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The R/S System: A New and Simple Approach to Determining Ligand Priority and a Unified Method for the Assignment and Correlation of Stereogenic Center Configuration in Diverse Stereoformulas Dipak K. Mandal Department of Chemistry, Presidency College, Calcutta 700 073, India;
[email protected] The configurational descriptor (R or S) to a stereogenic center in an organic molecule is specified after the establishment of a priority order of ligands attached to the stereogenic center according to the CIP sequence rules (1, 2). However, the existing schemes used for the application of the prime sequence rule (based on atomic number) to determine ligand priority are lengthy and cumbersome. Further, the assignment of proper descriptors is often difficult because the stereogenic centers are represented in diverse stereochemical formulas such as Fischer, flying wedge, zigzag, sawhorse, Newman, 3-dimensional cyclic structure, and cyclic conformation. This paper addresses these problems in two parts. The first part deals with a new approach providing an “at-a-glance” priority order of ligands differing in constitution. In the second part, a simple and unified procedure for the assignment and correlation of R or S configuration of a stereogenic center in varied stereochemical representations is presented. Determination of Ligand Priority The ligands (i.e., substituent groups) attached to a stereogenic center may differ either in constitution or in configuration. However, in the vast majority of organic compounds, the ligands differ only in constitution and their priority order is determined primarily by the sequence rule higher atomic number precedes lower. To apply this rule, several schemes have been developed, such as (i) tree-graph exploration (3); (ii) use of complemented (duplicate or phantom) atoms for multiple bonds (1, 3); (iii) graphical flowchart scheme (4 ); and (iv) ligand complementation when a ligand is polydentate or has a cyclic or bicyclic component (2, 5). The proper application of these schemes is not always simple and it involves a lengthy and complicated procedure in many cases. Presented here is a new approach with respect to the application of the above sequence rule for determining the priority order of constitutionally different ligands. This approach treats the ligands in their correct and proper bonding connectivity and proposes the following “application rules”. 1. Carbon–oxygen and carbon–nitrogen bond: Count the number of carbon–oxygen and carbon–nitrogen bonds at a similar carbon in ligands, taking a double bond as 2 bonds and a triple bond as 3 bonds. The rule is, greater number of bonds gives higher priority. Carbon– oxygen bond gets precedence over carbon–nitrogen bond. 2. Hydrogen atoms: Count the number of H atoms attached to the first atom (i.e., the atom directly linked to the stereogenic center) of ligands. The rule is, the fewer the
866
number of H atoms attached, the higher is the precedence. If the first atom provides no decision, proceed outwardly and count the least number of H atoms attached to a second atom; then, if necessary, proceed to a third atom, and so on. H itself is not considered as an outward atom (i.e., second atom, third atom, etc.). 3. Chain propagation vs chain termination: If the rule of H atoms cannot provide a decision, then compare the ligands as to whether a ligand possesses the next outward atom (chain propagation) or does not possess the next outward atom (chain termination). The rule is, chain propagation (CP) precedes chain termination (CT). A ligand chain is a chain of first and outward atom(s) in which no such atom is considered more than once and the stereogenic atom is excluded.
