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Dean H. Johnston, Otterbein University
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Symmetry planes in C4v molecules

How much detail do you go into when discussing symmetry planes in C4v molecules? There appears to be a semi-consensus that the vertical (σv) planes should contain as many atoms as possible, with the second set of planes (σd) bisecting the first.

But as I discuss in a blog post, this is not required and not always followed, especially if you're using computational chemistry software like Spartan. What do others do? Are you explicit about defining the difference between σv and σd, or do you not go into that much detail?

David Harding, Walailak University
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This is a problem I encountered when using the Symmetry website with my students. Both Dean and I would like to know very much what other members of the community think. The semi-consensus to place the vertical planes so that they contain as many atoms as possible seems to be more of a recent thing (see Introduction to Molecular Symmetry by J. S. Ogden, 2001 (https://global.oup.com/academic/product/introduction-to-molecular-symmet...). Is it the case that in Cotton's time, no such consensus existed and he simply chose to place the two sets of mirror planes in the way he did? Has this meant that it continues to be taught in this way even though it can be confusing for students? All thoughts and insights most welcome, David
Kari Young, Centre College
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I discuss the difference between σv and σ using the same "semi-consensus" explanation that Dean describes, but I tell students they will never be penalized for mislabeling or misusing v vs d. For the senior undergraduates in my inorganic courses, the distinction is interesting but not necessarily important.

For what its worth, Harris and Bertolucci use the same definition in Symmetry and Spectroscopy, "A point of nomenclature can be introduced before we leave the C4v point group. The C4v, exemplified by the molecule BrMn(CO)5...contains two kinds of vertical mirror planes. One kind goes through the central atoms...and is still designated σv. The other kind passes through the cental atoms but bisects the equatorial C-Mn-C angles. It is called a σplane, the 'd' standing for 'dihedral.'" (pp 18-19). This text was first published in 1978, while the first date on Chemical Applications of Group Theory is 1963.

We do however discuss in class the need for two different kinds of mirror planes designated differently. We also talk about of the x and y axes in other point groups are assigned somewhat arbitrarily and how we need to agree on which character tables to use. For example, the ones in Cotton's book are different from the ones in Miessler, Fischer, and Tarr (5th ed) for the C2v point group.  In class, I have never used the character table to "prove" the orientation of a molecule the way Dean does in his blog post, but I can imagine doing so in my office with a very interested student.

Joseph Keane, Muhlenberg College
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Per my other posts on symmetry topics, It's evident that I should not be voting on how σv vs σshould be defined.  However, I am happy to share the following excerpts from the current draft of my (POGIL) inorganic workbook.

"Reflections are further designated according to their orientations with respect to the rotation axes.  A reflection through a plane that is perpendicular to the principal rotation axis is called horizontal and symbolized σh.  A reflection through a plane that is parallel to the principal rotation axis is called vertical and is typically symbolized σv."

"In a rigorous analysis, vertical mirror planes that bisect acute angles formed by groups extending away from the principal rotation axes are labeled σ(for dihedral) rather than σv."

"Much like the difference between C2’ and C2’’, the σv vs. σd distinction is a minor point that typically does not impact our applications of symmetry at this level."

In discussion, I clarify that, while I like to see the C2’ vs. C2’’ and σv vs. σd distinctions in lists of symmetry elements/operations, I don't penalize as long as they get the complete counts (of Caxes and/or vertical mirror planes) correct.

My hope is that the above text reflects consensus.  Feedback from the VIPEr group has been helpful in the workbook's development, and I welcome any criticism of the above, either messaged directly or shared on the forum, no worries.

 

 

RozaGlice
Great post!
Sabrina G. Sobel, Hofstra University
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I agree with Kari Young and Joseph Keane. I define the vertical and dihedral mirror planes the same way as they do, but I do point out that Spartan and other common molecular modeling programs create arbitrary axes that may not correspond to what we do in the analog world. I don't make a big deal about the exact labeling of the vertical and dihedral planes as long as all are represented. Students need to have a clear consistent definition for their own analyses. Molecular modeling represents another level of complexity since it only shows plots of composite, mixed atomic orbitals without listing the mixing - you have to look at the output matrix to figure that out.

Adam R. Johnson, Harvey Mudd College
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Like others have said, I explicitly point out the 2 types of mirror planes in C4v but also say that I don't grade on the labels as long as it is used consistently. Similarly, I don't grade on the nomenclature of axis systems (is water in xz or yz?) becaue you get the same internally consistent answer no matter what. Conventions are useful but as long as the draw an axis system and define their symmetry elements using that axis system, I'm ok with it.