limited to molecules containing at least one unique atom and most informative for molecules with two or more unique atoms, it is noted that small molecules with one or more unique atoms are often used to introduce the concepts of symmetry and symmetry operations.
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ost modern undergraduate inorganic textbooks cover the basics of molecular symmetry, starting with symmetry elements and operations and working up to applications in vibrational spectroscopy and molecular orbital theory.1 In my experience, symmetry tends to be one of the more challenging topics in inorganic chemistry for undergraduates. This may be due to required 3D visualization of molecular structures and their manipulation in space. Some excellent computer tools have emerged in recent years that have made it significantly easier for students to visualize symmetry elements and the effects of symmetry operations, in particular those operations that cannot be performed on a physical model (such as reflection in a plane and inversion).2,3 These programs are excellent tools for in-class use and at-home practice in the identification of symmetry elements. Since adopting such tools in my classes, I have found that students have much greater success in identifying and understanding the effects of symmetry operations. However, with regard to identifying symmetry elements, I find that some students still have difficulty seeing that certain symmetry elements are not present; that is, convincing themselves of their absence. Sometimes proving that something is not there is much harder than proving it is present! Often a student unable to find a symmetry element will be reluctant to eliminate the possibility of its existence. To help students confidently eliminate the possibility of the presence of some symmetry elements in certain cases, I have found it helpful to point out the following simple rule: Unique Atom Rule: Every symmetry element must contain all unique atoms. The rule is useful for molecules that contain one or more unique atoms. It is the logical consequence of the fact that a unique atom must not move during any symmetry operation. Despite its simplicity and obvious nature, this rule is not generally explicitly stated in textbooks.1 Atoms can be unique by element identity or environment. Recognizing unique atoms by element type is trivial; recognizing unique atoms by environment requires consideration of the structure and symmetry properties of the molecule. The rule can be introduced initially in terms of unique element atoms within the molecule and later elaborated to include unique atoms in general. With this simple rule in mind, students not only can prove to themselves that certain symmetry Copyright r 2011 American Chemical Society and Division of Chemical Education, Inc.
Figure 1. Structures of CH2ClBr and ClF3O. Unique atoms are highlighted in blue.
Two simple examples are given in Figure 1. For CH2ClBr, the realization that all symmetry elements must contain C, Cl, and Br quickly leads to the conclusion that no Cn rotation axis can exist. The rule also makes the location of the only symmetry element, a σ plane, immediately apparent. The student can stop looking for additional symmetry elements at this point when he or she considers the unique atom rule. The disphenoidal structure shown for ClF3O is an example where the unique atoms are defined by environment as well as element. In this case, the O and Cl atoms are unique by element and the equatorial F atom is unique by environment. It is therefore immediately apparent that there can be no Cn rotation axis of symmetry as there is no single straight line containing the 3 unique atoms. It is also clear that the only plane of symmetry possible is the plane defined by the Cl, O, and equatorial F atoms. This is indeed a plane of symmetry and the student need not look further for additional symmetry elements because of the unique-atom rule. When students are asked to discuss this rule in class, they often create their own rules as a result of the requirements imposed by unique atoms. Some conclusions from a recent in-class discussion were Published: April 20, 2011 1010
dx.doi.org/10.1021/ed1011508 | J. Chem. Educ. 2011, 88, 1010–1011
Journal of Chemical Education
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• If there is one unique atom in a molecule, the only possible location for an inversion center is where that atom exists. • A molecule with more than one unique atom cannot have an inversion center. • If there are two or more unique atoms in a molecule, there can only be at most one Cn rotation axis. The unique atoms must all exist in a linear arrangement for this Cn axis to exist. • If there are three or more unique atoms in a molecule that are not arranged linearly, there can only be at most one plane of symmetry. The plane of symmetry, if present, is that defined by the unique atoms. There can be no additional symmetry elements and hence point group must be either Cs or C1. The student-derived rules are clear consequences of the unique-atom rule and probably not in themselves worth memorizing. However, it is an interesting exercise to see what conclusions students will draw from the unique-atom rule. This simple rule can lead to easier visualization of symmetry elements and, moreover, easier elimination of those that do not exist. Additionally, consideration of the consequences of the unique-atom rule can lead to interesting in-class discussions and student derived conclusions.
’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected].
’ REFERENCES (1) For example: Housecroft, C. E.; Sharpe, A. G. Inorganic Chemistry, 3rd ed.; Prentice Hall: New York, 2008. Atkins, P.; Overton, T.; Rourke, J.; Weller, M.; Armstrong, F. Shriver and Atkins’ Inorganic Chemistry, 5th ed.; Oxford University Press: Oxford, 2010. Miessler, G. L.; Tarr, D. A. Inorganic Chemistry, 3rd ed.; Prentice Hall: New York, 2010. (2) Charistos, N. D.; Tsipis, C. A.; Sigalas, M. P. J. Chem. Educ. 2005, 82, 1741. (3) Cass, M. E.; Rzepa, H. S.; Rzepa, D. R.; Williams, C. K. J. Chem. Educ. 2005, 82, 1742.
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