The above rules for assigning ligand priority are illustrated in Figure 1 with three sets of ligands: A1–A5, B1–B5, and C1–C5. For ligands A1–A5, the priority order is decided by the rule of hydrogen and the rule of chain propagation (CP) vs chain termination (CT). In each of these ligands, the first atom is carbon with no H atom attached to it; thus the first atom provides no decision. The least number of H atoms linked to a second atom (carbon) is 0, 1, 1, 1, and 3 for A1–A5, respectively, which determines the highest-priority ligand as A1 and the lowest-priority ligand as A5. Among the other three, the ligand A4 does not possess a third atom (i.e., CT) and thus has the lowest priority in the group of A2–A4. The ligands A2 and A3 possess a third atom linked to 1 and 3 H’s, respectively, which makes their relative priority A2 > A3. Thus the overall priority order is A1 > A2 > A3 > A4 > A5. For ligands B1–B5, the priority order (shown in Fig. 1B) is also determined on the basis of the rule of hydrogen and the rule of CP vs CT. The point to note here is that the ligand B2 possesses a seventh atom (i.e., CP), while the ligand B3 lacks the seventh atom (i.e., CT)—since, on going round the ring, the sixth atom gets linked to the first atom, which cannot be considered again as a seventh atom (see the definition of ligand chain in the rule of CP vs CT). The ligands C1–C5 possess carbon–oxygen bonds, which need to be considered first. The number of such bonds at the first carbon is 3, 2, 2, 1, and 1, respectively, which gives a partial priority order C1 > C2 = C3 > C4 = C5 as per the rule of carbon–oxygen bond. The complete priority order (shown in Fig. 1C) is then easily determined by the rule of hydrogen and the rule of CP vs CT. It may be mentioned that the relative priority of C4 and C5 is decided at the first carbon, and hence the counting of carbon–oxygen bonds at the second carbon in C5 does not arise.
Journal of Chemical Education • Vol. 77 No. 7 July 2000 • JChemEd.chem.wisc.edu
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H A
Ligands
A1
A2
at second atom ( )
0
1 1
at third atom ( ) Priority
A4
CH3 C CH3 CH3 A5
1
1
3
3
CT
CH3 (CH3)2C - CH CH3 A3
(CH3)2C - C(CH3)3
Least No. of H atoms
B
H C
CH
A1 > A2 > A3 > A4 > A5
Ligands
CH
CH2(CH2)2CH2CH3 CH n-C5H11
CH2(CH2)3CH2CH3 CHCH3 CH n-C6H13
CH
CH2
B1
B2
B3
B4
B5
1
2
2
2
2
at sixth atom ( )
2
2
3
CT
at seventh atom ( )
CP
CT
Least No. of H atoms at second atom ( )
Priority
B1 > B2 > B3 > B4 > B5
O C
Figure 1. Determination of priority order of ligands. The outward atom (i.e. second atom, third atom etc.) refers to the relevant atom other than H. CP: chain propagation (i.e. the outward atom considered exists); CT: chain termination (i.e. the outward atom considered does not exist).
OH C CH3 CH3
CHOHCOOH
C2
C3
C4
C5
2
2
1
1
at first atom ( )
1
1
0
1
at second atom ( )
0
0
at third atom ( )
CP
CT
Ligands
H C
OCH3 CH OH
C OH
C1 No. of carbon-oxygen bonds at first carbon ( ) 3
O
Least No. of H atoms
Priority
C1 > C2 > C3 > C4 > C5 O
D
Ligands
O C CH2CH3
O
C D2
D1
O Ligand chain
Priority
O C
N D3
F C
C O C
CHFCH2Cl CH CHBrCH2Br D4
C N
C
C C Br Br
CHFCH2I CH CHBrCH2Cl D5 F C
C C C Br Cl
D1 > D2 > D3 > D4 > D5
Note the following points: 1. When a decision can be reached directly on the basis of difference of atomic number of first or outward atom in the ligand chain, other rules do not apply. An example is shown in Figure 1D, wherein the priority order of ligands D1–D5 is determined as D1 > D2 > D3 > D4 > D5. It may be noted (3) that, for ligands D4 and D5, a third atom (Br vs F) decides the branch to be considered as the ligand chain and a fourth atom (Br vs Cl) decides the relative priority as D4 > D5. 2. The hydrogen isotope (D or T), if present in a ligand, is to be included in the counting of H atoms when using the rule of hydrogen. If this procedure fails to provide a decision, the sequence rule higher mass number precedes lower prevails. It therefore follows that –CH2CH2CH3 > –CD2CH3 > –CH2CH3.
3. The rule of hydrogen does not apply to the case when the same atom exhibits different valencies in 䊝 ¨ two ligands. For example, – NHMe2 precedes – NMe 2 because the lone pair has lower precedence than H.
