626 VI. CAROTENOIDS AND RELATED COMPOUNDS 



It has been calculated that if X and X' are both hydrogen atoms, they 

 would be 1.7 A. apart. Although this is somewhat less than the usual dist- 

 ance of the van der Waals contact, a molecule of this type can exist by re- 

 moving the strain to a considerable extent by small rotations out of the 

 coplanarity. If, on the other hand, X or X' is replaced by a methyl group, 

 the distance is only 1.6 A,, which is about one-half the distance of the van 

 der Waals contact. Such a compound would therefore be highly unstable 

 and could not exist. ^" The spatial relationship when two hydrogens or one 

 hydrogen and one methyl group occupy the positions a and a' in relation 

 to the double bond is illustrated graphically in Figure 14. 



Fig. 14. A graphic illustration of the positions occupied by 

 two hj drogen atoms or by one hydrogen atom and one methyl 

 group in a, a '-positions to a double bond when a cis configura- 

 tion exists. «i'«7 



The number of theoretically possible stereoisomers is therefore much 

 lower in the carotenoid molecule which contains branched chains than in 

 the unbranched aliphatic compound containing the same number of con- 

 jugated double bonds. The number is also lower when the carotenoids are 

 symmetrical, i.e., the two halves of the molecule are identical, than when 

 the compounds are unsymmetrical, i.e., the two halves of the molecule are 

 dissimilar. If n is the number of stereochemically effective double bonds, 

 the possible isomers can be calculated by the following equations: 



Unsymmetrical: N = 2"' 

 Symmetrical : 



n - odd A^ = 2^"-'^ -.(2^""'^/' + 1) 



n = even N = 2^""^-^(2'^''' + 1) 



The number of such possible isomers is calculated in Table 21. 



Since the natural carotenoids contain only 4 to 7 stereochemically effec- 

 tive double bonds, the largest number of stereoisomers possible is 128, 

 which is the case with lycoxanthin and rhodoviolascin.^*" The total num- 

 ber of isomers for the common carotenoids is summarized in Table 22. 



