IUPAC name for 1,2,3-trichlorocyclopropane?

Question

What is the IUPAC name for the two isomers of 1,2,3-trichlorocyclopropane? Similarly what is the name for isomers of 1,2,3,4-tetrachlorocyclobutane, 1,2,3,4,5-pentachlorocyclopentane, etc?

1,2,3-trichlorocyclopropane has two isomers, one of them with all the chlorine atoms facing in one direction and the other with one chlorine facing the opposite direction of the other two. In CIP rule, if two substituents on an atom differ only in their absolute configuration, R takes priority over S. However I have difficulty applying the rule here: two of the substituents are exactly the same. Nevertheless the two molecules are clearly distinct.

In practice the problem could be circumvented by using trans- and cis- prefix. But it does not address the key problem and fails on longer chains --- 1,2,3,4-tetrachlorocyclobutane has 4 possible arrangements, though not necessarily all of them have the problem.

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Here are the isomers of cyclobutane and their mirror images. I use + and - to denote a chlorine atom above or below the plane. The number in the parenthesis is the number of distinct molecules.

+ + | - -    (1)
+ + | - - 

+ - | - +    (1)
+ + | + +

+ - | - +    (1)
+ - | - +

+ - | - +    (1)
- + | + -

Answer 1

Achiral cyclic compounds like 1,2,3-trichlorocyclopropane may contain pseudoasymmetric centers.

Pseudoasymmetric centers have distinguishable ligands (“a”, “b”, “c”, “d”), two of which are nonsuperposable mirror images of each other (enantiomorphic). The lower case stereodescriptors “r” and “s” are used to designate the absolute configuration of pseudoasymmetric centers, for example (2⁠R,3⁠r,4⁠S)‑2,3,4‑trichloropentane:

Note that the stereodescriptors “r” and “s” 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”).

The configurations (“r” or “s”) at pseudoasymmetric stereogenic units are determined by application of the Cahn-Ingold-Prelog (CIP) priority system and the sequence rules. In particular, note that an atom or group with descriptor “R” has priority over its enantiomorph “S”. In order to establish the order of precedence of ligands in a stereogenic unit, the atoms of the stereogenic unit are rearranged in a hierarchical diagram, called a “digraph”. Descriptors specified in digraphs may correspond to the final descriptors or to temporary auxiliary descriptors used only for ranking ligands and never appearing as final descriptors.

Similar to the above-mentioned case of (2⁠R,3⁠r,4⁠S)‑2,3,4‑trichloropentane, the structure of (1⁠r)‑1,2,3‑trichlorocyclopropane contains one pseudoasymmetric center, which has two ligands that are nonsuperposable mirror images of each other:

The other isomer of 1,2,3‑trichlorocyclopropane is (1⁠s,2⁠s,3s)‑1,2,3‑trichlorocyclopropane, which contains three pseudoasymmetric centers. Each one has two ligands that are nonsuperposable mirror images of each other:

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It may not be obvious how to choose the stereodescriptors ‘r’ or ‘s’ for 1,2,3-trisubstituted cyclopropanes. The ranking is a complex process and requires the use of auxiliary descriptors.

Generally, the stereodescriptors ‘r’ and ‘s’ are assigned by applying the Cahn-Ingold-Prelog (CIP) Priority System as for the stereodescriptors ‘R’ and ‘S’. The order of precedence is reached by the construction of a hierarchical digraph and the application of the Sequence Rules.

The constitutional formula of a cyclic molecule is transformed into an acyclic digraph according to the methodology that is described in Subsection P-92.1.4.3 of the current version of Nomenclature of Organic Chemistry – IUPAC Recommendations and Preferred Names 2013 (Blue Book) and which has been recommended by Prelog and Helmchen.

In order to obtain the acyclic digraph of a stereogenic unit, the didentate ligand (i.e. the ring) is transformed into two monodentate ligands by leaving intact in each case one bond with the core of the stereogenic unit and cleaving the other bond. At the end of each of the two branches thus obtained, a duplicate atom of the core is attached. (Note that this methodology is similar to the case of multiple bonds.) For example, for the pseudoasymmetric stereogenic unit at the atom numbered ‘1’ of (1​r)‑1,2,3‑trichlorocyclopropane:

where $\ce{(C)}$ is a duplicate representation of the core of the pseudoasymmetric stereogenic unit.

As the digraph is acyclic, it is now possible to specify the stereodescriptor ‘R’ or ‘S’ for the stereogenic unit at the atoms numbered ‘2’ and ‘3’ in each branch. These are auxiliary descriptors that are different in each branch.

Since the auxiliary descriptors are different, they allow the branches to be ranked using Sequence Rule 5, which states that ‘R’ has priority over ‘S’.

P-92.1.3.5 Sequence Rule 5

An atom or group with descriptor ‘R’, ‘M’, and ‘seqCis’ has priority over its enantiomorph ‘S’, ‘P’ or ‘seq Trans’.

Therefore, the configuration of the pseudoasymmetric stereogenic unit at the atom numbered ‘1’ of (1​r)‑1,2,3‑trichlorocyclopropane can be determined to be ‘r’.

In the same way, the configuration of each pseudoasymmetric stereogenic unit of (1⁠s,2⁠s,3⁠s)‑1,2,3‑trichlorocyclopropane can be determined as ‘s’.