Figure 2 shows how the four ligands attached to a stereogenic center (starred carbon) in chiral molecules can be assigned an at-a-glance priority order by the present approach. In (᎑)-menthol (Fig. 2A), the ligands attached to a stereogenic center (*C-1) are OH, C-2 branch, C-6 branch, and H. The number of H atoms attached to C-2 and C-6 is 1 and 2, respectively (indicated by arrow). Thus the complete priority order is OH > C-2 > C-6 > H. In (᎑)-camphor (Fig. 2B), the stereogenic center (*C-1) is connected to C-2 branch, C-7 branch, C-6 branch, and CH3. C-2 is linked by a C=O; C-7, C-6, and methyl C are attached to 0, 2, and 3 H atoms, respectively. So the priority order is C-2 > C-7 > C-6 > CH3.
JChemEd.chem.wisc.edu • Vol. 77 No. 7 July 2000 • Journal of Chemical Education
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In the decalone derivative (Fig. 2C), the ligands attached to a stereogenic center (*C-9) are C-1 branch, CHO, C-10 branch, and C-8 branch. The number of carbon-oxygen bonds at C-1, aldehydic C, and C-10 is 2, 2 and 1, respectively, and no such bond exists at C-8. The number of H atoms attached to C-1 and aldehydic C is 0 and 1, and hence the priority order is C-1 > CHO > C-10 > C-8. A partial structure of cholestan-3-ol is shown in Figure 2D. The priority order of ligands (C-9 branch, C-5 branch, C-1 branch, and CH3) attached to the stereogenic center (*C-10) can be assigned using only the rule of hydrogen. The number of H atoms at C-9, C-5, C-1, and methyl C is 1, 1, 2, and 3, respectively. The least number of H’s attached to the next carbon (second atom) is 1 for C-9 branch and 2 for C-5 branch. Thus the priority order is C-9 > C-5 > C-1 > CH3. In the molecule shown in Figure 2E, the ligands linked to the stereogenic center (*C) are –CH 2 OCH 2 CH 3 ; –CH2CH2OCH2CH3; clockwise branch (–CH2OCH2CH2–) of the ring, and counterclockwise branch (–CH2CH2OCH2–) of the ring (see the definition of ligand chain in the rule of CP vs CT; *C is not included in any branch). The presence or absence of a C–O bond at the first carbon gives the partial sequence –CH 2 OCH 2 CH 2– = –CH 2OCH 2CH 3 > –CH 2 CH 2 OCH 2 CH 3 = –CH 2 CH 2 OCH 2 –. Now, –CH 2OCH2CH2– (2 H’s at the fourth atom) precedes –CH 2 OCH 2 CH 3 (3 H’s at the fourth atom). Again, –CH2CH2OCH2CH3 (2 H’s at the fourth atom and presence of fifth atom [CP]) precedes –CH2CH2OCH2– (2 H’s at the fourth atom and absence of fifth atom [CT]). Thus the complete priority order is clockwise branch > –CH2OCH2CH3 > -CH2CH2OCH2CH3 > counterclockwise branch.
B.
A. 1H
0H 3H
OH
2
7
2H
*1
H
O
1 6
6
*
2
2H C-2 > C-7 > C-6 > CH3
OH > C-2 > C-6 > H C=O & 1H
C.
2H OHC O 8
D. 3H
C=O & OH
2H
9
1H 1
1
9 10
* 10
C-O OH
2H
C-1 > CHO > C-10 > C-8
*
1H
5
HO 1H
H
C-9 > C-5 > C-1 > CH3 3H
E. 2H
CH2OCH2CH3
*
CH2CH2OCH2CH3
O
2H & CP 2H & CT
-CH2OCH2CH2- > -CH2OCH2CH3 > -CH2CH2OCH2CH3 >-CH2CH2OCH2(clockwise branch) (counterclockwise branch)
Figure 2. Priority order of ligands attached to the stereogenic center (*C). The arrows , , and label the first atom, second atom, and fourth atom, respectively, of the ligands. 0H, 1H, 2H, and 3H indicate the number of H atoms attached to the carbon marked by the arrow. CP: chain propagation; CT: chain termination.
