Optical rotations

Optical rotation is a general term which is used to include both circular dichroism and optical rotatory dispersion. These are closely related phenomena in the same way that absorption and ordinary dispersion (refractive index) are related. They can be interconverted by mathematical transforms. Whereas the common element in absorption and ordinary dispersion is the dipole strength of the transition, the common quantity in circular dichroism and optical rotatory dispersion is rotational strength. And, as will be seen below, the rotational strength of a transition may be obtained from either measurement. 

Optical rotations of starch acetates have, as a rule, been measured by means of the sodium-D-lines with chloroform or, less frequently, pyridine as the solvent. Although individual specific rotations have ranged from + 128 to +276 , the values reported for triacetates prepared by mild treatments seem to lie relatively close together, as indicated in Table I. 

Hawkins, Jones, Young Banana In chhro-Jorm +167° °C. 20 

Optical Rotation.—The c.d. spectrum of (—)-/raw-l,2-di-4-pyridyloxiran (26) has been determined and rotation strengths have been compared with calculated values. The configuration of (—)-(26) was shown as by comparison with (-f)-R-/rfl 5-stilbene oxide. 

Miscellaneous.—Dipole-moment measurements have been used to determine the conformational equilibrium between (27) and (28) for oxirans and thiirans. The small angle of the three-membered ring bends both axial and 

Computed atomic charges and binding energies from an INDO molecular orbital study of a-heteroatom nitrenes are consistent with their known reactivity towards olefins to give aziridines. Molecular orbital calculations on the reaction of propylene oxide and isobutylene oxide with hydrogen chloride and ammonia predict an orientation of addition in agreement with experiment. 

From semi-empirical molecular orbital calculations the /raw-isomer of diaziridine (31) is predicted to be more stable/ and in partial support of this 

Numerous lichen substances are optically active, e.g. the well-known usnic acid, which is found in the (-1-)- and (-)-form in hchens. The optical rotation is calculated according to the equation 

The fragmentation of usnic acid is quite different under positive and negative ionization Fig. 12. 

Ion a is formed via a retro Diels-Alder process and ion b arises by a transfer of the 3-hydroxy hydrogen to C-4. Contrary to the positive ion MS, the negative one shows only a [M-CHj]- peak corresponding to ion c. 

ORD and CD are very useful chiroptical methods, for the characterization and determination of the relative and absolute configuration of chiral compounds. Their application was reviewed by Snatzke (1968,1981,1982). ORD data are given either as [a]J with [a] the specific 

298 C17H30O4 Lactone carboxylic acid from Lecanora rupicola 

Mathematical definition yields the clockwise handness toward a positive z-direction as positive and vice versa, like angular momentum. As time proceeds, the two vectors at z0 contrarotate and combine to give a linear polarization halfway between them, 

Here it should be emphasized that chemical definition is exactly opposite. According to the convention in physics, the signs coincide with those in mathematics. The traditional chemical signs are converted, however. Thus, the sign in Eqs. (10) and (11) must be converted, as follows  

The signs of optical activity or of the Faraday effect (magnetically induced optical activity see Appendix) used by physicists are frequently opposite to the chemically defined ones. Furthermore, the handness in liquid crystals, such as cholestric or chiral smectic ones, often has been defined erroneously and thus confused. 

Rewriting the expression for O in terms of refractive indeces nL and nR, we obtain  

Experimentally, one can use degrees as the rotation unit, and decimeters for the optical path length then the experimentally obtained rotational angle a is defined as follows  

The second carbon from the left is an asymmetric carbon atom because it has four different groups attached to it—a methyl group, a hydrogen, a hydroxyl group, and an ethyl group. 

One ingredient in pharmaceutical cough medicine preparations is a flavor oil. Pharmaceutical companies that produce such preparations purchase the flavor oil in bulk quantities and then perform a laboratory analysis on a sample of it to determine its quality. The method of choice for this is refractive index. The flavor oil raw material must be within the refractive index specification limits established for it before it can be used in the cough medicine production process. 

