This paper describes the synthesis and characterization of a Cr(I) dimer with a very short Cr-Cr distance. Computational studies support fivefold bonding between the chromium atoms. I have used this paper to introduce metal-metal multiple bonds and discuss the molecular orbital interactions of homonuclear diatomics including d-orbitals. More generally, it is a nice example to stimulate the discussion of what constitutes a bond and the various interpretations of bond order.
Students are asked to read the paper and answer the discussion questions before coming to class. I used this paper in a second-year inorganic course after we had talked about MO theory of diatomics but fairly early in our discussion of transition metal chemistry. There is a Perspectives article in Science that goes along with this paper, but I decided not to give it to the students as I wanted them to work out the MO diagram for themselves.
Student performance on the discussion questions is assessed.
This was a great exercise, although I plan on modifying it a bit for next time. I will have students START with drawing the MOs for C2h symmetry rather than for linear. They are described in the paper and students can easily show how the orbital labels are derived from the character table. Surprisingly, the students wondered why the delta and Pi orbitals were NOT degenerate for C2h. This is a great lead-in for exploring the linear geometry where they are. As for determining the symmetry labels for D infinity h, the students had great difficulty because we did not do any examples for the linear groups. We always "cheated" by using the lower symmetry D2h group. Anyway, seeing the trig functions in the character table is quite scary for the students (and for me), but this paper provides a great example for tackling linear molecules. Since students already see that the delta and pi bonding MOs should be degenerate in the linear molecule, they should know to look at both together when assigning characters for the reducible rep. Assigning a value of 180 degress for phi will make those ugly trig functions turn into integers, and deriving the symmetry labels becomes a snap. As a follow-up, the paper by Hoffmann et al entitled "The Many Ways to Have a Quintuple Bond" allows students to confirm their assignments and explore some of the theoretical "problems" with having a true quintuple bond with a trans-bent geometry. Overall, this was a great exercise. I'm curious how others have students derive the symmetry labels for the linear system.
I used this example (modified somewhat) as a PS question in the fall - it worked well. Thanks!
I modified this question for use on my second midterm exam in inorganic chemistry this spring. I have become extremely bored with the diatomic molecules I ask them to draw MO diagrams for (O2, carbide, NO, cyanide, N2, yawn...) I presented this problem in four parts and gave them the ground state electron configuration of Cr(I). I also provided a set of x,y, z axes which I was hoping would help the students draw out the atomic orbitals. Most of the students did get the right MO diagram with a sigma, two pi, and two delta symmetry bonding orbitals. I had not spent any significant time on delta MO's in lecture, but we did start off the MO unit by looking at sketches of possible orbital overlaps and classifying them as bonding, anti-bonding, or non-bonding. One of the overlaps we looked at was a pair of d orbitals forming a delta symmetry MO, so they had at least had a brief intro to the concept.
The average score on this question was ~76%, which is similar to the average score on the exam overall.
Thanks Maggie! I intend to use this paper this year to talk more about MO diagrams and in particular as an introduction to transition metal species. I agree with Anne, that both I and the students are bored with those p-block elements. Figuring out the change in the axis system from the point group to the labeling of the MOs was a little confusing for me at first though!