The reflection invariance problems in stereochemical nomenclature for absolute configuration

1 Preamble

Enantiomers are differentiated based on their absolute configuration, which signifies the arrangement of ligands in 3D-space around the elements of chirality (Eliel et al., 1994; Gawley, 2005; Gawley & Aube, 1996; Talapatra & Talapatra, 2015; Tsogoeva, 2021; Wheeland, 1949). Different methods have been proposed to denote the absolute configuration of a chiral molecule. The initially introduced D/L nomenclature system (now used mainly for amino acids and carbohydrates) suffered from severe limitations and could not cover all types of chiral molecules. This was subsequently replaced with the R/S system introduced by Cahn, Ingold and Prelog (known as the CIP system). The method has wide acceptance and can be used to denote the absolute configuration of any molecule having central or axial or planar chirality. For molecules with helical chirality, the absolute configuration is denoted by P/M (Plus and Minus) nomenclature which is also used to specify the different gauche conformations containing rotatable C–C bonds.

2 Introducing the concept of reflection variance and invariance

Every molecule needs an identity which is its name as per IUPAC nomenclature system. From the name itself, one can draw the structure of a molecule. Alternatively, the structure of a molecule can be given a name as per the IUPAC rules. Molecules lacking any chirality element requires a nomenclature system that allows to draw the main chain and the connectivity of all the atoms present in the substituents. For these molecules knowing the constitution or atom-to-atom connectivity is sufficient to identify the molecule. In case of molecules with chiral elements, an additional parameter is required which is the absolute configuration or the three-dimensional arrangement of groups in space around the chiral element. This absolute configuration is expressed by descriptors R and S following the CIP guidelines. Since chiral molecules can have two different non-superimposable mirror image structures, the 3D-arrangement of groups around a chirality element should have mirror image relationship. Let us suppose one enantiomer has a chirality centre whose configuration as per CIP priority system is R. That means the direction of priorities from 1→2→3 is clockwise when viewed opposite to that the group of 4th or least priority (Figure 1). The enantiomer of the same molecule should then present an anticlockwise direction in in going from priorities 1→2→3 when viewed opposite to the 4th priority group and will thus have S-configuration. This argument gives rise to an apparent dogma that the mirror image of R molecule will always be an S molecule. During our interaction with students of chemistry at the undergraduate level, while teaching stereochemistry, very often we encounter a situation when a majority of students suffer from this dogma that mirror image of R is aways S and vice versa. To them, inversion of configuration means R going to S or the opposite while retention means R remaining R and so is true for S. This misconcept is an off-shoot of not knowing the difference between configuration and configurational descriptor as clarified in the next few lines. We must remember that R and S are only descriptors applied to denote the absolute configuration of a chirality centre and depends upon the priorities of the ligands attached to the centre. In a majority of cases, the priorities of the ligands remain the same in both the enantiomers and in those cases, the mirror image relationship between R and S enantiomers is indeed true. If, however, there is change of priority of any set of ligands going from one enantiomer to the other, the configurational descriptor for both the chiral centres remains the same. An opposite of this scenario may also be observed where the configurational descriptor changes although the configuration is retained. One of the possibilities when this may occur is while the priority order of the ligands has changed possibly due to replacement of one of the ligands by another one (from the same side in 3D-space) with a different CIP priority. All these as been exemplified later. The change of R descriptor to S in the mirror image is called reflection variance (Figure 1) while if R remains R (or S remains S) in the mirror image, that is called reflection invariance. A similar situation arises when dealing with P and M conformers of two enatiomeric molecules (like helicenes) or suitably substituted mirror image conformations like +synclinal and -synclinal gauche forms. The P form of one enantiomer should become M form in its mirror image giving rise to the paradigm that mirror image of P gauche form is always an M gauche form (Cahn & Ingold, 1951; Cahn, Ingold, & Prelog, 1956; Cahn, Ingold, & Prelog, 1966; Prelog & Helmchen, 1982) Here again, this is true only when the fiducial groups attached to carbon centres remain the same even in the mirror image. However, violations are known and in this manuscript, we wanted to highlight those special cases which show apparently anomalous reflection invariance or variance. We must, however, bear in mind that in the enantiomeric pairs, the ligands occupy exactly the mirror image positions, that is, the configuration always bears a mirror-image relationship (reflection variant) but the descriptors of configuration (like R/S or P/M) may or may not follow such paradigm.

Figure 1:

Few examples of reflection variance.

It has been mentioned in the text books and literature that this reflection variance is generally true except in case of pseudo-asymmetric carbons where reflection invariance is observed. Recently (Bhattacharya, Singha, Das, Gupta, & Basak, 2020), in an article, we have proposed a pilot atom-based approach, a concept already included in CIP system to assign the configuration to molecules with central chirality, following which one can overcome this reflection invariance problem for pseudo-asymmetric carbon.