John Hannon, an analyst for a pharmaceutical company, uses a refractometer for the determination of the quality of flavor oil used in cough medicine preparations. 

FIGURE 15.13 (a) A representation of a light beam with all wave planes shown as double arrows around the line 

Most of the time, enantiomers are found equally mixed together. Equally mixed enantiomers are not optically active because the rotation in one direction by one structure is canceled by the rotation in the opposite direction by the other structure. Hence, a sample of 2-butanol, for example, as normally obtained from a chemical vendor, is not optically active. An equimolar mixture of two enantiomers is called a racemic mixture and is optically inactive. Separation of a racemic mixture is not possible by conventional methods because the enantiomers are identical with respect to properties that are used to effect the separation. However, it may be possible to separate them by chemical methods, meaning that one may undergo a chemical reaction that the other does not. Some biological reactions are such reactions, and hence a single enantiomeric structure is sometimes found in nature. 

Introduction. Visible light is a form of energy transmitted by wave motion. The vibration of the waves of light is transverse they vibrate in a direction at right angles to that in which the waves are moving. Sound waves are longitudinal and vibrate in the same 

(6) Two halves of the field with different intensities of illumination, (c) Two halves of the field with uniform illumination (zero point of the instrument). 

For sodium light (D line, 5890 Angstroms wave length) the specific rotation [a] is calculated by the use of the following formula, applicable to solutions of pure liquids and compounds  

Put the contents of the volumetric flask into one of the clean and dry bottles. Wash the volumetric flask three times with distilled water. By means of the graduated pipette transfer 50 ml of the stock solution into the volumetric flask and dilute to 100 ml. Determine the rotation of this solution at the same temperature as used in the first solution. Dilute 50 ml of the second solution to the same degree, and determine its rotation. Using the formula, calculate the specific rotation for each concentration. Tabulate your observed data and calculations. 

The results of these studies (shown in Figs. 10.2 and 10.3) suggest that the experiment is capable of detecting an asymmetry of order 10 . 

Thus the existence of a parity-violating component interfering with the em interaction is confirmed The -dependence in (10.2.8) for the range 0.15 y 0.38 has been studied and is compatible with the SM result with sin 6w = 0.224 0.020—a further success for the theory. 

Another remarkable result of the interference between weak and em interactions is that the refractive index of a substance can be different for right and left circularly polarized light, even when the material is in a non-crystalline form. We shall consider the passage of a plane polarized 

hl are the refractive indices (complex if there is absorption) for right and left circularly polarized light of angular frequency u then at a point z inside the vapour 

It is easy then to see that the resultant electric field at 2 is plane 

Comparison with Eq. (3.78) shows that the Fourier components of the operator and the field are given as 

Insertion of these operators in Eq. (3.109) yields for the expansion of the time-dependent dipole moment 

Comparing this with the classical expansion of a time-dependent dipole moment in Eq. (7.18) we can identify the frequency-dependent polarizability tensor as a linear response function or polarization propagator 

In Section 7.1 we discussed that plane or linear polarized radiation can be expressed as the superposition of left-circularly polarized and right-circularly polarized waves with the same refractive index. If the refractive indices for left- and right-circularly polarized radiation, however, differ by 

In the derivation of the molecular properties, which give rise to this effect, we have to take the spatial variation of the electric field vector into account and can thus not make the dipole approximation, contrary to the last section. This implies that we have to include a contribution from the interaction with the curl of the time-dependent electric-field, V xS r,t), to the expansion of the induced dipole moment of a molecule in Eq. (7.18). However, Maxwell s third equation, Eq. (2.37) relates the curl of the electric-field vector to the time derivative dB r,t)/dt of the magnetic induction and we can thus alternatively replace the spatial variation and expand the induced dipole moment instead in the electric field and the time derivative of the magnetic induction of a monochromatic wave (Buckingham, 1967) as 

