Cahn-Ingold-Prelog Rules: More on Rings and Digraphs

How to Manipulate JSmol Structures

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This page describes how to treat small rings as substituents via the CIP method, how to convert cyclic compounds into acyclic digraphs and how to distinguish between duplicate and phantom atoms.

The 1993 update of the 1982 Cahn-Ingold-Prelog rules is located here.

  

(R)-Cyclopropyl-2-methylpropan-1-ol


The assignment of R/S-configurations to the enantiomers of 2-butanol is trivial by the CIP method. But how does one handle rings as substituents? The solution to the problem is to convert the structure to an acyclic version, a digraph as in 1a and 1b.

Using cyclopropyl alcohol 1 as an example, consider the path C4-C5-C6-C4 around the ring. The path C4-C5-C6-(C4 ), wherein the last term in the chain is a tetradentate, duplicate carbon attached to three atoms of atomic number zero (phantom atoms). The duplicate atoms, in this instance carbon, are enclosed in parentheses and still have their respective atomic number. The phantom atom ranks below hydrogen.

In digraphs 1a and 1b the number of the duplicate atom is displayed as (4). Alternatively, the path around the ring could also be traversed via route C4-C6-C5-(C4 ).

The red numbers in digraph 1b signify the sphere or the distance the atoms are remote from the center of stereochemistry. The oxygen, C2, C4 and H are in the first sphere with oxygen having the top priority and the hydrogen the lowest. The priority of the C2 and C4 chains must be determined. No priority can be assigned at sphere 1 because O>C2= C4>H. C2 and C4 are equivalent [C,C,H] in sphere 2. Sphere 3 breaks the tie where C4 [C,H,H] supercedes C2[H,H,H]. The priorities for C1 are O>C4>C2>H. The stereocenter is of the (R)-configuration.

Notice that spheres 4 and 5 were not utilized. Sphere 4 contains a duplicate atom (4) while sphere 5 contains six phantom atoms of at. no. = 0. Most of the subsequent digraphs will not display hydrogens or phantom atoms but their presence will be implied.


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(S)-1-Cyclopropyl-2-propylpentan-1-ol

Cyclopropyl alcohol 2 is a homolog of cyclopropyl alcohol 1. The digraphs display a high degree of symmetry. C5 and C11 bear a total of three hydrogens each in sphere 5 because they are methyl groups whereas the two duplicate carbons (C6) bear "three atoms each of zero atomic number". The priorities are O>C2>C6>H. The stereocenter C1 is of the (S)-configuration.

 

 


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(3S,4S)-4-Methylhex-3-en-1-ol

The C4 (S)-configuration of allylic alcohol 3 is determined in the first sphere: C4{C3[O,C,H]>C5[C,C,H]>C7[H,H,H]>H}. The analysis of the C3 stereochemistry is not as obvious. The bold lines in digraph 3b distinguish betwee C2 and C4. In sphere 3 [6,H,H]>[(2),H,H] because in sphere 4 (not shown) the former is terminated with [H,H,H] while the latter has [0,0,0] as terminators. Therefore, C4>C2 because every other atom is of higher priority than one with an at. no. = 0. The order of priorities is O>C4>C2>H. The stereocenter C1 is of the (S)-configuration.

 
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(1R,5S,6R)-5,6-Dimethylcyclohex-2-en-1-ol

As was the case with allylic alcohol 3, allylic cyclohexenol 4 displays symmetry in its digraphs. The C5 and C6 assignments are resolved at the sphere 2 level: (S)-C5 {C6[C,C,H]>C4[C,H,H]>C7[H,H,H]} and (R)-C6 {C1[O,C,H]>C5[C,C,H]>C8[H,H,H]}.

C1's assignment is resolved in sphere 2 (digraph 4b). The C6 route has [C,C,H;8,5,H] while the C2 route has [C,(C),H;3,(3),H]. The order of priority for C1 is O>C6>C2>H. The stereocenter C1 is of the (R)-configuration.


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(-)-α-Pinene

α-Pinene (5a) is a bicyclic monoterpene (C10H16) that occurs as both enantiomers in nature. [Note: The degree of unsaturation of α-pinene is 3, one double bond and two rings. Therefore, α-pinene is bicyclic.] The determination of the configuration at C1 and C5 is not trivial by just looking at structure 5 or 5a. Duplicate atoms are added to the double bond of 5 to form structure 5a. To assign the configuration at C1, digraph 5b is constructed. There are three carbon chains (C2,C6,C7) each of which splits into two additional pathways back to C1. Notice that there are six (1) terminations in the digraph. The six pathways are:

  1. 1-2-3-4-5-6-(1)
  2. 1-2-3-4-5-7-(1)
  3. 1-6-5-4-3-2-(1)
  4. 1-6-5-7-(1)
  5. 1-7-5-6-(1)
  6. 1-7-5-4-3-2-(1)

Hydrogen has the lowest priority and C7 (C,H,H) has the next lowest priority. Does C2 or C6 have the top priority? The distinction is made in sphere 2. C2 is bound to C3 , (C3) and C10 while C6 is bound to C5, C8 and C9. Only (C3) is monodentate and bound to 3 atoms with at. no. = 0. Therefore, given that O>C[H]>C(0)>H, the priority order for C1 is C6>C2>C7>H. The stereocenter C1 is of the (S)-configuration.

