I saw my former PhD boss (Fraser Stoddart) over the weekend and he had a challenge for me. And I can’t resist a challenge. He gave me a copy of the midterm he had just given his grad class and suggested I have a crack at question 1. Here it is:
1. Give the possible symmetries (point groups) for the following four objects, considering all of the possible permutations in which the objects may be assembled. In each case, identify the symmetry elements as well (50 pts).
a. A flat cardboard square, through the four corners of which four nails have been driven perpendicularly.
b. Ditto, with four right-handed screws replacing the nails.
c. Ditto, with one left-handed and three right-handed screws replacing the nails.
d. Ditto, with two left-handed and two right-handed screws replacing the nails.
Bonus: Identify any squares which are enantiomers of each other (1 pt each).
Hints: (1) Use scratch paper first! (2) Representing the cardboard squares as stereocenter-containing organic compounds may help your thought processes. (3) You should end up with 25-35 unique solutions to this problem.
Because we lead a kinda rock-and-roll lifestyle, my wife and I sat down the following evening to have a go at the question — she’s much better at this symmetry stuff than I am. It took us a good couple of hours (incidentally, that’s the time allotted for the whole midterm — 5 questions in total — not just question 1…), and we had to look up the flowcharts for assigning point groups, but we ended up getting them all right and just missed one pair of enantiomers. So, if you have an hour or two to kill and fancy getting your head around some stereochem/symmetry problems, give it a go. I’ll post up our answers in a few days. If you look hard enough on Twitter, you’ll find them there too.
Fraser pointed out that the question is not his; he took it from the 1966 edition of Introduction to Stereochemistry by Kurt Mislow.
One clue of my own: don’t forget about axes of improper rotation and centres of inversion… and good luck! Let me know how you do in the comments section.
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UPDATE — here are the answers