The reflection invariance in pseudo-asymmetric systems has only been briefly described in the literature or text books. Lately, we became interested to explore other systems and to find out whether such reflection invariance phenomenon does exist in those systems. In our search, we could find several classes of molecules where the absolute configuration around the element of chirality remains same in their mirror images (reflection invariant). In this manuscript, we discuss those reflection invariant cases and would like to propose ways to avoid the reflection invariance within the ambit of the CIP rules with minimal modifications in R/S and P/M descriptors. As we have already dealt (Bhattacharya et al., 2020) with the reflection invariance in molecules with pseudo-asymmetric centres, this part is not included in our discussion. However, we have taken up the spiro systems having both central and axial chirality, in which the spiro carbon can be considered to be a pseudo-asymmetric carbon in appropriate cases. It may be pertinent to mention here that Mislow et al. (Mislow & Siegel, 1984) in their 1984 paper, had commented about the pseudo-asymmetric centre like C-3 in meso trihydroxy glutaric acid and proposed that this centre be preferably called stereogenic but achirotopic (a concept to describe local chirality).

3 Necessity to conceptually differentiate between ‘configuration’ and ‘configurational descriptor’

Based on the previous discussions, it may be said that mistaking ‘configuration’ to be same as the ‘configurational descriptor’ for a given chiral molecule, is one of the major reasons for misinterpretation of reflection variance/invariance issues in stereochemistry. Conceptual clashes occur in the students’ mind if they are not aware of the fact that the configuration of a particular chiral molecule is absolute but the descriptors are not. The descriptors have been designed based on certain priority rules to assign the absolute configuration. So, it is of great importance to realise the difference between configuration and configurational descriptor and appreciate their mutual orthogonality. Following systems would help to exemplify the unusuality and highlight the complications of reflection variance or invariance generated thereof.

1. In S_N2 reactions occurring at a chirality centre, there is always an inversion of configuration (Walden inversion) but that does not mandate a change in the configurational descriptor. This depends on the relative priorities of the entering nucleophile and the leaving group. On the other hand, for S_Ni reaction, since the nucleophile attacks from the same side as that of the leaving group, the configuration is retained. However, if the CIP priority order of the entering nucleophile and that of the nucleofuge are not same, then the configurational descriptor may change (Scheme 1).

2. If one asks what is the stereochemical relation between the molecules (A^R)(A^S) C^S (B^R) (H) and (A^S)(A^R) C^S (B^S) (H), the answer will probably be diastereomers or epimers at the chirality centre C (Figure 2). This answer is, however wrong, and the two compounds are actually mirror images and hence enantiomers.

Scheme 1:

Change and retention in configurational descriptors for S_Ni and S_N2 respectively.

Figure 2:

Enantiomeric pair.

Consideration of the above molecules as diastereomers lead to further complicacy like their reactivity with achiral agent, say, the H replacement with bromine. Treating the two molecules as diastereomers will lead to the wrong impression that they will have different activation energies for bromination as reactions pass through diastereomeric TSs; actually, enantiomeric TSs are involved and hence the rate of bromination will be same for both.

The two structures (3a and 3b) are drawn in such a way (Figure 3) so that they don’t appear to be mirror images as is structure 3b’. Comparison of the H’s in structures 3a and 3b might give an impression that they are diastereotopic!

1. Writing one unequivocal structure for a chiral planar molecule with a defined configuration may lead to ambiguity. This is exemplified by the enantiomers 4a and 4b with both pS absolute configuration as shown in Figure 4,

Figure 3:

Topicity of the hydrogen atoms.

Figure 4:

Reflection invariance in enantiomeric systems having planar chirality.

1. It may be pertinent to mention here a similar phenomenon which happened for E/Z configuration. For this, reflection invariance is generally true. That is E should remain E in its mirror image; similar is for Z-configured molecule. However, there are reflection variance cases for E/Z systems also as indicated in the following example (Figure 5).

Figure 5:

Reflection variance in E/Z isomers.

1. [1,3] and [1,5]-sigmatropic migration of chiral alkyl groups offer interesting examples addressing the irregularities related to configurational inversion and retention. Due to geometrical reasons, usually suprafacial migration is favoured over the antarafacial mode for [1,n] shift when n is small (Fleming, 1999). In case of thermal [1,3] and photochemical [1,5], suprafacial migration induces the alkyl group to transfer with an inversion in configuration (Mislow and Siegel, 1984). However, for specific systems, like 6a and 6f (Scheme 2), the configurational descriptor is retained although the configuration is inverted. On the other hand, photochemical [1,3] and thermal [1,5], supramolecular migration induces the alkyl migration to proceed with a retention in configuration. Interestingly for the latter two rearrangements with 6a and 6f, the configurational descriptor is changed although the configuration is retained. The product formations can be rationalized through various approaches (Cahn and Ingold, 1951), one of which is FMO as shown in Scheme 2.

