Determining a Chiral Molecule's R/S Configuration Using the Rule of Multiplication Jin-Xian Wang and Chi Yang Northwest Normal University, 95 An Ning Road (E.) 730070,Lanzhou, China The most widelv acce~tedmethod for s~ecifvine the configuration about stereogenic center1 i s t h e - R I ~system. This determination involves a two-steo Drocess. The first step requires a n assignment of priority to each group about the stereogenic center. The second step involves a mental transfer of the two-dimensional figure into a three-dimensional model, followed by the determination of R or S . However. some individuals. narticularlv students being exposed fo; the first time to s&eochernic& considerations, often encounter difficultv in the absence of a three-dimensional model when required to draw or mentally visualize the DroDer arramement for snecifvine the confirmration. ~ i e t z e l i l provided ) a rule for mathemitical comparison of the nrioritv numbers of a chiral comwund in a Fischer Dmjection to make i t possible to determine whether thi arrangement of groups represents a n R or S confiiration without the need for any three-dimensional manipulation. Some recent articles report simple methods (2-13) for specifying the RIS configuration of a stereogenic center, but these methods are only applicable to Fischer projec(5).There is no uniform. simtions or ~ e r s ~ e c t i formulas ve ple m e t h o d for specifying t h e RIS configuration of a to a variety of c o n k-stereoeenic center that is andicable .. urational formulas. We have developed a simple, rapid, and general method for specifying the WS configuration of a stereogenic center. Now we report a new rule of multiplication that can be used to specify the configuration of a stereogenic center found in any configurational formula used to depict a chiral molecule. This rule is simple, general, and efficient, and it can be used in many cases. I t can be applied not only to Fischer nmiections. but also to wedee formulas.. *Dersoec" tive formulas, Newman formulas, cyclic molecules, and chiral axis molecules. I n addition, given the name of a chiral molecule, it is possible to write any kind of configurational formula for the molecule based on this information.
Table 1. Sign of Rules of Multiplication
;
&
&
-
.
-
&
Rules of Multiplication Assign the priority sequence for the groups attached to the stereogenic center based on the Cahn-Ingold-Prelog sequence rules, and express the sequence by 1 , 2 , 3 , 4 (where1 represents the highest priority p u p , 2 the second highest priority group etc.). Determine the Observational Gmup 'In this paper, the term "stereogenic center" is used as a replacement for the term "chiral center". See Mislow, K. Siegel, J. J. Am. Chem. SOC.1984, 106,3319-3328.
No
Determination Factor
"-" Sign
"+"Sign
A
Position of observational group
Forward or above the ring
Behind or below the ring
B
Sequence number of theobservational
Odd (1 or 3)
Even (2 or 4)
C
Spatial orientation of the three groups besides the observational group
~lodcwise
Counterclockwise
Table 2. Rules of Multiplication 1.
Multlply signs associated with the determination factors (AxBxC).
2
If the result of this multiplication is "+", then the configuration is "I?.
3.
If the result of this multiplication is v'; then the configuration is ''9..
In wedge formulas, Neu man formulas, perspective formulas, chiral aas, and Flaoher prolectmn, use enher the group that is lrnked to the skrw~wnwcenter and is in fmnt of rhr planc of thr papcr or the group that is linked to the sterewwnlc v n t e r and is behind the plane of the paper as theobservational group. (Since b; convention the vertical .. emuos mint into and . of a Fiseher nroiection . " bchnnd the plnnr of the pnprr, whllr chc hor~mntaigroups pomt fwward and out of the plane of the paper, thrs means that any group attached to a stereogeniccenter can serve as the observational group in a Fischer projection. In Newman formulas and Perspective formulas, the observational group for the stereogenic center nearest to the observer is the group linkedto the stereogeniccenterthat is behind the vlane of the naner. . . while the observational group for thp sterengemc crnter fnrth~stfrom the nhserver is the group lmked to the dereogenw center that la ~n fmnt of t h p plane of the paper, In cyclw compounds, use as the observational group either the p u p attached to the stereogenic center that is above the ring or the group attached to the stereogenic center that is below the ring. Determination Factor A (Table 1) Define a n y ub~ervatiunalpoup that is in front uf the plane of paper nr "+", while any observational group that
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373
Table 3. Determination of RIS Configuration Configurational formulas
I
Observational group
CHO
c3
c2
c3
c2
COOH
COOH
OH
COOH
Br
Determination factor
B -
+
+
-
-
-
-
+
-
1
S
R
R
R
S
R
S
S
R
S
RIS Configuration Name
S-) Glyceraldehvde
(2R,3R)-(+)-Tartaric acid
(2R,35)-2- BromodChlorobutane
(ZR,3S)-Z-(+)-Tartaric (1S,2@-1,2-Dihydroxyacid t,2-Cyclopropanedicarboxvlic acid
aOb~ewationalgroup can be determined randomly. The result is the same. Viewed from Y.
