The detection of stereogenic units in a molecule isn't always a trivial task. This is illustrated by two previous blog posts (post 1 post 2) where the stereogenic units do not have 4 topological different ligands. The posts also list the set of rules that enable the detection of these stereogenic units as can be found in the referenced paper[1]. While there are only 3 rules, the amount of code needed to implement them is big. The rest of this blog post will describe an alternative method to detect these stereogenic units from a paper by the same authors[2].
A potential stereogenic center is any atom with at least 3 heavy atom neighbors. For some atoms (e.g. nitrogen), the barrier of inversion is low and these atoms are not stereogenic centers. The definition for a tetrahedral stereogenic atom is now:
A potential stereogenic centre really is a stereogenic centre if there exists no automorphic permutation causing an inversion of the configuration of only the potential stereogenic centre under consideration.
If there exists at least one automorphic permutation causing the inversion of the configuration of only the stereogenic centre under consideration, then the potential stereogenic centre can be a stereogenic centre if the number of topologically equivalent neighbours (ligands) of potential stereogenic centre is less than or equal to the number of configurations of these ligands.
At first sight, the new definition is much simpler compared to the 3 rules. However, when it comes to implementing this, there is a catch. The second part of the definition requires the number of configurations of a topologically equivalent ligand to be computed. This could eventually leads to code comparable to the previous rules. Nevertheless, the definition is brief and easy to remember. The need for the automorphic permutations limits it's manual use though.
To illustrate how the definition works, a few examples will be covered next. The first example is the most simple case where there are 4 different ligands.
For these cases, there exists no automorphims that only invert the center. In fact, for molecules like these there is only the identity permutation. The next example illustrates where an automorphism exists that inverts the potential stereogenic center only.
In both cases, there will exist an automorphism that will invert the center (i.e. exchange the two equivalent methyl groups). Therefore, both potential stereo centers are not stereo centers.
A more interesting example is 1,4-dihydroxy-cyclohexane. In this case, there are 4 automorphisms but none of them invert only center 1 or 4. 2 of the 4 permutations invert both center 1 and 4. Atoms 1 and 4 are therefore stereogenic centers.
The second part of the definition correctly identifies the central stereo centers in the following molecules. In all 3 cases, the number of configurations for the ligand is greater than the number of equivalent ligands.
The number of equivalent ligands are 3 for the two structures on top and 2 for the bottom structure. For the top two, the number of configurations is 4 (>= 3). Likewise, the number of configurations for the bottom structure is 2 (>=2). The central stereogenic center is successfully found in the 3 cases.
Finally, two examples where the number of configurations in the equivalent ligands is lower than the number of equivalent ligands. In both cases, there are 3 equivalent ligands and only 2 configurations for the ligand (2<=3). The central atoms are therefore not stereogenic since at least one configuration will be duplicated.
From the last two figures, it should be clear that counting the number of configurations in a ligand is not the same as the number of stereo centers times two. The paper doesn't really go into the details on how to do this. However, another concept introduced by the paper might be useful here: a set of interdependent stereo centers. These sets can be found be inspecting the automorphisms. A set can contain one or more stereo centers and these sets are the independent stereogenic units in a molecule. Some examples showing the sets of interdependent stereo centers in different colors should make this easier to understand.
For all examples given above, the number of configurations is the same as the number of interdependent sets of stereo centers in the ligand times 2. Unfortunately, this is not true in all cases. Below is an examples where this would not work.
Until I find a good way to count the number of configurations, the new definition is not preferable over the old rules. I'll keep looking though and will post my findings. Suggestions are always welcome of course.
[1] M. Razinger, K. Balasubramanian, M. Perdih, M. E. Munk,
Stereoisomere Generation in Computer-Enhanced Structure Elucidation,
J. Chem. Inf. Comput. Si. 1993, 33, 812-825
[2] M. Perdih, M. Razinger, Stereochemistry and Sequence Rules: A Proposal for Modification of Cahn-Ingold-Prelog System, Tetrahedron: Asymmetry, 1994, Vol. 5, No. 5, 835-861 http://dx.doi.org/10.1016/S0957-4166(00)86237-0
1 comments:
@Tim, great writeup. One small correction:
"For some atoms (e.g. nitrogen), the barrier of inversion is low and these atoms are not stereogenic centers."
Quaternary ammonium salts and n-oxides would be the exceptions to this rule.
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