Assignment and Correlation of Absolute Configuration Various methods have been devised for assigning the R/S configurations to stereogenic centers in projection or perspective formulas (5–16 ). Eliel has addressed this problem in 3D formulas by formulating a scheme for eight possibilities of ligand permutation (5). Wang and Yang reported a mathematical procedure for specifying the R/S configuration in a variety of stereochemical formulas (17 ). However, when a stereogenic center is represented as a Fischer projection, the assignment is straightforward and simple. If the lowest-priority ligand is on the vertical line of the Fischer projection, the array of the remaining three in descending priority sequence gives the correct descriptor, R for clockwise and S for counterclockwise; but if the lowest-priority ligand is on the horizontal line, the opposite assignment is correct (8). The procedure for the transformation of a pertinent stereogenic center in any stereochemical representation into a Fischer projection, for assigning the R/S configuration, is as follows. For a stereogenic center, any two ligands in a plane (a and b in Fig. 3) are chosen, and a clockwise arc (through the tetrahedral angle) is drawn from a to b taking the stereogenic atom as geometric center. The stereoformula is transformed into a Fischer projection (Fig. 3), in which the vertical line is defined with the ligand a (at the initial position of the arc) at the top and the ligand b (at the final position of the arc) at the bottom. The ligands c (in front) and d (in rear) would then occupy the horizontal right and horizontal left positions, respectively. One may also consider a counterclock868
vertical bottom horizontal left a
b d
clockwise arc
c
d a
vertical top
c b horizontal right
Figure 3. Mnemonic for transformation of 3D structure into Fischer projection.
wise arc (b → a), when the ligand c (in front) would take up the horizontal left, with the ligands b and a being placed, respectively, at the vertical top and vertical bottom of the Fischer projection. The procedure is illustrated with two examples in Figure 4. Figure 4A is for a wedge/dash structure (e.g., flying wedge, zigzag, and 3D cyclic structure) and Figure 4B is for conformational formulas (Newman, sawhorse, chair, and other cyclic conformations). In the 3D cyclic structure (Fig. 4A), each of nine stereogenic centers is labeled with its descriptor. The Fischer projections for stereogenic centers, C-5 and C-10 are drawn for illustration. For C-10, a clockwise arc (C-5→C-1) is drawn when 10-methyl is in front and C-9 is in rear. The descriptor assigned for C-10 is S. The same result (descriptor) is obtained whether one defines a clockwise arc (C-9→C-5) when C-1 is in rear or a clockwise arc (C-1→C-9) when C-5
Journal of Chemical Education • Vol. 77 No. 7 July 2000 • JChemEd.chem.wisc.edu
In the Classroom
20
A.
H
17
13
H 1
HO
14 8
3
H
H
H
5
4
3S, 5S, 8R, 9S, 10S, 13R, 14S, 17R, 20S B.
9-C
2
1
CH3
10
4
C-1
3
6
H
C-4
C-6
7
5 4
2
C-5
9
10
2
1
C-10
3
5S
10S
CO2H 1 2
Ha 3
Hb
CO2H
H
CH3 Hb
H
2
4
C-3
2-C
2
2
3
Ha
OH
OH
CH3 3
1
2S
2S
Ha : pro-R Hb : pro-S
C.
