Cahn-Ingold-Prelog Rules: duplicate vs. phantom atoms

How to Manipulate JSmol Structures

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   While the descriptors R/S are employed in the CIP system to describe absolute configuration of tetracoordinate chiral centers, the lower case r/s descriptors are applied to the configuration of pseudoasymmetric centers.The rules for assigning these descriptors are addressed in the examples below. The 1993 update of the 1982 Cahn-Ingold-Prelog rules is located here.  


Fig. 1

 

 

(1S,5S)-α-pinene

1,4-Dimethylcyclohexane

The trans-stereoisomer (Fig. 1), as represented in 1a, has a plane of symmetry through C1 and C4 and a two-fold axis of symmetry along the x-axis that passes through the center of the C2-C3 and C5-C6 bonds. The pseudo-asymmetric carbons C1 and C4 are equivalent owing to the two-fold axis. The configurational assignments will be the same.

At C1 the lowest priority (4) atom is hydrogen and the methyl group ranks third. But how does one chose between the chains C2-C3-C4 and C6-C5-C4 for the remaining two priorities? They are essentially mirror images of one another. Therein lies a solution!

Digraph 1b is constructed by following the path from C1 (red dot) to C2-C6 and terminating in a phantom carbon atom (C1; red dot) that has a mass of zero. The same process may also proceed from C1 to C6-C2 terminating in a phantom C1. These two chains are enantiomeric and temporary configurations (Ro/So) can be assigned to each based on the "chiral" center at C4. The lefthand C4 of 1b is assigned an Ro configuration with priorities C3-C2-C1>C5-C6-C1(phantom)>CH3>H. Conversely, the enantiomeric righthand C4 chain is of the So configuration.

Therefore, C1 has the top two priority chains as Ro and So. Because R has priority of S, the same is true for Ro and So. The configuration of C1 is r given Ro>So>CH3>H. By symmetry C4 is also of the r-configuration. Structure 1c is a condensed version of 1b.

cis-1,4-Dimethylcyclohexane (Fig. 2) has a plane of symmetry through C1 and C4 and a two-fold axis of rotation orthogonal to the plane of the ring. Both of these pseudoasymmetric centers will have the same configuration. The only difference between digraph 2b and 1b is the stereochemistry at C1 while the Ro/So assignments remain the same. The priorities remain the same, Ro>So>CH3>H. Both C1 and C4 have the same s-configuration.


Fig. 2

cis-1,4-Dimethylcyclohexane


Fig. 3


trans-1-Methyl-4-propylcyclohexane

1-Methyl-4-propylcyclohexane

These two stereoisomers, Figs. 3 & 4, provide an interesting comparison to Figs. 1 & 2, respectively. Note that the temporary Ro/So assignments in 1-methyl-4-propylcyclohexanes are opposite those in 1,4-dimethylcyclohexanes. This is the result of a change in priorities. In digraph 3b the propyl group takes priority over the chain bearing the phantom atom. The carbon of the terminal methyl group of the propyl chain has an atomic number of six while the terminal phantom carbon (red dot) has an atomic number of zero. Therefore, the assignment of So to the lefthand center of C4 arises from the priorities C3-C2-C1>propyl>C5-C6-C1>H. The same reasoning applies to the Ro assignment in 3b as well as 4b. The C1 center of the trans-isomer (3c) is of the s-configuration while the cis-isomer (4c) has the r-configuration at C1.

The Ro/So assignments for C1 in 3d are the same as in 1b. The configuration at C4 in 3d is "r" following the priorities C3-C2-C1>C5-C6-C1>propyl>H [Ro>So>propyl>H]. The same arguments may be applied to the C4 s-configuration of the cis-isomer (Fig. 4).

The only difference between 5a and 6a is the configuration at C1. All other assignments remain the same. The priorities are Ro>So>CH3>H and C1 is of the r-configuration.The assignment at C4 in 4d is the opposite of 3d because the Ro/So assignments have been switched at C1. The priorities are Ro>So>CH3CH2CH2>H and C4 is of the s-configuration.

Fig. 4



cis-1-Methyl-4-propylcyclohexane



Fig. 5


trans-4-Methylcyclohexan-1-ol

4-Methylcyclohexan-1-ol

These trans/cis isomers of 4-methylcyclohexan-1-ol, Figs. 5 & 6 respectively, have the same temporary configurations at C4 (5b & 6b) as was observed in Figs. 1 & 2. The major difference lies in the Ro/So assignments in 5d & 6d where the priorities are OH>C3-C2-C1>C5-C6-C1>H. The assignment of C1 (5c & 6c) has priorities OH>Ro>So>H while C4 (5e & 6e) has Ro>So>CH3>H.

Fig. 6


cis-4-Methylcyclohexan-1-ol


Fig. 7

trans-1,3-Dichlorocyclobutane

1,3-Dichlorocyclobutane

These trans/cis isomers have the same symmetry as Figs. 1 & 2. Thus, C1 and C3 are identical in each stereoisomer and there will be a single r/s assignment. The trans-isomer has an r-configuration at C1, and of course at C3, with priorities Cl>Ro>So>H.

Fig. 8

cis-1,3-Dichlorocyclobutane


Fig. 9


trans-Decalin

Decalins

trans-Decalin has the same symmetry as trans-1,4-dimethylcyclohexane (Fig. 1) and trans-1,3-dichlorocyclobutane (Fig. 7) but the analysis is not as simple as these earlier cases. At C1, C6 has the highest priority and the hydrogen has the lowest. How does one assign Ro/So designations to distinguish C2 from C10? In 9b the bond between C1 and C10 and a phantom atom C1 is created (blue dot) with mass zero. Now the vertical plane of symmetry has been eliminated and C6 has become "chiral". At C6, C1>C5>C7>H because the C7 chain terminates at C1 of mass 12 (red dot) while the C5 chain terminates in C1 (blue dot) of mass zero. Therefore, C6 is assigned as Ro, which begins at C2. Similarly, 9c, the mirror image of 9b, is assigned as So. Relative to C1 (9d), C2 = Ro and C10 = So. Thus, at C1, C6>Ro>So>H and C1 is of the r-configuration.

A similar analysis in Fig. 10 assigns the s-configuration to the methine carbons in cis-decalin.

 

Fig. 10


cis-Decalin



Fig. 11


[2.2.1]-Bicycloheptane

[2.2.1]-Bicycloheptane

[2.2.1]-Bicyclohexane (11a) has two planes of symmetry. One passes through C1-C7-C4 and the other through C1 in addition to the C2-C3 and C5-C6 bond. The latter plane dictates that whatever the assignment is at C1, it will be the same at C4. To determine the configuration at C1, priorities must be establised for C4. Clearly, hydrogen has the lowest priority while C7 has the highest because C7-C1 outranks C3-C2 and C5-C6in 11b. Placing the thumb of your right in the direction of the hydrogen at C4, your fingers point from C7 to C2 to C5. The chain C2-C3 is Ro. Likewise, your left hand assigns the chain C5-C6 as So. Returning to C1, the priorities are C7>Ro>So>H. C1 and C4 are of the s-configuration.

[2.1.1]-Bicyclohexane

[2.1.1]-Bicyclohexane (12a) is similar to the previous example, 11a. While the hydrogen at C3 still has the lowest priority, the bold chain C2-C6-C5-C1 has the second lowest priority. A decision must be made about the chains C3-C2-C1 and C3-C4-C1. Applying the hand rule as above, the assignments are So and Ro, respectively. At C1, the priorities are Ro>So>C5-C6>H. C1 and C3 have the r-configuration.

Fig. 12


[2.1.1]-Bicyclohexane