Smith interpreted his results in terms of an equilibrium between two 

Dependence of Optical Rotalim on pH. Carpenter, Dahlberg, and Hening (1928) studied the effect of pH on the specific rotation of 0.7 % 

Dependence of Optical Rotation on Other Added Substances. Katz and Wienhoven (1933) have reported the effects on optical rotation of a wide variety of substances. Those which diminished the numerical value of the specific rotation at 15° were observed qualitatively to lower the rigidity, and some of them prevented gelation at 15°. The latter compounds have already been mentioned under melting points. Others which caused a substantial numerical decrease in specific rotation at a concentration of 1 Jlf were thioacetamide, iodoethanol, sodium heptylate, sodium caprylate, and sodium isophthalate. The effectiveness of large anions is apparent, as in the depression of the melting point. 

FIGURE 2.4. Linearly polarized light as a vector sum of left and right circularly polarized hght. 

Biot introduced the convention that a rotation of the plane of polarization in the clockwise direction to an observer viewing the beam as it is going away is said to be positive, and is 

FIGURE 2.5. The rotation of plane-polarized light. The counterclockwise rotation shown in this figure is denoted as ( ) and is called levorotatory. See color insert. 

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Circular dicliroism has been a useful servant to tire biophysical chemist since it allows tire non-invasive detennination of secondary stmcture (a-helices and P-sheets) in dissolved biopolymers. Due to tire dissymmetry of tliese stmctures (containing chiral centres) tliey are biaxial and show circular birefringence. Circular dicliroism is tlie Kramers-Kronig transfonnation of tlie resulting optical rotatory dispersion. The spectral window useful for distinguishing between a-helices and so on lies in tlie region 200-250 nm and hence is masked by certain salts. The metliod as usually applied is only semi-quantitative, since tlie measured optical rotations also depend on tlie exact amino acid sequence. 

Tinoco I 1963 The exciton contribution to the optical rotation of polymers Radiat. Res. 20 133-9... 

An example of a chiral compound is lactic acid. Two different forms of lactic acid that are mirror images of each other can be defined (Figure 2-69). These two different molecules are called enantiomers. They can be separated, isolated, and characterized experimentally. They are different chemical entities, and some of their properties arc different (c.g., their optical rotation),... 

The third method is of limited application and is used only in special cases, The second is the most accurate and rapid method, and is of considerable technical importance. The chemical method (described below), although less accurate than the polarimetric method, is of great value for the estimation of sugars in biological fluids. In fact, for such purposes, it is often to be preferred to the polarimetric method owing to the probable presence of other substances having high optical rotations. 

The small capital letter prefix refers to configuration, related to n glyceraldehyde, and not to the direction of optical rotation. The sign of optical rotation is expressed as (+) and (—) or as d and I or by the words dextro and Uuvo. Th is we have n.( —)-fructose and ,-(+).arabinose. 

Only three not four stereoisomeric 2 3 butanediols are possible These three are shown m Eigure 7 10 The (2R 3R) and (2S 3S) forms are enantiomers of each other and have equal and opposite optical rotations A third combination of chirality centers (2R 3S) however gives an achiral structure that is superimposable on its (2S 3R) minor image Because it is achiral this third stereoisomer is optically inactive We call achiral mole cules that have chnahty centers meso forms The meso form m Eigure 7 10 is known as meso 2 3 butanediol... 

Section 7 4 Optical activity, or the degree to which a substance rotates the plane of polarized light is a physical property used to characterize chiral sub stances Enantiomers have equal and opposite optical rotations To be optically active a substance must be chiral and one enantiomer must be present m excess of the other A racemic mixture is optically inactive and contains equal quantities of enantiomers... 

The optical rotations just cited for each isomer are those measured immediately after each one is dissolved m water On standing the rotation of the solution containing the a isomer decreases from +112 2° to +52 5° the rotation of the solution of the p isomer increases from +18 7° to the same value of +52 5° This phenomenon is called mutarotation What is happening is that each solution initially containing only one anomeric form undergoes equilibration to the same mixture of a and p pyranose forms The open chain form is an intermediate m the process... 