2. Intramolecular rearrangements with chiral migrating groups are often considered to apparently involve a retention in the configurational descriptor of the migrating group since the bond-breaking (with the migration origin) and bond-making (with the migration terminus) are concerted and hence occur from the same side (Sykes, 1986). However, careful inspection reveals that the descriptor remains unchanged only when the migration origin and the terminus possess the same CIP priority order with respect to the migrating group. Following is an example (Scheme 3) of a Beckmann rearrangement (Blatt, 1933) in which the product (obtainable as per the established mechanism) reveals that the migrating group undergoes a change in its configurational descriptor which is rationalizable based on the previous arguments.

Thus, in this case, the configuration conceptually remains unchanged while it is the configurational descriptor that changes.

1. It is often a matter of confusion specially among the student community that configurational descriptor of a stereogenic centre only changes when bond with that atom is broken or a new bond is formed (except for conformational enantiomers or diastereomers). However, there may be examples where this convention is violated. Following is an example which shows the formation of cyclic phenonium ion 8c from β-phenyl alcohol derivative 8a by the treatment of HBr. Here, none of the bonds directly existing with the sp³ stereogenic carbon (highlighted in red) in the substrate alcohol is broken or newly formed, yet it undergoes a change in its configurational descriptor (Scheme 4).

Scheme 2:

[1,3] and [1,5]-sigmatropic migrations of chiral alkyl groups.

Scheme 3:

Beckmann rearrangement with change in configurational descriptor of the chiral migrating group.

Scheme 4:

Change in configurational descriptor without any bond breaking or making with the chirality center.

This is rationalizable when we notice that the CIP priority order of the four ligand groups bonded to the sp³ stereogenic carbon (highlighted in red) is different in the cyclic phenonium derivative (intermediate product) as compared to the acyclic alcohol (9a). Here also, the configuration conceptually remains unchanged.

4 Examples of special cases of reflection invariance in (i) spiro systems, (ii) planar chiral systems, (iii) mirror image conformations: a pilot-atom based proposal to make the R/S relations consistent

4.1 Spiro systems (Eliel et al., 1994; Gawley and Aube, 1996; Moss, 1999; Talapatra and Talapatra, 2015; Wheeland, 1949)

We start with a chiral spiro system. The spiro carbon atom, when attached to two sets of mutually different ligands in the two arms of a ring, becomes a chirality centre and the molecule becomes chiral. Apart from having a chirality centre, the molecule also possesses a chirality axis. Normally while assigning absolute configuration of such a system, chirality centre gets priority over chiral axis. For molecules with one pair of ligands residing in the arms of a particular cyclic ring having same constitution but different configurations (enantiomorphic), it makes the spiro carbon a pseudo-asymmetric centre. Expectedly, following the CIP norms, the configuration of the spiro carbon for both the enantiomers 9a/9b turned out to be s (lower case indicating pseudo-asymmetric carbon) and is thus reflection invariant (Figure 6A). Another similar example of reflection invariance is shown in case of the enantiomeric pair 9c/9d containing enantiomorphic chirality centres attached to the same ring of the spirane.

Figure 6:

Assignment of R/S descriptors for some spiro systems. (A) Reflection invariance of the configurational descriptors for the enantiomers obtained using the existing rules. (B) Pilot atom-based approach of assigning the configurational descriptors giving reflection variance.

4.1.1 Possible solution

By adapting our previously proposed pilot atom-based approach (Bhattacharya et al., 2020), in which the non-enantiomorphic group with higher priority should be considered as pilot atom. such invariances can be successfully dealt with (Figure 6B).

4.2 Systems with planar chirality (Bach, Mazur, Hamama, & Lauderbacka, 1972; Bickelhaupt & de Wolf, 1993; Cram et al., 1974; Cope & Metha, 1964; Cram & Steinberg, 1951; Cram, Allinger, & Steinberg, 1954; Eliel et al., 1994; Gawley and Aube, 1996; Hopf, 2000; Kane, de Wolf, & Bickelhaupt, 1994; Lopez & Palomo, 2022; Otsubo & Misumi, 1978; Talapatra and Talapatra, 2015; Tobe & Weber, 1994; Wheeland, 1949)

In ansa compounds or p-cyclophanes where the 2-dimenesionally chiral aromatic ring(s) is/are attached with enantiomorphic ligands, interesting situation arises while assigning absolute configuration to the two enantiomers where the chiral ligand has higher priority over the de-symmetrizing ligand. The absolute configurational descriptors (pR/pS) for such aromatic rings with planar chirality remain the same, i.e. reflection invariant. Two different cases (10a and 10b; 10c and 10d) are described to elaborate the scenario (Figure 7A).