The configuration of C5 is detailed in digraph 5c. In sphere 2, C1, C8 and C9 are bound to C6, which takes top priority. The distinction between the C4 and C7 pathways is resolved in sphere 3. The C7 pathway displays C4, C6, and H [C,C,H] while the C4 route reveals C2, (C2), and H [C,(C),H] in sphere 3. The C7 path takes precedent over its C4 counterpart. The C5 priorities are C6>C7>C4>H. The stereocenter C5 is of the (S)-configuration.


(1S,5S)-α-Pinene
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(+)-Camphor

The assignment of configurations at C1 and C4 of camphor is easier that the case of α-pinene. Examination of structure 6 or digraph 6a reveals for C1 that the C10-methyl group has the lowest priority [H,H,H] while C2 has the highest priority [O,O,C]. There is no tie to break between C7 [C,C,C] and C6[C,H,H]. The priorities for C1 are C2>C7>C6>H; C1 has the (R)-configuration. This result is born out in a more formal way in digraph 6b.

As with C1, C4 has no ties to break. In digraph 6c, sphere 1{C7 [C,C,C]}>sphere 2{C2[O,[O],C]}>sphere 3{C1[C,C,C]}>H. The priorities for C4 are C7>C3>C5>H; C4 has the (R)-configuration. For both C1 and C4 it is the spheres alone that determine priorities since there are no ties to be resolved.


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(+)-Myrtenal

Enantiomer 7 of myrtenal is a natural product and the oxidation product of (1S,5S)-α-pinene 5. In digraph 7b the hydrogen is the lowest priority group; C7 [C,H,H] precedes it. C2 and C6 are the same in sphere 1 because they have the equivalent patterns [C,C,(C); 3,10,(3)] and [C,C,C; 5,8,9], respectively, in sphere 2. The decision is made in sphere 3. The C2- C10 route displays {O,[O],H} while the C6 route reveals [C,C,H] in sphere 3. A single oxygen takes priority over any carbon. The priorities for C1 are C2>C6>C7>H. The stereocenter C1 is of the (S)-configuration.

For stereocenter C5, C6 takes top priority while the distinction between C4 and C7 is resolved in favor of C7's [C,C,H] over C4's [C,(C),H] in sphere 3. Notice that these determinations are made prior to sphere 5 where the oxygens appear. The priorities for C5 are C6>C7>C4>H.The stereocenter C5 is of the (R)-configuration.

The same conclusion for C5 is reached in the circular digraph 7d. Sphere 3 has a tie between C2 and C6 for the C7 --> C1 path versus C2 and (C2) in path C4 --> C3. The tie is broken in sphere 4 where the red ovals cancel each other but the green oval supercedes the phantom atoms in the blue oval. Duplicate atoms, which are in the same nth sphere as a non-duplicated atom, are equal to one another [C = (C)]. It is only in the (n+1)th sphere that a distinction is made.



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(1S,4S,5S,6R,8S)-(+)-Sativene

(arbitrary numbering system)

Sativene is a tricyclic sesquiterpene that has five stereocenters. Four of the assignments are straightforward, solvable at the first or second sphere level. However,the C5 stereocenter solution is a bit more complex. In partial digraph 8c the three carbons, C4, C6 and C8, contiguous with C5 are equivalent since they each protrude into sphere 2 as C4[3,11,H], C6[1,9,H] and C8[7,10,H], all of which satisfy [C,C,H]. These data are listed in the chart below. The blue pattern in the chart for sphere 3 assigns C4 to a priority just above the hydrogen in sphere 1. The pattern [14,15,H;C,C,H] in the path from C4 ranks lower than those from C6[2,7,12;C,C,C] and C8[1,13,(13);C,C,(C)], both of which are equal to each other. Sphere 4 resolves this tie. While C6[8,13,(13)] = C8[2,6,12] and C6[3,H,H] = C8[(7),H,H], C6[H,H,H] prevails over C8[0,0,0]. Thus the order of priorities is C6>C8>C4>H. The stereocenter C5 is of the (S)-configuration.



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(1S,5S)-5-Methylbicyclo[3.1.0]hex-2-ene

There are two stereocenters, C1 and C5, in the small, bicyclic alkene 10. Digraph 10b has hydrogen as the lowest priority group in sphere 1. Sphere 2 distinguishes among the remaining three groups. The 1--->5 path has [7,6,4;C,C,C] while the 1--->2 route shows [3,(3),H;C,(C),H and the 1--->6 path displays [5,H,H;C,H,H]. The order of priorities at C1 is C5>C2>C6>H. The stereocenter C1 is of the (S)-configuration.

The sphere 1 C7 Methyl has the lowest priority for C5 in digraph 10c. The 5--->1 path in sphere 2 reveals [6,2,H;C,C,H]; route 5--->4 has [3,H,H;C,H,H]; and 5--->6 displays [1,H,H;C,H,H]. The tie between the last two paths is broken in sphere 3 as the 5--->6 route has [7,2,(5);C,C,(C)] priority over 5--->4 that has only [2,(2),H;C,(C),H]. The order of priorities at C5 is C1>C6>C4>C7. The stereocenter C5 is of the (S)-configuration.



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