The distribution between the a and p anomenc forms at equilibrium is readily cal culated from the optical rotations of the pure isomers and the final optical rotation of the solution and is determined to be 36% a to 64% p Independent measurements have established that only the pyranose forms of d glucose are present m significant quanti ties at equilibrium... 

The specific optical rotations of pure a and p o mannopyranose are +29 3° and -17 0° respectively When either form is dissolved in water mutarotation occurs and the observed rotation of the solution changes until a final rotation of +14 2° is observed Assuming that only a and p pyranose forms are present calculate the percent of each isomer at equilibrium... 

A particular carbohydrate can mterconvert between furanose and pyra nose forms and between the a and (3 configuration of each form The change from one form to an equilibrium mixture of all the possible hemi acetals causes a change m optical rotation called mutarotation... 

Mutarotation (Section 25 8) The change in optical rotation that occurs when a single form of a carbohydrate is allowed to equilibrate to a mixture of isomeric hemiacetals... 

Specific Rotation. Optical rotation is caused by individual molecules of the optically active compound. The amount of rotation depends upon how many molecules the light beam encounters in passing through the tube. When allowances are made for the length of the tube that contains the sample and the sample concentration, it is found that the amount of rotation, as well as its direction, is a characteristic of each individual optically active compound. 

Optically Inactive Chiral Compounds. Although chirality is a necessary prerequisite for optical activity, chiral compounds are not necessarily optically active. With an equal mixture of two enantiomers, no net optical rotation is observed. Such a mixture of enantiomers is said to be racemic and is designated as ( ) and not as dl. Racemic mixtures usually have melting points higher than the melting point of either pure enantiomer. 

The sign of optical rotation is placed in parentheses, (-f) for dextrorotary, (—) for levorotary, and ( ) for racemic, and placed before the formula. The wavelength (in nanometers is indicated by a right subscript unless indicated otherwise, it refers to the sodium D-line. 

Physical Properties. When crystaUized from aqueous solutions above 5°C, natural (R-R, R )-tartaric acid is obtained in the anhydrous form. Below 5°C, tartaric acid forms a monohydrate which is unstable at room temperature. The optical rotation of an aqueous solution varies with concentration. It is stable in air and racemizes with great ease on heating. Some of the physical properties of (R-R, R )-tartaric acid are Hsted in Table 7. 

The a-carbon of glutamic acid is chiral. A convenient and effective means to determine the chemical purity of MSG is measurement of its specific rotation. The specific optical rotation of a solution of 10 g MSG in 100 mL of 2 A/HQ is +25.16. Besides L-glutamic acid [56-86-0] D-glutamic acid [6893-26-1] and the racemic mixture, DL-glutamic acid [617-65-2] are known. Unique taste modifying characteristics are possessed only by the L-form. 

The melting points, optical rotations, and uv spectral data for selected prostanoids are provided in Table 1. Additional physical properties for the primary PGs have been summarized in the Hterature and the physical methods have been reviewed (47). The molecular conformations of PGE2 and PGA have been determined in the soHd state by x-ray diffraction, and special H and nuclear magnetic resonance (nmr) spectral studies of several PGs have been reported (11,48—53). Mass spectral data have also been compiled (54) (see Mass spectrometry Spectroscopy). 

Specific optical rotation values, [a], for starch pastes range from 180 to 220° (5), but for pure amylose and amylopectin fractions [a] is 200°. The stmcture of amylose has been estabUshed by use of x-ray diffraction and infrared spectroscopy (23). The latter analysis shows that the proposed stmcture (23) is consistent with the proposed ground-state conformation of the monomer D-glucopyranosyl units. Intramolecular bonding in amylose has also been investigated with nuclear magnetic resonance (nmr) spectroscopy (24). 

The concentration of a pure sugar solution is determined by measurements of polarization (optical rotation), refractive index, and density. 

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