O
O 1
3
H
2
Cl 3
1
O
2
Cl
H
1
H 3
H
in Figure 4C. The stereogenic center (C-2) of 2-chlorocyclohexanone is linked to four ligands: –Cl, C-1 branch, C-3 branch, and H. At first, the absolute configuration of C-2 is defined in the 3D cyclic structure by a clockwise arc (H→Cl) when C-1 is in front and C-3 in the rear. The equivalent chair conformation and Newman projection are then readily obtained by correlation (i.e., H→Cl clockwise arc, front C-1 and rear C-3). The descriptor for C-2 as determined from the transformed Fischer projection (not shown) is S. This method for assigning and correlating stereogenic center absolute configuration has several advantages. It requires a minimum of spatial imagination and serves as a general, unified procedure for all stereochemical representations. The method is not only fast and simple to use, but also flexible in the sense that one is free to choose any pair of ligands for defining the clockwise (or counterclockwise) arc and thereby recognizing the front or rear ligand. Lastly, the procedure is also useful for assigning descriptors to stereoheterotopic (enantiotopic or diastereotopic) ligands in any stereoformula.
2 H
Cl
Figure 4. Assignment and correlation of absolute configuration in stereoformulas. A: (3S, 5S, 8R, 9S, 10S, 13R, 14S, 17R, 20S)Cholestan-3-ol. B: (2S)-3-Hydroxy-2-methylpropanoic acid (Ha: pro-R; Hb: pro-S). C: Correlation of (S)-2-chlorocyclohexanone in 3-dimensional cyclic structure, chair conformation, and Newman projection. (Numerals in circle represent priority order of ligands).
is in rear. The stereogenic center, C-5 is designated as S from the Fischer projection drawn by tracing a clockwise arc (C-10→C-6). The descriptors for other stereogenic centers are derived similarly. The molecule in sawhorse representation (Fig. 4B) contains a stereogenic center (C-2) and a prostereogenic center (C-3) with two diastereotopic ligands (Ha and Hb). The descriptor for C-2 is assigned as S from the Fischer projection drawn for a clockwise arc (CO2H→CH3). For assigning descriptors to Ha and H b, a clockwise arc (Hb→OH) is considered to draw the Fischer projection shown. For Ha, the sequence is OH > C-2 > Ha(D) > Hb, and for Hb, the sequence is OH > C-2 > Hb(D) > Ha. Hence, Ha is pro-R and Hb is pro-S. An example of correlation of absolute configuration in three stereoformulas (3D cyclic, chair, and Newman) is shown
Acknowledgment I would like to thank the anonymous referees for helpful suggestions. Literature Cited 1. Cahn, R. S.; Ingold, C.; Prelog, V. Angew. Chem., Int. Ed. Engl. 1966, 5, 385–415. 2. Prelog, V.; Helmchen, G. Angew. Chem., Int. Ed. Engl. 1982, 21, 567–583. 3. Eliel, E. L.; Wilen, S. H.; Mander, L. N. Stereochemistry of Organic Compounds; Wiley: New York, 1994; pp 103–112. 4. Starkey, R. J. Chem. Educ. 1995, 72, 315–318. 5. Eliel, E. L. J. Chem. Educ. 1985, 62, 223–224. 6. Dietzel, R. A. J. Chem. Educ. 1979, 56, 451. 7. Idoux, J. P. J. Chem. Educ. 1982, 59, 553. 8. Epling, G. A. J. Chem. Educ. 1982, 59, 650. 9. Brun, Y.; Leblanc, P. J. Chem. Educ. 1983, 60, 403–404. 10. Ayorinde, F. O. J. Chem. Educ. 1983, 60, 928–929. 11. Diehl, J. W. J. Chem. Educ. 1984, 61, 90. 12. Beauchamp, P. S. J. Chem. Educ. 1984, 61, 666–667. 13. Huheey, J. E. J. Chem. Educ. 1986, 63, 598–600. 14. Aalund, M. P.; Pincock, J. A. J. Chem. Educ. 1986, 63, 600–601. 15. Kotera, M. Bull. Chem. Soc. Jpn. 1986, 59, 639–640. 16. Ruekberg, B. J. Chem. Educ. 1987, 64, 1034. 17. Wang, J. X.; Yang, C. J. Chem. Educ. 1992, 69, 373–375.
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