Symmetry and Group Theory- Point Group Tips and Practice 7 (K2ReH9)

Time to add another example to point group practice problems. I got this complex from the publication below:

http://pubs.acs.org/doi/abs/10.1021%2Fic50014a026
S. C. Abrahams, A. P. Ginsberg, K. Knox

Inorg. Chem., 1964, 3 (4), pp 558–567

Publication Date: April 1, 196

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Dr. Frank Hoffmann was very kind enough to contact me and "make the threecapped trigonal prism  visible through the polyhedral representation in VESTA.." So, he sent me the Vesta file and I just changed the color of the atoms so that it looks clear on my blog's template. You can see the screenshots below.  As I mentioned in my other posts, there is a free online course named "The Fascination of Crystals and Symmetry" on iversity.org . The course has started three weeks ago. So, you are not late to register and start enjoying the symmetry. Just check it out:

https://iversity.org/courses/the-fascination-of-crystals-and-symmetry

 Hydrogens are black, potassium ions are blue and rhenium ions are shown as pink.

 ------------Update-----------


I tried to draw and show the geometry, but I really couldn't figure out how I am supposed to show it using a software. I think you can see one of my unsuccessful attempts on Avogadro below.

  an unsuccessful drawing attempt!

Anyway, you can see the metal complex here:

 

 http://pubs.acs.org/doi/abs/10.1021%2Fic50014a026

So, the principal axis goes through the center of the "triangles." Then it is very easy to see that there is a C3 rotation axis. Now it is time to look for a perpendicular C2. You can see it (actually three of them) going along one of those equatorial atoms (7, 8, 9). Obviously, we are assuming that this is a perfect geometry with equal angles and bond lengths. This says that our point group will be D3. 

There is a mirror plane going through atoms #7, #8 and #9. This means there is a perpendicular mirror plane divides complex into two equal "parts." Finally, this mirror plane tells us that the point group is D3h.

If you had difficulty to follow how I found out the point group, you can look at the very simple "flowchart" I made here. 

Actually, this is a  really nice paper with a molecular orbital diagram too. I feel like it is an inorganic chemistry lecture. Also, this complex was one of the first ones that helped chemists think as "M-H bond as a normal covalency." [1].

Reference :

1. Crabtree, H.R. The Organometallic Chemistry of the Transition Metals , John Wiley and Sons, 2001. Print.