In the Classroom
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; dkmandal@cal.vsnl.net.in
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
In the Classroom
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 – N̈Me2
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
867
In the Classroom
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.
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JChemEd.chem.wisc.edu • Vol. 77 No. 7 July 2000 • Journal of Chemical Education
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