FIGURE 106.-Fischer projectional formulas and the corresponding names for the

pentoses, hexoses, and heptoses.

5. CORRELATIONS BETWEEN OPTICAL ROTATION AND STRUCTURE

Study of the relationship between structure and optical rotation began with Van't Hoff [39], who advanced the principle that the optical rotation of the molecule is equal to the algebraic sum of rotations due to the constituent atoms, the rotations of which change from A to A when the atomic configuration is replaced by its mirror image. Accordingly, Van't Hoff represented the optical rotations of the open-chain modifications of the four pentoses in the following

"Since the sum of No. 2, No. 3, and No. 4 is equal to A+B+C, the rotation of arabinose (probably the highest) should be equal to the rotations of xylose, ribose, and the expected fourth type taken together." This concept, which is designated as the principle of optical superposition, has been applied to the sugars, sugar acetates, glycosides, and many sugar derivatives. Van't Hoff's fundamental principle may be valid provided the asymmetric carbon is replaced by its mirror image and no other changes follow. But each atom in the molecule influences the neighboring atoms, and consequently a stereoisomeric change results in a new distribution of atoms, electrons, and electromagnetic fields so that the conditions necessary for the valid application of the principle are not realized. The effect of changes in the configuration of neighboring groups on the optical rotation of an asymmetric carbon was noted by Rosanoff [40] and by Freudenberg and Kuhn [41]. The configurations of the atoms adjacent to a given asymmetric carbon appear to alter its optical rotation markedly, while the configurations of the atoms separated from the given asymmetric carbon appear to have less influence.

According to the principle of optical superposition, the optical rotation of the sugar is equal to the algebraic sum of the partial rotations at each of the asymmetric centers. For example, the molecular rotation of a-d-lyxose is represented by Aoн-R2-R3+R1, where Дon, R2, R3, and R, are the partial rotations at carbons 1, 2, 3, and 4. The optical rotations and configurations of the pentoses, hexoses, and heptoses are given in table 52.

TABLE 52.-Optical rotation and configuration for the pyranose sugars

The value for twice the rotation (2R) of an asymmetric carbon, perhaps better called the rotational difference, may be obtained by subtracting the equations representing the optical rotations of the separate sugars in such a manner as to eliminate all of the variables except one. Some values calculated in this manner are given in table 53. In order to bring out relations between the various values for the rotational differences and the configurations of the neighboring groups, the configurations of the contiguous groups are indicated by the symbols given in the column on the right. The first term in the symbol represents the configuration of the carbon which lies above the one under consideration, when the formula is written with the reducing group uppermost, while the second term represents the configuration. of the carbon which lies below.

323414° -42-29

The rotational difference corresponding to the first, or reducing carbon, has been designated 2Aon in accord with the terminology originated by Hudson. The numerical values for 2Аон obtained from the alpha and beta modifications of arabinose, glucose, and galactose, and other sugars having like configurations for carbons 2 and 5, are approximately 17,000, while the values from the rotations of mannose and talose, and other sugars having unlike configurations for carbons 2 and 5, are considerably lower, approximately 10,000.

TABLE 53.-Differences in molecular rotation (principle of optical superposition)

1 Hydroxyls on carbons 1 and 4 are cis or trans, as indicated. ? Carbon 1 in a-l-arabinose and in a-l-ribose (Hudson's nomenclature) has the same configuration as carbon 1 in the 8-d-aldobexoses. See footnote 39.

The difference in the optical rotations of two sugars of diverse configuration for carbon 2 gives 2R2, a value which has been called the "epimeric difference" [42]. The optical rotation of an asymmetric carbon which lies between two asymmetric groups is influenced by the configurations of both groups [43]. There are four arrangements or combinations involving the configurations of the carbons which lie on either side of carbon 2. These are represented symbolically in the following manner: (1) a, +; (2) α, −; (3) ß, +; (4) ß, —. Epimeric