VI
gure 1. Determination of a chirai molecule's WS configuration using the rule of multiplication. group) attached ta the stereogenic center (Factor C), determine the RIS wnfiguratian. If the composite sign produced when all three determination factors are multiplied together is "+"then the configuration is R; whereas, if the mmposite sign produced when all three determination factors are multiplied together is "-" then the configuration is S. (Table 2).
Figure 2. Based on the wmpound's names write RIS configuration formulas (Fischer projections). is behind the plane of paper is "-". Any ubsewalionol noup lrnked to a stereogcnic ccnrrr thnt is pnrt of a ring syscrm is " *" whrn a is above the ring and - ' whrn it is below the ring. Determination Factor B (Table 1) An observational gmup that receives an odd number (1or 3) in the priority sequence is "+"; whereas, if it receives an even number (2 or 4) in the priority sequence it is "-". Determination Factor C (Table 1) Ignoring the observational group, when the spatial orientation of the three other groups linked to the stereogenic center is clockwise (mine fmm hieher to lower orioritv) assign a "+" value; whereas, if it is munterdodrwise assign a "-' value. According to the position of the observational group (Factor A), the priority sequence number (odd or even) of the ahservational group (Factor B), and the direction of spatial orientation of the three other groups (besides the observational
374
Journal of Chemical Education
Applying the Rules of Multiplication To Obtain a 3-D Configurational Formula Based on a Compound's Name For t h e determination of chiral molecule RIS configuration, see Figure 1a n d Table 3. Based on t h e wmpound's name, write t h e RIS wnfiguration formulas. Procedure: (1)Write the condensed formula. (2) Assign the priority sequence for groups attached ta the stereogenic center based on the sequence rules. (3) Write the RIS configuration formulas from the rule of multidieation. The following example illustrates t h e procedure for t h e compound (2R,3S)-2-chloro-3,4dihydroxybutanal
~-.~-~~~ ~~~~~
c4
c2
c3
c1
*Cz: C1> CHO > CH(0H)-CH20H > H 1
2
3
4
*C3:
OH > CH(C1) -CHO > CH20H > H 1
2
3
4
Fischer pmjectians2( F i g . 2 1. Newman formulas and perspective formulas3( F i g . 3). Literature Cited 1. 2. 3. 4. 5.
6. 7. 8. 9.
Dietrel,R.A..J . Chem Educ. 1919,56,451. Idowt. J. P. J Chem. Edur.1982.59.553. Epling, G.A. J. C h . Edw. 1982,59,650. Ayorh~de,F. 0.J . C h m Educ. 1983,60,92&929. E1iel.E. L. J C h m . Educ. 1985, 62,221-224. Ruekberg, Ben.J. C h m . Edue. 1981.64.1034. Nasipuri, Dhanonjoy J. Chem. Educ. 1889,66,48%484 Reddy,K R. N. J Chem. E d w . 1989,66,478. Mattem, D. L. J. C h m . Educ. 1985.62, 191.
2The Ci and OH groups are used as the observational group in
Fi ure 2. %he observational groups are
2 Figure 3. Based on the compound's name write RIS configuration formulas (Newman formulas and perspective formulas). 10. 11. 12. 13.
Zhang, LHuarue TongboafChmistqJ,19886.39-41. Ye, F;Zhang, Guobh.Huarue Tbngboo ( C h u o l s t ~ )1, 9 8 6 , 4 1 4 JNorthweat TPach. Coll. 1981, 87-99. Wang, Wane J.-X.: Gao. H. J. Ni Teach. CoU. 1983.3751.
in Figure 3
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Number 5
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