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I have several classes of problems I'm facing in which I'd like to be able to discuss stereochemistry of non-tetrahedral centers. Specifically, I'd like to be able to check that the absolute configuration around a (for instance) trigonal bipyramidal transition state matches the absolute configuration that I've calculated.

For instance, these (chemically meaningless) trigonal bipyramidal structures are not superimposable: non superimposable trigonal bipyramidal molecules

What's a good resource discussing "higher order" stereochemistry? I'm particularly interested in classification of stereochemistries and in exchange rules for different orderings (analogous to the parity rules for tetrahedral centers). I'm coming from a computational/algorithmic slant.

The best (only) resource I've found so far is the opensmiles specification: http://opensmiles.org/opensmiles.html#_trigonal_bipyramidal_centers. I'm happy to purchase a book, or academic paper, or read program source code.

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closed as too broad by Mithoron, Todd Minehardt, airhuff, Melanie Shebel, bon Jul 29 '17 at 7:10

Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. Avoid asking multiple distinct questions at once. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

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I'm not sure how easy this is to implement algorithmically, but for what it's worth, the official IUPAC recommendations are as follows.

Section P-93.3 in Nomenclature of Organic Chemistry – IUPAC Recommendations and Preferred Names 2013 (Blue Book) describes the guidelines for assigning configuration at non-tetrahedral atoms. The portions of this answer will be quoted from there.

These guidelines, and further details on certain aspects, are also discussed in Nomenclature of Inorganic Chemistry – IUPAC Recommendations 2005 (Red Book) (link), section IR-9.3.

Stereodescriptors for nontetrahedral configurations are composed of three parts.

(1) A symbol indicating overall geometry called the 'polyhedral symbol';

(2) A symbol called the 'configuration index' that describes the configuration of ligands around the central atom;

(3) A symbol indicating the 'absolute configuration' associated with the central atom called the 'chirality symbol'.

For the first example you provided:

tbp structure

which is a trigonal bipyramid, the appropriate 'polyhedral symbol' is TBPY-5 (P-93.3.2, Blue Book). The numbers in red are the priorities according to the Cahn–Ingold–Prelog system, which will soon be required.

The 'configuration index' is

a series of numbers to identify where each atom or group is located. It is based on the CIP priority order of the atoms attached. The atom or atoms with highest priority are given priority number one '1'; the next priority number two '2', and so on. [...] (P-93.3.3.1)

For a trigonal bipyramid, this "consists of the priority numbers of the two apical atoms (lower number first if different), representing the reference axis of the system" (P-93.3.3.5.1). In this case, the two apical atoms have priority numbers 1 and 2, so the configuration index is simply 12.

The 'chirality symbols' available for a trigonal bipyramidal system are 'A' and 'C'.

The atoms in the plane perpendicular to the reference axis are viewed from the side with the atom or group of highest priority on the reference axis. If the direction from the atom in this plane with highest priority to the atom with the next higher priority is clockwise the chirality symbol is 'C', if anticlockwise 'A' (P-93.3.4.2.1).

Looking along the reference axis (which is the axis containing the axial ligands), from the direction of the higher priority atom (oxygen), the equatorial ligands decrease in priority going in a clockwise order. So, the chirality symbol is C. (Essentially, this is analogous to assigning an R-configuration for an ordinary chiral carbon.)

The three parts of the stereodescriptor are enclosed in parentheses and separated from each other by hyphens and cited at the front of the name separated from it by a hyphen. (P-93.3.1)

The full stereodescriptor is therefore (TBPY-5-12-C).

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