Figure 7:

Assignment of R/S descriptors for some systems showing planar chirality. (A) Reflection invariance of the configurational descriptors for the enantiomers obtained using the existing rules. (B) Pilot atom-based approach of assigning the configurational descriptors giving reflection variance.

4.2.1 Possible solution

In order to avoid this reflection invariant descriptors for enantiomeric systems as shown in Figure 7A, the following considerations can be made:

1. The pilot atom should remain same in both the enantiomers. That means the two pilot atoms should have a mirror-image relationship.

2. The pilot atom should be selected in that enantiomer first which is nearer to the R-configured ligand (higher priority) and also to the de-symmetrizing substituent. In case where two de-symmetrizing substituents are present, higher priority substituent is considered.

The examples in Figure 7B can help to clarify the above points.

4.3 Mirror image conformations: reflection invariance in P/M nomenclature

4.3.1 P/M gauche conformations (Eliel et al., 1994; Gawley and Aube, 1996; Mancinelli, Bencivenni, Pecorari, & Mazzanti, 2020; Talapatra and Talapatra, 2015; Testa & Gassman, 1979; Wheeland, 1949)

As mentioned earlier, a P/M descriptor system is adapted for naming the gauche forms and a set of rules are in place for the assignment when the molecules are represented in Newman projection. The most important aspect of finding out P/M nomenclature is to identify the fiducial groups at both the front and the back carbons. The rules are summarized below:

1. Selection of the fiducial atom/group

   1. If all substituents are different when considered separately for the front and rear carbons, then the priority sequences for the substituents on front and the rear carbon atoms are decided individually as per the CIP sequence rules. The topmost priority groups are considered as the fiducial atoms/groups.

   2. In case where two out of the three ligands attached to the front or the back carbon are identical, the unique (non-identical atoms) are considered as the fiducidal atoms/groups.

1. Deciding the directional sense for assigning the configuration

   1. Looking from the top face (side of the front carbon atom), if one moves in a clockwise direction upon going from fiducial atom/group in the front carbon to the fiducial atom/group in the rear carbon, covering the smaller angle, then it is said to have P (plus) descriptor. On the other hand, if the direction is anticlockwise, it is said to be in the M (minus) form. The same approach is also applicable while looking at the molecule from the side of the rear carbon atom.

Some examples of use of the above rules to designate the P and M gauche conformations with mirror image relationships are shown in Figure 8A.

Figure 8:

Assignment of P/M descriptors for mirror-image conformations of molecules with/without chiral substituents. (A) Reflection variance of the conformational descriptors for systems devoid of chiral substituents. (B) Reflection invariance of the conformational descriptors for systems having chiral substituents, obtained using the existing rules. (C) Reflection variance of such conformational descriptors obtained using the pilot atom-based approach.

For molecules with three chiral ligands, two of which are enantiomorphic and the other ligand has lowest priority, such mirror image relationship between P and M forms (reflection variance) can be violated. A few examples of such systems are depicted in Figure 8B.

4.3.2 Possible solutions

The reflection invariance problem for P/M gauche forms can be overcome if the priority is decided in relation to the configurational descriptor of the pilot atom (group) keeping in mind that RR > SS > RS > SR. The pilot atom is the non-enantiomorphic ligand. According to this nomenclature system the reflection variance in mirror image conformers is restored (Figure 8C). This also demonstrates the scope of our proposed rules for assigning configuration for pseudo-asymmetric carbon.

5 Conclusions

The reflection variance/invariance problem is a fundamental concept in stereochemistry. The existing system of assigning configurational descriptor may fail to affect reflection variance for the enantiomeric molecules like the ones possessing a hybrid of central with either axial or planar chirality. Similar apparent ambiguities are also observed for mirror image conformations of systems with chiral substitutions. This may lead to unwanted confusion in the mind of students owing to a general misunderstanding of the similarity between ‘configuration’ and ‘configurational descriptor’. An attempt has been made to elucidate the difference between these two allied concepts through suitably chosen examples. Further, a simple pilot-atom based approach has been proposed which modulates the established CIP priority sequence to introduce the reflection variance for the enantiomers and thereby remove the existing anomaly observed under the conventional protocol.