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As far as I know, the central carbon shouldn't be a chiral center because it has two identical substituents. And yet, these two compounds should be different from each other.. Is it possible to denote the central carbon with R/S convention? They seem to be meso-compounds, but I'm unsure of their naming.

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In this case, there are 3 stereogenic centers, they are $\ce{C-3}$, $\ce{C-4}$, $\ce{C-5}$

$\ce{C-3}$,$\ce{C-5}$ are straightforward. Using the main CIP rules (1-3), we get $\ce{C-3}$ to be $R$ and $\ce{C-5}$ to be $S$

The term 'pseudoasymmetric' is defined in Subsection P-92.1.1 (d) of the IUPAC Blue Book as follows.

Stereogenic units are called pseudoasymmetric (center, axis or plane) when they have distinguishable ligands 'a', 'b', 'c', 'd', two and only two of which are nonsuperposable mirror images of each other (enantiomorphic). (…). The 'r/s' (…) stereodescriptors describing a pseudoasymmetric stereogenic unit are invariant on reflection in a mirror (for example 'r' remains 'r', and 's' remains 's'), but are reversed by the exchange of any two ligands ('r' becomes 's', and 's' becomes 'r'). Lower case stereodescriptors are used to describe pseudoasymmetric stereogenic units

$\ce{C-4}$ is a pseudo asymmetric center since two groups attached differ only in stereochemistry. In such a scenario, we turn to CIP rule 5, which states

Atom or group descriptor 'R', 'M' or 'Seqcis' precede 'S', 'P' and 'Seqtrans', respectively.

That is, $R$ > $S$ in priorities

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Now, using this, we can now name the compound using the following rules.

P-91.2.1.1 Cahn-Ingold-Prelog (CIP) stereodescriptors

Some stereodescriptors described in the Cahn-Ingold-Prelog (CIP) priority system, called 'CIP stereodescriptors', are recommended to specify the configuration of organic compounds, (…), and in the nomenclature of natural products (…). The following stereodescriptors are used as preferred stereodescriptors (…):

(a) 'R' and 'S', to designate the absolute configuration of tetracoordinate (quadriligant) chirality centers;

(b) 'r' and 's', to designate the absolute configuration of pseudoasymmetric centers;

(…)

P-14.4 NUMBERING

When several structural features appear in cyclic and acyclic compounds, low locants are assigned to them in the following decreasing order of seniority:

(…)

(j) When there is a choice for lower locants related to the presence of stereogenic centers or stereoisomers, the lower locant is assigned to CIP stereodescriptors Z, R, M, and r (pseudoasymmetry) that are preferred to E, S, P, and s, respectively, which are preferred to the non-CIP stereodescriptors cis, trans, or r (reference), c, and t (…).

(…)

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Therefore this compound will be named (3R,4r,5S)-3,5-dichloro-4-methylheptane

Similarly for the other case, where the methyl group points away from you, we get:

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As noted by Safdar, the two chiral compounds are meso-compunds. Like for meso-tartaric acid, there a is a mirror plane in the molecule. It is possible to name them unambiguously, too. You may use a page like the one about e.g., ChemDraw to train yourself in this part of chemical nomenclature:

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While the compound is chiral, it is better to speak about the three atoms with wedges attached to them as stereogenic centers. As you will learn later on, there equally is e.g., axial chirality.

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  • $\begingroup$ I usually say "chirality center" to distinguish it from whether or not the compound is chiral or not, but thanks, I'll start using stereogenic center instead. $\endgroup$
    – Quantonium
    Jun 2 at 17:05
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The central $\ce{C}$ is said to be pseudochiral. This means that its chirality will depend upon the configuration of the branches attached to it. For example, in the compounds you've drawn, the central $\ce{C}$ indeed is, in fact, achiral. They are diastereomers and not enantiomers, and both are meso compounds, hence optically inactive.

However, if you had drawn one of the $\ce{Cl}$ in dash position, then both your compounds would again be diastereomers, but they would be optically active and the central $\ce{C}$ would be chiral, since the attached groups are different.

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