Answer 2

Contrary to what I believed earlier, cis- and trans- notation is unambiguous for cyclic compounds and is accepted by IUPAC, though not without some tweak. According to the rule of assigning cis- and trans- in gold book:

The appropriate reference plane of a double bond is perpendicular to that of the relevant σ-bonds and passes through the double bond. For a ring (the ring being in a conformation, real or assumed, without re-entrant angles at the two substituted atoms) it is the mean plane of the ring(s) … If there are more than two entities attached to the ring the use of cis and trans requires the definition of a reference substituent.

In the isomer of trichlorocyclopropane which has all three chlorine atoms on the same side, I can choose any one as the reference and the other two should thus be cis. The name should be r-1,c-2,c-3-trichlorocyclopropane. The other isomer is named r-1,c-2,t-4-trichlorocyclopropane.

However I'm still not sure whether and how CIP rule could be used. This page, which gives additional examples of c- and t- naming, merely states CIP could be used without substantiation.

Answer 3

The preferred absolute stereochemical configuration notation using the R/S, r/s, … stereodescriptors and CIP rules (as in Loong's detailed answer) might be in some cases quite difficult for human chemist to construct or decipher, like in this case.

There's also a non-preferred, but simpler method using cis/trans notation (IUPAC BlueBook 2013 P-93.5.1.2) for cycles with two stereocenters, and r/c/t (reference, cis, trans) notation (for more ring stereocenters), already mentioned by ℵ_ϵ.

P-93.5.1.3 Relative configuration; the stereodescriptors ‘r’, ‘c’, and ‘t’

P-93.5.1.3.1 When one substituent and one hydrogen atom are attached to each of more than two positions of a monocycle, the steric relations of the ligands are expressed by adding ‘r’ (the reference ligand) after the locant of the lowest numbered of these ligands, and ‘c’ for ‘cis’ and ‘t’ for ‘trans’ (as required) followed by a hyphen and the locant of another ligand, thus expressing the relationship to the reference ligand. The relative configuration is expressed by these stereodescriptors. Furthermore, racemates may also be denoted by this method. For preferred IUPAC names, the preferred stereodescriptors are those used in the CIP priority system described in P-91 and P-92, With stereodescriptors such as ‘R’ and ‘S’ to describe absolute configuration and the prefixes ‘rel’ to express relative configuration and ‘rac’ for racemates, as described in P-93.1.3.
The notation consisting of adding ‘r’ (for reference substituent) followed by a hyphen and the locant of the lowest numbered of these substituents and ‘c’ (for cis) and ‘t’ (for trans) (as appropriate) followed by a hyphen and the locant for another substituent, as used in the 1993 Guide to IUPAC Nomenclature of Organic Compounds (ref. 2), is no longer recommended.
(…)

P-93.5.1.3.2 When two different ligands are attached at the same position of a monocycle, then the lowest-numbered ligand named as a suffix is chosen as reference ligand. If none of the ligands is named as a suffix, then that the ligand of the pair of ligands having the lowest number and Which is higher ranking in the Sequence Rule is chosen as a reference ligand. The relationship of the Sequence-Rule-higher ranking at geminally substituted positions, relative to the reference group, is cited as ‘c’ or ‘t’, as required.
(…)

Example 3:

(1R,2R,3s,4S,5S,6s)-1,2,3,4,5,6-hexachlorocyclohexane (PIN)
1r,2c,3c,4t,5t,6t-hexachlorocyclohexane

Explanation: In this compound, different numberings are necessary in accordance with the precedence of ‘R’ ligands and ‘cis’ arrangements for lowest locants (…)

The notation is for relative stereochemical configuration. But, since each of the six structures in your question is achiral as a whole (superimposable with its mirror image, i.e. a meso form), the relative stereochemical configuration completely describes the absolute configuration as well.

We get the following names

(1s,2s,3s)-1,2,3-trichlorocyclopropane (PIN)
1r,2c,3c-trichlorocyclopropane

(1r)-1,2,3-trichlorocyclopropane (PIN)
1r,2c,3t-trichlorocyclopropane

(1s,2s,3s,4s)-1,2,3,4-tetrachlorocyclobutane (PIN)
1r,2c,3c,4c-tetrachlorocyclobutane

(1R,2r,3S,4s)-1,2,3,4-tetrachlorocyclobutane (PIN)
1r,2c,3c,4t-tetrachlorocyclobutane

(1R,2R,3S,4S)-1,2,3,4-tetrachlorocyclobutane (PIN)
1r,2c,3t,4t-tetrachlorocyclobutane

(1r,2r,3r,4r)-1,2,3,4-tetrachlorocyclobutane (PIN)
1r,2t,3c,4t-tetrachlorocyclobutane

Please note that

• PIN states for ‘preferred IUPAC name’;
• the numberings for the name pairs do not match (the PIN names are just for reference or comparison), the second one is generally shifted and/or reversed (one can easily deduce that e.g. for the mentioned IUPAC P-93.5.1.3.2 example 3 structure, hexachlorocyclohexane, the two pseudoasymmetric carbons (3s,6s) from the PIN name correspond with carbons 2 and 5 from the non-PIN name illustrated by the formula), as for the r/c/t notation, atom with locant 1 (reference r) and the numbering direction is chosen so that as much as possible subsequent descriptors are c (cis), then t (trans), it's quite easy;
• the r stereodescriptor has completely different meaning in both stereochemical notation systems;
• the r/c/t descriptors are not in parentheses before the complete name, but directly after the locants in the name;
• there are also older obsolete/incorrect variants for this notation with dashes, like
  • r-1,c-2,c-3-trichlorocyclopropane (IUPAC 1993, R-7.1.1),
  • 1-r,2-c,3-c-trichlorocyclopropane (IUPAC BlueBook 2013, first uncorrected release, some parts).