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

manner:

"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 Aо-R2-R3-R4, 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.

903232 O-50 - 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 2Аon 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 B-d-aldohexoses. 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

pairs corresponding to the first group are not known products at present but would be represented by a-d-gulose and a-d-idose, or by a-d-allose and a-d-altrose. In the hexose series the second group is represented by a-d-glucose and a-d-mannose, and by a-d-galactose and a-d-talose. The epimeric differences obtained from these pairs, +14,930 and +14,900, are in excellent agreement. The third group is represented by B-d-allose and B-d-altrose, and by B-d-a-glucoheptose and B-d-B-glucoheptose. The epimeric differences for these pairs are -5,940 and -6,010. Since these sugars have not been extensively studied, it is quite possible that B-d-altrose or B-d-ß-glucoheptose may be improperly classified. The fourth group is represented in the hexose series by B-d-glucose and B-d-mannose, and by B-d-galactose and B-d-talose. The epimeric differences obtained from these pairs are +6,430 and +7,130. The epimeric differences obtained for various configurations bring out the need for considering the configuration of adjacent groups in making comparisons, and emphasize the complex character of the problem.

The rotational differences for carbon 3, obtained from sugars which represent three possible combinations for the configurations of the adjacent groups, give values of approximately 16,000, -3,000, and +8,000. The differences in these values show that the configurations of the adjacent carbons influence rotation. Data are not available for calculating the rotational differences for the fourth group. For two of the configurations, the comparisons give results in approximate agreement with one another.

The data available for calculating the rotational differences for carbon 4 in the hexose series are limited to only one combination for the configurations of the adjacent carbon atoms. Four calculations from the optical rotations of eight sugars give values in approximate agreement with each other, namely, -6,940, -6,140, -6,970, and -5,440. These values are in accord with those obtained in the heptose series for substances of like configuration, but they are not strictly comparable with those obtained from the pentoses, because the pentoses differ from the hexoses and heptoses in the substituent group on adjacent carbon 5.

The determination of the optical rotation of carbon 5 is complicated, because any change in its configuration affects the adjacent ring oxygen, which in turn determines the alpha and beta positions of the first carbon. Consequently, the rotational differences for carbon 5 (2R,) include any changes which may be induced by the dissymmetry of the molecule as a whole. The data at hand are not sufficient to evaluate this factor. The comparisons involving the optical rotations of allose and altrose do not appear to be in accord. The discrepancy may be caused by improper classification, erroneous optical rotations, or unknown structural differences, such as differences in the conformation of the rings.

The rotational differences clearly show that optical rotation is not uniformly an additive property and that dissimilarity in the configurations of the contiguous atoms results in deviations from the Van't Hoff theory of optical superposition. The work of Tschugaeff, Kuhn, Lowry, and others [24, p. 429] shows that each asymmetric carbon in an optically active substance gives rise to one or more partial rotations, which may be correlated with absorption bands of characteristic frequency having their origin in particular electronic transitions

taking place in the molecule. These transitions are not influenced greatly by atoms or groups at some distance from the asymmetric. carbon but are influenced by the neighboring groups. The optical rotation in the visible spectrum is chiefly governed by the absorption bands nearest the wave length used for the rotation measurements. Since the bands are not located at the same wave lengths for all sugars, the partial rotation varies in irregular fashion with the wave length. For this reason the difference in the rotations of two sugars depends in part on the light used for making comparison, and it is obvious that the optical rotations cannot be rigorously represented by the simple algebraic equations suggested by Van't Hoff.

Nevertheless, the active part that the principle of optical superposition has played in the development of carbohydrate chemistry is sufficient justification for continuing its use. It has been amply demonstrated that substances of similar structure and configuration give approximately like rotational differences.

For correlating optical rotation and structure, Hudson [32] has noted a number of approximations which are expressed in several empirical rules. The so-called first rule of isorotation relates to the optical rotation of the glycosidic carbon. If the formulas for alpha and beta glucose are written as ring structures differing solely in the configuration of carbon 1, and if the rotation due to the end asymmetric carbon is A, and the rotation due to the rest of the molecule is B, the molecular rotation of one isomer will be +A+B, and the rotation of the other isomer will be -A+B. The sum of the rotations is +2B and their difference +2A. When the molecular rotations of the alpha and beta modifications of glucose, galactose, and lactose are compared on the one hand, and the molecular rotations of lyxose, rhamnose, mannose, and 4-glucosidomannose are compared on the other hand, it will be observed that the differences in the molecular rotations for the alpha-beta pairs in each group are nearly constant. The members of the first group have the configuration H-C-OH for the carbon adjacent to the glycosidic group, while the members of the second group have the configuration HO-C-H. Many similar comparisons reveal that the rotational difference, 2A, is nearly constant for substances which have like glycosidic groups, like ring structures, and like configurations on the adjacent carbon atoms. This approximate equality is the basis of the first rule of isorotation which states that the rotation of the glycosidic group is affected in only a minor degree by changes in the structure of the remainder of the molecule provided the changes are not on the contiguous atoms.*

40

Hudson's second rule of isorotation relates to the optical rotation of the rest of the molecule. The sum of the molecular rotations of the alpha and beta sugars, +2B, varies from sugar to sugar, but if the sums of the molecular rotations of the sugars are compared with the sums of the molecular rotations of the methyl glycosides, it will be observed that the values of 2B obtained for the sugars are in close agreement with the values of 2B' obtained for the glycosides. This is the basis for the second rule of isorotation which states that changes in the structure of the glycosidic carbon affect in only a minor degree the rotation of the remainder of the molecule. As may be observed from data given in table 54, the values for 2B are in approximate agreement

40 Hudson's original rule does not exclude changes on the contiguous atoms.